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Lunar Siyuz flight

Posted by: Ekkehard Augustin - Sat Oct 08, 2005 11:50 am
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Lunar Siyuz flight 
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Contents

Round Trip: Applying the Apollo 14-numbers properly now
Round Trip: Final results without the correction factors
Round Trip at correction factors
Lunar Orbital Trip
Adding a third hint regarding the calculation of landers
How to apply the functions
The Landing Trip
Excel spreadsheet
Appendix
Applying numbers completely: Dummies
Round Trip: Resulting Amounts, Prices etc.
Correction factors
Without correction factors
- Prices at expendable QuickReach for the CXV, Falcon 9 S9 as tanker and $ 0.65 per kg cerosene
- Prices at reusable QuickReach for the CXV as well as for the tanker and $ 0.65 per kg cerosene
- Prices at expendable QuickReach for the CXV, Launchpoint Technologies maglev for the 100 kg-tanker at $ 50,000 and $ 0.65 per kg cerosene
- Prices at expendable QuickReach for the CXV, Launchpoint Technologies maglev for the 100 kg-tanker at $ 18,900 and $ 0.65 per kg cerosene
Correction factor for TPI only
- Prices at expendable QuickReach for the CXV, Falcon 9 S9 as tanker and $ 0.65 per kg cerosene
- Prices at reusable QuickReach for the CXV as well as for the tanker and $ 0.65 per kg cerosene
- Prices at expendable QuickReach for the CXV, Launchpoint Technologies maglev for the 100 kg-tanker at $ 50,000 and $ 0.65 per kg cerosene
- Prices at expendable QuickReach for the CXV, Launchpoint Technologies maglev for the 100 kg-tanker at $ 18,900 and $ 0.65 per kg cerosene





Round Trip: Applying the Apollo 14-numbers properly now

I formerly reduced the weight of the Apollo SM by the weight of the electrical equipment of 1,200 kg. The reason was something like the circumstance that the round-trip doesn’t include requirements of an orbital trip or the like. I now add again these 1,200 kg and apply the complete 24,523 the Apollo SM weighs inclduing the propellant. Otherwise the numbers still weren’t properly applied like is now possible that there is a solution for the lander

The weight of the lander to be added also is 14,696 kg.

Without the correction factors the amount of propellant in the case of a cylindrical tankis a bit less than 54,000 kg now. This number is much more correct that the earlier one because for some good reasons the earlier calculations didn’t apply the number(s) properly and have been meant for purposes of demonstration merely.

This means a reduction by around 7,700 kg which is around 12.5% of the former result – showing the importancy of the lander and the thoughts about it.

If the correction factor for TPI is applied the required amount of propellant is down to 32,600 kg only.

The weights of the hardware in the case without correction factors are 5,968 kg of vehicle + tank + engine without propellant – far below the existing vehicles applied – and 59,893 kg including propellant which is far below the total weight in the case of Apollo 14 before the beginning of Translunar Injection.

The correction factor for TPI drops these weights to 5,931 kg – a slight drop only – and 38,490 kg.

So up to now no caculation linearly up has been done – which means that the saftey margins are kept.



Round Trip: Final results without the correction factors

Without the correction factor the prices per apssenger at 5 passengers to be flown are between $ 26.3 mio at a spherical tank, price = variable costs per passenger without no safety margins and $ 57 mio initially cylindrical and including depreciations and safety margin(s) – if an expendable QuickReach and a Falcon 9 S9 is applied.

If the QuickReach is reusable instead and used for the tanker also the prices are down to $ 276,000 spherical + variable costs = price without safety margin and $ 11.5 mio initially at a cylindrical tank and including depreciations and a safety margin.

But most interesting are the number if Launchpoint Technologies‘ maglev would be applied if it works and is available in 4 to 5 years

At the maximum costs they are telling the prices would be $ 7.6 mio spherical + price = variable costs + no safety margin to $ 22.4 mio initially at cylindrical tank + depreciations + safety margin. If their number for the 3,000-launches-per-year-case is applied the prices drop down to $ 5.4 mio spherical + price = variable costs + no safety margin to $ 18.4 mio initially with cylindrical + depreciation + safety margin

So Launchpoint Technologies theoretically allow a price drop down to less than $ 10 mio for the round trip in 4 to 5 years.

And the correction factors aren’t applied yet!



Round Trip at correction factors

At application of the correction factor for TPI the prices drop by a bit less than a third of the prices without the correction factors – for the case of the expendable QuickReach and the Falcon 9 S9.

If the reusable QuickReach is applied instead of the expendable and the Falcon then the minimum price got is dropped by MORE than a thrid – the price then is at a bit more than $ 176,000. This is very close to the earlier result of $ 170,000 when the calculations were very raw and unstructured etc. But it is the price in the case of a spherical tank while in the cylindrical case the price is above $ 200,000 – around $ 256,000.

Very interesting again are the results in the case of launching 100 kg-tankers by Launchpoint Technologies‘ maglev. This way the prices theoretically might be down to $ 4.8 mio to $ 6.2 mio at the minimum and $ 17.4 mio to $ 19.8 mio in four to five years – nearby future in difference to the potential reusable QuickReach applied for the year 2030 which 23 years away.

So with correction factors Launchpoint Technologies theoretically allow for prices around $ 5 mio – the maximum prices include depreciations for lost-in-space-costs and investments.

Like I said in the previous post I also applied the correctiuon factor for EOI – Soyuz-Soyuz – additionally. But this increases the required amount of propellant by less than 100 kg only – this has a neglegible impact on the costs and prices only

Because the information under www.astronautix.com that NASA 20 cents only per kg of cerosene in 1980 I applied that price too – but the resulting prices in the case of the reusable QuickReach for the CXV as well as the tanker drop by $ 2,000 only.



Lunar Orbital Trip

During the earlier unstructured calculations I calculated the price for a lunar orbital trip as part of the calculation of the price of a landing trip. If I remember correct this was after the Apollo-like landing trip but before that landing trip that included refuelling at the Moon.

Because of structured and systematical calculations I here calculate the lunar orbital trip before any landing trip

Since an orbital trip includes two more phases – Planetary Orbital Insertian POI and Trans Earth Injection TEI – two more correction factors seem to be required. Since there are no manned vehicles except Apollo that have done POI and TEI Apollo is the only existig vehicle that can be applied here. I continue to apply Apollo 14 because I have all the numbers about it that the formular(s) need.

The only correction factors that can be calculated are Apollo-Apollo factors. For the tank inside the Apollo SM I apply a diameter of 3.8 m which would mean a wall 1 cm thick.

The data and informations available to me mean that Apollo carried a payload during POI that consisted of 2,143.56 kg reserved propellant, 14,696 kg Apollo LM including its propellant and

One aspect is essential and very important here and must be considered. While the Saturn IV B is used during one phase only and then expended something like that is NOT the case in POI. No tank of the Apollo SM is expended after POI and the Apollo SM was carried in total and as a whole throught POI as well as TEI. This requires to establish virtual tsaging.

Sources listed much earlier provide informations about how much propellant was consumed during POI and how during TEI. This allows to apply those portion of the Apollo SM and its tanks the known portions of propellant required as different stages and thus tanks. The split needs to be done so that one of the virtual stages and tanks does have no top adn the other no bottom because the weight must be applied as it is.

Since the Apollo SM carried 18,413 kg propellant and – like calculated much earlier – 11,647.44 kg of it were consumed during POI and another 4,622 kg during TEI there were 2,143.56 kg propellant as payload. Then of the weight of the stage of 3,110 kg (Apollo SM – propellant – engine) 1,967.280639 kg were POI, 780,6669201 kg TEI and 362.0524412 kg payload.

So during POI a payload of 2,143.56 kg propellant + 362.0524412 kg tank + 14,696 kg Apollo LM was carried.
For TEI the question is if the 1,143.56 kg üpropellant still were there. It would mean a safety margin to suppose that they have been consumed – then the weight the TEI-propellant was required for would be less resulting in higher propellant requirements per kg compared to the assumption that the 2,143.56 kg were NOT consumed in the lunar orbit. Since the Apollo LM was left at the Moon a payload of 362.0524412 kg tank + 1,967.280639 kg POI-tank were carried. That tank of the previous phase mustn’t be applied as tank because it was not for a future phase.

The length of 7.56 m has to split into three parts also but only two of them will be applied because the length of payload has no impact. To do that I simply calculate the volume of the POI and the TEI-propellant and then apply the diameter of 3.8 m supposed and the formular for the volume of a cylinder

I am getting very short length – because of this the weight of top and bottom is relatively high. By the way – I am not sure if the tanks are cylindrical or spherical. I can’t but apply cylindrical values. AsAss sr that is an error it contributes to the correction factor(s)..

The length of all the tanks together – including the payload portion is 1.591722322 m – leaving 5.968277678 m for top and bottom. The POI-part is 1.006869616 m long, the TEI-part 0.399551435 m. I could split the remainder into two parts according to these length – but is that justified?. Under www.bernd-leitenberger.de it is said that the bottom-parts of rockets are used to attac h engines etc. – in so far it would be injustified. On the other hand no engine is attached to the top – from which it could be concluded that the top is lighter than the bottom. So I split the 5.9... m according to the length of the tanks. Then the POI-part of top + bottom is 4.272744247 m long – meaning a total length of the virtual POI-stage of 5,279613863 m. For the TEI-part then a top of 1.695533431 m and a total length of 2.095084866 m is got.

I had to calculate the engine Isp by multiplying the Isp listed under www.astronautix.com by 9.81 m/s because under www.bernd-leitenberger.de it is said that in difference to Germany in the US ve is divided by g – but the spreadsheet up to now uses the german versions.

For the calculation of the POI correction factor the TEI weights have to included via a dummy for TEI.

The POI correction factor is 0.875136699 then – obviously too few propellant is calculated here. This means that the correction factor must be applied – in difference to the Apollo-Soyuz case in TPI where an amount of propellant was calculated that was too high in comparison to the capacity of the Block DM applied for Soyuz.

TEI now needs a EOI-dummy because there can be no payload/cargo for TEI – such cargo does make sense only if it will be delivered somewhere which then means an EOI. The correction factor got is 0,999227652.

This all now simply needs to be added to what makes up the round trip up to now to create the orbital trip.

Then without the correction factors 56,936.07906 kg of propellant are required in the cylindrical case and a total cylindrical weight without propellant of 5,908.878942 kg. Obviously all weights are below the weights of the applied existing vehicles and that safety margin is kept.

The prices wuthoiut the correction factors are as follows:

$ 27,330,553.09 to $ 39,894,384.86 variable costs at expendable QuickReach and Falcon 9 S9
$ 30,063,608.4 to $ 43,883,823.34 price including depreciations
$ 41,063,608.4 to $ 54,883,823.34 initial price
$ 35,000,000 to $ 50,000,000 price including safety margin
$ 46,000,000 to $ 61,000,000 initial price including safety margin

$ 283,474.6422 to $ 422,666.8811 variable costs at expendable QuickReach and Falcon 9 S9
$ 311,822.1064 to $ 464,933.5692 price including depreciations
$ 11,311,822.11 to $ 11,464,933.57 initial price
$ 360,000 to $ 520,000 price including safety margin
$ 11,360,000 to $ 11,520,000 initial price including safety margin

If Launchpoint Technologies launch 100 kg-tanks the price is between $ 5.4 mio and $ 23 mio.

I applied a cerosene price of $ 0.20 for the reusable QuickReach-case and the Launchpoint Technologies-case

There obviously is a significant reduction compared to the round trip which is puzzlinge at the first glance. This has to do with the circumstance that the weight of the hardware is increased slightly only by the increased required amount of propellant. The propellant is very cheap compared to the hardware which is valid for the costs of transportation into LEO also. May be it will be thought about it more later – whenever that will be.

If all correction factors are applied the required amount of propellant is down to 45,448.87613 kg and the empty weight of tanks plus vehicle together is very slightly reduced only to 5,906.432221 kg.

The impacts on the prices are

reduction by $ 5 mio to $ 7 mio variable costs at expendable QuickReach and Falcon 9 S9
$ 5 mio to $ 8 mio price including depreciations
$ 5 mio to $ 8 mio initial price
$ 7 mio to $ 10 mio price including safety margin
$ 7 mio to $ 10 mio initial price including safety margin

$ 52,000 to $ 80,000 variable costs at expendable QuickReach and Falcon 9 S9
$ 57,000 to $ 88,000 price including depreciations
$ 57,000 to $ 88,000 initial price
$ 60,000 to $ 100,000 including safety margin
$ $ 60,000 to $ 100,000 initial price including safety margin

$ 282,000 to $ 1.6 mio are the reductions if 100 kg-tanks would be launched by Launchpoint Technologies.

The reduced numbers are the more correct numbers because they are corrected by the correction factors

The landing trip now can be calculated by simply calculating the lander and adding it and its propellant to the weight of the potential part of the calculations.



Adding a third hint regarding the calculation of landers

The recent calculations of the round-trip applied a correction factor of Apollo to Soyuz – and this then was used for the calculation of the CXV-like vehicle.

In difference to that up to now the calculation of landers aaren’t done yet to calculate a third lander. This wasn’t valid because there was a problem to be solved prior to that.

There also was a concept by Space Adventures and the Russians that applies a tank/stage the calculation of the CXV-like vehicle uses also – but no such concept by companies etc. like Space Adventures or the Russians is known regarding landers up to now and no such tank was used in the calculation of landers up to now. This might cause confusion.

And the Block DM obviously can be used with several different payloads and thus vehicles also while all the tanks of landers seem to be bound to those particular landers. The tanks seem to be integrated into them which seems to be not the case regarding Saturn IV B, Block DM and the like. Personally I have problems to imagine an Apollo LM tank or stage to apply as a standard while I have no problems to imagine the application of a Block DM as such a standard.



How to apply the functions

All the functions are related to one phase. This means that they can be applied properly to the existing landers only. One of them can be applied to potential landers also if the reduction in safety linked to doing so is considered to be acceptable

First there are the functions relating the weight of the carrier to the total amount of propellant. Since the carrier itself (the vehicle without the engine, tanks/stages and payloads) requires a share only of this total propellant it seems that the function (or its result) must be multiplied by a share. This share is known for existing landers. This is valid also for engines and payloads.

But there is a problem. For potential landers heavier than the existing ones the share might be shifted because of the higher amounts of propellant required and the heavier stages required because of the larger amounts of propellant.

Of course the ratio between the landers and engines will be applied – but this tells shares in kg only but not in percentage or fractions.

One way out is to calculated the volume of the total amount of propellant. From that a given tank/stage can be applied to calculate the new one.

Then the last group of functions can be applied to check the result. The last group realtes the combined weight of the lander and the tank/stage to the total amount of propellant. If the function and the way described above are sufficiently close to each other then the way can be applied.

But then the last group of function should be applied directly.

The result to be compared could be checked via the function relating the carrier-weight to the weight of the tank/stage as well. So this second group of functions could be applied alternatively – and should.

This second group of functions is telling something that is derived by the formular(s) in parallel for the potential lander or vehicle – but it’s done there NOT for the existing landers that are expendable.

In so far the first group of functions should be applied for the share the heavier EXPENDABLE carrier would require of the total propellant while the second group of functions should be applied to calculate the tank/stage of that EXPENDABLE carrier that never existed – like the potential lander.

To this now the formular(s) can be applied

The alternative is to apply the last group. Then the result of the function would have to be split via a ratio between carrier and tank/stage. This would mean to assume that this ratio is constant – which is too unsafe in my eyes. Because of this the second group of functions has to be applied then since it is telling a changing ratio.

This last group might be applied to the reusable lander also that is got if the functions are NOT applied to get a heavier expendable carrier that never existed. This can be done because the total weight of the lander plus the tank/stage is considered and this combined weight would be valid allways for the potential reusable lander.



The Landing Trip

Ass illustrated in the previous post there are some problems to find proper correction factors for existing expendable landers. So the first but highly unsafe option is to leave away all correction factors and simply apply the ratios and shares going into the formualr(s). Then the result for a lander weighing 3,600 kg (to keep comparability to earlier calculations) and using a stage/tank derived from the Block DM as standard is a required amount of propellant of 10,554 kg to 10,555 kg for landing and launch together.

Since the weight of the lander is more than twice the weight of the expendable Apollo LM carrier this appears to be doubtful. The weight of the Block DM might justify the result since it is lighter than the Apollo LM DS and the non-carrier-part of the Apollo LM AS together but it is NOT justified if the 3,600 kg for the reusable lander is added.

Because of this an expendable virtual lander weighing 3,600 kg has to be applied. The requirements of this lander can be calculated by applying the function(s).

This is quite similar to the adjustments of propellants and tanks of the existing vehicles doing TPI, POI, TEI and EOI.

The functions are applied like this:

If the amount of propellant or weight of stage/tank is let’s say 7,123 then 7,000 is taken and the values higher by 25%, 50% and 75% of 1,00 are added. Next 10 % of 7,123 are added to that number and it is compared to 7000 + 25% of 1,000, + 50% of 1,000 etc. Then that value is applied that is above 7,123 + 0.1 * 7,123. If the highest value is exceeded then the number is rounded up to the next full 100. This is already applied for the prices that include a safety margin – but here a function is selected this way – it will be that function that deliveres a weight above the result of the method described. Of the functions listed in the previous post it is the function delivering the result 9,314.172129563 kg for the landing part of the Apollo LM DS.

Next this will be done for the stage/tank also. Here the sum of the carrier weight, its ascent propellant, its ascent engine and its ascent stage has to be applied here.

This leads to the calculation of the propellant and the stage for the launch. Because no regression was possible here the functions for the landing part must be adjusted to the launch part. The weight of the Apollo LM AS has a ratio of 0.456564768 to the Apollo LM DS. At the Luna 15 this ratio is much less. To be on the safe side I round up to 0.5 and then add another 0.25 – supposing that 0.75 might be sufficient. The difference to the landing part is that the propellant for launch mustn’t be included now.

Since the weights of the carrier and the engine are given and the weight of the stage is calculated via the function all shares are known now and all can be calculated.

The complete Apollo LM including propellant weighed 14,696 kg 10,523 kg of which were propellant and the remaining 4,173 kg Apollo LM carrier, Apollo LM DS and the non-carrier part of the Apollo LM AS. In comparison to the virtual pendant got and applied here consist of a weight for carrier + landing part + launch part of 3,600 kg + 2 * 113 kg + 6,284.333 kg =10,110.333 kg and requires an amount of propellant of 27,053.436 kg. This is the virtual larger expendable lander – it is 2.4228 times as heavy as the Apollo LM and requires 2.571 times ist propellant.

The formulars next apply the 3,600 kg as weight of the reusable carrier but apply a Block DM as stage or tank. The required amount of propellant then is 14,236.26584 kg. That the propellant requirements are that smaller than in the expendable case seems to be puzzling – but the Block DM weighs 0.136 kg per kg propellant while the Apollo LM DS weighs 0.229kg per kg propellant and the Apollo LM AS 0.229 kg per kg propellant too. This expalins it very far – the numbers for the Apollo LM DS and AS are neraly twice those for the Block DM. From the AS and DS the engines have been subtracted and from the AS the carrier too – I applied weights calculated like described in one or two of the most recent posts. Afew economies of scale are involved also because the unification of the seperated tanks of the expendable version removes one top and one bottom formerly required because of the requirement to keep the tanks separated.

The propellant is calculated into LOX/cerosene now and the Block DM is applied. From this a weight for the stage of 2,069.79 kg for the stage/tank follows if it is cylindrical. The spherical alternative I don’t consider yet here.

This means a hardware weight of 3,600 kg + 2,069.79 kg + 230 kg engine = 5,899.79 kg. Then including the propellant the cargo for the vehicle traveling between Earth and Moon is 20,136.05584 kg.during POI and 5,899.79 during TEI and EOI because then the propellant of the lander is consumed totally.

For the trip from Earth to Moon and back then a required amount of propellant of 69,639.97281 kg is got and the total hardware weight is 31,947.43065 kg – but this I needed to check in short. It turns out that it includes the propellant for the lander for example.

In difference to the round trip I never tried the orbital trip and the landing trip before this post yet. This has to do with the payload/cargo only. It turned out in the last few moments that the payload-term isn’t flexible enough.

This finding means that it should be suspected that the propellant calculated is too high. The hardware weight isn’t the value got but 17,711.17081 kg only. This is less than the weight for TPI and POI for the existing vehicles – but it is more than during TEI and EOI for those vehicles.

So it may be that it is required now to do regressional anlysis for the vehicle(s) traveling between Earth and Moon.

At the amount of propellant got here the prices range from $ 977,102.5471 at reusable QuickReach and $ 0.20 per kg cerosene to $ 122 mio initially including safety margin, depreciations at expendable QuickReach, Falcon 9 S9 for the tanker and $ 0.65 per kg of cerosene.

If Launchpoint Technologies‘ maglev and 100 kg-tankers would be applied the prices got for the round trip would be kept nearly that would be theoretically possible in 4 to 5 years.



Excel spreadsheet

There are tables of correction factors now – one for each phase. Also a table of tankers into LEO has been added. A table of taxis for passengers into LEO doesn’t seem to make sense at present since except for the CXV numbers for reusable vehicles seem to be missing. I didn’t cehck that but I remember investment and development about other vehicles only. But this may change quickly and so a table of taxis will be added with one vehicle only which is the CXV.

A table of propellants has benn added too which simply lists the prices of the propellants. The spreadsheet uses it for the calculations of the price(s) by the amounts of propellant calculated.




Throughout this post the engine-Isp was applied instead of the propellant Isp – I later will check if this means least costs in all cases or if that’s not the case. I will post the minima and the maxima then only. It will take a while until I’ll do that.



I remember that I announced to list some further results of tests of the regeressional got functions in this post which I didn’t now. But besides the checks required like mentioned above there are some other checks interestng because there are two reusable landers already. So the announced checks will be delayed to the interesting other checks – in the next post I hope.





Dipl.-Volkswirt (bdvb) Augustin (Political Economist)

Appendix

Applying numbers completely: Dummies

To calculate the round trip properly by applying the numbers of Apollo completely a dummy has been applied for the phase POI earlier. This dummy is required to include all numbers. The Apollo SM and the Apollo LM are payloads towards the Moon and this concept is based on the thought that payloads make sense in POI and EOI only since they have a destination – and at the destination an orbital insertion is required.

To avoid multiple calculation of objects that exist only once the payload is included in the phase at ist destination only and from there included also into earlier phases carrying it also and thus has an impact on the amount of propellant required in those earlier phases.

But except of the payload all other numbers for the phases not goenthrough during a round trip – POI and TEI – are left zero.

This is a second dummy because that applied earlier means different numbers. Consequently there are both a second test Apollo against Soyuz and a second round trip now.



Round Trip: Resulting Amounts, Prices etc.

Correction factors

Apollo-Soyuz correction factor = 3.271641733
Soyuz-Soyuz correction factor = 0.997199543 from TPI



Without correction factors

Required amount of propellant = 53924.67619 kg cylinbdrical vs. ...

- Prices at expendable QuickReach for the CXV, Falcon 9 S9 as tanker and $ 0.65 per kg cerosene

variable costs per passenger = $ 37,995,897.02 cylindrical vs $ 26,298,243.52 spherical
price incl. depreciation = $ 41,795,486.72 cylindrical vs. $ 28,928,067.87 spherical at 10 % of price
initial price per passenger = $ 52,795,486.72 cylindrical vs. $ 39,928,067.87 spherical
price incl. safety + rounded = $ 46,000,000 cylindrical vs. $ 32,000,000 spherical
initial incl. safety + rounded = $ 57,000,000 cylindrical vs. $ 43,000,000 spherical



- Prices at reusable QuickReach for the CXV as well as for the tanker and $ 0.65 per kg cerosene

variable costs per passenger = $ 406,487.1259 cylindrical vs $ 275,221.1613 spherical
price incl. depreciation = $ 447,135.8385 cylindrical vs. $ 302,743.2775 spherical at 10 % of price
initial price per passenger = $ 11,447,135.8 cylindrical vs. $ 11,302,743.28 spherical
price incl. safety + rounded = $ 500,000 cylindrical vs. $ 350,000 spherical
initial incl. safety + rounded = $ 11,500,000 cylindrical vs. $ 11,350,000 spherical



- Prices at expendable QuickReach for the CXV, Launchpoint Technologies maglev for the 100 kg-tanker at $ 50,000 and $ 0.65 per kg cerosene

variable costs per passenger = $ 9,399,477.827 cylindrical vs $ 7,541,570.661 spherical
price incl. depreciation = $ 10,339,425.61 cylindrical vs. $ 8,295,727.727 spherical at 10 % of price
initial price per passenger = $ 21,339,425.61 cylindrical vs. $ 19,295,727.73 spherical
price incl. safety + rounded = $ 11,400,000 cylindrical vs. $ 9,200,000 spherical
initial incl. safety + rounded = $ 22,400,000 cylindrical vs. $ 20,200,000 spherical



- Prices at expendable QuickReach for the CXV, Launchpoint Technologies maglev for the 100 kg-tanker at $ 18,900 and $ 0.65 per kg cerosene

variable costs per passenger = $ 6,045,362.968 cylindrical vs $ 5,341,573.706 spherical
price incl. depreciation = $ 6,649,899.265 cylindrical vs. $ 5,875,731.076 spherical at 10 % of price
initial price per passenger = $ 17,649,899.26 cylindrical vs. $ 16,875,731.08 spherical
price incl. safety + rounded = $ 7,400,000 cylindrical vs. $ 6,600,000 spherical
initial incl. safety + rounded = $ 18,400,000 cylindrical vs. $ 17,600,000 spherical



Correction factor for TPI only

Required amount of propellant = 32,559.66405 kg cylindrical vs. 21359,66649 kg spherical

- Prices at expendable QuickReach for the CXV, Falcon 9 S9 as tanker and $ 0.65 per kg cerosene

variable costs per passenger = $ 24,526,687.67 cylindrical vs $ 17,465,839.27 spherical
price incl. depreciation = $ 26,979,356.44 cylindrical vs. $ 19,212,423.2 spherical at 10 % of price
initial price per passenger = $ 37,979,356.44 cylindrical vs. $ 30,212,423.2 spherical
price incl. safety + rounded = $ 30,000,000 cylindrical vs. $ 21,200,000 spherical
initial incl. safety + rounded = $ 41,000,000 cylindrical vs. $ 32200000 spherical



- Prices at reusable QuickReach for the CXV as well as for the tanker and $ 0.65 per kg cerosene

variable costs per passenger = $ 255,341.5345 cylindrical vs $ 176,107.7739 spherical
price incl. depreciation = $ 280,875.6879 cylindrical vs. $ 193,718.5513 spherical at 10 % of price
initial price per passenger = $ 11,280,875.69 cylindrical vs. $ 11,193,718.55 spherical
price incl. safety + rounded = $ 320,000 cylindrical vs. $ 214,000 spherical
initial incl. safety + rounded = $ 11,320,000 cylindrical vs. $ 11,214,000 spherical



- Prices at expendable QuickReach for the CXV, Launchpoint Technologies maglev for the 100 kg-tanker at $ 50,000 and $ 0.65 per kg cerosene

variable costs per passenger = $ 7,260,199.161 cylindrical vs $ 6,138,743.406 spherical
price incl. depreciation = $ 7,986,219.077 cylindrical vs. $ 6,752,617.746 spherical at 10 % of price
initial price per passenger = $ 18,986,219.08 cylindrical vs. $ 17,752,617.75 spherical
price incl. safety + rounded = $ 8,800,000 cylindrical vs. $ 7,600,000 spherical
initial incl. safety + rounded = $ 19,800,000 cylindrical vs. $ 18,600,000 spherical



- Prices at expendable QuickReach for the CXV, Launchpoint Technologies maglev for the 100 kg-tanker at $ 18,900 and $ 0.65 per kg cerosene

variable costs per passenger = $ 5,234,988.057 cylindrical vs $ 4,810,172.15 spherical
price incl. depreciation = $ 5,758,486.863 cylindrical vs. $ 5,291,189.365 spherical at 10 % of price
initial price per passenger = $ 16,758,486.86 cylindrical vs. $ 16,291,189.36 spherical
price incl. safety + rounded = $ 6,400,000 cylindrical vs. $ 6,000,000 spherical
initial incl. safety + rounded = $ 17,400,000 cylindrical vs. $ 17,000,000 spherical


End of Appendix



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Post    Posted on: Sat Jan 13, 2007 8:12 pm
Conetnts

Landers Statistically Involved: Propellants via Regressional Functions
Regressional Function Selected
Tests by Micro-Space’s Lander



Landers Statistically Involved: Propellants via Regressional Functions

For Lunar 9 no Isp-ratio of propellants can be calculated because it consumed a particular propellant www.bernd-leitenberger.de doesn’t list an Isp for. For this reason only non-standarduized propellants can be calculated. The amounts calculated for Luna 9 are all too low – the best result is less than the correct number by around 5%. The stages are too high by between 761% and 1714% - that’s not reasonable.

