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Cost of a T-Space CXV launch

Posted by: Andy Hill - Tue Aug 23, 2005 8:03 am
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Cost of a T-Space CXV launch 
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Post    Posted on: Tue Sep 13, 2005 11:56 am
Thank You Very Much, whonos, for helping out regarding the O2 and doing the required corrections concerning the other data.

Obviously the propellant is not the large cost factor included in the 20 million flight costs of the CXV. So I'll continue now.

Let's have a look on the surface and the weight of the booster. The surface I calculated for the full-scale booster is 19.57541292 times that of the Drop Test Article and since I take the DTA-weight of 2018 lbs as the weight of the surface material here I get a full-scale weight of 39,503.18327 lbs. To this I add the weight of 8,100 lbs the Drop Test Article representing the CXV had which was full scale. This means I get a total weight of 47,603.18327 to be launched by the propellant we calculated the costs of.

To this the weight of the propellant has to be added.

Next I am going to look for reasonable approach of Economics to apply the less than 5 million $ for the DARPA-booster. That approach I am looking for because I am interested in the upper boundary - which I try to get by calculating too high costs. There is an upper boundary already - they must be assumed to be less than 20 million because that are the flight costs of the CXV according to t/Space.

Given the $76,202.2 in total you calculated as propellant costs, whonos, theknown upper boundary already has been reduced. The stronger argument is that the propellant costs for DARPA will be much less than $76,000 while the whole booster - propellant included - will cost less than 5 million dollars. There seems to be a huge gap between the propellant costs and the non-propellant-material of the booster.



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Post    Posted on: Tue Sep 13, 2005 12:19 pm
I suspect a large part of the costs will be taken up by recovery / refurbishment of both stages and the CXV itself.

I seem to remember reading somewhere that the cost of cleaning and reburbishing the SRBs on the shuttle were nearly as expensive as making new ones for each flight. The cost of filling the SRBs with propellant would be the same irrespective of whether they were new or not and this is probably the same for the CXV launch vehicle.

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Post    Posted on: Tue Sep 13, 2005 12:56 pm
From earlier posts and missing informations that Airlaunch's booster would be recovered I am assuming currently that the booster won't be recovered and thus not refurbished. As a consequence this recovery and refurbishments can't be included into the cost - this is a later consideration I am already thinking about.

I am looking for what I can calculate to some degree and then look on what's left. Currently any recovery costs and refurbishment costs will be included in this "what's left".

I have to think about some additional results currently.



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Post    Posted on: Wed Sep 14, 2005 12:28 pm
In between I am making use of the information that the booster of the 1000-lbs-DARPA-payload will cost less than 5 million dollars.

I remember that I would have to use the Ziolkovsky-formular in principle and that this would result in exponential reductions of the required amount of propellant if the weight of the payload to be launched is reduced linearyly - but I am interested in the upper boundary of weight, volume and surface and so calculate linear reductions. So I avod using the Ziolkovsky-formular here.

The weight of the CXV plus the boster calculated up to now is 47,603.18327 lbs. This is the theoretical full scale booster. It has a volume of 376.4186656 m^3 and a surface of 376.4186656 m^2. The weight divided by 8,100 lbs/1,000 lbs then is 5,876.936206 lbs. This is the DARPA payload plus the booster. Since the payload is 1,000 lbs the remaining 4,876.936206 lbs are the weight of the booster. The volume of that booster has to be calculated by diving th volume of the booster for the CXV by 8,100/1,000 too which results in a volume of 46.4714402 m^3 for the boster of the DARPA payload.

If I assume now that the radius of the DARPA-booster is 0,5 m - the radius of the DARPA payload - then the booster will have to be 59.16927536 m long. This results in a surface of 187.4565571 m^2. Since the booster will cost less than 5 million dollars the surface material will cost less than 5 million dollars too.

From this I can calculate the upper boundary for the costs of