Applying the functions for Surveyor leads to better results. Four of the functions deliver between 47% and 52% more propellant than Surveyor really consumed – so here is a safety margin got. The stages calculated are between 327.5% and 769% too heavy which again is unreasonable and too light is not possible. One of the functions applying the sum of the weight of the stage and the weight of the carrier results in propellant amounts higher than the correct value by 8.5% to 13.5% - I would prefer one of the other functions I talked about previously.

In the case of Ranger all propellant amounts got are too high by between 2104% and 11601% - highly unreasonable which is a bit better for the stages (exceeded by 621% to 1296%.)

Last Luna 15 because I don’t want to repeat the Apollo LM although I didn’t list the results of very few functions for it yet: the functions applying the carrier only by between 4% and 32% too few propellant but the functions applying the complete hardware 37% to 64% above the correct value while the stages are too light by 38% to 67%.

For the Apollo LM all values are reasonable and moderate. The unreasonable values will be caused by the circumstance that Luna 9 to Ranger partially were designed to crash into the lunar surface instead of doing a soft landing and so had too few propellant to do a soft landing. But Surveyor is an exception of that. But Surveyor didn’t have a retrun-stage and ist return-propellant. I would have preferred to not apply those three – but I needed additional values besides Luna 15 and Apollo LM.

In total the unreasonable values enable moderate and reasonable safety margins for the Apollo LM – so the functions as wholes can be applied for calculations linearly up beyond the Apollo LM I think.



Regressional Function Selected

Doing the checks I thought over the selection of the regressional function for the stages of the larger virtual expendable labnder. Iselected that function that overapproximates the weight of the stages. Such a safety margin results in an underapproximation of the amount of propellant – und thus removes safety margins of the costs instead of keeping or increasing them.

Because of this a correction of the calculations of the previous post regarding the numbers applied really is required partially at least - I will select another function.

For the Apollo LM the stage-weights are all a bit too high – by between 2.5% and 54%. This needs to be handled a bit to keep safety margins. The point is that the higher the weight of the total hardware the less the propellant calculated per kg of hardware – and this at the expendable site of the functions. This would underapproximate the required amount of propellant of the reusable vehicle.

Since there seems to be no really systematical way out I think about to take the differences negatively – in contrary to getting positive results.



Tests by Micro-Space’s Lander

I am not sure about the follwing properties of Micro-Space’s Lander:

1. It has four tanks of 4 inch diameter – I am not sure if 1 inch are 2.5 centimeters or 2.54 centimeters. But the volume will be larger at 2.54 centimeters. And this would result in a larger weight of the volume around the volume of the propellant.
2. From Richard Specks answer(s) to me in the General Micro-Space Forum section I only know that the oxidizer is H2O2. But I do not know what the fuel is. Because of this I am going to apply oone minimum and one maximum density mix and one minimum and one maximum Isp mix.
3. I do not know the engine Isp.

Under www.bernd-leitenberger .de there are densities available only for the mixes with ADMH and Hydrazine – 1.24 g/cm^3 and 1.26 g/cm^3.

The mix with ADMH is the one with the minimum Isp also while the mix with the maximum Isp is with Beryllium hydride. For this mix I will apply the lower density of the two known to me at present. The calculations can be redone later if/when someone else or I myself find the densities missing.

I translated the weights Richard Speck has listed into kilograms and apply his explanation that one lander will be used for descent while the other will be used to fuel the first one for ascent. Since the fuelling lander obviously would NOT have to carry back any payload I suppose that it can return into orbit like the first one. This I necessaryly suspect to involve a problem – so I have to think about it again later.

The translation of the weights results in 22.68 kg for the empty lander, 272.16 for the propellant and 10.89 kg for the four tanks together which I need to consider to be the stage.

Obviously this is lighter than the lightest lander applied to get the regressional functions. I can calculate down from that lightest lander – Luna 9 – to find a correction factor but I can NOT test what I did in the previous post because it wouldn’t be a calculation linearly up.

But there is one difference between Micro-Space’s lander and the Apollo LM – the weight of the astronaut as payload is much larger than that of the empty lander and ist tank/stage while the weight of the astronaut is neglegible compared to the weight of the Apollo LM. So I add the weight left for the astronaut. This is listed to be 250 pounds which are 113.4 kg. This weight added to the other 33.57 kg of the empty lander including stage then are 146.97 kg – which is more than for the Luna 9 not only but is very close to Surveyor also.

So this way I can test the regressional function(s) as well as a calculation linearly down now. Of course I need to speculate a bit about the weight of the engine. Looking onto the image of the lander on Micro-Space’s homepage each engine seems to have a length of 20% of the length of one tank and there are four engines. This might suggest 2 kg to 3 kg for all engines together. I am not sure but this I suspect to be too low. Because of this I increase that to 6 kg.

At a density of 1.24 g/cm^3 the volume of the propellant plus oxidizer is 0.2195 m^3. 2.54 cm per inch are 0.0254 m – then 4 inch are 0.1016 m. I suppose the walls to be 0.005 thick for the calculations and thus have to apply a diameter for the volume of the propellant of 0.0916 m. Then the volume of the propellant in all four tanks together would be 33.3054 m high – 8.32635 m per tank each of the four (makes me doubt the more my numbers). Supposing a thickness of top and ttom of 0.04 m together I then get 33.3454 m length for the stage. The legs etc. I suppose to be neglegible light.

About all this I will ask Richard Speck in the General Micro-Space Forum because it’s speculation, there is the opportunity to ask and correct the calculations according to his answer – but I am aware that the data or some of them may be a technical or a business secret.

For now I apply the data listed here.

I need to speculate and think abut Luna 9‘s engine. The problem is that I find the data I needed to apply are a bit unclear. It is said that the ebngine has been thrown away before touch down and that this has been done a couple of time before it – the engine hasn’t been landed. The data above mean that I the engine of Micro-Space’s lander would have a weight of 1/21 of the lander itself. Applying this to Luna 9 would result in 3 kg to 4 kg for ist engine – let’s say 4 kg. I have no Isp for the propellant but one for the engine – 2727. This I will apply now – although this doesn’t fit no way into the regressional function because it is based on the Isp of the propellant and must be doubted to a large degree.

Luna 9 didn’t have no launching part – because of this I apply the two phases landing and launching without links and connections between them now – like I applied the Soyuz-Block DM-TPI as their EOI.

Applying the same regressional function applied for the potential reusable lunar lander weighing 3,600 kg I get for the Micro-Space lander 377.1023 kg of propellant – this is more by 38.559% - which would be a formidable safety margin. It should be a bit more moderate though to keep comparability perhaps. In so far the method of applying regressional functions has passed this first test successfully.

This test also proposes a solution for the problem that the stage-weights got by the regressional functions reduce the safety margin(s) – it shows that the required amount of propellant got tends to be too high even if the application of the function for the stage is kept unchanged. The advantage also is that the effects of both the regressional propellant-function and the regressional stage-function are combined and because of this show in this case that this perhaps might be keeping a sufficient safey margin. The Micro-Space lander could be a very good benchmark for the selection of the function(s) to be applied.

Of course the numbers applied must be doubted. ...

Because of this and because of something looking strange I do the break at this point and will continue in the next post where I hope to test via Pixel also.

Of course both the Micro-Space lander and Pixel will be used as normal landers for the calculations of the landing trip once the tests are finished, the strange thing is looked into and the inflexibility regarding paylaods is removed properly. I hope to be at that point at the end of the next post.



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Post    Posted on: Sat Jan 27, 2007 6:57 pm
Contents

Richard Speck’s informations about the correct data: Applying Engine Weight and Thickness
Richard Speck’s informations about the correct data: Applying all data listed
Remark regarding comparisons between this thread and post and Richard Speck’s answer to me
Pixel
Other Checks mentioned in the pre-previous post



Richard Speck’s informations about the correct data: Applying Engine Weight, Thickness and Isp

Thank You Very Much, for the data, Richard Speck. Aa first step I apply the values for the weight of the engine, the thickness of the tank walls and the Isp resulting from the information about the propellant(s) separated from the other data to only correct the data applied in the previous post. Later in this post the complete data you posted in your very positive answer to me will be applied.

About how I suppose the Isp I will talk in the next chapter in short.

The data are applied by adding another version of the Micr Space-lander where the engine is listed to weight 4 kg instead of 6 kg while the weight of the carrier is increased by 2 kg. The thickness of the tank-walls of 0.0005 mm instead of 0.005 mm results in a diameter for the volume of the propellant of 0.1006 m instead of 0.0916 m only.

The tanks would be a bit smaller now – a bit more than 6.9 m high.

The result at the two corrected values is a required amount of propellant of 513.1932721 kg which still is above the correct value by 88.57%. So the two correction done here still lead to the result that the rgeressional function applied in the calculation of a reusable lander weighing 3,600 kg is safe.

The value got now is below the value calculated in the previous post. This is because I detected that I according to the informations Richard Speck posted as answer to a much earlier post of mine doubled the weight of the propellant because two landers are used in his concept but didn’t double the weight of the empty lander and the tanks also. This I corrected for the 4 kg-engine and the 0.0005 mm-thickness.

So I have to redo the calculation of the previous post now. The value resulting for the speculated data of the previous post then is 512.2766595 kg which is by 88.23% above the correct value

Up to this point the regerssional functions seem to establish a sufficient safety margin.



Richard Speck’s informations about the correct data: Applying all data listed

Thank You Very Much again, Richard Speck, for posting the complete data – this enables to apply date here that are reality and thus tend to improve the realism and correctness of the data and the results of the calculations of landings here.

The data listed in Richard Speck’s answer are

    - propellant: 90% Hydrogen Peroxide, desity 1.35gm/ml
    a mix of Methyl Alcohol and Hydrazine, density of Methyl Alcohol about 0.9gm/ml.
    - engine weight: 4 kg
    - thickness of tank walls 0.0005 mm
    - length of tanks: 1.8 m
    - outer diameter of tanks: 0.1 m
    - number of tanks: 10
    - required amount of fuel: 900 pounds


The 900 pounds of fuel mean that another error occured in the previous post as well as in the previous step – I neglected the circumstance that the second lander consumes 300 pounds of fuel additionally to the 300 pounds for carrying the astronaut to the lunar surface and another 300 pounds to carry him back to orbit. The tanks required to carry 300 pounds down to the lunar surface by the second lander I also neglected.

I corrected this all which doesn’t change the previous results. This will be due to the additional tanks to carry the fuel for launch by the second lander. This means that the corrected results of both the previous post and the previous chapter still say that the regressional functions establish a sufficient safety margin. But in difference to those two a comparison to 900 pounds is required which are 408,233133 kg. The safety margin now is 25.72% and 25.49%.

Obviously the correction still keeps the regressional functions to establish a safety margin – only the percentage is reduced.

But does this hold also if the complete data are applied Richard Speck posted?

Obviously the propellant-mix assumed is wrong – not ADMH is used but Methanol plus Hydrazine. For this I do not know any Isp. This also is valid for 90% Hydrogen Peroxide. Under www.bernd-leitenberger.de I only find the Isp for 95% Hydrogen Peroxide with Hydrazine listed to be 2760 but no Isps where Methanol is involved. I do not know if the methyl-group of ADMH might be used as a substitute or not and so will do that no way. But the Isp for Hydrogen Peroxide with ADMH als is listed as 2760. So I will apply 2760.

The tanker-list for landers of the Excel-spreadsheet requires all tanks involved to be listed as one huge tank. This menas that the 10 tanks per lander are taken as one huge tank. The two landers Richard Speck applies plus the tanks to carry the fuel down to the lunar surface also are taken as one reusable lander. I suppose that the tank weight is kept except for the aditional tops and bottoms for the six tanks – but the former four will be shorter now. In so far I suppose that I do not have to apply a significant higher tank weight.

This way the regressional functions result in a required amount of propellant of 407.8382835 kg for the Micro Space-lander at the data Richard Speck posted. This now obviously is a little bit too few – the complete safety margin is gone

At this point now I do what I already thozght about in the previous post – for the stage I now apply another regerssional function of the four available that results in a lighter stage. I select that one that calculates the lightest stage for the Apollo LM – that stage still is by 55 kg to 56 kg heavier than the actaul stage was.

The new result is 686.1383567 kg. – there seems to be a safety margin again now of 68.08%.

Obviously the safety margin can be kept – simply by the selection of another regeressional function: There is sufficient flexibility up to now.

This means: The regressional functions paased the test against the Micro Space-lander successfully. And the test says that the stage has to ba calculated by the regressional function resulting in a light stage-weight.



Remark regarding comparisons between this thread and post and Richard Speck’s answer to me

It might be argued that the results of the calculations here are considered to be wrong because Richard Speck explicitly has said that to reuse the lander isn’t wirth the expenses etc. since it is that cheap and that he explicitly say that this would change only when the costs per kg drop below $ 220/kg.

I have no doubts that Richard Speck is right in that – and because of his business, his insights, his experiences and his knowledge of more detailed data his calculations allways will be more correct than those of each poster at this message board who is no producer of rockets or space vehicles.

But this does NOT mean that the results I am calculating in this thread are wrong – the point is that NO direct comparison is valid.

The reasons are crucial differences of the conspets. In this thread I apply a vehicle travelling between Earth and Moon that NEVER LANDS. This means also that LUNAR LANDERs applied in this thread NEVER will LAND ON EARTH.

The Excel-spreadsheet also calculates the minimum number of flights and passengers required to make the prices calculated possible. These numbers I am neglecting a bit ta present – they will be considered later a bit closer to find out the required scale of business and the ways and opportunities available to get to that scale of business.

So: Of course Richard Speck is correct and I never would try to argue against what he said – I myself in turn calculate concepts here that are quite different to his one. But bith his concept and those applied here can use the Micro Space-lander.

During the earlier unsystematical calculations I also considered the concept to leave the lander on the Moon completely and to apply a lander-like lunar tanker travelling between the lunar surface and a lunar orbit. This the Micro Space-lander also could be used for – in Richard Speck’s concept the lander carrying the launch-fuel for th lander carrying the astornaut is left on the Moon. Later this lander could be refueled by lunar ressources if they would allow for production of Hydrogen Peroxide, Methanol and Hydrazine... I do not know if this is possible – it requires carbon for example. But earlier I applied lunar Hydrogen and Oxygen. This Iwill repeat later.

In particular a comparison between this post and the previous one would be invalid because I am applying the Micro Space-lander here only to find out if the regressional functions lead to a safety margin.


Pixel

To apply the data James Bauer of Armaidllo Aerospace posted when he answered to my question in the General Armadillo Aerospace Forum section I first calculate the weights from gallons and liters. According to the post(s) 10 to 12 gallons of 55 gallons of Ethanol are left – so obviously 45 to 43 gallons are consumed. I will use 45 gallons. Since one gallon is 4.546 liters 45 gallons are 204.57 liters = 204,570 cm^3. At 0.7894 g/cm^3 these are 161,487.558 g = 161.487558 kg.

The 220+ liters of LOX because of the density of 1.141 g/cm^3 weigh 251,020 +g = 251.020+ kg. So a weight of 422.507558 kg has to be applied for propellant. The volume of this propellant seems to be 424,570 cm^3 = 0.424570 m^3.
The Isp of LOX/Ethanol is 2740 according to www.bernd-leitenberger.de

From a picture published I suppose the four spherical tanks to have a dimater of 0.8 m each. Then the four together have a volume of 1.072 to 1.073 according to the formular for a spherical volume. There seems to be a lot of volume around the propellant.

Since I need to apply a cylindrical tank I calculkate a height of such a tank by applying the diamter of 0.8 m and get 2.1333 m.

James Bauer told me that Pixel weighs 640 pounds. These are 290 kg to 291 kg.

Up to here the Isp seems to be a bit less only than that in the case of the Micro Space-lander while the amount of propellant is a bit more but not too much. This might outweight each other perhaps.

The height I get for the cylindrical tank is much less compared to the Micro Space-lander which will be so because I kept the diamter at 0.8 m. If I would have applied 0. M the height would be more similar to Micro Space.

But the weigh of Pixel is more than the weight of two Micro Space-landers, their engines, three Micro Space-tanks and one astronaut together.

This means that I cannot conclude from similarties to the Micro Space-lander that the regressional function would successfully pass a test against Pixel too.

So I have to talk to Armadillo Aerospace – in particular I must ask for the weight of the tanks and the engine.



Other Checks mentioned in the pre-previous post

The cause and the solution for the inflexibility are found and fixed. The weights of the lander, ist tank/stage, engine and propellant will be added automatically while it will be possible also to insert additional cargo that is freight really. This way it is avoided that the lander could be forgotten but trips can include freight also that needs to be inserted explicitly.

The data required to get regressional functions for TEI, EOI, TPI and POI are selected and the functions are about to be found. But first it is required to look again if they are needed already. This can be done when the solution talked about is inserted into the Excel-spreadsheet.

Also a check for negative values will be of help and assistance but I at present still have only vague ideas about it.

One of the constants at present is taken from two different tables for two different cells in parallel. That’s no problem but is a possible source of errors – I still must check the reasons from which this resulted.



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Post    Posted on: Sat Feb 10, 2007 10:33 pm
Contents

Remark regarding the list of landers
Armadillo Aerospace: The Additional Informations about Pixel
Testing the regressional functions against Pixel
Summary of Tests
Check of the Reason(s) for Application of two different Tables for two different Cells
Orbital Trip calculated Three Posts ago
Landing Trip calculated Three Posts ago
Remark about the Impact of the Additionally Required Safety Margins
Regarding the Safety Margin(s) for EOI and TPI
Landing Trips with Alternative Landers
Lunar Falcon
CXV-like lander
Apollo LM-like lander
Pixel
Micro Space
Appendix
List of Upper Stages involved into the Regressional Functions for TPI/EOI




Remark regarding the list of landers

In the previous post I redid a calculation because data applied earlier were wrong. This alone would be no problem – but the data applied partially were wrong and partially noit that wrong.

Because of this those data will not be available in the lists of the Excel spreadsheet.



Armadillo Aerospace: The Additional Informations about Pixel

As James Bauer of Armadillo Aerospace told me in the Q&A-tnread in the General Armadillo Aerospace Forum section the engines of Pixel weigh 45 to 50 pounds while the tanks weigh 90 to 95 pounds – and both these weights are part of the total weight of Pixel of 640 pounds he told me of last year. The seat added in between weighs 25 pounds I have to add to the 640 pounds.

Since James Bauer did NOT say that Pixel couldn’t be applied like Micro Space’s lander I suppose that it can be applied that way. But I suppose that it would be NOT required to refuel Pixel after landing by fuel carried by a second Pixel.

The infomration about the weight of the tanks I understand to refer to all four tanks together. Then the translation of pounds into kg results in a weight slightly above the weight of the tanks of Micro Space’s lamder only – like the amount of propellant. I apply the lower value to keep the required amount of propellant per kg of hardware as high as possible

The information about the engine(s) I apply according to that about the tanks.

Since the tanks and the engines are part of the 640 pounds 505 pounds are left for the remainder of Pixel to which 25 pounds for the seat have to be added. Then this reaminder is 50% heavier than Micro Space’s lander.

This makes me think again about Pixel being applied like the Micro Space-lander – I didn’t ask for engine Isps yet and have propellant Isps for earthian sea level only. So it may be that the correct values not available to me would make me cease the thinking.

So based on the data available I decide to apply Pixel for another test.



Testing the regressional functions against Pixel

That lander applied to get the regressional functions the weight of the carrier-part of which is closest to the weight of Pixel but weighs still less than Pixel – that lander is Surveyor.

Applying a diameter of 0.7 m for a cylindrical volume of the propellant of Pixel and the same regressional functions applied for the test against the lander of Micro Space a required amount of propellant of 1,155.735 kg is got – which is by 173.54% above the correct value.

This means that the regressional functions have paased successfully the test against Pixel also.

More yet seems to result from this: Another of the four functions for the propellant might be applied in combination with another one of the four functions for stages.

The only problem might be considered to be that the alternative set of functions might fail the test against the Micro Space lander. But there seem to be ways out:

1. That function that passes the test against Pixel but not that against Micro Space might be one boundary of a corridor while that function passing the tests agaisnt both landers might be the other boundary of that corridor.
2. Pixel is heavier than the Micro Space lander and is closer to landers heavier than Pixel – and thus might have to be considered to be more relevant.

Of course there is the additional problem that it has not been said explicitly yet that Pixel can be applied like the Micro Space lander or – more precisely – two of them.

But this also might be solved because the functions used for this test here resulted in a value 2.7354 times the correct value – the too high value might cover the requirements of an alternative Pixel that really can land on the Moon and return into orbit again.

Summary of Tests

All in all the regressional functions have been testetd against three vehciels now – Apollo LM, Micro Space and Pixel. They have successfully passed all these tests and thus seem to provide a sufficient safety margin

While it is correct to apply a function leading to high values for the propellant afunction leading to low values must be applied for stages here.

This will have to be considered to be valid for regressional functions for rockets later also.

There might be two functions forming a corridor of safety margins – meaning one function of lower boundaries of a safety margin and another function of upper boundaries of the same safety margin.

Which of four regressional functions must or can be applied depends on the stages, engines or prpellants to be applied by the potential lander.

The four regressional functions available are the one got via the statistical regression, a second one where the error of the constant is added to that constant, a third one where the error of the factor of the variable is added to that factor and the fourth one where both the error of the constant is added to the constant and the error of the factor is added to that factor.



Check of the Reason(s) for Application of two different Tables for two different Cells

The two different cells contain the weight of cargo. Up to the previous post it wasn’t clear yet if the lander has to be taken into account separatedly from freight or if this is NOT the case.

To avoid waste of time the lander was NOT taken into account separatedly. But it had to be expected that the tank of an existing lander has to be adjusted if the exisitng and the potential lander consume different propellants of different density – this continues to be possible. This would mean that adjustment like that of the stage of the Saturn IV B have to be calculated. And this in turn means two different values for the weight of cargo – lander plus freight – which require two different cells.

Then there would be two different values for the propellant of the existing lander – the original one and the one resulting from the adjustment.

The calculation of the landers is separated from the other calculations but the results go into those other calculations. The point where they are used in those other calculations is where the adjusted Saturn IV B is calculated. Before that adjustment is done the non-adjusted lander is part of the numbers.

To also keep oversight etc. two tables were applied.

But it turned out that adjustments of lander tanks will NOT be done a way that has an impact on cargo.

The lander will be kept precisely separated from the vehicle travelling between Earth and Moon and from freight.

The only question left is if the freight of the potential vehicle can or must be considered to be the same like that of the existing vehicle. This is NOT possible because the freight of the existing vehicle is used ONLY to calculate linearly down the propellant of a potential vehicle lighter than the existing one including ist freight. The freight of a potential vehicle MUSTN’T be predetermined by the Excel spreadsheet – and so two different cells are required but their valued will be inserted by a user freely. This menas that the values MUSTN’T be taken from a table automatically.

Of course a freight inserted by a user would be inserted into a table descirbing a trip – but this is quite another table than a table doing calculations or adjustments like the one being part of the reasons looked for.

The Excel spreadsheet has been improved according to this now.



Orbital Trip calculated Three Posts ago

After the corrections are done the required amount of propellant is dropped by around 2,000 kg applying the correction factors.

This results in a drop of the formerly calculated costs and prices of between around $ 1 mio at expendable QuickReach plus Falcon 9 S9 as tanker and around $ 11,000 at reusable QuickReach used as tanker also..

This difference has been caused by the removal of the second table applied for cargo as well as by the formerly inflexible handling of the case that a lander might be carried.



Landing Trip calculated Three Posts ago

It turns out that the amount of propellant got was nearly correct – it was higher formerly by less than 500 kg.

The weight of the lander including tank/stage is 5,762.398049 kg 3,600 kg of which is the carrier part. The tank/stage of the vehicle travelling between Earth and Moon weighs 2,081.546683 kg, the vehicle itself 3,600 kg and the engine 230 kg. This is a total of 11,673.94473.

Checking this against the existing vehicles applied the total hardware weight is above the weight of the existing vehicle(s) in EOI and slightly above the weight in TEI but below the weight in POI and TPI.

This seems to call for regressional functions now – but let’s look for the weights including the propellant for the lander that is carried during POI additionally to the lander itself. The amount of propellant calculated is 14,236.26582 kg like in the former post. Then the total weight in POI is 25,910.21055 which is below the weight valid in the case of the existing vehicle. This also holds for TPI.

So the former result still holds after the correction of the Excel spreadsheet are done.

Please note urgently: These calculations only provide a comparison to the result of an earlier post. I didn’t make sure that the regressional function(s) applied fit into the criterions found via Pixel, Micro Space or Apollo LM.



Remark about the Impact of the Additionally Required Safety Margins

Since the propellants and hardware weights got already for the landing trip already include a safety margin the additional safety margin(s) to some degree are safety margins of safety margins. In TEI the hardware weight got for the potential case is above the existing vehicle by around 100 kg only! For EOI this is a bit different – the potential case is above the existing case by around 2,000 kg which is more than a fourth of the weight of the existing case. But a safety margin of a safety margin is included here also.

In short – the additional regressional functions for the vehicle travelling between Earth and Moon increase the probability that the resulting prices and costs are sufficiently safe.



Regarding the Safety Margin(s) for EOI and TPI

Although it is NOT required yet to include a safety margin into the propellant amounts calculated for TPI it will be enabled already because of the requirement of a safety margin for EOI.

The reason is that there were no EOI yet and has to be substituted by the value for TPI for this reason. This already has been done before a safety margin for EOI became required..

This means that it already becomes possible to consider vehicles travelling between Earth and Moon here that are very much larger or heavier than what I was considering during the unsystematical calculations last spring and summer.

Since there are values available for TEI that seem to allow for getting a safety margin for TEI an opportunity to get a safety margin for POI seems not to be required yet. But I will enable a safety margin for POI also – for several reasons:

1. It is not sure that the data available for TEI are that different that they allow a statistical regression.
2. I am not sure if there are more than two values available – at present I have in mind only two: Luna 15 and Apollo CSM.
3. There nonethelss safety margins for three phases will be available – so why not adding the remaining one? Then all is complete and it saves the time to get it later.

POI can be used as a substitute in TEI if the data are insufficient..

I am already working on the regressional functions required for TPI (and EOI). The upper stages involved are listed in the Appendix..

In principle I could do like I did regarding the lander heavier than the Apollo LM. I already tried the regression for the orginal propellants – neglegging the effects and impacts of the differences between different propellants – and the degree of determination is 87.49% - this would be sufficient since regarding the landers I accepted 68% as sufficient.

But looking at a diagram got via Excel I saw amplitudes, volatility and erratic peaks that made me doubt if this would be sufficient. I felt too much doubts and so treid and played around how it all could be improved. The idea came up to me to distinguish two groups of values – an upper group and a lower group. This way I got a degree of determination of 97.98% for the upper group and of 98.586 for the lower group.

This is speaking for that split for now. But it isn’t sufficient yet to use it for calculations – regressions are required also for the different propellants calculated into one standard propellant for all upper stages involved like done regarding the landers.

Also a transparent and systematical way has to be applied for doing the split because there will be the opportunity that each one of you who wants to apply another group of upper stages is can do that.

This I will enable for the landers also – but I don’t think that it will have any significant impact on the results got up to now.



Landing Trips with Alternative Landers

Two lannders need safety margins not available yet – the numbers will be listed in the next post. One lander still needs considerations of how to calculate the numbers to be applied



Lunar Falcon

I didn’t find time yet calculate the Lunar Falcon a new way. I have in mind to apply the relation between the weights of the Saturn V and the Apollo LM. But there are a few alternatives. Since the Apollo LM had to go an altitude of 111 km only from lunar orbit to lunar surface or back the ratio might have to use the requirements for this altitude on Earth. On the other hand this wouldn’t be the orbital altitude the earthian Falcon V would go to.

Next the Saturn V has three stages for the launch while the Apollo LM has only one – the Falcon will have two.

I nonetheless suppose that the case of the lunar Falcon will require safety margins for EOI and TPI at least – which means that it will have to be calculated for the next post.



CXV-like lander

Because of the reqirement of safety margins for EOI and TEI no safey values are possible yet. The numbers already got aren’t sufficiently based on the criterions found by the tests against Pixel, Micro Space and Apollo LM.



Apollo LM-like lander

This case requires not a single safety margin for the phases TPI to EOI.but I didn’t find time yet to apply the proper safety margin(s) (regressional functions).



Pixel

To properly calculate a trip using Pixel the circumstance has to be handled that Pixel can carry one astronaut per landing only. Because of this five landings are required to carry five astronauts down to the lunar surface.

The amount of propellant required for one landing is automatically applied by the Excel spreadsheet. This now means that Pixel needs to refueled four times if each passenger is carried after the previous one has been landed and returned (another mode is possible but would require more thoughts I want to avoid at present). The propellant to be refueled now can be freight only – the flexibility established regarding landers and freight turns out to be required now.

Since Pixel consumes 422.507558 kg of propellant there is freight of 1,690.030232 kg involved in this trip. But this freight exists during TPI and POI only because the propellants for the lander are totally consumed when the vehicles and passengers leave the Moon for Earth. And calculation mustn’t apply the frieght twice because there is only one freight – the formulars take it as part of POI only.

Result: The amount of propellant for TPI to EOI is 46,548.90005 kg only – very close to the orbital trip.According to www.astronautix.com Ethanole costs $ 0.16 only which is more than the LOX-price. And the weight doesn’t have that much an impact on the transportation costs. So this landing trip would have costs and a price at the level of the orbital trip!



Micro Space

Here in priciple the same is valid like for Pixel. The difference is that an ampunt of proepllant of 408.233133 kg is required which is less than in the case of Pixel. The freight then is 1,632.932532 kg. The same result holds like for Pixel. The costs and price of the trip would be higher by a few thousand dollars because of the high H2O2-price of $ 1 to $ 2 but this small portions won’t weigh to the vast majority of passengers I suppose.





Numbers of costs etc. for the landing trips calculated here I will list later. The next post will include a comparison to a document you sent me, Stefan, - this I already announced several posts ago but needed to delay it because it turned out that something was improper – sorry for the long delay.

And I hope to consider the landing trip that includes refuel by lunar ISRU that had been considered zthe unsystematical and intransparent way only up to now.





Dipl.-Volkswirt (bdvb) Augustin (Political Economist)

Appendix

List of Upper Stages involved into the Regressional Functions for TPI/EOI

OAM
Titan 2-2
Burner 2
FW-4D
Agena D
Centaur C
Agena B
Luna 8K72-2
Molniya 8K78M-3
Molniya 8K78-3
Proton 11S824
Proton 11S824M
Saturn IV B


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Post    Posted on: Thu Mar 01, 2007 12:45 pm
Contents

Apollo LM-pendant. CXV-pendant, lunar Falcon: Selection of Functions best adjusted to Micro Space and Pixel
The Weight of the Falcon-derived Lander
Three Heavy Landers: Weights and Amounts
The Vehicles travelling between Earth and Moon: Phases TPI and EOI
The Vehicles travelling between Earth and Moon: Phases POI and TEI – ineresting...
Removal of Negative Values
Landing Trips sufficiently based on Safety Margins
Comparison to unsystematical calculations
Futron Report Stefan Sigwarth sent me – comparison
Refuelling at the Moon
The Safety Margins via Regressional Functions
Excel spreadsheet
Appendix
Lunar Orbital Vehicles for Regressional Analysis
Orbital Trip: Results avoiding negative values



Please select the points from the contents you are interested in in particular, if there are such points– due to time and other aspects it wasn’t possible to keep this post shorter

Apollo LM-pendant. CXV-pendant, lunar Falcon: Selection of Functions best adjusted to Micro Space and Pixel

In between it turned out that the amount of propellant listed when the regressional functions had successfully passed the test against Micro Space were too small – the correct value is 754.8362177 kg which menas that the functions are safer yet than thought. A few small corrections of numbers have been done and I tried to find the earlier not that correct values again to get the former value again – for checks – but failed. May be I come across those values later again. So I accept the higher value now.

Next I recognized that the correct data about the Micro Space lander mean that it is heavier than Surveyor now The regressional functions still pass the test but this is not the focus now.

There are two different sets of four rgeressional functions. The one is based on amounts of different propellants that are not recalculated into amounts of a standard propellant while the other is based on amount of propellant recalculated by Isp into amounts of one stnadrad propellant. What the standard propellant is depends on the propellant the selcted existing lander used.

Now Luna 9 and Surveyor used different propellants. So the standard is changed now and the constants and factors of the regressional functions of that set based on a standard are changed also. The value got now is 687.3489003 kg – very close to the value got earlier. May be the wrong values used earlier are close now but I don’t look for them now.

This value is got by the combination of a propellant function selected by the system of safety margins already applied and explained earlier. The amount of propellant of Surveyor was increased by 10% as safety margin. Next the next quarter above the correct amount of propellant Surveyor used was looked for – the amount was around 564 kg and the next quarter is 575 kg. And finally the value including the 10%-margin is rounded up to 630 kg. Then the three are compared to each other. The maximum of them is used then to find that regressional function for the propellant that is above but closest to that maximum. There might be functions resulting in higher values but these are not selected. This keeps it all systematical.

This also describes how Micro Space’s lander and Pixel can be used to select the regressional function for the stage: Since the earlier posts indicated that lighter stages have to be prefered over heavier ones that function is to be selected that is below but closest to the correct weight of Micro Space or Pixel. To the correct weight of these vehicles the 10%-margin is to be added, second the next quarter above the correct value has to be selected and the rounded up 110%-value has to calculated. The miniumum of those three is that weight of the tank/stage of Micro Space’s lander or Pixel that includes the systematically got maximum safety margin. It may be puzzling that I continue to calculate three values above the correct one – I do so because the amount of propellant is increased and requires a larger and thus heavier tank/stage.

That regressional function is the optimal one that results in that value for the stage that is below the value with the minimum systematical safety margin but closest to it among all the other above it.

It turns out that applying Surveyor results in values high above the correct one for Micro Space for all four regressional functions – they are all between 7 times and 20 times the correct value. To handle this there are the follwoing alternatives:

1. Application of a lighter existing lander. This would be Luna 9. But the values still would be high above the correct ones and above the level required because the constants alone already are high above the correct values.
2. Application of Micro Space (Pixel) directly. The values still would be slightly above the correct ones.
3. Division of the results of the regressional functions by that power of ten that drops them to that power of ten the correct values are at.

Using Micro Space and applying the third alternative that function is the best adjusted that results in the lightest stage – it still is very slightly above the correct value.

This results in the required amount of propellant of 687.3489003 kg.

At present the third alternative seems to be the most proper in this situation.

Under the perspective of the safety margin however the value got for the propellant includes it might be more proper to keep that margin systematical. This menas the selection of a combination of rgeressional functions instead of a function for the propellant and the stage separatedly. The functions selcted might be qutie different ones than those selected up to now. There are sixteen combinations each of which have to be inserted into the formulars.

This may be interesting and reasonable and I am thinking about enabling this method – but I am doubting abouzt it also on the other hand. It would mean to limit the safety margin included into the amount of propellant got – but I don’t know what upper limit might be correct. Each limit may be too few propellant.

So I neglect this method for now – the propellant depends on the weight of the hardware as independent variable and to this weight safety margins are applied.

That far the regressional functions best adjusted by Micro Space.

So now the adjustment by Pixel. First it is to be clarified that the too high amount of propellant got by the regressional functions is changed a bit in this case also. This caused by improvements of the selection of the regressional function for the propelannt. The amount is dropped by around 43 kg.

But the new amount is got by a function that is NOT the best adjusted function. That function is applied to calculate the weight of the tank or stage that results in the lightest tank/stage. But the method described above regarding the best adjusted function for the stage of Micro Space’s lander selects the function that results in the next heavier stage.

This function best adjusted to Pixel leads to a required amount of propellant of 1,039.716855 kg – still high above the correct value.

So now the propellant function is selected automatically via the given correct value while this is not possible regarding the stage function since ist selction is NOT based on the propellant here.

The function for the stage needs to be adjusted by the existing reusable landers – they are

267.1013157 kg + 0.389875022 * weight of lander (best adjusted to Micro Space)
267,1013157 kg + 0,542930878 * weight of lander (best adjusted to Pixel)

This means that the stage-function must be selected manually by choice of the lander it should be best adjusted to.

Up to now two landers are available only for best adjustments – Micro Space and Pixel. In the future the lander of Masten Space Systems can be added – at present I am not sure to what degree the hardware Masten is developing really will be opertaed at the Lunar Lander Challenge.at the XPRIZE CUP.

So the functions, the formulars and – to some degree at lest- the Excel spreadsheet are ready to calculate a reusbale pendant of the carrier part of the Apollo LM, a CXV-like lander and a Falcon-derived lander. But first an idea about the weight of the Falcon-derived lander needs to be got.



The Weight of the Falcon-derived Lander

Like already said in the previous post the Apollo LM will be applied to derive this weight.

Let’s start with the launch. The amount of propellant required at launch is 2,356 kg while the weight of the Apollo LM AS is 2,189 kg.

Regarding the launch of the Falcon V as actually designed by SpaceX I again considered the weight of 154,500 kg liested by SpaceX. During the former unsystematical calculations I applied this as empty weight. Now I compared it to the weight of existing expendable vehicles and think that the value is too high for an empty vehicle – in particular since it is kept as light as possible.

The problem now is that I have no safe idea about how much of that weight is hardware and how much propellant.

Because of this the weight of the Apollo LM AS and ist propellant should be applied in total which is 4,545 kg.

The value 154,500 will be the weight without the payload. The maximum possible weight of the payload listed is 5,400 kg. So 159,900 kg have to be applied.

According to www.bernd-leitenberger.de the Saturn V could launch 133 tons into an orbit at 185 km altitude – a value applied also by others discussing at this mesage board. This required a total weight of hardware plus propellant of 28,585.415. To this a portion of the third stage has to be added. This portion I didn’t calculate as precise value here because for a few reasons.

In difference to the Apollo LM AS the Saturn V consumes two different propellants – LOX/Cerosene and LOX/LH2. I couldn’t find the altitude where the first stage separates from the upper two. This keeps me from applying the altitude of 100 km I said to want to apply in the previous post.

Next precision would require to calculate the LOX(LH2 into LOX/Cerosene for all stages and them to calculkate it into N2O4/ADMH to get the correct ratio to the Apollo LM AS.

Third thrust would have to be applied here.

All this would require a lot of time again – simply for just one calculation that I don’t think to be applied for other cases again.

Since hydrogen has a density of 25% to 33.333% that of LOX/Cerosne the two upper stages together would be lighter that the actual ones. This might allow for adding one third of the weight of the empty third stage. This would mean a weight of 32,585.415. But the Isp of LOX/Cerosene is below that of LOX/LH2 by a bit less than a quarter – the reduced weight of the two upper stages would be iincreased then by one quarter of the new value.

So it may be that applying a total weight of 32,000 kg has a tendency of being too much if all stages would consume LOX/cerosene. This would result in too large a ratio. Since the Isp of LOX/Cerosene is less than that of N2O4/ADMH – propellant of the Apollo LM AS – the ratio would be smaller if this would be calculated into LOX/Cerosene.

The ratio mustn’t be too high because this would reduce the weight of the Falcon-derived lander too much. Because of the Isp-ratio I decide to increase the weight of 32,000 kg by 6,000 kg to 38,000 kg and the total weight of the Apollo LM AS up to 5,000.

Then the ratio is 7.2. The over 80,000 kg of LOX/LH2 plus 8,000 kg of the Saturn VI B I cosider to be part of the payload launched into the arthian orbit. Now I divide the weight of the Falcon V designed plus the maximum payload by these 7.2 getting 22,208.33... kg for a lunar Falcon-derived vehicle that launches from the Moon.

This doesn’t include the landing yet. To include it Micro Space’s approach would be the best to be applied – one lander that launches and arrives inorbit empty. The same lander has arrived the lunar surface empty as well. Next there is a second lander delivering fuel to the surface and being empty as well when touching down. These two landers I added on to one lander.

To do so regarding the Falcon-derived lander also the amount of propellant is required. Since it is not listed by SpaceX I am going to try now to conclude to it. A look into the data about the Soyuz-rocket available under www.bernd-leitenberger.de shows that the weight of the empty Soyz-rockets is 23 tons to 24 tons allways (as far as detailed numbers are available there). It is not clear how much lighter the designed Falcon V is if empty. For simplicity let’s assume that it weighs 21 tons and divide it by 7 for the Moon. The Syouz-data I am referring to don’t include a payload. The Falcon V designed can carry 5,400 kg. This leaves 16,808.33... kg for the stage/tank plus propellant. The 21 tons of empty weight of the Falcon designed divided by 7 would mean a weight of 3 tons of the empty lunar stage/tank. This would mean 13,808.33... kg of propellant which would be LOX/Cerosene required by a launching Falcon-derived lander. One such lander would deliver 5,400 kg of propellant to the lunar surface at the same requirement of propellant.

The 13,808.33... kg would launch 8,400 kg – 5,400 kg payload plus 3,000 kg tank/stage. The same amount would deliver that weight to the surface. The first landing would include a carrier for people and/or payloads that are no propellants. A second identical lander would deliver 5,400 kg of propellant – but it would launch a smaller weight. In principle only 3,000 kg have to be launched then that can be assumed to need 5,000 kg of propellant only. Then 34,5 landings are needed. This means

13,808.33... kg for the landing itself.
34.5 * (13,808.33... kg + 5,000 kg) = 648,887.5 kg for all deliveries and the final launch of the tanker-lander
13,808.33... kg for the launch

676,504.166... kg of propellant in total. The hardware used in this calculation weighs 11.400 kg in total.

Obviuosly I have got a horrible weight again.

There is one uncertainty regarding the data – calling SpaceX’s homepage only a grey area was displayed when I tried to check, if 5,400 kg payload is correct or if 4,500 kg has to be applied. May be I reconsider this later but I am not sure.

Of course most of the horrible weight is freight – as weight of the lander itself 46,425 kg only are to be inserted as propellant and 11,400 kg for the carrier, its stage and the empty weight of the tanker delivering propellant from the orbit to the surface. Of the amount of propellant 27,616.66... kg are landing and launch of the lander and 18,808.33... kg are one landing and one launch of the tanker.

The the freight is 630,079,166... kg.



Three Heavy Landers: Weights and Amounts

Applying the formulars for the landers including the rgeressional functions the vehicle travelling between Earth and Moon has to carry:

Code:
lander               tank/stage   adjusted to   prop.         tank/stage   carrier

Reus Apollo LM-pnd   Block DM     Micro Space     6,321.637     858,085    1,535.667
Reus Apollo LM-pnd   Block DM     Pixel           5,752,21594     780.793    1,535.667
CXV-pendant          Block DM     Micro Space    16.045.599   2,177.993    3,600
CXV-pendant          Block DM     Pixel         14,276.769   1,937.896    3,600
Falcon-derived       Falc.-der    -             676,504.167   6,000        5,400


The table shows that the adjustment to Pixel results in less weight. This has to do with the circumstance that the regressinonal function best adjusted to Pixel gets the heavier stage. While the effect seems to moderate for the Apollo LM-pendant I consider this NOt to be the case regarding the CXV-pendant and will apply the adjustment to Micro Space only for the landing trips that don’t include refuelling. This I do to keep the highest systematical safety margin.

To apply these values now the regressional functions for the vehicle travelling between Earth and Monn are needed.



The Vehicles travelling between Earth and Moon: Phases TPI and EOI

The correct original values for the amounts of propellant consumed in TPI can be divided into an upper and a lower group by the regressional function that doesn’t apply the errors of the constant and the factor. That function can be used to calculate the values. Then the correct values are compared tto these results – those vehicles the correct values for are aboce the results are the upper group while those below the results are the lower group.

The function got by the vehicles listed in the previous post consists of the factor 1.652758829 and the constant 5,690.160714. Because I changed something a bit here the degree of determination again- it’s 89.19%

Next the regressional analysises for each the upper and the lower group is done. Without the errors the function for the upper group consists of the constant 12,840.57038 and the factor 1.509869128 – which means a much higher level but a slightly smaller slope. Because of the smaller slope it might be that another function must be applied – this will be decided by an adjustment to the payload to be accelerated. Since no reusable vehicle like Micro Space’s lander or Pixel is available there is no other choice. The adjustment will be done like for the landers. The function(s) will be tested against the Saturn IV B.

The lower group consists of the factor 1.99668784 and the constant 1,417.48481 – because of the higher slope this function might deliver more proper results even for a heavier vehicle than the function of the upper group.

Up to this point the propellants haven’t been calculated into one standard propellant. For this standard propellant all the regressions have to be repeated now. The upper and the lower row might look quite different then. And this really is the case – one of the rockets that were in the upper group in the non-standard propellants case is moved to the lower group now and the degree of determination is increased from between 93% and 94% up to over 97%.

It also turns out that the lower group of the standard propellant(s) case – degree of determination between 82% and 83% only – results in a regressional function of a slope that results in propellant amounts very high above those resulting by the functions got for the upper group – the highest values among all the functions. But this doesn’t mean yet, that the function for the lower group will be applied – among the other functions there is one best adjusted.

For the stages it’s all quite similar except for the circumstance that no standardization is involved. There are five groups – all rockets, rockets of the non-standardized upper row, the rockets of the non-standardized lower row, the rockets of the standardized upper row and the rockets of the stnadradized lower row.

Since there are no reusable vehicles that can be appled to select the best adjusted regressional stage function the method applied for the propellant will be used here.

The constants of the regressional propellant functions listed up to here are valid for the Saturn IV B only since I apply that stage to test the functions. In difference to that the constants and factors of the regresional stage functions are independent of the propellant – and so they are valid for each upper stage.

One aspect I have to mention here – the Block DM is NOT included into the statistics. This also holds for the Soyuz-capsule. I didn’t include them because of a difficulty with the informations available. The articles about the two companies working on private lunar trips are quoted to have said that the Block DM will be used. But that stage will be modified. The modifications up to now never have been specified. This means that the informations required for the regression are too incomplete.

So far the functions for TLI and – as substitutes – for EOI.



The Vehicles travelling between Earth and Moon: Phases POI and TEI – interesting...

What’s left are the functions for POI and TEI. TEI will be derived from or substituted by POI because the Apollo CSM had been used for both these phases in total and provides a ratio between the propellant requirements of the two phases. Because of this the TEI-function simply is the POI-function times that ratio here.

The appendix containes a list of the vehicles used for the regressional analysis.

It turns out that the propellant function based on original propellants and the propellant function based on standardized propellant(s9 as well as the stage function all have a degree of determination extremely close to 100%! For the propellants the degree of determination is above 99.99% - for the stages it is above 99.9999%.

This might mean that the resulting function without the errors is that safe that no safety marginbs are required.

More yet – using the functions to calculate the propellants it turns out that the results are above the correct amounts but that slightly that the differences are below 1% of the correct values.

Obviously the desired safety margins can’t be got this way and appear not to be required – but should I rely on that? I am feeling doubts.

But what to do? Regarding the propellant function(s) to me the best way appears to be to simply apply the method already established for landers and the other two phases and to subtract the constant(s) of the functions from the maximum value and to divide the remainder by the weight of the Apollo CSM including all its freights then. This way a larger factor is got that provides a sufficient safety margin.I decide to select the constant of that function that is above but closest to the correct value – this keeps the factor as high as possible.Here the function is got via the POI-propellant – because of this the ratio between the TEI-propellant and the POI-propellant will be applied to get the function for TEI.

Regarding the stage or tank there really is no problem because a light stage weight improves the safety margin of the propellant and the finding about the function means that the values all fit into the principle that that function to be selected leads to a result that is below but closest to the safety margin value.

The formular developed earlier menas that a too high value for one phase has an increasing effect on the values of the previous phases – so the overall safety margin is increased by doing as described.



Removal of Negative Values

The checks for negative values added to the Excel spreadsheet in between have indicated that during the calculation of the orbital trip negative values have occurred. Becuase of this I discovered that randomly the value of the diamter of the volume of the propellant had been altered – I corrected it to 6.46 m again which I seem to have have selected when i started to calculate the round trip.

This also has an impact on the results for all the landing trips.

The new results are slightly higher than the earlier ones – they are listed in the appendix.

Please note: The cylindrical weight of the vehicle plus the empty stage or tank resulting now is by a few hundred kilograms above the weight of the existing vehicle plus the existing stage applied. This means that the regressional functions must be applied for the orbital trip also now – but for EOI only.

Regarding the regerssional function it turns out here that neither the standard-propellant – LOX/cerosene – upper row nor the standard-propellant lower row is best adjusted but the standard-propellant original set of rockets – non-split. If the propellants weren’t standardized this row would be much more adjusted but I wouldn’t trust the result because of differences in density and Isps.

Regarding the stage function one of the functions for the non-standard-propellant lower row-rocket-set is best adjusted – the standard-propellant-rocket-sets all result in weights high above the maximum value – please remember: stages have to be calculated light instead of heavy.

Using the function it turns out that they result in less propellant instead of more meaning a smaller tank instead of larger one. The explanation seems to be that the CXV is by 3,650 kg lighter than the Soyuz – the functions have to be applied so that the weight of the CXV is applied to calculate a virtual lighter Soyuz.

So there is no chance at present than to accept the unsafe result that is got without the functions – and it is not that much of a problem I think because the calculation of the price(s) involves an additional safety margin.

Regarding those prices and variable costs to which no safety margin is applied the following reasoning means that they may safe also: The calculation really has gone linearly down which is safe. Some of those safe values then have gone into the calculation that results in the value above the safe limit the existing vehicle sets.. The other phases where the existing vehicle is much heavier than the weights resulting from the calculation also may have the effect of keeping the results safer than they are looking – the resulting weights are below the weights of the existing vehicles in TPI, POI and TEI.



Landing Trips sufficiently based on Safety Margins

It is to be expected that the values for all the landing trips are above the limit set by the existing vehicle in EOI at least in the case of a cylindrical tank because this already is the case for the orbital trip – but what about the case of a spherical tank?

Micro Space’s lander as the lightest already results in a total hardware weight above the limit set by the existing vehicle. The application of the regressional function results in less weights yet. So I here also prefer to not apply the functions – in TPI to TEI the resulting weights still are below the existing weights provided by the Saturn IV B, the Apollo CSM and the Apollo LM.

The values in the case of Micro Space are as follows:

proepllant for travelling Earth-Moon-Earth: 46,699.6571 kg cyl. 33,898.9555 kg sph.
propellant for the lander has benn listed already – per landing as well as for 5 landings in total
total propellant costs for 5 landings: $ 1,326.76

At tanker Falcon 9 S 9 and taxi CXV with expendable QuickReach2

variable costs $ 34,727,824.59 cyl. vs. $ 26,657,839.47 sph.
price $ 38,200,607.05 cyl. vs. $ 29,323,623.41 sph.
initial price $ 49,200,607.05 cyl. vs. $ 40,323,623.41 sph.
price including safety margin $ 44,000,000.00 cyl. vs. $ 34,000,000.00 sph.
initial price including safety margin $ 55,000,000.00 cyl. vs. $ 45,000,000.00 sph.

At tanker and taxi CXV with reusable QuickReach2 each

variable costs $ 369,814.25 cyl. vs. $ 279,256.40 sph.
price $ 406,795.67 cyl. vs. $ 307,182.03 sph.
initial price $ 11,406,795.67 cyl. vs. $ 11,307,182.03 sph.
price including safety margin $ 460,000.00 cyl. vs. $ 350,000.00 sph.
initial price including safety margin $ 11,460,000.00 cyl. vs. $ 11,350,000.00 sph

At tanker Launchpoint Technologies and taxi CXV with expendable QuickReach

variable costs $ 5,848,739.41 cyl. vs. $ 5,363,208.79 sph.
price $ 6,433,613.35 cyl. vs. $ 5,899,529.67 sph.
initial price $ 17,433,613.35 cyl. vs. $ 16,899,529.67 sph.
price including safety margin $ 7,260,000.00 cyl. vs. $ 6,600,000.00 sph.
initial price including safety margin $ 18,260,000.00 cyl. vs. $ 17,600,000.00 sph

As can be seen by a comparison to the values for the orbital trip the differences to that trip are small only – and it turns out that Pixel would increase the prices by that small values that they aren’t worth to be listed – I will do that in another post in an appendix. John Carmack, this doesn’t mean that I don’t consider Pixel to be essential – I do that really, but at this point I don’t get additional insights.

The situation regarding the weights also doesn’t change.

So it’s time now to look at the landings trips using heavy landers.

Let’s start with the reusable pendant of the Apollo LM.

This now is a case where the application of the regressional function really establishes a safety margin – the resulting weights are higher than without the function. In so far the heavy landers may mean safe values.

Since the Apollo LM carried two persons only five passengers would require three flights. This means that additioanlly to the propellant the formualr(s) calculate for the lander 11,504.43188 kg freight are to be carried.

The calculation assumes a Block DM as stage or tank for the lander. This means that the lander hardware in total is lighter than in the case of the actual Apollo LM. That’s the reason why less propellant is calculated than the Apollo LM needed.

No function needs to be applied for TPI and POI yet – but the function for TEI must be applied now.

Interestingly the function results in less propellant with the reusable pendant of the Apollo LM – so I switched the function off again. The situtation is analogous to that with Micro Space but one additional safety margin has been added.

The values are:

proepllant for travelling Earth-Moon-Earth: 76,460.0587 kg cyl. 67,385.419 kg sph.
propellant for the lander 17,256.64782 kg
total propellant costs for 3 landings: $ 11,216.82

At tanker Falcon 9 S 9 and taxi CXV with expendable QuickReach2

variable costs $ 63,082,107.26 cyl. vs. $ 57,361,154.68 sph.
price $ 69,390,317.99 cyl. vs. $ 63,097,270.14 sph.
initial price $ 80,390,317.99 cyl. vs. $ 74,097,270.14 sph.
price including safety margin $ 78,000,000.00 cyl. vs. $ 70,000,000.00 sph.
initial price including safety margin $ 89,000,000.00 cyl. vs. $ 81,000,000.00 sph.

At tanker and taxi CXV with reusable QuickReach2 each

variable costs $ 687,993.64 cyl. vs. $ 623,795.60 sph.
price $ 756,793.00 cyl. vs. $ 686,175.16 sph.
initial price $ 11,756,793.00 cyl. vs. $ 11,686,175.16 sph.
price including safety margin $ 840,000.00 cyl. vs. $ 760,000.00 sph.
initial price including safety margin $ 11,840,000.00 cyl. vs. $ 11,760,000.00 sph

At tanker Launchpoint Technologies and taxi CXV with expendable QuickReach

variable costs $ 7,554,674.68 cyl. vs. $ 7,210,473.60 sph.
price $ 8,310,142.15 cyl. vs. $ 7,931,520.95 sph.
initial price $ 19,310,142.14 cyl. vs. $ 18,931,520.95 sph.
price including safety margin $ 9,200,000.00 cyl. vs. $ 8,800,000.00 sph.
initial price including safety margin $ 20,200,000.00 cyl. vs. $ 19,800,000.00 sph

As n be seen by a comparison to the result for Micro Space the price with a reusable pendant of Apollo LM would be significantly higher – there may be passengers who prefer Micro Space or Pixel for this reason and the market might rule out the reusable Apollo LM-pendant. If other aspects will or would change the preferences should be discusssed in the Public Perception section partially at least or in another thread.

What now about the CXV-like lunar lander? For this lander no propellant would have to be carried as cargo because it would carry five people down to the lunar surface and back again by one landing.

The function for TEI still results in less propellant – but the weights resulting mean that the function for POI must be switched on now.

It turns out that the regressional POI-functions increase the result a bit again but not to the number resulting if only the function for EOI is switsched on.

I was trying around a bit and found that switching on the EOI-functions and the POI-functions with keeping switched of the TEI-functions increases the weights while switching off EOI and TEI but keeping switched on POI results in an astronomical number of more than 37 mio kg of propellant.

A look at the factors and constants shows that they are relatively small for TEI but relatively high for EOI. It can be expected mathematically that the linear functions have a range where their results are below the real existing data and another range where they are above those data – this is the explanation for what turned out.

The result simply is that the price of a landing trip using a CXV-like lander would be significantly above the according numbers for the reusable Apollo LM-pendant – which might change if the lander would be left on the Moon. This will be considered later. The numbers for the CXV-pendant are ranging from $ 125,000,000.00 initial price cylindrical including safety margin at tanker Falcon 9 S ) with taxi CXV with expendable QuickReach2 to $ 782,416.42 variable costs spherical at tanker and taxi CXV with reusable QuickReach each.

The propellant required is aclose to the 100,000 kg-mark – without the lander the propellant for has been listed earlier already..The propellant for the lander would cost nearly $ 28,000.

The lunar Falcon I consider only for comparisons. It requires the TPI-functions to be switched on. Then the result is more than 2.6 mio kg for the travel between Earth and Moon to which the more than 676,000 kg for the lander itself would have to be added.

The propellant for the lander would cost $ 439,727.71. The total price would be ranging between $ 2,051,000,000.00 and $ 19,260,809.39.



Comparison to unsystematical calculations

Looking into the table posted around 9th of July 2006 it seems that spherical at least lower prices and costs are got now – cylindrical the prices are slightly above the earlier ones.

The landing trips are to be had significantly cheaper also – but at using Micro Space or Pixel only. For those cases drops by between a fourth and a third are resulting. The reusable Apollo LM-pendant would increase the price by around two thirds.

Interestingly 100kg-tankers launched by Launchpoint Technologies‘ maglev theoretically could keep the price maximum very close to the result got earlier – and this value might be possible in four to five years, if they succeed until then, if the technology would be used for such tankers and if the vehicles for and towards the Moon were available then. Four to five years would mean 2011/2012 – t/Space recently said they might have ready their orbital vehicle in 2010 when they reported that they and NASA have closed a Space Act Agreement.

The price got for the lunar Falcon is above the earlier result by $ 400 mio to $ 600 mio.

There seems to be a tendency to both directions and a visible relevancy of the spherical case – but up to now I have looked at this not enough yet.



Futron Report Stefan Sigwarth sent me - comparison

Hello, Stefan,

I have gone through the report and looked at the launch prices and the payloads. Without doing any calculations it quickly was clear that the costs and prices I am calculating here based on the Falcon 9 S 9, the CXV, QuickReach2 and Launchpoint Technologies never can be achieved by the expendable rockets in use at present.

This I tend to suppose to be one of the major reasons why there is going on not more in space and regarding Moon and Mars.

I will read the report several times more to link it to the calculations and results of this thread later. May be it will be based on $ per kg, may be the base will be distance or the like.



Refuelling at the Moon

Unfortunately it is not possible yet to calculate trips during which the vehicle travelling between Earth and Moon is refuelled at the Moon.

But the landing trips calculated in this post are of interest for such trips. Several trips calculated carry freight and this freight is propellant.

I am not sure if it is correct to apply earthian prices for propellant found or created at the Moon but it is required to apply a price. Involving freight may be of help. I might include deliveries of propellant from Earth – similar to a comparison that was involved in at least one of the last unsystematical calculations earlier. I am thinking about a way to rawly approximate the costs of the transportation along the three-months-trajectory t/Space are talking about in one of their documents.

How the formulars are to be applied for the case of refuelling has been described eralier in an appendix already when I derived the formular(s).



The Safety Margins via Regressional Functions

It turned out that the regressional functions found and applied not neccessaryly result in higher values than the linear calculations up by ratios and shares.

This may mean that the data the regressions are based on include ways and techniques to reduce propellant requirements and tank weights that cannot be taken into account the way the calculations are done. This would favor the idea that the real future prices may be less than those calculated here. Then the formulars and functions would be overapproximating the prices – which is intended.

Another point is that I at present don’t see a better way to get additionally required safety margins a systematical way. I am looking for them and might extend something I have done but it’s looking a bit chaotic to me.

The functions will be of use later again but they will not be required for the refuelling trips to be calculated next.



Excel spreadsheet

This all took much more time than I thought because it had to be incorporated into the Excel spreadsheet in several cells including some additional control-cells. Several new tables had to be added and new columns had to be added to exisiting tables.

These enhancements are new sources of errors which occurred really and required corrections of calculations.

So prior to further calculations the trip design table at least has to be modified and improved.

Since it seems to me that there are aspects, links, connections, functions, terms etc. that may appear strange, puzzling, wrong or something like that I am thinking about commenting them in teh Excel spreadsheet – this also is a help for me myself as areminder.







Dipl.-Volkswirt (bdvb) Augustin (Political Economist)



Appendix

Lunar Orbital Vehicles for Regressional Analysis

Code:
name               total weight   empty weight   prop.

Lunar Prospector      296.4          158.7          137.7   Hydrazine
Clementine            424            228            195     N2O4/Hydrazine
Explorer 49           328            215.8          112.2   solid
Explorer 35           104.3           73.3           31     solid
Apollo CSM         45,024.8       33,377.3      11,647.4   N2O4/ADMH


For the second to fourth vehicle there are different data available about the total weight. I selected those data, that arithmetically fit best into the data available about empty weight and propellant.

The empty weight of Explorer49 is calculated from the avilable data.

Regarding Explorer35 the empty weight is calculated as well plus there is the problem that except for the total weight to data about IMP-D was referred. I had no chance but to apply the information that except for the weight the data are identical. From this I suppose that the amount of propellant is idnetical. From this I concluded the empty weight.

I also wanted to include Lunar Orbiter, but no data except for the total weight are given, The same holds for the russian Lunas. It’s a pity that there are as many lunar orbiters as rockets having launched them but that much less data about them are available than about those rockets.

Data that can be used for a regressional analysis of stages or tanks are available about the two Explorers and the Apollo CSM only – about Clementine and Lunar Prospector I didn’t find any up to now.




Orbital Trip: Results avoiding negative values

Correction factors applied – no regressional functions applied

Required amount of propellant: 43,782.8529 kg cylindrical 28,458.7194 kg spherical
Weight of required tank/stage: 5,942.9840 kg cylindrical 3,862.9213 kg spherical
Weight including vehicle: 9,772.9840 kg cylindrical 7,692.9213 kg spherical

Cylindrical – higher than safe limit by 561.7829 kg: price/variable costs

Bold values trustworthy

tanker Falcon 9 S 9/taxi CXV with expendable QuickReach2

variable costs $ 31,602,156.62
price $ 34,762,372.28
initial price $ 45,762,372.28
price including safety margin $ 40,000,000.00
initial price including safety margin $ 51,000,000.00

tanker and taxi one CXV with reusable QuickReach2 each

variable costs $ 334,739.36
price $ 368,213.30
initial price $ 11,368,213.30
price including safety margin $ 420,000.00
initial price including safety margin $ 11,420,000.00

tanker Launchpoint Technologies/taxi CXV with expendable QuickReach (4 to 5 years in the future)

variable costs $ 5,660,683.61
price $ 6,226,751.97
initial price $ 17,226,751.97
price including safety margin $ 7,000,000.00
initial price including safety margin $ 18,000,000.00

Spherical: price/varibale costs

tanker Falcon 9 S 9/taxi CXV with expendable QuickReach2

variable costs $ 21,941,316.72
price $ 24,135,448.39
initial price $ 35,135,448.39
price including safety margin $ 28,000,000.00
initial price including safety margin $ 39,000,000.00

tanker and taxi one CXV with reusable QuickReach2 each

variable costs $ 226,329.63
price $ 248,962.59
initial price $ 11,248,962.59
price including safety margin $ 280,000.00
initial price including safety margin $ 11,280,000.00

tanker Launchpoint Technologies/taxi CXV with expendable QuickReach (4 to 5 years in the future)

variable costs $ 5,079,439.23
price $ 5,587,383.15
initial price $ 16,587,383.15
price including safety margin $ 6,200,000.00
initial price including safety margin $ 17,200,000.00

Regressional function applied for EOI – correction factor for EOI set to 1

Required amount of propellant: 31,932.8395 kg cylindrical 20,755.9613 kg spherical
Weight of required tank/stage: 4,334.4903 kg cylindrical 2,817.3666 kg spherical
Weight including vehicle: 8,164.4903 kg cylindrical 6,647.3666 kg spherical



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Post    Posted on: Wed Apr 04, 2007 9:11 pm
Contents

Remark regarding the Application of the Regressional Functions
Modifications and Improvements of Tables of the Excel Spreadsheets: Impacts
Lunar Tankers: Think of a Detail of the Falcon-derived Lander
Deliveries of propellant or freight to the Moon
Former unsystematical calculation: Three possible cases to be distinguished
Original Refuelling Trip
Part One-Calculation(s)
Part Two-Calculation(s)
Total of the two Calculations.
Excel spreadsheet
Appendix
Calculation of reusable lunar tankers




Remark regarding the Application of the Regressional Functions

I reconsidered how I applied the regressional functions to check if all was correct. Doing so I needed to clarify it to myself again and because of this it might be of help to clarify it publicly here too.

Phase-internal:

1. The purpose of the regressional functions is to enable the replacement of the amount of propellant and the
weight of the stage or tank of an existing vehicle by that amount of propellant and that weight of stage/tank a virtual version of that vehicle would require that would have a weight different to the real existing vehicle. This means that all other properties of the existing vehicle are kept unchanged.

The weight of the virtual existing vehicle allways is equal to the weight of the potential vehicle because that weight is above the weight of the real existing vehicle – including freight etc.!

2. The regressional functions describe a relation between the different amounts of propellants existing vehicles required and the weight of those existing vehicles themselves – this weight DOES NOT INCLUDE the weight of the STAGES or TANKS because that weight also is calculated by other regressional functions and because the amounts of propellant applied to get the regressional function(s) for the propellant include the propellant required to accelerate the stages/tanks.

3. The result of the regressional functions for the propellant because of 2. and the trailing issue of 1. completely replaces the real amount of propellant the real vehicles needed.

4. The result of the regressional functions for the stages/tanks because of 1. COMPLETELY replace the total weight of the stage/tank of the real existing vehicle.

Cross-phase:

1. The amounts of propellant the existing vehicles required that are used to get the regressional functions is related to the weight of the vehicles only – but include amounts also that were required to accelerate the additional masses of stages/tanks and propellants required for future phases.Because of this it is NOT allowed but invalid to apply the functions to the weight(s) of those stages and propellants for future phases.

2. The new amounts of propellants and weights of stages must be applied to get the proper ratios – and thus in opposite to excluding them from the application of the functions still must be added on across the phases for the ratios like done if the functions are not applied

From these 4 points it follows that NO amount of propellant and NO weight of a stage or tank of the real existing vehicle can be involved into the formulars no more – it MUSTN’T be done and WOULD BE TOTALLY WRONG. All the other weights - freights, landers and vehicles are already involved completely.

This means that the formular(s) is /are modified essentially if the function(s) must be applied because the functions involve several data of the existing vehicle as a TOTAL THAT IS NEITHER DETAILED NOR STRUCTURED FOR THE VIRTUAL VERSION that are DETAILED FOR ITS REAL VERSION.

This is a complex change that required longer conscious and concentrated thoughts and thinking by me when I thought it over and checked it. This can NOT be seen by looking on the Excel formulars or on the mathematical formulars.



Modifications and Improvements of Tables of the Excel Spreadsheets: Impacts

Doing the modifications and improvements it turned out that at least one cell contained an expression that had to be altered. Before the modifications and improvements the contents of that cell appeared to be completely correct but when they have been prgressed that far already that the cell in question was the sinmgle one left yet it turned out that its contents has become a mix of the concept for the normal case where no regressional functions are required and the concept for the other case requiring the regressional functions.

That cell is part of the phase TEI – that phase the regressional functions are kept switched off in the previous post. It was the mix of switched-off and switched-on that unveiled the problem.

Because of this more modifictaions were required.

The solution of these previously unrecognizable problems has an impact on the results

One tricky column is left yet where it is unclear what the most proper handling of a mix is – at present mixes seem to be inescapable regarding that column. This will be investigated much later when the complete spreadsheet will be checked for erros, mistakes etc. finally before releasing the spreadsheet for public use.

The impact on the results for Microspace and Pixel are very small only – below $ 2,000, which has to do with very small errors regarding the costs for the propellant of the lander. A landing via Pixel is more expensive than a landing via Micro Space by less than 1% only – so again I don’t list the numbers in this post.

Regarding the orbital trip with all functions switch off there are no changes of numbers that could be detected without a lot of closer looks.

But with the EOI-function switched ON the amount of propellant required is by a little bit more than 15,850 kg higher now than got in the previous post. This is by a little bit more than 3,000 kg more than with the function switched OFF. The variable costs in the cylindrcal case are increased by a fifteenth – more than 6.667%. For now this hint may be sufficient.

So obviously there is an impact on this trip – the safety margin is increased by an amount that can be detected easyly.

The result for the CXV-like lander is kept – merely because I listed it not in detail in the previous post. The amount of propellant is bit higher above the 100,000 kg-mark now – by a few 1,000 kg. The costs of the propellant for the lander are between $ 9,000 and $ 10,000 without the transporation costs.

The prices are dropped for this trip – from $ 125 mio down to $ 81 mio in the cylindrical case with Falcon 9 S 9 and expendable QuickReach2 for the CXV as taxi.

The astronomical number is dropped by 9 mio kg to 10 mio kg..

The EOI-function alone results in an amount of propellant of between 99,400 kg and 99,500 kg.

For the Apollo LM-pendant the amount of propellant with the EOI-function switched on is increased by a bit more than 8,400 kg. The price for the cylindrical case with Falcon 9 S 9 and expendable QuickReach2 is increased by $ 5.358 mio – a bit less than 8.333%.

Withoput the EOI-function the amount of propellant is by 15,400 kg below the now got correct value while the variable costs are $ 9.658 mio below the result got via the EOI-function. So regarding the amount of propellant there seems to be a safety margin of around 22.2%.

Up to this point the results are:

    orbital trip looking unchanged
    Micro Space landing trip-numbers slightly increased
    Pixel landing trip-numbers slightly increased
    Apollo LM-pendant landing trip-numbers increased
    CXV-oendant landing trip-amount of propellant looking increased – but prices dropped


What’s left is the landing using the Falcon-derived lander. I had a look onto the price(s) only – and interestingly the cylindrical price is by $ 300 mio BELOW the price got the unsystematical way now. Spherical the price is dropped by $ 537 mio.

A surprise – at the first glance.

But the earlier unsystematical calculations last summer didn’t take into account economies of scale regarding the multiple Block-DMs. They simply had been added on applying their total weight of 2,300 kg which includes the engine and the tops and bottoms. But one very huge Block-DM neeeds only one engine, only one bottom and only one top.

Next the lunar Falcon itself is much lighter now – 11,400 kg including ist tanker instead of 100,000 kg.

The price drop for the CXV-pendant-based landing trip will have to do with improvements of the calculation of the propellant costs of the lander as well as with the improvements of how the weight of that propellant is included into the formulars now. This has removed error-causing violations of the concept and system and other mistakes and errors that were indetectable because of those violations.



Lunar Tankers: Think of a Detail of the Falcon-derived Lander

The Falcon-derived lander included a second lander that returns into the orbit empty and lands again carrying an amount of propellant equal to the weight of the carrier-part of the first lander. It returned several times and refueled the first tanker before that lander returned as well as the second one at the end of the visit to the lunar surface.

That second lander was nothing else than a tanker that was carried from Earth to the Moon and back again. But a portion of the propellant this second lander delivered down to the lunar surface the lander required itself to be able to return into the orbit.

Here now this tanker will not langer be carried from Earth to Moon and back – it will stay on the Moon allways. So the vehicle travelling between Earth and Moon no longer will require propellant to carry the weight of this tanker.

Of course this means that there is an investment to carry the tanker to the Moon one-way. But this investment I will consider later like I still have to do regarding other investments I did not consider yet.

I in between inserted this tanker into the tanker table and allowed to use all the lunar tankers to be calculated as tankers that are carried between Earth adn Moon alternatively to using them as tankers staying at the Moon and not carried back to Earth.

It also is possible now to use these tankers as if they simply would be freighters between surface and orbit that carry freight to the orbit and nxt carry other freight down from the orbit – this enables to apply the Excel spreadsheet for calculations beyond what is in focus here at present.

So there are now landers, tankers/freighters that both either can be carried from Earth each trip or brought to the Moon to stay and do service there.



Deliveries of propellant or freight to the Moon

Like in the earlier unsystematical calculations the calculations here apply the chance that there might be deposits of water ice or hydrogen at least on the Moon that are sufficient to be used as propellant in combination with lunar oxygen bound in lunar Regolith. This would mean that no deliveries from Earth are needed.

But the landers applied in this thread up to now don’t consume LOX/LH2 but N2O4/Aerozin50, LOX/cerosene, H2O2/Methanol/Hydrazine or LOX/Ethanol. Since at present there are no or no sufficient lunar layers or deposits of nitrogen or carbon are known these two at least or the propellants including them would have to be delivered from Earth. Because of this real freighters will be calculated that like the concept of t/Space will travel slower than the passenger flights.

Since less velocity means exponentially less required amounts of propellant here again I suppose calculations linearly down to be safe – like done regarding the reduction of weight where the velocity of the existing vehicle has been kept.

If the weight of the potential vehicle(s) of all the systematical calculations done up to now is kept but the time for one complete trip – including the return to Earth – is increased by any factor then the required amount of propellant should drop exponentially. So a linear reduction should include a safety margin that exponentially grows with the factor. The amount by which the factor reduces the requirement linearly could be added to the weight of the potential vehicle then because it wouldn’t be consumed. Since the talk at present is about deliveries the vehicle in total could be considered to be freight plus engine, stage/tank for landing and launch and propellant for landing and launch. May be that I will apply only a portion of the propellant that won’t be consumed.

This is a trade of velocity for propellant here (freight in general) like t/Space have in mind according to their document.

In this case the total weight towards the Moon would be kept but some propellant simply would be shifted to become cargo itself or to be replaced by cargo (equipment for mining, electrolysis, radiation shielding, artificial atmosphere and much more).

Another possibility might be to increase the weight towards the Moon from the weights considered by the systematical calculations. Then the propellants calculated would be kept as they are but a longer time of travel would be got. This time would have to be increased exponentially – at present I am not sure if I can find a linar calculation of time up that includes a sufficient safety margin.

The increased time means another trajectory towards the Moon (or another planet...) which has no impact on what’s considered here. It will mean higher communication costs if the level of autonomy is assumed to be where it was at the time the existing vehicles went to the Moon. But I up to now have no data about communication costs while changes in autonomy will be involved in the the investment into the vehicles and thus in the depreciations of that investment.

This enables to consider and involve costs of delivery/transportation, frequency of delivery and coordination of delivery with passenger or cargo trips.

In principle this is the same like for trucks on Earth – they either consume more Diesel or gasoline than a much lighter five-person-car or they need more time to go the same distance.

This opens the door to the possibility and opportunity to consider and discuss a wider earthian-lunar or even interplanetary economy because machines and other equipments could be delivered and the optimal purposes for vehicles of different capacities regarding weight of freight, velocity and frequency of delivery could be indentified.

When the cargo has been offloaded at the Moon the vehicle can be assumed to return to Earth empty – but it may be interesting to consider it going back loaded...

Here I will go on to consider the costs and price of lunar passenger trips.



Former unsystematical calculation: Three possible cases to be distinguished

Via the earlier unsystematical calculations a vehicle has been considered that used a huge Block-DM that could be fueled by LOX/cerosene or alternatively LOX/LH2. There two additional alternatives – the vehicle could have one smaller Block-Dm for LOX/cerosene to be used towards its destination plus a reusable version fo an existing LOX/LH2-stage or it could have a LOX/LH2-stage that alternatively can be fueled by LOX/cerosene.

These three cases will be considered before involving deliveries.



Original Refuelling Trip

The original trip where the vehicle was refueled at the Moon used a Blcok-DM that was assumed to be capable to be fueled with LOX/LH2 alternatively – it was assumed that the engine can consume that propellant.

I remember to have described already which way a landing trip with refuellling can be calculated in an Appendix much earlier since 30th of September 2006 but can’t find the description at the moment.

So I repeat the method here: The difference to all what has been done up to now is that the calculations are split.

The first calculation considers TPI and PIO only – the variables and parameters for TEI and EOI are set to zero and the correction factors as well as other parameters and variables that might cause callers of fractions to be zero are set to 1. This calculation also includes propellant delivery into LEO, taxi into LEO and the landings

The second calculation considers TEI and EOI while for TPI and POI all is set to zero or one.
Here the refuellings are involved.

So there is a Part One-calculation and a Part Two-calculation.



Part One-Calculation(s)

The propellant required for TPI and POI resulting is 12,388.91832 kg of LOX/cerosene in the cylindrical case.

Then the following variable costs per passenger for TPI + POI without the landing(s) and refuelling(s):are got:

Falcon 9 S 9, expendable QuickReach2: $ 13,096,936.224 cyl. – $ 7,946,585.688 sph.
Falcon 9 S 9, reusable QuickReach2: $ 9,121,936.223 cyl. - $ 3,971,585.688 sph.
reusable QuickReach2, reusable QuickReach2: $ 126,819.476 cyl. - $ 69,024.489 sph.
Launchpoint Technologies, expendable QuickReach2: $ 4,547,067.734 cyl. - $ 4,237,196.921

Up to this point everything is promising a lot. I leave away depreciations, safety margins and initial prices for now and list them when the trip is calculated completely.

The costs of the propellants of the landers are as follows:

Micro Space $ 816,466 per passenger
Pixel $ 67.60 per passenger
Apollo LM-pendant $ 82,831.91 per passenger
CXV-pendant $ 1,855.98 per passenger

I leave away the Falcon-derived lander here because I used only to look for an upper boundary for non-refuelling landings.

It seems that of these only the Apollo LM-pendant could increase the price significantly – the impact on the case of a reusable QuickReach2 as LEO-tanker as well as as LEO-taxi would be huge.

But all these tankers would require deliveries because their propellants include carbon or/and nitrogen. Since the present calculations don’t include deliveries these landers can’t be applied here.

Here only lunar ressources of water ice, bureid hydrogen and in Regolith bound oxygen are available. So landers are required that consume LOX/LH2. Micro Space and Pixel are existing reusable landers – I don’t recalculate them into LOX/LH2-consuming landers. The Apollo LM also is an existing lander but an expedable one – so I calculated a reusable version of it that consumes LOX/LH2. This I also did for the CXV-pendant.

Both the calculations still assume that a Block-DM can contain LOX/LH2 and its engine can consume it without problems. This is done to keep it all fitting into the concept – it will be changed in further steps.

The results now are as follows (costs per passenger):

Apollo LM-pendant on LOX/LH2 $ 2,124.205 at $ 0.56/kg - $ 13,655.603 at $ 3.6/kg
CXV-pendant on LOX/LH2 $ 1,765.706 at $ 0.56/kg - $ 11,350.966 at $ 3.6/kg

I formerly applied $ 0.56 as price of LH2 which is a subsidized price – it was the only one I could find last year. In between I found $ 3.6 under www.astronautice.com and applied it also. Both these prices are high above the price of LOX – so the numbers above include a safety margin which is required because up to now costs of transportation of production equipment are included. This will stay uncahnged because I do not know the required investments. May be that I will consider deliveries of LH2 at least but that’s not sure.

As can be seen the Apollo LM isn’t threatening the low prices no more. N2O4/ADMH is very expensive - $ 24 – in comparison to LH2.



Part Two-Calculation(s)

The phases TEI and EOI together would require 13,344.266 of LOX/cerosene cylindrical – but here no refuelling of LOX/cerosene is possible. This would require deliveries and here no deliveries are considered.

Because of this now a CXV consuming LOX/LH“ will must be calculated that uses a Block-DM and the same engine as before. The weight and the Isp of the engine are kept. May be that something like that – done also for the two LOX/LH2-landers in the previous chapter – is wrong but at present I don’t see any good chance to find abetter way that completely fits also in what has been done in the previous chapter. The engine must be the same – no way out. There might be a way out in a later step perhaps.

Now 13,247.56 kg are got - less by less than 100 kg. Since I can’t find an error at present I suppose that it has to do with the low density of LH2. I tried in short the engine Isp of the Apollo CSM and found a drop by around 3,000 kg. This seems to confirm that I was right above and that I applied the Apollo CSM-engine during the unsystematical calculations.

The variable costs per passenger now are $ 1,483.7264 cyl. and 974.50 sph. Since transportation costs and taxis into LEO mustn’t be included here this is the propellant only. Again I delay all the other numbers regarding prices until everyting is complete – but in principle the costs of both calculations together are those got in the Part One-calculation to which only the propellant costs for the landers and the tankers have to be added yet (and their depreciations of course that haven’t been considered yet...).

What’s left now is to calculate the costs of refuelling. These are the propellant costs and depreciations of the tankers.

In the unsystematical calculations last year I simply applied the lander(s) as tankers. Because of all the distinctions applied by the formular(s) it is possible to improve that now.

First tanker-versions of Micro Space and Pixel are ruled out completely for now because these would require deliveries. This also holds for the tanker of the Falcon-derived lander. So what’s left are the Apollo LM-pendant on LOX/LH2, the CXV-pendant on LOX/LH2 and Launchpoint Technologies.

Second the tanker-versions of the non-launchpoint Technolgies-tankers left include a weight that only has to do with life support, shielding and other human-related equipments. And in particular they include equipment that has to do with return to Earth and communications to Earth. Because of this the weight of the carrier-part of the Apollo LM can be considered to be propellant for refuelling. This also holds for the CXV of which only the weight of the Block-DM is going to be considered to be left after the vehicle waiting in the lunar orbit is refuelled. So in difference to the landers not only the weight of the propellant for the launch – which was the landing in the case of the landers! – is removed at retrun to the lunar surface but the weight of the carrier-part of the Apollo LM as well as the weight of the CXV itself also. This means that less propellant is required to return to the lunar surface than was required for the launch of the lander(s).

Third the tanker of Launchpoint Technologies could launch much more than 100 kg from the lunar surface.

Before the vehicle waiting is refuelled – at launch – the tanker-versions of the Apollo LM-pendant and the CXV-pendant – both on LOX/LH2 – have that weight the according landers have including the carrier part. So this could be copied from the according landers. But a portion of the propellant calculate for launch back to the vehicle in orbit now will have to be considered to be a part of the amount for refuelling – because the weight of the carrier-part or the CXV is part of that amount now also and will not return. The tanker will be light in the second phase of ist flight and so will not need a portion of what the landers need – this portion must be added to the weight of that what accords to the carrier-part or the CXV.

The calculations are described in the Appendix.

The Apollo LM-pendant-derived tanker carries 2,307.182557 kg of propellant and consumes 5,550.522997 kg of propellant – the CXV-pendant-derived tanker delivers 5,327.967986 kg and consumes 14,037.26209 kg.

If the Apollo LM-derived tanker on LOX/LH2 is applied 5.728011294 flights are required to fuel the vehicle for the reutrn flight to Earth. Each flight costs $ 3,108.292878 at a LH2-price of $ 0.56 and $ 19,981.883 at a LH2-price of $ 3.6. Then refuelling costs 17,804.34 at the low price but $ 114,456.45 at the high price. Per passnger these are between $ 3,500 and $ 22,900 – seems to be not that much of a threat to low prices.

Using the CXV-pendant-derived tanker on LOX/LH2 2,480414255 flights only are required with costs per flight of $ 7,860.87 at the lower LH2-price and $ 50,534.14 at the higher LH2-price. Refuelling this way costs $ 19,498.21 at the low price but 125,345.61 at the high price – between $ 3,900 and $ 25,100 per passenger which again is not that much of a threat to low prices.

The third possible tanker is a lunar Launchpoint Technologies maglev. Since the lunar gravity is much less than the earthian one a higher weight can be launched at the same consumption of electricity. This electricity would be for free on the Monn if it is supposed to be solar power. But I need a price and apply the price the company is speaking of at 3,000 launches per year. When I calculated the lunar Falcon V I applied a factor of 7.2 by which the lunar Falcon 5 would be lighter than the earthian one. Regarding the maglev there is nothing to be calculated lighter – so I suppose that simply the weight that can be launched is increased by that factor of 7.2 – meaning that a lunar Launchpoint Technologies maglev would launch 720 kg instead of 100 kg.

Then 18.355 maglev-launches would be required that would cost $ 18,900 kg each. So refuelling this way would cost 346,908.65 – $ 69,381.73 per passenger which is a threat to the low prices. But to mention it again – solar power is for free and only depreciations may have to be paid which will be significantly less than $ 18,900.

To these costs of transportation of propellant from the lunar surface into the lunar orbit only the costs of that delivered propellant have to be added – and these costs are between around $ 7,400 and $ 47,600 – the later of which might threten the low prices.



Total of the two Calculations

In between several things changed my mind – I will NOT list the exact prices got because there are too many alternative landers and tankers that have an impact on the price in particular by the 10% for depreciations. Instead I talk about what the results are around.

At Falcon 9 S9 plus expendable QuickReach2 the variable costs per passenger would be around $ 13.1 mio cylindrical and around $ 8 mio sphercal. The price would be ranging between $ 8.75 mio and $ 14.6 mio. Initial price would be between $ 19.75 mio and 25.6 mio. The price including safety margin would be $ 10 mio spherical and $ 16.2 mio cylindrical while the initial price including safety margin would be $ 21.2 mio and $ 27.2 mio.

The reusable QuickReach instead of the expendable one drop that all by $ 4 mio..

But if the tanker into LEO also would use the reusable QuickReach2 it would be really interesting.Spherical the trip could cost $ 85,000 – if and only if the LH2-price is $ 0.56 - at $ 3.6 the trip would cost $ 155,000. Cylindrical these would be higher by less than $ 60,000. The price would add $ 8,500, $ 15,500 or $ 6,000 – the initials would add $ 11 mio.

With Launchpoint Technologies as tanker into LEO the prices would be below $ 20 mio initial and below $ 6 mio else.



Excel spreadsheet

In between the spreadsheet can apply different numbers of passengers for the travel between Earth and Moon on the one side and for the landing on the Moon on the other side.

This allows to calculate trips where the number of passengers carried into the lunar orbit is higher than the number of passengers carried down to the lunar surface. Such trips are nothing else than an integration of orbital trips with landing trips in one trip. They are of meaning for entrepreneurs because they no longer would have to wait until a landing trip is complete or an orbital trip is complete.

Example:

The CXV-like vehicle has a capacity of 5 passengers. There should be 5 passengers to operate at minimum costs, keep a minimum price and thus operate optimally.

But there are 3 orbital passengers only and 2 landing passengers only – so neither the orbital trip alone nor the landing trip alone would be optimal or/and at minimum costs and price. But the two together are at optimum, minimum costs and minimum price as long as a lander is applied that carries no more than 2 passengers.

The cargo of the potential vehicle has been split now into two categories while the cargo of the existing vehicle is kept as it was. The two categories for the potential vehicle are landers and their propellant as one categorie and other freights as the second category.

These are not split regarding the exisitng vehicle because no changes are possible or allowed for them. In difference to that the cargo of the potential vehicle can be changed according to your ideas. You also can select or add other landers – but then the propellant to be carried has to be adjusted to the lander and the number of landings and launches it has to do because of the number of people to be carried down to the surface. To assure that this adjustment is done the required amounts of propellant are calculated regardless of the lander being a calculated potential one or an existing one listed in the table of reusable landers

In the case of the lunar Falcon the tanker for it is connected to it and handled like a lander. In principle that tanker is an integral part of the lunar Falcon because I introduced it as a substitute for a heavier lunar Falcon that would carry its launch propellant itself.

The lander calculations for the phases TPI to EOI are kept together as an additional section now that follows the result(s) and control cells (except for the selection of the regressional function(s)) of the other sections.

The spreadsheet is enabled to distiguish if the lander, tanker and their propellants are carried or if they are kept at the other planet. This property is incorporated into the design of the trip. The trip design additionally distiguishes if Part One-calculation or another calculation is to be done.




This took a long time now because of a lot of modifications of the spreadsheet, several checks but very much work at the job also. So this should it be for this post now.

But it is just at the beginning. It is required to look into the next two steps and the deliveries from Earth...



Dipl.-Volkswirt (bdvb) Augustin (Political Economist)




Appendix

Calculation of reusable lunar tankers

To get the propellant the mpty tanker needs at landing the calculations to get the according phase for the lander can be applied. The according phase for the lander is the LAUNCH – not the landing. The reason is that the lander already has consumed some propellant before the launch when carried by the vehicle travelling between Earth and Moon while the tanker already has consumed some propellant before the landing – the two start their operations from opposite locations simply: The lander in the orbit when carried from Earth, the tanker from the lunar surface when kept on the Moon.

Since the talk is about the tanker-versions of the Apollo LM-pendant on LOX/LH2 and the CXV-pendant on LOX/LH2 and these two are based on the expendable Apollo LM with the rgeressional functions switched on... –since this is the case consistency requires to go on this way although the empty tanker is lighter than the expendable Apollo LM.

The only way avoiding iterational calculations seems to be by shares. First the share of the launch-propellant of the lander the stage and engine required is calculated. Next the weight of a tank/stage is calculated that would have a capacity equal to the amount of propellant according to the share got. Then the difference between the weight required for the total amount of propellant for the lander and the weight required for that amount of propellant the stage itself required is the empty tank-weight to be landed if the carrier-part of the lander would not be there at launch.

At the tanker the required tank-weight at launch of that tanker is less than at the lander. So keeping the weight required at the lander means to apply too heavy a tank/stage – this means a safety margin. Thus is is safe to do so – plus it would be tricky to avoid it.

Then the difference has to be applied as the weight of the vehicle at landing of the tanker.

The total propellant of the reusable lander Apollo-LM-pendant on LOX/LH2 was 6,322.038438 kg. These require a tank/stage weighing 858.138988 kg. The engine weighs 230 kg. So the carrier-part of 1,535.667116 kg and those two in total weigh 2,623.806104 kg. Of these the carrier part has a share of 58.5282241% - so it can be supposed that it causes that 58.5% of propellant also. This is valid for landing as well as for launch. Since only the launch of the lander is of interest here only that share of propellant needs to be applied that was consumed at launch. This amount is 1,927.830889 kg 58.5% of which are 1,128.325183 kg.

So 799.5057066 kg are left the stage and the engine required at launch. These require a tank or stage weighing 108.4590611 kg only.

The difference between 858.138988 kg and 108.4590611 kg is 749.679927 kg. Applying this weight and the Block-DM the amount of propellant the tanker requires at landing results in 1,156.315448 kg. This number means that of 1,927.830889 kg of propellant the lander needed to launch 771.5154413 kg are shifted to delivered propellant. Since the weight of the carrier-part of the lander too is propellant to be delivered the tanker delivers an amount of propellant of the sum of those two- which is 2,307.182557 kg

The total amount of propellant the tanker requires is reduced by that number also and thus is 5,550.522997 kg. The weight of the lander inclduing stage and engine then is 983.4152527 kg.

The CXV-pendant leads to the following numbers: 15,765.23007 kg total propellant at lander ==> required tank weighing 2,139.936148 kg; engine weighs 230 kg, carrier-part weighs 3,600 kg ==> total weight 5,969.936148 kg ==> share of carrier-part 60.3021525%; amount of propellant at launch of the lander was 4,230.390499 kg ==> carrier part causes 2,551.01653  ==> stage and engine required 1,679.373969 needing a tank weighing 227.9543683 kg ==> resulting weight to be applied as vehicle-weight at the tanker is 1,911.981779 kg ==> 2,502.422513 kg required to land the tanker ==> 1,727.967986 kg shifted to the amount of propellant that is freight; weight of carrier-part is also propellant as freight now ==> total amount delivered is 5,327.967986 kg of propellant at a total consumption of 14,037.26209 kg while the tanker weighs 2,135.385739 kg


End of Appendix


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Post Simplified:   Posted on: Tue Apr 17, 2007 9:22 pm
My oversimplified effort: Near term Lunar landing and return (coach) $20 Million.

Much less than the current price of Russian launch to ISS with EVA. (I will never pay to go into orbit – or to the Moon – and just look out of a window.)


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Post    Posted on: Tue May 01, 2007 5:05 pm
Hello, rpspeck,

Thank You Very Much for your short feedback. I remember well that I asked you which way you got your result. The reason was that I was interested in the way you got it - I that time couldn't find out that way that quickly and consider it to be a very good check for the results I am getting here.

Unfortunately it is required that I redo the calculation of the step 1-trip to rule out possible application of errored or wrong numbers - there is a short remark about it below. So for now it should be suspected that the numbers for step 1got in the previous post may be too low.



Contents

Refuelling landing trip with Block-DM: Short Review
Unintended Safety Margin Detected...
Part Three-calculation(s)
Tank of an existing LOX/LH2-stage:
Weight of the Tanks to be applied as cargo
How to apply the Excel spreadsheet?
Thickness of the Sides of the External Tank
Flight back to Earth: Weight of the LOX/LH2-Tank
Completing the calculation of the Step 2-Trip
Costs/Prices of Step 2-Trip
Appendix
Revision of The Calculation of Reusable Lunar Tankers



Refuelling Landing Trip with Block-DM: Short Review

The main property of the calculation of the refuelling landing trip to be seen in step 1 in the previous post is that the calculation has to be done in two steps. The reason for this is that the formualr(s) and the Excel spreadshett allways consider four phases of flight between Earth and Moon. Regarding a refuelling trip this would mean that the refuelled propellant would be considered as if it was carried from Earth by the vehicle doing the refuelling landing trip – which would lead to wrong results. And so the flight from Earth to Moon has to be calculated separatedly from the flight from Moon to Earth.

To do that it should be recalled that the flight from Earth to Moon consists of the phases TPI and PIO. Since the two remaining phases are NOT part of this flight all the variabls and parameters have to be kept zero or one. The flight from Moon to Earth consists of TEI and EOI only and so the variables and parameters of the two previous phases have to be kept zero or one.

The consequence is that the results are independent of each other except for the aspect that identical existing and potential vehicles and identical standard-tanks for the potential vehicle are applied.

This independency means the risk that for one and the same tank to be used in both parts of the trip – towards the Moon and away from the Moon – two different weights might be got. This is a logical contradiction that must be avoided.

Have a look to the previous post – the flight towards the Moon required 12,388.91832 kg while the flight away from the Moon back to Earth required 13,247.56 kg – a difference of nearly 1,000 kg meaning that the tank at the flight back to Earth suddenly was larger and thus heavier. This would have to be taken into account at the flight towards the Moon but wasn’t.

How this can be done has been shown in the previous post by the calculation of the propellant the tanker(s) require to land again.

The weight of the larger tank has to be calculated. Then the weight for the smaller tank has to be subtracted and the result has to be inserted into the other trip as cargo which is an analogon to the vehicle-weight at the landing of the tanker(s).

Finally that flight where the cargo has to be inserted has to recalculated – so in truth the calculation consists of three steps instead of only two. This will be done here later.

Let’s have a short look onto the difference. It is 955.34768 kg – these are 6.3% of the capacity of one Block-DM. This Block-DM weighs 2,070 kg without the engine. Then the weight to be added seems to be 129.68 kg which is sounding neglegible and to be supposed to be too high because the top and the bottom would have to be subtracted because they are there already – but I will do the third step to demosntrate the effect and to rule out possible errors of future calculations.

Such errors are to be expected beginning at the next step. That step removes the assumption that the Block-DM is fueled with LH2 at return to Earth. Instead the return will apply an existing LH2-stage as standard-tank for the potential vehicle. LH2 has a much smaller density than cerosene and thus causes a larger tank to be required which will be heavier. Second that LH2-stage may be heavier because of the additional weight of the pressurization and the cryogenics for the LH2.

Usually the situation of having one tank but two equations a system of two equations would be applied to. But I am doubting if it is worth that pain which I suppose to require longer time than the formular(s) already available and programmed into the Excel spreadsheet.

So I prefer another way here. The additional weight will require more LOX/cerosene to go from Earth to Moon. This extra propellant NORMALLY would also add weight because it requires a larger and thus heavier tank. But this tank already has been added – to some degree at least. It is that portion of the tank included as cargo for now. To what degree has it been added? 1000 kg of LOX/LH2 require by three to four times the volume 1000 kg of LOX/cerosene require. On the other hand the Isp of LOX/LH2 is a bit more than 1.3 times that of LOX/cerosene – nearly 4/3. Consequently the additional LOX/cerosene would require a third to a fourth of the tank only the LOX/LH2 would require but a third more of LOX/cerosene is needed. Let’s have a look into a short example:

a) 1000 kg of LOX/LH2 replaced by LOX/cerosene in part one means that a volume of a tank sufficient for 1000 kg of LOX/LH2 is uased by 25% only.
b) The same replacemnet means that because of the difference in Isp 1000 kg of LOX/LH2 would have to be replaced by 1,300 kg of LOX/cerosene.
c) Form a) AND b) follows that an amount of LOX/cerosene is needed to replace 1000 kg of LOX/LH2 that uses the tank sufficient for that amount of LOX/LH2 up to 33% to 34%

This is a very raw approximation but it shows that it seems to be likely that the additional volume will be more than the new amount of LOX/cerosne will require: To add the cargo simply and then recalculate it all is sufficient.

Next from the new amount to be got the original amount can be subtracted to find out how much of the as cargo added tank is used in between during the travel from Earth to Moon. This is nothing else than a check if the thinking described here is sufficient. It also might add another safety margin.

I have in mind the idea to also do a check by calculating the use of LOX/cerosene during the travel from Moon to Earth – but I am not sure because this calculation nonetheless will be of interest later when deliveries via freighters will be included.



Unintended Safety Margin Detected...

I in between detected an unintended safety margin – caused by a small error. This error caused the propellant required by tha lander waiting on the lunar surface for the vehicle coming from Earth.to be included as if that propellant would be carried from Earth. This error had no effect on the amount of propellant required but on the variable costs only – they were too high by $ 76,000 to $ 77,000 for the Part 1-calculation in the case of using Launchpoint Technologies as tanker into LEO and CXV with expendable QuickReach2 as taxi into LEO. Since it were the costs of the propellant for the lander the error will be the same for all cases where Launchpoint Technologies is applied. The drop will be much higher at more expensive tankers.

This error has been removed now.



Part Three-calculation(s)

I am going to concentrate on the CXV-pendant on LOX/LH2 as lander and the Apollo-LM-pendant-derived tanker here.

The weight of the sides of the tank calculated was 2.63878227 kg – which is sounding incredible to me at present. May be that the sides of the tank(s) of the Block-Dm are thicker and thus heavier than supposed. This has to do with the problem that there seem to be no data about the correct inner diamter of the tank(s) of the Block-DM and other stages. The diameter(s) supposed mean that more than 99% of the complete weight of the Block-DM without the engine are the weight of the top and the bottom.

The weight of the sides of the tank for part 2 needs to be 10.3553174 kg – like suspected the replacement of cerosene by LH2 increases the reuqired tank by nearly 4 times.

At this point I found that the way the required tank was calculated if it contains another propellant than previously was improper. I corrected the way and get a slöightly different amount of propellant required now. It is by less than 100 kg more now. This will be so for the landers and thus the tankers also – but the calculated amounts of propellant are less than for the vehicle returning to Earth by a factor of 4 at least. In so far this is neglegible for now. I will take into account the small correction later – I already have recalculated the capacity of the Block DM for LH2 for use here and will apply it to the LH2-based landers also.

By the way – part 2 mustn’t include lost-in-space-costs because they are included into part 1 completely already.

Obviously the tank calculated in part 2 is by 7.716535126 kg heavier than that calculated in part 1. So these 7.716535126 kg have to be inserted as cargo into part 1 now.

The required amount of propellant got in part 1 is increased by a bit less than 16 kg now. This increases the weight of the tank required for going from Earth to Moon by 0.003391447 kg only – which shows that the tank is sufficient for both directions now. The costs and prices are increased very slightly only.

Regarding the additional weight of tank to be carried as cargo from Earth to Moon I do NOT calculated a separate value for the spherical case – this is an additional safety margin in that case.

The resulting total numbers are


Code:
Launchpoint Technologies, expend. QuickReach2
             cylindrical     spherical
var. costs    4,477,372.09    4,165,433.06
price         4,925,109.30    4,581,976.36
price init   15,925,109.30   15,581,976.36
price safe    5,606,200       5,204,200
safe init    16,606,200      16,204,200
                                   
reusable QuickReach2, reusable QuickReach2
             cylindrical     spherical
var. costs      119,613.83       59,983.62
price           131,575.22       65,981.98
price init   11,131,575.22   11,065,981,98
price safe      146,200          74,200
safe init    11,146,200      11,074,200
                                   
Falcon 9 S 9, reusable QuickReach2
             cylindrical     spherical
var. costs    7,852,277.95    2,695,385.15
price         8,637,505.73    2,964,923.66
price init   19,637,505.73   13,964,923.66
price safe    9,606,200       3,404,200
safe init    20,606,200      14,404,200
                                   
Falcon 9 S 9, expendable QuickReach2
var. costs   11,827,277.95   11,827,277.95
price        13,010,005.73   13,010,005.73
price init   24,010,005.73   24,010,005.73
price safe   14,406,200      14,406,200
safe init    25,406,200      25,406,200


The case where the tanker into LEO as well as the taxi into LEO use a reusable QuickReach2 – second case – results in numbers far below those got in the unsystematical calculations even if the tank is cylindrical.

In so far the low costs and price of those former calculations are confirmed now.



Tank of an existing LOX/LH2-stage:

But it was assumed that the Block DM can carry LH2 instead of cerosene. This assumptions will be removed now to improve the safety of the numbers. At the return flight the vehicle will use a scaled version of an existing tank or stage that was or would be fueled with LOX/LH2.

At this point I was checking how to handle the new tank because up to now the potential vehicle and the landers and tankers allways applied the Block DM during this thread.

1. New check required to get a correction factors?
The Apollo-Soyuz-correction factor was got applying two different tanks/stages both of which I know about that they can be used to fly towards the Moon. Do I know that about other stages also? This seems to be NOT the case. Does this rule out modern LOX/LH2-stages? What was behind the checks done earlier? The size of the tank? For the potential vehicle the Block DM has been scaled – so size was NOT the reason. Was it the weight of the combination of vehicle, stage/tank and others? Obviously NOT. Was it a matter of the ratio between the existing vehicle and the potential vehicle? Sounds familiar – and is correct indirectly: The adjustment of resulting propellant amounts is behind the correction factor(s) and these amounts determine the size of the tank/stage.

So no new check required. But no new check is possible because no vehicle has flown towards the Moon using modern tanks/stages as far as I know.

2- Can the available and possible factors be applied to modern tanks/stages?
The weight of the Block DM was part of the calculation of the available and possible correction factors while the modern ones are NOT and CANNOT be. But is that of meaning here? The factor is a number correcting overapproximations that are invalid because the approximated amount doesn’t fit into the capacity of a tank although it is known that that capacity is sufficient or possible underapproximations that might remove the safety margin(s).

Sounding as if the exisitng factors can be applied but what about the different propellants involved into the Apollo-Soyuz-check? There also is an Apoloo-Apollo-check.and a Soyuz-Soyuz-check which are all involving identical propellantsa for the existing and the potential vehicle. A Soyuz-Apollo check seems to be of interest here. It could be avoided by applying Apollo in EOI instead of Soyuz – but this would be off the system and might get results that differe from the application of Soyuz very much.

3. Must the engine be changed?
Please recall that the engine has been moved from the stage to the vehicle. The tank of the stage may have been optimized to the engine – but was that of meaning in the formulars? No, it wasn’t. If the stage was optimized then this optimum has been applied as base. If this turns the tank and the results suboptimal then this means that the costs got are higher than they would be in reality – which is nothing else than a safety margin.

Does keeping the engien andanger correctness? Up to now it was supposed that the Block DM might have reduced correctness – to cahnge the tank only already improved the correctness. Changing the engine reduces comparability to the other calculations May be that the stresses a particular temperatures causes to different engines are different also and that this results in different materials the engines are made of and that this mans changed weights. But there are other arguments that counteract to this.

The best way will be to look at the weights of the engines attached to the existing stages/tanks.

All in all it seems to me that modern tanks can be applied without severe problems. There are explicit safety margins that might be sufficient to handle errors involved by modern tanks.

But are the modern tanks worth to be applied or would it be sufficient to apply the Saturn IV B? To answer this questionthe ratio between the weight of propellant contained and the weight of the stage without the engine can be used. This ratio is 8.9...at the Saturn IV B.

I checked the stages Centaur V1, the Delta 4H-2, the Delta RS-68, The Centaur G, the Titan 5 and the External Tank of the Space Shuttle. There are no data about the weights of the engine of the Delta 4H-2 and the Titan 5. The others are listed under www.astronautix.com as follows:


Code:
stage         gross     emoty    engine       mass engine

Centaur V1     22,825    2,026   RL-10A-4-2     167
Delta RS-68   226,400   26,760   RS-68   6,597
Centaur G      23,880    2,775   RL-10A-3A      141
External T.   750,975   29,930   none            0


At this point the light weight of the engines of the Centaur V1 and the Centaur G may be signs that it is sufficiently safe to NOT change the engine of the potential vehicle because the engines of those stages are much lighter. The only aspect not known here if the engines are destroyed after burn out of the satges or if they are not. So I continue to apply the engine of the Block DM.

After subtraction of the weight of the engines – multiplied by 2 in the case of the Centaur G because it has two engines – from the emty weight(s), subtraction of the empty weight from the gross weight and division of the results. The Centaur G is ruled out because the quotient is below 8.9. Of the remaining stages the External Tank has by far the best qutient. The next best is the Centaur V1 but it is far below the External Tank.

Because of this I prefer the Externak Tank now although I am thinking about the possibility that the Centaur V1 might be the safer choice – perhaps I will apply that too later (just for a check perhaps).

This tank has to be applied to the landers also now – these two have to be recalculated as well as the lunar tankers derived from them.



Weight of the Tanks to be applied as cargo

Now there are tank-weights as cargo at both the flight towards the Moon and the flight back to Earth which was NOT the case when only the Block DM was applied.

Again I think that an equation system isn’t worth the pain in this case. Since the required amounts of propellant aren’t known yet in this case the way to do a raw approximation needs to be extended a bit.

1. During the flight towards the Moon the LOX/LH2-tank is cargo completely while during the flight back to Earth the Block DM-derived tank is cargo completely.
2. In the Block DM-only-case an increase of the capacity by 1,000 kg resulted in an increase of the tank-weight by 7 to 8 kg only and these required 16 kg additional propellant during the flight towards the Moon
3. The sides of the tank sufficient for the complete amount of LOX/LH2 required to return to Earth weighed around 10.4 kg.
4. Most of the weight of the empty tank was the weight of top plus bottom.
5. The Excel spreadsheet lists the weight of top + bottom of the Saturn IV B to be around 11,000 kg and the weight of the top + bottom of the Block DM to be around 2067 kg.

These data enable a very raw approximation. Obviously point 5 suggests that the cargo during the return flight is much lighter than the cargo during the flight towards the Moon. Because iof this it is likely that the effect of the cargo on the required amount of propellant and thus the weight of the LOX/LH2-tank is the smaller one by far. This favours the idea to do the part-2-calculation first.

Point 4 means that most of the weight of the cargo during return is included by the top + bottom already while point 2 means that the weight of the Block DM-derived tank as cargo would be increased by 10% of the weight of top + bottom only if the capacity would be increased by 25,837.5 kg of propellant – this is got by a division of 10% of 2067 by 8. To increase the weight of the cargo to 3,000 kg an additional capacity of aroung 100,000 kg seems to be required. It seems to be very unlikely that those high capacities will be required.

Point 2 also means that the additional weight of 10% of the weight of top + bottom would increase the required amount of propellant by 413.4 kg only.if the talk were about LOX/cerosene.

So it seems that it will be sfae to apply a cargo weighing 2,300 kg during the return flight. To apply the formular(s) – the Excel spreadsheet – to this will tell the weight of the required LOX/LH2-tank based on the External Tank of the Space Shuttle. To that weight the part 1-calculation can be applied and will tell the weight of the Block DM-derived tank got This can be compared to the 2,300 kg – if it is below that the calculations seem to be safe and a portion of the 2,300 kg need to be applied as cargo.



How to apply the Excel spreadsheet?

What is going to be done now is the design of a trip. Up to now all the trips could be designed in one complete step – except for the correcting calculation at the beginning of this post.

There might be separate sub-trips for the lander, the tanker as well as those two separate sub-trips known already. Or the sub-trips for the lander and the tanker can be integrated into the known sub-trips. This has been down in the previous step.

Why I am thinking about that here? The reason is that the part 2-calculation is going to be done first – but this would require to know the numbers of the tanker which need to be derived from the numbers of the lander. But the numbers of the lander aren’t avaliable yet because they will be calculated as part of the part 1-calculation using the External Tank instead of the Block DM.

Because of this I at present prefer to calcualte a torso-part 2 missing the tanker. I am not sure at the moment if this will be enabled via dialogs, buttons etc. already being established but it might be possible using via general opportunities I will provide to modify trips regardless of which ones they are.



Thickness of the Sides of the External Tank

To keep comparability I had in mind to suppose the side of the External Tank to be as thick as those of the Saturn IV B – but this results in negative values of variables which means that the sides of the External Tank are thinner (assuming that tank being a cylinder at least).

Trying several alternative thicknesses it turned out that a thickness of 4 cm resulted in positive but too few amounts of propellant – far below 10,000 kg. This low value I am doubting too much since at the Block DM led to more than 10,000 kg of LOX/LH2.

A thickness of 3 cm results in 21,691.18783 kg without the cargo yet to be inserted while 1 cm results in 58,318.98729 kg. There were reasons to suppose 1 cm thickness of the side of the tank(s) of the Block DM while the also were reasons to suppose 14 cm thickness of the tank(s) of the Saturn IV B. The Block DM was small while the Saturn IV B was large or even huge. Since the External Tank is huge in comparison to the Block DM also it seems to be reasonable to suppose a thickness of 3 cm instead of 1 cm only.



Flight back to Earth: Weight of the LOX/LH2-Tank

It difference to the first alternative there is cargo during this flight now. This causes one problem – the existing vehicles don’t carry cargo or no significant cargo at least. The cargo ratios and shares are zero because of this and so the Excel spreadsheet wouldn’t take into account the cargo. This problem might be handled via several alternatives:

1. Applying the existing vehicles of TPI and POI for EOI and TEI as well
2. Giving up the approach to handle the empty tank(s) as cargo and incorporating them into the tank applied
3. Inserting the cargo and it’s propellant share and ratio of TPI and POI into the existing vehicles of EOI and TEI
4. Calculating an enhancement of the EOI- and TEI-weights via the formular(s) and then applying alternative 3
5. Applying the regressional functions.

Alternative 1 would mean to give up comparability. During the development of the Excel spreadsheet I once applied this alternative for other reasons and got quite different results than by keeping Soyuz. Since the correction factors had the value 1 that time it may be that a correction factor would be of help. It would be a particular correction factor because it wouldn’t adjust a resulting amount of propellant to the known correct amount like the Apollo-Soyuz-correction-factor – it would modify a cargo-carrying Apollo into a cargo-carrying Soyuz instead. One way to get this correction factor might be to apply the Apollo as existing vehicle during TPI as done up to now while replacing the potential vehicle CXV by the potential vehicle Soyuz to which the cargo would be added. The real amount of propellant (which would be the complete capacity of the Block DM at present since there are no other informations) would be divided by the result. To avoid the inroduction of an additional correction factor into the formular(s) this virtual Soyuz-flight would be added to the list of TPI-vehicles The same procedure would be done for TEI.

Alternative 2 would mean to establish the possibility to add weight to the tank weight the formular(s) calculate – which in principle is the same as to add the tank as cargo but uses the ratio and share of tank weights instead of those of the cargo.

Alternative 3 is a restriction of alternative 1 to the detail cargo. The Soyuz of EOI wouldn’t be replaced by the Apollo completely but the ratio and the share of the cargo of Apollo would be applied to handle the cargo virtually to be added to Soyuz.

Alternative 4 would first calculate a Soyuz with cargo as potential vehicle from the real Soyuz and add the result to the table of EOI-vehicles.

Alternative 5 would take into account that a Soyuz with cargo is heavier than the existing Soyuz...

All these alternatives would have to be applied to POI accordingly – Apollo reaplacing by Apollo with cargo.

As long as the tank for the previous phases is concerned all these alternatives can be applied – but the problem will return if and when cargo instead of tank(s) is to be carried from Moon to Earth.

Alternative 2 can be applied simply by adding the emty tank to the weight of the top and the bottom of the tank applied – which is the External Tank for now. This means that this alternative can be applied only if the regerssional functions are not applied. A look to the empty weight for the tank plus the vehicle shows that the weight of the Soyuz plus the Block DM is exceeded already – the functions must be applied and so the addition to top plus bottom can’t be applied. There may be a way to add the tank not used to that part of the formular that calculates the side of the tank – but unfortunately operations that were required during development of the formular make it difficult to identify the correct term the extra weight can be added to. May be that during a later check the correct term will be found. This check I consider to be required because of modifications done when I included the regressional functions.

Alternative 4 can be applied very easyly because it only is a modification of the Apollo-Soyuz-check – but it also would mean that later an in principle potential vehicle would be applied as a virtual existing vehicle to a final potential vehicle. It is like copying a copy – errors etc. could cumulate or even multiply. The choice of this alternative requires to insert the correction factor the Apollo-Soyuz-check resulzed in. That check can be used directly because the cargo is not part of the design of that trip and thus can be inserted after the selection of the trip. What’s speaking for this alternative is that it means that one and the same method is applied like for the previous potential vehicles – this keeps transparaency of what is done

Alternative 1 would be very simple but – as remarked above – hurt comparability. May be I try it to see the impact but for now it is ruled out.

Alternative 5 is the application of the regressional functions to the existing vehicle. It wouldn’t be worth the pain to incorporate the regressional functions for existing vehicles – the best way would be a calculation outside the spreadsheet and to add the result(s) to the list of vehicles.

Alternative 3 would mean to look for the ratio the formualr(s) result in for another existing vehicle that really carried cargo. It seems that this only might be Apollo since it is the only vehicle that was heavier than Soyuz. But it seems to be tricky to find out how the cargo anmd the cargo ratio of Apollo have to be handled to apply it properly at Soyuz

I select alternative 4. The problem is that the check is a torso and can’t take into account the cargo the way it is done for a complete trip. So I temporaryly add it directly to the weight of the vehicle. It would also be possible to add a vehicle to the list of potential vehicles that is a Soyuz pluy cargo. Might be that I add a possibility and column particularly for exchanging tanks – but that’s far from sure.

The result is that 18,933.0892 kg of LOX/cerosene are required and a Block DM-version weighing 2,076.459139 kg. I had in mind to calculate alternative numbers via the regressional functions outside the spreadsheet but think now that there would be no comparability because the methods are that different to each other. Itried a few calculations which were ranging between 20,500 kg and 70,000 kg of propellant and above a weight of 5,000 kg of the tank

Next the length of the tank has to be calculated. Here the difference between the real capacity of the Block DM and the capacity of the virtual existing one is applied using the formular of the cylindrical volume of the propellant weight. There is a third value required – the diameter of the volume of the propellant. This diameter has been supposed to get the correction factor – and exactly this supposed diameter must be applied here. The resulting prolongation of the tank is 0.351 meters.

Please keep in mind urgently: a diameter must be applied here that ahas been supposed earlier already – there is absolutely NO freedom to apply another supposed diameter here. On the other hand everyone is FORCED to calkculate another correction factor and other values if he or she wants to apply another diameter here than all those applied in previous calculations.

Since an „existing“ vehicle for EOI is got now the vehicle for TEI has to be considered. A look into the list of the TEI-vehicles shows that Apollo was carrying a freight of more than 2,300 kg weight... – which was empty tank-capacity. So the freight was heavier than that one to be applied here no only – it was tank of nearkly the same weight as to be assumed for the potential vehicle here. This means that the existing Apollo in TEI can be applied directly here – it is NOT REQUIRED to calculate a virtual existing vehicle for TEI.

So all seems to be ready now to do the part-2-calculation. But the results need to be checked if the total empty weights are still below the existing weights.

The required amounts of propellant got now are 21,226.40688 kg without cargo and without correction factors, 26,362.19486 kg including cargo but without correction factors, 31,682.88423 kg with freight and correction factors and 25,510.53869 without freight but with correction factors. Obviously the freight of 2,300 kg increases the amount of propellant required by 5,300 kg to 6,200 kg of LOX/LH2. I also tried the Satrun IV B to get a comparison – the result is 45,754.05714 kg of LOX/LH2. If the Centaur V1 is applied assuming the same thickness as for the External Tank the result is a required amount of propellant of 20,940.21376 kg LOX/LH2 – it seems that the Centaur V1 proves to lead to the lowest cost. And the costs are below those using the External Tank by more than a third. This result seems to mean that the required amount of LOX/LH2 is below that amount required for economies of scale of the External Tank!! But it also might mean that the External Tank isn’t that far developed regarding savings of weight as the Centaur V1 is.

Because of this all I now decide to give up the External Tank and to apply the Centaur V1 now. The tank reauired for the return to Earth using LOX/LH2 now weighs 1,860.019578 kg while the complete combination of vehicle, cargo (Block DM-version), engine and tank weighs 7,990.019578 kg. So no regression functions are required – everything is within the safety margins.

Now the part 1-calculation can be done because the weight of the tank being the cargo carried from Earth to Moon is known now - 1,860.019578 kg.



Completing the calculation of the Step 2-Trip

The required amount of LOX/cerosene at carrying the cargo calculated is 41,373.9559 kg. Then the Block DM-version weighs 2,075.564282 – which means that the weight of the tank applied in the part 2-part was a bit too high. I added the difference to the cargo of the part 1-calculation which increased the amount of propellant by less than 1,200 kg. As can be seen in step 1 where only the Block DM was used this doesn’t increase the weight of the tank that much.

Since the Centaur V1 now has to be applied as tank/stage for the reusable tankers also now the tankers ahve to be recalculated. At this point it turns out that there is a problem with the description of that calculation in the appendix of the previous post. I myself had to have a look there to do the calculation and detected that small or few details seems to be missing – it is unclear to me what I have done. So I thought about it another time and now again describe in the Appendix, how it is done. At present there is a table in the Excel spreadsheet I can apply but the table might be removed again later.

The calculation of the tanker first requires to calculate the lander. The Apollo LM-derived lander requires 5,874.609043 kg in total and 1,791.392584 kg at launch while for the CXV-derived lunar lander 14,210.55026 kg in total and 3,813.212781 kg at launch are the results. These numbers lead to an Apollo LM-based tanker consuming 5,079.970325 kg in total, 996.7538658 kg for landing and delivering 2,330.305834 kg or a CXV-based tanker needing 11,735.1006 kg in total, 1,337.763118 kg to land and delivering 6,075.449663 kg.

It turns out that the CXV-based tanker leads to by around $ 3,000 less refuelling costs than teh Apollo LM-based tanker – meaning only $ 600 per passenger. Because of this keep the Apollo LM-based tanker now.



Costs/Prices of Step 2-Trip

The calculation results in the follwing numbers:

Code:
Lpoint, expendable         cylindrical   spherical
variable costs              5623395,17    4460973,74      
price                       6185734,68    4907071,11      
initial price              17185734,68   15907071,11      
price + safety margin       6809200       5407200      
init. price + safe marg.   17809200      16407200      
                                         
reusable, reusable                        
variable costs               335457,25     117322,67      
price                        369002,98     129054,94      
initial price              11369002,98   11129054,94      
price + safety margin        409200        143200      
init. price + safe marg.   11409200      11143200      
                                         
Falcon, reusable                          
variable costs             26860052,50    7564986,58      
price                      29546057,75    8321485,24      
initial price              40546057,75   19321485,24      
price + safety margin      34009200       9207200      
init. price + safe marg.   45009200      20207200      
                                         
Falcon, expendable                        
variable costs             30835052,50   11827277,94      
price                      33918557,75   13010005,73      
initial price              44918557,75   24010005,73      
price + safety margin      38009200      14406200      
init. price + safe marg.   49009200      25406200      


As turns out the numbers are all significantly higher than in the first step. This already was catching the eye when the amounts of propellant have been calculated. The difference is that high that I am suspecting that I by error applied wrong numbers either for the step 1-trip or for this step. I will have to check the step 1-trip merely but will do that later because there will be a better opportunity to do that.

Obviuosly the cylindrical price remains by nearly 75% above $ 200,000 here and only the spherical case is below $ 150,000 – both at reusable QuickReach2 which would mean in 2030 earliest. But launchpoint Technologies as tanker with an expendable QuickReach2 still is a moderate price for a landing trip to the Moon.

I had one short and very limited look to a part 1-calculation for this step without any payload instead of the Centaur V1-version. There is a remarkable drop but I have to do a complete calculation later. This means that it sems to be likely that the step 2-trip is suboptimal by its own nature.



By the way – I randomly detected that the correction factors also correct the results für errors of data and logic. This is no surprise in principle but confirmed now by observation and random.







Dipl.-Volkswirt (bdvb) Augustin (Political Economist)



Appendix

Revision of The Calculation of Reusable Lunar Tankers

Like I said above I couldn’t totally recall reading the preious post how the tankers were calculated. However there is another reason also to do this revision – obviously the previous calculation didn’t distiguish between the top-plus-bottom psrts of the tank/stage and the sides which should be corrected now.

The calculation is based on the calculation of a lander – this means that the required amount of propellant got for a lander is applied. This amount is in a tank – and this tank of the lander has to be applied also. Up to now the same standard tank has been applied for the landers that was applied for the vehicle going forth and back between Earth and Moon. So the data about this standard tank have to be applied – including diameters supposed.

The standard tank has a standard capacity the amount of propellant required by the lander needs to be divided by to be able to calculate the weight of the tank of the lander. Because a weight of the top plus bottom of the standard tank has been calculated by the formualr(s) this weight has to be applied while the reuslt of the division is multiplied by the weight of the side of the standard tank calculated by the formular(s) also – giving the weight of the side the tank has in the case of the lander. Both these weights together are the weight of the tank of the lander.

The tanker will have the same engine as the lander – this was hurt for one lander in the appendix of the previous post. So next the total weight of the hardware of the lander needs to be applied.

Like already described and applied for the Earth-Moon-vehicle each part of the lander causes one share of the total propellant of lander according to the share that part has on the total weight of the hardware of the lander. At this point the phase considered starts to be of meaning. During the first phase of the operations – landing of the lander carried from Earth and/or launch of the tanker waiting on the Moon from the lunar surface – the weights of the bothe vehicles are equal. So I don’t do a particular calculation of that phase here. During the second phase however there is a significant difference that is essential – at the lander all the weight propelled during the first phase is carried during hte second phase also while this NOT the case at the tanker because the tanker has fuelled the propellant carried into the vehicle returning to Earth. I apply the total weight of the carrier-part of the lander to not to be carried during the second pahse (landing of the tanker).

So the amount of propellant required for the landing of the tanker is reduced to the share of tank/stage plus engine in comparison to the lander. To calculate the amount the amount is required the lander consumed at launch and must be multiplied by the share of the tank and the engine. The formular(s) calculating the total propellant for the lander do that split for landing and launch – thus the data needed are available.

The amount got needs to be divided by the capacity of the standard tank. The result multiplied by the weight of the side of the standard-tank leads to the weight of the side required for that version of the tank that has the capacity to contain the propellant to carry the tank/stage plus the engine.

Another portion of the tank to be landed is empty – and a part at least of that portion was required during the first phase of operation (landing of the lander or launch of the tanker). Above it has been said that the tanker will need the same amount propellant during th first phase as the lander did. The lander carried an amount of propellant for the second phase that was larger than in the case of the tanker because the tanker doesn’t keep a weight the lander kept. To keep the way described here simpla but correct that amount of propellant the lander needed for the second phase but the tanker does not is a portion of the freight now while the weight of that portion of the tank that contained this freight replaces the carrier-part of the lander. Then the empty portion of the tank can be considered to be divided into two portions – the capacity required to launch the tanker and the remaining capacity that contains a portion of the freight.

The capacity needed for the first-phase-propellant is calculated dividing that propellant by the standard-capacity and multiplying the result by the weight of the side of the standard-tank. Adding the weight of top plus bottom the weight of the tank/stage of the tanker is got. The portion of the tank containing a portion of the freight during the first phase is got by subtraction of the now got tank/stage from the tank/stage of the lander. The number before the subtraction is the total weight of the hardware of the lander.

Next this tanker.weight is divided by the total weight of the lander hardware to multiply the result by the propellant the lander consumed during the second phase of its operation – the result is the propellant the tanker needs for landing. The subtraction of this amount from the amount the lander consumed plus the weight of the carrier-part of the lander results in the weight of the propellant delivered while on the other hand the addition to the amount of propellant at launch of the tanker – which is the amount at landing of the lander – results in the total amount of propellant the lander needs.



Last edited by Ekkehard Augustin on Sat Jan 26, 2008 9:13 am, edited 1 time in total.



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Post    Posted on: Wed May 16, 2007 9:12 am
Contents

Step 3-trip: LOX/LH2 only plus Centaur V1
Assuming the Requirement of Deliveries
Tanker going from Earth to the Moon
Empty Tanker returning to Earth
Impact of Location of the LH2 delivered





Step 3-trip: LOX/LH2 only plus Centaur V1

To add this step 3 has the following purposes only:

    Safer calculation of LH2 applying an actual LH2-tank
    Enabling a comparison to a correctly calculated step 1-trip
    Enabling a comparison to a trip consuming kerosene only instead of LH2
    Enabling simplifications

The part 1-calculation results in a required amount of propellant of 29,913.13045 kg of LOX/LH2 for the trip from Earth to Moon in the cylindrical case and 7,819.648062 kg in the spherical case – by the way: The third case spherical + top plus bottom is much close to the spherical value...!

These two amounts cost $ 16,751.35 and $ 4,379.00 if $ 0.56 per kg is applied.

The lander applied is the Apollo LM-pendant consuming LOX/LH2.

The part 2-calculation results in 14,796.12111 kg LOX/LH2 cylindrical and 10,252.25839 kg spherical required. Since this means a very different weight of the tank this part 2 must be modified now – instead of part 1 in the to be doubted step 1-results. The obviously not used part of the weight of the part 1-tank needs to be added as cargo. The amount is by 50.54 % less than in part 1. The total weight of the cylindrical tank got was 1,924.804995 kg from which 1,708.828998 for top plus bottom are to be subtracted. Then the multiplication of the percentage with the difference between those two results in a cargo of 109.15 kg.

This leads to the final value of 15,087.68882 kg for the required amount of propellant for the return to Earth. This is the cylindrical value – the spherical one is 10,542.29455 kg.

These two cost $ 8,449.11 and $ 5,903.68 at $ 0.56 per kg LH2.

The prices got are

Code:
Lpoint, expendable          cylindrical   spherical
variable costs               5141414.03    4302187.06
price                        5655555.43    4732405.77
initial price               16655555.43   15732405.77
price incl. safety margin    6406600       5404600
init.price incl.safe marg   17406600      16404600
                                   
reusable, reusable                 
variable costs                243427.77      85907.48
price                         267770.55      94498.22
initial price               11267770.55   11094498.22
price incl. safety margin     306600        104600
init.price incl.safe marg   11306600      11104600
                                   
Falcon, reusable                   
variable costs              18890034.47    4960352.23
price                       20779037.92    5456387.46
initial price               31779037.92   16456387.46
price incl. safety margin   25006600       6004600
init.price incl.safe marg   36006600      17004600
                                   
Falcon, expendable                 
variable costs              22865034.47   11827277.94
price                       25151537.92   13010005.73
initial price               36151537.92   24010005.73
price incl. safety margin   30006600      14406200
init.price incl.safe marg   41006600      25406200


Obviously the prices are significantly cheaper now than in step 2. The reason will be that a complete tank to be carried as cargo is avoided now. It can NOT be considered to be due to using LH2 instead of kerosene because this would require a comparison to a correct calculated step 1 which isn’t available yet since the step 1 calculated must be checked yet.

One point must be mentioned in short here: The required amount of propellant for the return to Earth is by around 50% less than for the flight from Earth to the Moon. This can be supposed to be an impact of the significant different existing vehicles applied in TPI and EOI. The weights are very different. It will be looked at later.

Assuming the Requirement of Deliveries

The simplest refuelling trip considered above opens the simplest way to handle the doubts regarding the existence and availability of sufficient deposits of hydrogen or water ice on the Moon.

The reason is that only the delivery of hydrogen needs to be considered. But this also holds for other fuels that don’t include oxygen. The only one applied in this thread up to now is kerosene. All the other fuels include oxygen – H2O2, Hydrazine, Methanole, Ethanole, N2O4 and ADMH – which will require additional calculations before refuelling any vehicle.

In so far the first deliveries considered only will add the possibility to refuel earthian hydrogen or kerosene at the Moon plus lunar oxygen got out of lunar Regolith and to add landers and tankers consuming kerosene instead of LH2.

One question regarding deliveries might be if tankers are still required really. The point is that only hadrogen, kerosene – and later other chemicals – will be delivered but no LOX. Since LOX can be got from lunar Regolith the costs of carrying LOX from Earth to Moon can be avoided – this means that at a given capacity more LH2 or kerosene can be carried and the costs per trip can be kept at a lower level. The lunar LOX still needs to be carried up to the vehicle in the orbit – so a tanker still is required.

A second question is if the delievred amount of LH2 or kerosne really needs to be carried down to the lunar surface. Tankers or lnaders can get the required LOX at the lunar surface... – but what about the LH2 or kerosene they also need? Obviously at least a portion of the delivered fuel must be carried down to the lunar surface to enable the delivery of LOX into the lunar orbit – in principle this is the first small example of trade between the Earth and the Moon: The Moon gets LH2 or kerosene for LOX it gives up in favor of the vehicle returning to Earth!

The answer to the seond question also means that the tanker already is on the Moon when the vehicle doing the delivery arrives. How this situation is established will be considered later because it is an investment. The tanker already being on the Moon means that it is fueled with hydrogen or kerosene already and that it also has added lunar LOX already.

At this point the third question is of meaning: Should the delivered fuel be kept in orbit? To landed would add costs of delivery from the lunar surface into the orbit that can be avoided by keeping fuel for the vehicle leaving the lunar orbit for Earth in to orbit. On the other hand the lunar garvity field includes an anomaly that causes low lunar orbits to be unstable. I am informed that this is of meaning for orbits at or below 50 km – I am not sure about the life time of the orbit(s) of Apollo 8 and Apollo 11 to Apollo 17. So there are two possibilities: Keeping the portion of LH2 or kerosene for the vehicle in orbit or landing it.

A third possibility is to split the amount delivered into a portion to be landed for use by the tanker and another protion to be kept in orbit to refuel the vehicle returning to Earth.

If the complete amount is kept in orbit the tanker only would have to carry the LOX required for landing from the lunar surface but could refuel the kydrogenor kerosene required to land from that amount – this doesn’t have no impact though because the lander also would have to rtefuel the amount of hydrogen or kerosene required for the next launch from the lunar surface.

If the portion is partially kept in orbit and partially landed then the tanker neither needs to carry LH2 for its landing into the orbit because it can refuel there nor is it required to carry LH2 down to the surface for the next launch. So in this case the tanker might be modified so that the costs of delivery of lunar LOX into the lunar orbit are reduced. In the three steps that didn’t require delivereies of fuel the tanker had to carry the total amount of LOX and LH2 required for the landing with it into the orbit. This requirement can be removed now. This seems to reduce the required capacity of the tank(s) menaing less weight of the tank and reducing the amount of propellant the tanker consumes. This again keeps the level of costs low.

If on the other hand the complete delivery must be landed the tanker still might be modified as described because there is a period of time where a portion of fuel is available on the lunar surface as well as in orbit – but for refuelling a trip that doesn’t do a delivery the tanker will have to be as it was in the three steps calculated up to now. This would mean two kinds of tankers – one kind to land a delivery and one kind to refuel a vehicle from the delivered amount.

So there are the following cases

    total amount of LH2 delivered kept in orbit + one normal tanker consuming LH2
    portion of the amount of LH2 delivered landed + one lighter tanker + one normal tanker (both consuming LH2)
    total amount of LH2 delivered landed + one lighter tanker + one normal tanker (both consuming LH2)
    total amount of kerosene delivered kept in orbit + one normal tanker consuming kerosene
    portion of the amount of kerosene delivered landed + one lighter tanker + one normal tanker (both consuming kerosene)
    total amount of LH2 delivered landed + one lighter tanker + one normal tanker (both consuming kerosene)

For the landers the same is valid as for the tankers in principle except for the circumstance that the third alternative – temporary availability of LH2 or kerosene in the orbit – normally doesn’t exist for them because the delivered amount usually would have been removed from the orbit when they are operating.

The costs of the delivery will be calculated as costs of the hydrogen or kerosene made available on the Moon totally. In so far this all has an effect on the costs of landing on, launching from and refuelling at the Moon only. Since www.astronautix.com explicitly mentions a difference of costs for one and the same fuel caused by environmental requirements and according laws that are of no meaning on the Moon it will be interesting to compare that difference to the costs that result from the calculations going to be done – if the difference is larger then LH2 or kerosene delivered to the Moon will be cheaper.

The aspect of meaning here is that the freighter doing the delivery will traval at a significanlty less velocity.

And it will start to make sense to calculate a refuelling trip using kerosene only instead of going towards the Moon by kerosene but returning to Earth by LH2.



Tanker going from Earth to the Moon

To involve deliveries first remember what has been said two posts earlier:
Quote:
Since less velocity means exponentially less required amounts of propellant here again I suppose calculations linearly down to be safe – like done regarding the reduction of weight where the velocity of the existing vehicle has been kept.

If the weight of the potential vehicle(s) of all the systematical calculations done up to now is kept but the time for one complete trip – including the return to Earth – is increased by any factor then the required amount of propellant should drop exponentially. So a linear reduction should include a safety margin that exponentially grows with the factor. The amount by which the factor reduces the requirement linearly could be added to the weight of the potential vehicle then because it wouldn’t be consumed. Since the talk at present is about deliveries the vehicle in total could be considered to be freight plus engine, stage/tank for landing and launch and propellant for landing and launch. May be that I will apply only a portion of the propellant that won’t be consumed.
Quote:
In this case the total weight towards the Moon would be kept but some propellant simply would be shifted to become cargo itself ... .


This needs to be a bit more detailled first now.

The process is that the tanker will leave the earthian orbit loaded with cargo, It will arrive at the Moon loaded with this cargo – meaning that there in principle is no difference to step 3 since the cargo is an analogon to the vehicle and a portion of the tank and the propellant of step 3. When the tanker is offloded it will leave the lunar orbit and later enter the earthian orbit – but NOW the cargo will be OFFLOADED. This means that the part 1-calculation of step 3 above can be applied but the return to Earth needs to be recalculated because there is no analogon to the vehicle, a portion of the tank and the propellant of step 3 no more – the cargo has been removed.

Like in step 3 the tanker will be refuelled at the Moon but it seems to make no sense to refuel hydrogen there – this would mean to pump off the amount the tanker needs to return and to repump it later again. If the complete freight would be landed that amount would first be landed and relaunched to the tanker later which would be a waste of the hydrigen the lunar tanker consumes. What will be refuelled only will be lunar LOX. Of course this will mean consumption of delivered hydrogen but this an’t be avoided.

So the calculations of deliveries need to be kept split like the steps 1 to 3. But the are different to those steps because of offloading and the availability of lunar LOX combined with assuming the absence of any lunar hydrogen.

The shift of propellant – becoming possible because the longer flight time reduces the required amount of propellant - to the amount of cargo will NOT be done directly because this involves a possible error. The shift means an increased weight of cargo compared to its analogon og step 3. Because of this the reduced amount of propellant will be calculated and subtracted from the originally calculated one.

The result is the amount that can be considered to have become additional cargo now. For this amount one or more additional delivery flights will be assumed – using the same or a smaller tanker. This means that more than one engine, more than one top plus bottom of the tank and more than one amount of propellant required by the additional engines and tops plus bottoms will be involved.

In the reality there would be only one vehicle for the amounts considered separatedly here – menainf only one engine, only one top plus bottom and propellant for these one engine and one top plus bottom only. This would mean economies of scale neglected the way described – this adds a safety margin regarding the propellant

To avoid useless complexity and expenses of time amounts below the weight of the analogon(s) of step 3 will be replaced be the total weight of the analogon(s).

There are two perspectives of consideration that make sense – the time of three months t/space are talking about and that amount of time sufficient to keep refuelling at the Moon advantageous and favourable. May be that the both idenatical or tthe second one doesn’t exist. The first perspective can be found easyly the way described while the second possibility requires to apply the result of the part 2-calculation of step 3. That result is based on a price of $ 0.56 per kg of LH2 but www.astronautix.com lists maximum price/cos of $ 3.60 per kg of LH2 – so there also is a result b to be got by deviding the expenses for the propellant by 0.56 and next multiplying it by $ 3.60.

There are two different amounts of propellant listed for step 3 – each of them is the result of one of the two part i-calculations. The part 1-result is 29,913.13045 kg. This amount will be used here.

The complete time of the trips calculated up to now is six days – three towards the Moon and another three back to Earth. Since only the tme towards the Moon is considered here three days is the valid time of the step 3-trip to be applied here.

Originally 3 days required 29,913.13045 kg of LOX/LH2. At present the design of the delivery trip is that it needs 90 days – three standard-months of 30 days – towards the Moon. It carries the equivalent or analogon of the CXV weighing 3,600 kg. The engine needs to be kept off theat weight because it is required also if the CXV or its analogon wouldn’t be there. This means that only 997.104348333... kg would be required to carry 3,600 kg from Earth to the Moon – the original amount for 3 days has been divided by 30 to increase the time from 3 days to 90 days.

The original amount minus the new amount is giving 28916,026101666... to be shifted to cargo. This divided by 3,600 is giving 8.0322294726851... flights. Because that is that close to 8 this number of flights will be applied now. So the amount of LOX/LH2 to deliver 28,800 kg of LH2 from Earth to the Moon is these eight delivery flights plus the first delivery flight calculated times the amount required by the first calculated: (8 + 1) * 997.104348333 kg = 8,973,939135 kg of LOX/LH2.

Please note urgently:

    The approach to calculate linearly down via division by time appears to deserve lots of doubts or be wrong because the more days are assumed the more the required amount of propellant approaches 1 kg and less – but in parallel the more days required are applied the more delivery flights are got the way applied.

    The required amount got that way invloves (1 + n) engines plus (1 + n) tanks plus (1 + n) the amount of propellant one engine and one tank required – but the result got via that calculation is considered to be required for the delivery of the total amount of propellant of those (1 + n) flights by a tanker having (1 + n) the capacity of those smaller tankers, doing one flight only, having one engine only, having one tank only and thus requiring propellant for that single plus that single tank only.

    That applied to the above calculation menas that the calculation giving a required amount of 8,973,939135 kg involves 1 + 8 = 9 engines weighing 230 kg plus 1 + 8 = 9 tanks plus 1 + 8 = p amounts of propellant required for one such engine plus one such tank: 2,070 kg engines + X kg tanks + Y kg propellant for one engine plus one tank while the vehicle assumed to do the delivery has one engine only of 230 kg weight, one tank only and needs for those two together one amount of propellant only but will require 8,973,939135 kg of LOX/LH2 to deliver 29,913.13045 kg to the Moon in 90 days.

    The delivery does NOT involve a vehicle weighing 3,600 kg – this is turned into LH2 here.

In so far some of the doubts at least seem to be got rid of. And there are safety margins applied to get prices and costs.

So let’s consider those prices and costs now. In the step 3-trip all the costs and prices for the delivery already are calculated except for one portion. The weight to be delivered as well as depreciations and safety margins all is involved and the transportation costs and the price of LH2 already are included. The only portion to be added now is the delivery of 3,600 kg plus 8,973,939135 kg minus 997.104348333... kg

The 3,600 kg originally were the weight of the CXV-like vehicle waiting in LEO and never being landed on and launched from the earthian surface again. That’s turned into LH2 now which again and again will have to be launched because it is completely consumed again adn again. The weight subtracted from the total amount of propellant the delivery needs was already involved in the amount delivered into LEO from Earth.

The transporattion costs to deliver the additional 11576,83478666... kg of LH2 and LOX/LH2 are at

    Falcon 9 S 9 $ 36,484,570.24
    expendable QuickReach $ 32,157,874.41
    reusable QuickReach $ 401,973.43
    Launchpoint Technologies $ 2,188,021.77


The amount to be added costs $ 6,483.0274805333... .

The numbers listed for the step 3-trip must be modified a bit. The prices/costs of the landing(s) and the refuelling at the Moon have to subtracted. Second the prices are per paasenger – so they have to be multiplied by the number of passengers (5) and finally the costs of the taxi into LEO have to be subtracted.

I stored both the result of the final part 1-calculation and the result of the part 2-calculation – so the result without refuelling already is available.

Up to this point the total costs of the complete delivery are between variable costs of $ 800,000 spherical and delivered into LEO by a reusable QuickReach and initial price including safety margin $ 243 mio cylindrical delivered into LEO by a Falcon 9 S 9 – these are total flight costs resutling from the part 1-calculation.

All flights of the lunar tanker and the flight back to Earth will use portions of the amount of LH2 arriving at the Moon by this delivery flight.

Because of this next the amount is to be calculated the tanker requires to return to Earth.



Empty Tanker returning to Earth

Like already mentioned above the part 2-calculation now requires to list a new potential vehicle as empty tanker. This vehicle simply has no vehicle-weight here but an engine and a tank.

The calculation by the formular(s) and the Excel spreadsheet results in a required amount of propellant of 6,051.938287 for the return to Earth – within three days. This time for return may be reasonable to enable a quick follow-on delivery but 90 days would save LH2 for refuelling other vehicles at the Moon. This would reduce the required amount down to 201,7312762333... which are to be multiplied by (1 + 8) again giving 1,815.5814861 kg. This amount is required to return the engine and the tank for the propellant the tanker needs for the flight back to Earth.

This can’t be sufficient yet because the flight towards the Moon required much mmore propellant. So a second calculation is required where the difference of the two is carried as cargo. Here again the low values to be doubted must be applied to get the new result of the calculation that next will be modified from 3 days to ninety days and to one flight instead of 9 then. This now means that the virtual existing Soyuz carrying payload must be used again instead of the real Soyuz carrying no payload.

Now a required amount of 5,639.50064 kg for the return to Earth within 3 days is resulting.- meaning 187.983354666... for 90 days. This means that the one tanker that carried the complete amount delivered requires 1,691.850192 kg of propellant. This amount lower than the previous one is due to the cargo-carrying virtual existing Soyuz. Behind the reduction will be the circumstance that the heavier parts of the tank and the whole object aren’t increased but cause the larger amount of the propellant – meaning degression of costs and economies of scale.

The amount of 1,691.850192 kg is taken from the LH2 delivered – but partially only because lunar LOX is consumed also. So this value needs to be split and the LH2-portion then must be subtracted from the amount delivered – which means that this amount of LH2 is part of the costs or price of the amount left at the Moon.

At this point an aspect is of meaning I didn’t need to apply up to now – the mix ratio. I had problems to find the number(s) and ended up with two values listed under www.bernd-leitenberger,de. There the amount of oxygen seems to be the larger one which I have problems to believe because of other explanations an descriptions given there. Because of this I suppose that much more hydrogen than oxygen is consumed. The values listed are 5.5:1 and 5:1, Since the first of these means more hydrogen I apply it to have another safety margin. The division of the number got above by 5.5 + 1 and next the multiplication of the result by 5.5 results in 1,431.57 kg taken from the hydrogen delivered.

Then 28,481.565 kg of LH2 are available at the Moon. These obviously cost between $ 28.42 per kg spherical at reusable QuickReach2 and $ 8,566.79 cylindrical at the Falcon 9 S 9. Now the second number is an initial price including safety margin. I don’t think that this is a situation valid for such deliveries. Deliveries won’t include the lost-in-space costs an initial price includes because those costs will have been depreciated totally other ways the time when deliveries will start to be done But even then the upper boundary still is at several thousand dollars per kg of hydrogen.Except for the reusbale QuickReach Launchpoint technologies combined with spherical tanks is the only chance to keep the price/cost around $ 1,000. Below $ 100 is possible only if no safety margin is applied in the Launchpoint Technologies case.In the case of the reusable QuickReach2 the price/cost are far below $ 100 allways if the initial prices are excluded.

But this isn’t sufficient yet to determine what the costs of the trips might be at deliveries.

One number has been left out of consideration like in previous calculations – the weight of the tank the LH2 is carried in. The weight of this tank seems to be less than 1,000 kg and it may be a portion of the tank the propellant for the transportation is contained by. That tank may be defuellable for purposes of delivery. But of course it would be interesting to calculate the tank for transportation explicitly which would have to be done as additional cargo.



Impact of Location of the LH2 delivered

There were three alternative possibilities listed above. Here I start with

a) delivered LH2 kept ina lunar orbit

Of course lunar oxygen will have still to be delivered into the orbit. This price or costs of this lunar oxygen will be kept at $ 0.56 or $ 3.60 per kg like the price of LH2 on Earth and like applied for lunar LH2 earlier.

Of the 15,087.68882 kg LOX/LH2 required to return to Earth in step 3 12,766.51 kg are hydrogen while the remainder of 2,321.18 kg are oxygen. These are to be multiplied by $ 0.56 giving $ 1,299.86 which isn’t that much obviously.

To this the costs of the delivery from the lunar surface have to be added. The amount to be delivered is nearly one capacity of the former Apollo LM-pendant-derived tanker only – only one launch of the tanker is required to deliver the required amount of oxygen.

For one launch plus one landing the tanker needs 3,746.42 kg of LOX/LH2 which according to thoughts told above are simply distributed over the whole flight differently than in previous posts – the tanker carries no LH2 for landing at launch but refuels it in orbit from the delivered amount. The amount required to launch here will be considered to be taken from the delivery also because this really must be done to be able to do a second launch later again. This means that the whole requirement has to be split now into hydrogen and oxygen – 3,170.05 kg LH2 and 576.37 kg oxygen.

The oxygen costs $ 322.77 while the hydrogen – taken from the delivered amount costs $ 90,082.13. So the refuelling costs $ 90,404.90.

Next there is the landing which also requires LH2. The Apollo LM-pendant consumes 5,874.609043 kg of LOX/LH2 according to the previous post. Of these 4,970.82 kg are LH2 and 903.79 kg oxygen. The oxygen costs $ 506.12 while the LH2 costs $ 141,254.20 – $ 141,760.32.

Together with the refuelling these are $ 232,165.22.

What’s left now are the oxygen and the hydrogen for the return to Earth. $ 1,299.86 are listed above for the oxygen – what about the costs of the hydrogen? Given the amount calculated above the required amount costs $ 362,781.49. Addition of the oxygen results in $ 364,081.35.

Then in total at the Moon costs are caused of $ 596,246.57.

These are the costs/price for the flight back to Earth only including refuelling and lander. To this the costs/price of the flight towards the Moon must be added which are $ 410,763.90..

So the complete trip costs $ 1,007,010.47 – $ 201,402.10 per passenger and thus price/cost per ticket.

Compare this to the price/costs got above for the step 3-trip using a resuable QuickReach2 both for taxi and delivery of fuel into LEO assuming lunar ressources of hydrogen: $ 85,907.48 – the impact of the absence of lunar hydrogen and the reuslting requirment to deliver it would add costs of a bit more than $ 115,000 per passenger. This a bit less than 150% of the $ 86,000 – may be that this might be correct for the other alternatives listed above also. Multiplying them by 2.5 may be a reasonable rule of thumb but I didn’t check it yet.

For comparison have a look to the costs of the landing trip without carrying all the propellant from Earth (three posts ago): $ 279,256.40 – the delivery-based trip still seems to be advantageous economically.

Important remark: The result got here is invalid for t/Space’s concept and mustn’t be taken as argument regarding that concept because they don’t have in mind such a delivery but simply split the trip calculated three posts ago to get it cheaper. Their three-month delivery trip is a delivery from Moon to Earth which is the opposite of what I considered in this post.

Pleaso note also: The delivery has been calculated here only to get the lunar price/costs per kg LH2 – the amount itself would have to be much larger and/or there would have to be a whole fleet of tankers.

b) portion für lander and tanker landed onto the Moon

In this case the costs of the landing have to be added. The lander has to fly three times and consumes 4,970.82 kg of hydrogen. The ltnker has to fly one time and consumes 3,170.05 kg. So 18082,51 would have to be landed. Ignoring the cahnce the the tanker could be a bit smaller in this case – like mentioned above – 7.76 flights of the tanker are required. These 24,598.69 kg of hydrogen in total cost $ 699,012.55 – meaning additional $ 139,802.51. Adding this to the price/costs above the result exceeds the price/costs of a non-refuelling landing-trip mentioned above.

So this case is ruled out.

c) landing the complete amount delivered

Because of the result under b) this case isn’t worth to be calculated.



I neglected the oxygen under b) because it has no effect on the result – the case is ruled out: why calculate the costs of the lunar oxygen?

If there are no deposits of hydrogen on the Moon a lunar depot delivered from Earth is economical only if it can be left in a lunar orbit it seems. In reality it would have to much much larger than the amount applied here for economical reasons I suppose. The depot would have to be safe against the anomaly of the lunar gravity field or it would have to be able to handle it for years at least - better yet for decades.



The calculation of deliveries will be incorporated into the Excel spreadsheet as far as possible and as far as that makes sense, Any table of prices or costs will be listed later (if at all). The consideration of deliveries isn’t finished yet...







Dipl.-Volkswirt (bdvb) Augustin (Political Economist)


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Post    Posted on: Wed Sep 19, 2007 4:15 pm
Contents

Checked and found
Improved and systematical calculation
Landing the complete delivered propellant
Landing that portion of LH2 required to deliver LOX and to land people or cargo
Lunar Prices of delivered Hydrogen at $ 0.56 per kg on Earth
Economic Meanings: Ratios
Considering the results
Shackleton Crater Company
Application to Trips: Selection(s) and Constraint(s)
Trips based on Deliveries
Excel spreadsheet
Oxidizer/Fuel Ratios
Appendix
Lunar Prices of delivered Hydrogen at $ 0.56 per kg on Earth
Trip-prices at delivery of LH2



Checked and found

Looking for mix ratios to complete the data about vehicles, landers and tankers in the according tables because the incorporation of deliveries require them I began to wonder about the data I found and had a look into www.bernd-leitenberger.de and Wikipedia. I thought a bit about the informations and then became aware of a misunderstanding of mine. It is now clear to me that a mix ratio of 5.5 means 5.5 times as much LOX as LH2. The misunderstanding was caused by the information that that number means a surplus of hydrogen over oxygen which I understood as absolute from the german text. But the correct understanding is that so much hydrogen is fueled that it is not completely burnt with oxygen to water which only would be achieved at a mix ratio of 8.

The consequence of the error is that I applied too much of the delivered hydrogen, got too high a price (as it seems to me this moment) and too high portions of the delivery consumed per landing, launch, TEI and EOI.

Since all the calculations are done in this post using the Excel spreadsheet and since the error had NOT gone into the spreadsheet before doing new calculations the numbers in this post do NOT involve the error of the previous post.

Interesting point: There are prices that are significantly increased now while others are reduced. The reason is that the relation between LOX and LH2 has been changed by the correction so that larger amounts of LOX have to be carried from the lunar surface into lunar orbit than before. These deliveries consume LH2 carried from Earth to the Moon that at their arrival already have costs there that are nearly 100 times their costs on Earth. Those prices that include lost-in-space-costs or high safety margins thus include also a factor that overlays the impact of the change.



Improved and systematical calculation

There was one error in the previous post regarding the lunar LH2-price. The way of calculation didn’t take into account some details resulting in different cases – besides the misunderstanding talked about above. So I thought about it and extended the calculation of trips to the calculation of deliveries. This also turns it more systematical because it fits optimally into the approach.

The incorporation of the calculation into the Excel spreadsheet results in calculating the price of the delivered hydrogen – or any other propellant – a different way. More essential is that the calculation is more correct and it turned out that in the previous post I seem to have lost out of sight 3,600 kg of hydrogen delivered.

The way of calculation now is that first only the deliverey into the lunar orbit is calculated – giving a price if the tanker wouldn’t return but stay in the lunar orbit completely for ever. Next it has to be taken into account that of course the tanker will return to Earth – and will have to take a portion of the LH2 delvered to do so. This amount is multiplied by the price into the lunar orbit without the return. The result is divided by the amount left at the Moon and then added to the price into the lunar orbit without the return. Third the delivery of oxygen into the lunar robit has to be included now which hasn’t been done in the previous post because the amount of oxygen is that smal and in particular much smaller than the capacity of the tanker(s) applied up to now in the case of deliveries.

It could be assumed that one of the tankers already applied will be used but the capacity will be used to around 10% only – but I have my doubts if that is reasonable. The result may be wrong but too small to be of meaning and so on. Another way would be to calöculate as if the capacity would be used completely – but this would leave the question what will happen to the amount of oxygen not required. The most proper solution would be to calculate another lunar tanker for very small amounts - but this I am missing a reasonable base for because the lunar tankers already calculated are based on existing or virtually existing landers of knwon or given capacity. Micro Space or Pixel have the proper capacities it seems – but they can’t be applied at present because they consume propellants not available at the Moon at present even at delivery of hydrogen.

I suppose the second alternative to be the best one and apply it in the Excel spreadsheet. The required amount of propellant needs to be split in LH2 and LOX. The LH2 has to be multiplied by the price got n the step that includes the return of the tanker to Earth while the LOX the tanker neeeds will be multiplied by $ 0.56 since this is the earthian price of the more expensive LH2 on Earth which allways has been applied for LOX up to now to have a safety margin. Then the dollars are divided by the capacity resulting in the transportation costs per kg of delivered lunar LOX. This is mulötiplied by the amount to be delivered. This amount also is multiplied by $ ß.56. Both products are divided by the amount of LH2 left at the Moon and added to the price got before calculating the costs of the lunar LOX.

It turns out that the cylindrical values seem to be lower than calculated in the previous post while the spherical values are significantly higher than in the previous post. I check what the reason of the increase of the spherical values might have been and recognized that it has been the circumstance that I didn’t apply a distinction between the spherical case and the cylindrical case. This meant that I applied twice the amount of delivered LH2 as is correct. Regarding the reduction in the cylindrical case the reaon is that I lost out of sight 3,600 kg of LH2. This error or difference was of meaning at more than one step of calculation.

Another interesting result is that the initial prices in the spherical case are higher than in the cylindrical case. The reason is that the lost-in-space-costs applied are identical in both cases while the amount delivered in the spherical case is around half that delivered in the cylindrical case.

The results got now are listed in the appendix – there are two cases now that exceed the maximum price got in the previous post both of which are spherical. The numbers are got applying the Apollo LM-derived tanker with a Centaur V1-derived tank and consuming LOX/LH2.

The Excel spreadsheet also calculates deliveries of cargos that aren’t consumed. In this case – not going to be applied here – you have to decide previously if you want to apply the case that LH2 or another propellant has to be delivered or if it is available via ISRU. If you decide that LH2 must be delivered and the delivered equipoment (being an investment!) is required to do the rfeuelling landing trip a threefold-calculation would be required. First the delivery of LH2 or another propellant has to be calculated to get the LH2-price to be applied for the return to Earth. Next this price has to be applied to get the complete costs of the equipment which then are the complete costs to deliver the equipment and then to return to Earth + the value of the equipment itself which is its market- or production-price. And finally the refuelling trip would have to be calculated using the lunar LH2-price got. This trip involves the share of depreication invloved into each price as long as at least one component of the complete equipment isn’t depreciated completely. The complete value of the equipment including the transportation costs of the delivered one(s) will have to divided by the depreciation share of the price to get the number of trips to be required until the compete equipment is depreciated – turning the depreciation share into a (perhaps additional) profit.



Landing the complete delivered propellant

Before going on now the impact of landing the delivered LH2 will be considered. The calculation of the price if the LH2 is left in orbit also tells the amount of LH2 left after the tanker returned to Earth. From this the lunar tankers – now landing the delivery instead of carrying propellant into the orbit – must be refuelled to land the remainder.

The Apollo LM-derived tanker using a Centaur V1-derived tank/stage and consuming LOX/LH2 has a capacity of 2,330.305834 kg and consumes propellant of 3,746.418356 kg per mission. Of these 3,170.046302 kg are LH2 and 576.3720548 kg are LOX. The remainder left in orbit after the tanker returned to Earth will be divided between capacity and consumption according to these numbers.

So the remainder can be divided by the sum of capacity and amount to be consumed to find the number of flights required and possible to land the delivery. It’s a bit more than 5 in the cylindrical case here. This means the consumption of more than a third of the LH2 left. The precise ratio between consumption and landed amount got is 0.247337515. Then the new price – regardless of which of the cylindrical alternatives is considered (I didn’t check it though) – is „(1 + 0,247337515) * price at keeping in orbit + LOX-costs of the landing per kg of the LH2 reaching the lunar surface unconsumed (this is less than $ 1 that can be replaced by $ 1)“. This means that the prices listed for the case that the delkivery is kept in orbit are increased by a fourth.

In the spherical case the ratio turns out to be identical which is no wonder.

The ratio can be applied to the numbers listed in the appendix in the first two columns of the table of lunar LH2-prices – the results are listed in the other columns.

It is important to mention here that this is a talk about logistics and economical planning of trajectories now.

The Excel-spreadsheet will not list these ratios explicitly but as part of formulars only. The reason is that the values depend on the data of the tanker to be selected for carrying LH2 down to the lunar surface.



Landing that portion of LH2 required to deliver LOX and to land people or cargo

In difference to above the tanker wouldn’t be refulled from the LH2 kept in orbit completely but only to that amount that is required to land the tanker – for the next launch the tanker would be refuelled on the lunar surface. The tanker would have to land those amounts of LH2 only that are needed to deliver oxygen into the orbit and to launch landers that carry passengers or non-propellant payloads.

This means that the tank used to launch or land the tanker could be a bit lighter. But the difference in weight will be neglegible and the difference in LH2 taken from the orbital depot is in focus here. Instead of 576.3720548
kg it will be 423.0253062 kg only. The remainder required for the next launch will be fueled on the lunar surface.

The tanker and the passenger-vehicle for the trips now will get their return-LH2 from the orbital depot – but to deliver lunar LOX into the orbit the landed portions of LH2 will be consumed. This combination keeps it less expensive than in the case that the complete delivery is landed.

The empty tanker needs for its launch only 153.3467486 kg of the landed LH2 (recall that at present this is a tanker carrying LH2 from the orbit down to the lunar surface instead of the opposite order) but it carries 2,330 kg LH2 as freight. The complete oxygen required for both launch and landing is taken from the Moon.

So the amount of LH2 to be taken from the orbital depot for consumption must be divided by the amount to be landed (=capacity) to get the LH2-consumption per kg of LH2 carried to the surface. This must be multiplied by the orbital price of the LH2 and then added to that price. This is the LH2-portion of the price the LH2 has on the lunar surface – together with the LOX-portion of the price the price of LH2 on the lunar surface is got that must be applied also in the case that the LH2 is NOT applied as fuel but for the production of water for example, for lunar industrial purposes, fuel cells or the like.

To get the correct price for the LH2 on the lunar surface as fuel another LH2-portion of the price has to be added – the amount of LH2 required (by the particular tanker in use at present) to launch again empty must be divided by the amount of LH2 remaining on the lunar surface. Then the price on the lunar surface has to be multiplied by the result which next has to be added to the price valid on the lunar surface – this is the LH2-portion of LH2 as fuel on the lunar surface.

So next the LOX consumed to carry the LH2 down to the surface has to be divided by the amount of LH2 landed – the result has to be multiplied by the LOX-price. Adding this to the LH2-portion of the lunar surface-LH2-price results in the LH2-price valid on the surface as long as the LH2 is NOT consumed as fuel..

What’s left is the LOX-portion of the LH2-price of LH2 as fuel. This means that additionally to the LH2 consumed to launch into the orbit to get to the depot the consumed amount of LOX at that launch has to be divided by the amount of LH2 left on the lunar surface. The result has to be multiplied by the LOX-price and then added to the LH2-portion of the price of LH2 as fuel.

The two LOX-portions together are less than $ 1 here – which would be quite different if the LOX would have to be delivered.

The reason why there are different prices for LH2 as non-fuel and LH2 as fuel is that LH2 as non-fuel doesn’t need to be replaced. If for example the LH2 is used to produce water it allways can be got back for other purposes by electrolysis based on solar power. This I at present assume to be possible for other applications also. Replacements are required if the cracking of LH2-including chemicals etc. is not desired or possible – but then it can be assumed here that the replacement also won’t leave the lunar surface again. The most essential and important application of course will be flights from one lunar surface point to another one!!!

In the case of the Apollo LM-based tanker the ratio now is 0.181532098 for the landing of the LH2 + this 0.181532098 * 0.070440804 for consuming the landed LH2 + 0.070440804 incorporating the differnce to the surface-price = 0.264760169 and then added to 1 – a very little bit more than the ratio in the case of landing the delivery in total. But this will NOT be involved into refuelling the vehicle that returns to Earth but to landers and tankers for that vehicle only. The price of the landed LH2 then is „(1 + 0.181532098 + + 0.070440804 + 0.181532098 * 0.070440804) * price at orbital depot + LOX-costs of the landing per kg of the LH2 reaching the lunar surface unconsumed and launching the empty tanker (this is less than $ 1 that can be replaced by $ 1)“.

The ratio can be applied to the numbers listed in the appendix but the results can be applied for landings and launches only – regarding refuelling they would have an impact on the costs of the oxygen only. The results of the application of the ratios are listed in the appendix.

Like in the previous chapter the Excel-spreadsheet will not list these ratios explicitly but as part of formulars only. The reason is that the values depend on the data of the tanker to be selected for carrying LH2 down to the lunar surface.



Economic Meanings: Ratios

Up to this point the orbital prices are multiplied by the follwing economic ratios:

1. LH2-consumption at return to Earth/(LH2 delivered - LH2-consumption at return to Earth) = LH2-consumption at return to Earth/LH2-depot left in lunar orbit

This is the share of the LH2-consumption at return of the orbital LH2-depot – called scd here.This tells the share of the costs until lunar orbit that has to be added to incorporate the costs of the retrun of the tanker to Earth.

2. 1 + scd This is the ratio the LH2-price without return has to be multiplied by to get the correct LH2-price in the lunar orbit.

3. LOX-consumption at return to Earth/(LH2 delivered - LH2-consumption at return to Earth) = LOX-consumption at return to Earth/LH2-depot left in lunar orbit

This is the ratio of the LOX-consumption at return to the orbital LH2-depot – called rcd here. This is the LOX delivered from the lunar surface.

This ratio is applied to the price per kg LOX. Since for all propellants consumed the price of the more expensive propellant in the non-delivery-case is applied here and this price is $ 0.56 for LH2 $ 0.56 are applied.

Then the price is (1 + scd) * no-return-LH2-price + rcd * ISRU-LOX-price = orbital return-LH2-price without LOX-transportation-costs.

4. LOX-consumption at return to Earth/(LH2 delivered - LH2-consumption at return to Earth – LH2-consumption at transportation of lunar LOX) = LOX-consumption at return to Earth/(LH2-depot left in lunar orbit – LH2-consumption for transportation) = LOX-consumption at return to Earth/LH2-depot left in lunar orbit after transporation requirements.

This is the ratio of the LOX-consumption at return to Earth to the orbital depot left after reduction by the amount consumed by transporation plus the amount consumed by return to Earth.

This ratio is multiplied by the costs of LOX-transportation per kg.

5. (LH2 delivered - LH2-consumption at return to Earth – LH2-consumption at transportation of lunar LOX)/(capacity of lander + LH2-consumption of lander) = LOX-consumption at return to Earth/(LH2-depot left in lunar orbit – LH2-consumption for transportation)/(capacity of lander + LH2-consumption of lander) = LH2-depot left in lunar orbit after transporation requirements/(capacity of lander + LH2-consumption of lander)

This is the number of flights required and possible to land the delivered LH2 some of which necessaryly is consumed at carrying the delivery down to the lunar surface. This is called nof here.

The number of flights is multiplied with the LH2-share of the propellant-consumption of the tanker and – separately – with the LOX-share of that consumption.

6. LH2-consumption for landing/LH2-amount landed = LH2-amount required per kg of carried LH2.

This is the LH2-portion of the real costs of the transportation of LH2 from the orbit to the lunar surface – called rct1 here.

7. LH2-consumption for launch/LH2-amount to be landed = LH2-amount required to get to the LH2 delivered per kg of LH2 to be transported

This is the LH2-portion of the real costs of the launch of the empty tanker from the lunar surface into the lunar orbit – called rce1 here.

8. 1 + rct1 + rct1 * rce1 This is the ratio the orbital LH2-price covering the return to Earth has to be multiplied by if a portion only of the delivered amount is carried down to the lunar surface.

These are combined with the following technical ratio:

mix ratio



Considering the results

Looking into the table of LH2-prices in the appendix it catches the eyes that the prices are higher if the LH2 is landed partially only.

At first glance this is puzzling. The explanation is that in the case that the complete delivery is landed all LH2 consumed to landed the delivery are taken from the amount of LH2 that it still in orbit and is cheaper there than that on the lunar surface while in the case of landing a portion of the delivery only some amounts of LH2 consumed are taken from what has been landed which is more expensive than what’s kept in orbit.

That the prices in the cases of partially or totally landed deliveries are higher than in the case of consumtion or application of the delivery on the lunar surface has to do with the circumstance that nothing has been taken from it yet to launch again something.

This point could be considered to be an artificial distinction hurting the market principle. It seems to mean that there are amounts of LH2 not avilable for other purposes than launching vehicles. This is reasonable though because indeed already here on Earth substances and chemicals that can be consumed as fuel as well for other pusrposes are reserved and thus stored for application as fuel. The tank of a car or the tanks at gasoline stations are examples of that.

But here this still looks strange etc. because the next launch of the tzanker carrying down LH2 allways is added to the costs of the landed amount.

So let’s solve this by the thought that there might be a tanker capable of carrying down the whole delivery at once and keeping that delivery for purposes on the surface only – in total or to an overwhelming large part. Then the calculates surface prices are reasonable and the other prices will be valid that moment only when there is a nexxt launch of that tanker and for that portion only the tanker is consuming right then.

Really the price for sonsumptions or application on the lunar surface is a step of calculation here only that is required to get the final LH2-price at partial landing of LH2. But it can be of use for a particular purpose.

Finally it can be doubted if the alternative to land the delivered LH2 partially only is reasonable and economical at all since the price is higher then compared to landing it in total. But this appears so only if the prices are compared simply. It may turn out to be economical if it is applied in combination with the amount left in the orbital depot. This will be considered later.



Shackleton Crater Company

Since there are prices of delivered LH2 now it will be interesting to have a first look to Shackleton Crater Company now. This means that I now assume again that there is lunar LH2 and deliveries aren’t required – but might they be reasonable despiate the lunar availability? This can be a question of the price Shackleton Crater Company takes. The minimum price of the delivered LH2 listed in the appaendix for the case that the LH2 is applied or consumed on the surface only is $ 57.82. Why not deliver LH2 even if there is LH2 on the Moon but costs $ 57.82 or more? This would not be worth the expenditure and pain. May be that only this price coveres the lunar production costs of LH2. But what if it includes a profit margin? Then Shackleton Crater Company would find it interesting to set a lower price, miss a portion of the profits and the deliveries wouldn’t be economical indeed.

Instead of profit the price of $ 57.82 might include depreciations that would fall apart later – then the lunar production is interesting and economical too because it is known that it will lead to lower lunar prices in the future.

So what might that mean for Shackleton Crater Company? May be that the earthian production price is valid on the Moon also like assumed in earlier posts already. Then the pice of $ 57.82 can be considered to include depreciations of $ 57.82 - $ 0.56 = $ 57.26. Shackleton Crater Company and Stone Aerospace have said that $ 15 bio are required to start production of lunar LH2 and other fuels on the Moon. $ 15 bio divided by $ 57.26 result in 261,962,976 kg of LH2 to be sold to depreciate the $ 15 bio completely. This amount would mean 17.465 flights back to Earth or elsewhere or equivalent consumption or application of lunar LH2 on the lunar surface. Of course LH2 delivered into the orbit would have a higher price because lunar LH2 would have to be consumed at launch and landing of the tanker but the price could be dropped below $ 57.82 so much that the orbital price is at or less than the orbital price at delivery from Earth. I didn’t look for that price in this post.

But the price might be at $ 10,728.80 at delivery as well as production costs plus depreciation. Then the margin of depreciation in that price would be $ 10,728.24. At investments of $ 15 bio the production of 1,398,180kg would be sufficient for total depreciation. Then 94 flights back to Earth, to elsewhere or the equivalent of consumption or application on the lunar surface would be sufficient for total depreciation – which is a quite reasonable number.

This underlines the meaning and importance of the private struggle for cheap and general access to space. The more the privates succeed the more likely cheap return and permanent presence on the Moon and other planets.



Application to Trips: Selection(s) and Constraint(s)

I was thinking about the recalculation of the refuelling landing trip consuming LOX/LH2 only and thought about limiting the number of alternatives to what I usually list.

There is at least one constraint to be obeyed to – only those lunar LH2-costs or –prices are valid that are based on the same earthian price as applied for part 1 – towards the Moon – of the refuelling trip. If for example the delivery is based on an earthian LH2-price of $ 0.56 then the lunar price mustn’t be applied to refuelling trips that a price of $ 3.60 per kg of LH2 is applied to – but only to refuelling trips that as well apply an earthian LH2-price of $ 0.56.

But what about the other numbers to be selected?

Must a delivery trip assuming a certain tank-diameter applied to trips only where the same diameter is assumed? At first glance the delivery trip simply might have used another tank/stage than the refuelling trip and the difference seems to be valid. But thinking about the hardware the assumption is applied to it turns out that it is the same hardware – and if the same tank or stage has been produced two or more times the diameter reasonably must be assumed to be identical. This rules out mixes of deliveries using the same hardware as the refuelling trip but assuming a different diameter witth that refuelling trip.

What if the delivery trip and the refuelling trip consume different propellants? These of course can be mixed – on Earth it’s usual that the tanker delivering gasoline („Benzin“ in German) consumes Diesel while other cars consume the gasoline delivered by consuming Diesel.

Next there are the five alternative costs/prices I am listing. The situation here is that the delkivery trip and the refuelling trip don’t use identical tanks/stages. This allows for the situation that the tank/stage of the one is already depreciated completely while that of the other is not. This means that a mix of variable costs for the one trip and price including depreciation for the other is valid. If both trips use an identical tank/stage instead then there is only one point where a mix is allowed – for the one trip the final depreciation has to be done and the other is the first that is free of depreciations

What about the initial prices? If one of the trips has to depreciate lost-in-space costs then the other might have finished the depreciation already – the mix is valid if the tank/stage used is not identical. If they are identical there is one situation where a mix is valid – analogous to what has beens aid regrding depreciation of hardware.

A mix of a passenger trip with safety margin with a delivery trip without safety margin is not allowed if the same existing tank/stage or vehicle is applied because each margin handles uncertainties and a mix would mean a mix of more uncertainnty with less uncertainty for the same existing hardware applied. If the existing hardware applied to do the calculation(s) is different the mix of safety margins seems to be valid because the numbers etc. about one existing hardware might be more safe or provide more safety than the numbers about the other. A mix of a delivery trip with safety margin with a passenger trip without safety margin seems to be allowed also because the way of calculation starts at variable costs that don’t include a safety margin and then proceeds towards the safety margin(s). In this case the price of the delivered LH2 or other propellant already includes its own safety margin. Both the stage/tank and the vehicle are to be considered because both have an impact on the safety margin. Since the stage/tank of the existing vehicle is handled here as an integral conponent of the existing vehicle this is no problem regarding the Excel spreadsheet.

Essential and important: All the mixes considered are mixes of a passenger trip with a delivery trip carrying LH2 here.

The Excel spreadshett will NOT rule out mixes that are allowed once only because the spreadsheet can’t know how often the mix will be applied and when. There may be limited chances to establish a capability but it isn’t worth the pain. So be cautious regarding this and allways check if you or the poster have/has in mind the allowed single situation or if you or she/he is talking about repeated situations. If the forbidden mix of safety margins occurs the Excel spreadsheet will list zeros.

Regarding the existing hardware the Excel spreadsheet considers all phases calculated because one phase with different existing hardwares between passenger and delivery trip already means a difference impacting the safety margin which allows for the mix of a safety margin passenger trip with a non-safety margin delivery trip.

One more point is that landers and tankers as well as the vehicle returning to Earth have to be fueled or refueled. It may be that the landers and tankers consume other propellants than the vehicle returning to Earth. What desrves a few thoughts is the question if the landers might consume different propellants than the landers. On Earth there seem to be such differences since some rockets consume LOX/LH2, others LOX/cerosene, yet others N2O4/ADMH and yet others solids etc.

I am not sure if this should or could be applied to other planets – at present at least I have some doubts. First there ISRU-propellants obviously avalable on the Moon seem to be very limited to LOX/LH2, on Mars to LOX/LH2 and LOX/methane, on the Moons of the gas giants to LOX/LH2. There are no market prices on those planets at present and so there are no local economic factors which a choice might be based on. These are sufficient reasons to apply the same propellants for landers and tankers here. It also avoids useless complexity of the Excel spreadsheet.



Trips based on Deliveries

The complete set of lunar LH2-prices has increased the possible number of trip costs or prices by very much now.

So because the number of results listed should be kept where it was up to now additional constraints shouldbe inmtroduced now that aren’t caused by logics or so.

1. Before any consideration of deliveries of LH2 from Earth to Moon only one lunar LH2-price existed and thus was applied to each combination of tanker into LEO and taxi into LEO. Now that there are several lunar LH2-prices for each LEO-tanker-LEO-taxi-combination only thos lunar LH2-prices will be applied where the delivery applied the same LEO-tanker as the trip does.
2. To get the variable costs as price of a trip now up to five lunar LH2-prices exist now instead of one. So here to calculkate the usual five alternative kinds of trip prices only the according kind of LH2-price will be applied This means:

To get the variable costs of a trip the lunar LH2-variable-costs-price will be applied and only that price – to get the price of a trip including the depreciation only the lunar LH2-price including depreciation will be applied. Initial prices will be calculated applying inital luna LH2-prices only and so on.

3. As far as there are particular illustrations that are of meaning a few additional calculations only will be listed separatedly from the usual list.

One point I should mention here. The refuelling will be done by a lunar tanker. If the delivery in total or partially is kept in the lunar orbit then the following is valid:

1. If the delivery is landed partially then the tanker consumes the more expensive landed LH2 at launch but the cheaper LH2 kept in orbit at landing
2. The vehicle to be refuelled will refuel LH2 from the orbital depot. This will drop the required number of tanker flights if the amount of LH2 is larger than the required amount of LOX – which of course is the case. So the Excel spreadsheet will apply that to get proper results.

Point one is valid for landers also – I will add according columns in the table of reusable landers but apply the results got by the table calculating propellants for landers derived and calculated from existing landers.

Please look into the list of trip-prices based on deliveries and compare them to the list four posts ago – it seems that most of the prices at delivery of LH2 are BELOW the prices without delivery and without refuelling. At delivery the trip-prices seem to be less by between around 10% and 65% - I didn’t calculate the percentages though. There are exceptions – at a reusable QuickReach2 for both the taxi and the tanker into LEO as well as at a reusable QuickReach2 for the taxi and Launchpoint Technologies as tanker the initial prices and the initial prices with safety margin in case of delivery are HIGHER than in the earlier list. And the non-imitial price including safety margin at cylindrical tank and QuickReach2 both for taxi and tanker is higher also..

I think I can cancel the former idea to look for those deliveries or delivery prices that break even with prices without refuelling – a significant number of prices at delivery of LH2 are below the non-refueling prices at a delivery time of 90 days towards the Moon and 90 days back to Earth. Except for one all prices higher at delivery are initial prices – but for most alternative calculations the lost-in-space costs applied are very different from those applied in the much earlier non-systematical calculations. I think them to be improper – I should remark at this point that I will have to recalculate all results when the Excel spreadsheet is complete for the Moon. The all initial prices may be LOWER at deliveries.

So delivery of LH2 to the Moon if there is no hydrogen on the Moon may be advantageous – although the relations between the earthian prices of LH2 and other propellants may change that. But that’s a question of available ressources and markets that mustn’t have an impact here.

This also means that up to now the calculations are speaking for t/Space’s concept of using tankers and let them go along trajectories requiring longer times.

The prices considered up to now don’t include landing the LH2 yet. So let’s have a look on it and do some comparisons. The variable costs in the case that a QuickReach2 is applied for the taxi and the tanker, the LH2-price in lunar orbit is the cheapest of the list in the appendix, tha tank is spherical and the fuel is landed partially only the trip price is $ 133,452.38. If all the propellant is landed then the trip price is $ 183,012.86 – by a bit more than 37% higher than at landing a part of the delivery only. Compared to the orbital price of $ 130,459.91 a partial landing of the delivery doesn’t have that a large effect on the trip-price – less than 3%. The initial price including safety margin at expendable QuickReach2 for the taxi, Falcon 9 S 9 for the tanker, the LH2-price at delivery of LH2 into LEO via the Falcon and towards the Moon using a spherical tank and a cylindrical tank applied for the trip towards the Moon the trip price at partially landing the fuel is $ 48.2 mio – which again is reasonable compared to a delivery totally kept in orbit. The difference is 0.4% only. If the fuel is landed totally the trip price is $ 63.6 mio – by nearly 32% in comparison to keeping the complete delivery in the lunar orbit.

In the first case it still is cheaper to deliver the LH2 than to carry it during the trip – but in the second case (Falcon 9 S 9, expendable QuickReach2, etc.) the case of partially landed delivery only reamins cheaper than the no-delivery-case while the case of totally landed delivery is more expensive than the non-delivery-case by $ 8.6 mio – a bit more than 15.63%.

So it seems that here a difference has been found that shows that progress of vehicle development, trip-demand and selection of a vehicle can turn a decision to land delivered fuel from more expensive to cheaper.

The reusable-QuickReach-case still seems to mean that the delivery-concept of t/Space is advanatgeous.



Excel spreadsheet

To avoid waste of space the spreadsheet now applies a VBA-macro to copy the delivery price into the according field for landers and tankers if part 1 is calculated while it copies it into the field for the vehicle if part 2 is considered and the value of the field for tha tankers has been inserted already.

I had to check out several things which isn’t that a funny thing to do it privately. It is possible to get a condensed list automatically simply by using columns and insert Excel-functions into them but this makes the spreadsheet grow rapidly. Perhaps it would grow that large that it can’t be emailed. So I looked for replacements after applying that way the first time.

The combo boxes for prices include additional informations to assist the choice.

The lost-in-space-costs or their maximum can be inserted. The reason in particular are remarks of Robert Bigelow that the russian launch costs have been held low artificially. Another reason is that th exchange rtae of the Dollar to the Ruble is volatile, that the applied $ 65 mio are estimated by entrepreneurs and other people familiar with spaveflight and that prices and costs can change at all.



Oxidizer/Fuel Ratios

I enhanced the tables of potential landers, reusable landers and potential vehicles by the Oxidizer/Fuel Ratio. As far as www.astronautix.com lists the ratios I inserted those numbers, other may be from www.bernd-leitenberger.de. The ratio for Pixel is calculated from the numbers James Bauer told me a while ago in the Q&A-thread in the General Armadillo Aerospace Forum section.

A few posts ago I transformed thos numbers into kilograms. I got 161.487558 kg of Ethanol consumed and 251.020+ kg of LOX. So the Oxidizer/Fuel Ratio of Pixel seems to be 1.55.

The ratio of Micro Space’s lander I have to ask for because I don’t trust no conclusions of mine from the numbers Richard Speck told me to that Oxidizer/Fuel Ratio.

The Part 2-calculations require the Oxidizer/Fuel Ratios of the vehicles travelling between Moon and Earth also. Regarding these ratios there is one question to be answered: What ratio to apply to the CXV-pendant on LOX/LH2? The only ratios available are the one for Soyuz and the one for Saturn V and – if I remember correct – for the engine of the Centaur V1. The Soyuz-ratio can be applied to the CXV-pendant because the Block DM is applied for it here – but the Block DM consumes LOX/cerosene instaed of LOX/LH2.

For the lander Apollo LM-pendant on LOX/LH2 applaing an adjusted version of the Centaur V1 the ratio of that stage’s engine and of the Saturn V#s J-2 is used. This seem to be speaking for using that ratio for the CXV-pendant on LOX/LH2 also. But I tried to look into it a bit closer and more cautious. The ratio of the Block DM is a bit less than 97% of the optimal LOX/cerosene-ratio of 2.56 while the ratio of the J-2 is a bit less than 92% of the optimal LOX/LH2-ratio of 6.0. Since the ratio is NOT applied to calculate the amount of propellant but the costs of that propellant the criterion has to be which ratio results in the higher costs – meaning another safety margin.

Since LH2 is more expensive than LOX that alternative should be chosen for the CXV-pendant on LOX/LH2 that results in the higher amount of LH2. That is the lower ratio of the two. That of the J-2 is 5.5 while the other is 6.0 times a bit less than 97% = a bit more than 5.8. This seems to be speaking for 5.5 where the amount of LH2 per kg of LOX is higher. So this ratio will be applied here.











Dipl.-Volkswirt (bdvb) Augustin (Political Economist)



Appendix

Lunar Prices of delivered Hydrogen at $ 0.56 per kg on Earth

Based on:

Tanker(s) based on Apollo LM-pendant on LOX/LH2
90 days towards the Moon (Apollo-, Soyuz- or CXV-trip times 30)



Code:
             orbital depot only   surface depot only          split
              cyl.      sph.      cyl.       sph.      cyl.       sph.

                               reusable QuickReach 2 

var. costs     78.16     48.47     98.26      61.22     99.67      62.11
price          82.71     52.25    103.92      65,94    105.42      66.91
init.price   1788.89   4986.29   2232.11    6220.35   2263.33    6307.28
price +       311.91     57.24    389.82      72.16    395.31      73.29
safe mar.
init.price   2018.09   4991.28   2518.00    6226.57   2553.22    6313.58
+ marg.
                              Launchpoint Technologies

var. costs    277.19    214.53    346.51     268.35    351.39     272,14
price         301.61    234.88    376.97     293.73    382.27     297.88
init.price   2007.79   5168.92   2505.15    6448.14   2540.19    6538.25
price +       330.83    262.21    413.42     327.83    419.23     332.45
safe mar.
init.price   2037.01   5196.25   2541.60    6482.24   2577.15    6572.82
+ marg.
                                    Falcon 9 S 9

var. costs   4169.84   3403.17   5201.96    4245.67   5274.66    4305.02
price        4575.85   3741.57   5708.39    4667.76   5788.17    4733.00
init.price   6282.03   8675.60   7836.58   10822.17   7946.08   10973.37
price +      5073.16   4145.91   6328.70    5172.11   6417.15    5244.39
safe mar.
init.price   6779.34   9079.94   8456.89   11326.52   8575.06   11484.77
+ marg.



(continuation)

             surface consumption
              cyl.       sph.

             reusable QuickReach 2

var. costs     92.91      57.82
price          98.28      62.30
init.price   2114.19    5892.02
price +       369.09      68,19
safe mar.
init.price   2385.00    5897.91
+ marg.
             Launchpoint Technologies

var. costs    328.07     254.03
price         356.92     278.07
init.price   2372.83    6107.80
price +       391.44     310.37
safe mar.
init.price   2407.35    6140.09
+ marg.
                Falcon 9 S 9

var. costs   4927.36    4021.52
price        5407.07    4421.34
init.price   7422.98   10251.06
price +      5994.66    4899.08
safe mar.
init.price   8010.57   10728.80
+ marg.




Trip-prices at delivery of LH2

production price $ 0.56
The list does NOT contain all possible prices that can be calculated based on the list of possible prices because )of restrictions explained in the text (constraints)

Code:
cylindrical   spherical     cyl. at acc    cyl.      sph.
                            sph. LH2-      acc. LH2-price   
                            deliv.price

reusable QuickReach2 taxi and tanker            

  330499.59     130459.91     295988.45     78.16     48.47
  369359.51     147570.07     330429.62     82.79     52.25
13550583.16   16441710.23   17638218.96   1788.80   4986.29
  750000.00     170000.00     386000.00    311,99     57.24
14140000.00   17300000.00   18400000.00   2018.09   4991.28
            
Launchpoint Technologies tanker expendable QuickReach2 taxi            

5459796.54    4508720.72    5386969.88    277,19    214,53
6036991.21    4981428.29    5951683.12    301,69    234,88
19218214.87   21275568.44   23259472.45   2007.79   5168.92
6860000.00    5540000.00    6600000.00    330.83    262.21
20140000.00   22600000.00   24800000.00   2037.01   5196.25
            
Falcon 9 S 9 tanker reusable QuickReach2 taxi            

23732464.95    8277218.32   22841446.44   4169.84   3403.17
26624766.47    9468028.91   25558199.09   4575.85   3741,57
39805990.13   25762169.07   42865988.42   6282.03   8675.60
32000000.00   10980000.00   29200000.00   5073.16   4145.91
44200000.00   27800000.00   48000000.00   6779.34   9079.94

Falcon 9 S 9 tanker expendable QuickReach2 taxi            

27707464.95   12252218.32   26816446.44   4169.84   3403.17
30997266.47   13840528.91   29930699.09   4575.85   3741.57
44178490.13   30134669.07   47238488.42   6282.03   8675.60
36000000.00   15780000.00   35200000.00   5073.16   4145.91
50200000.00   32600000.00   53000000.00   6779.34   9079.94



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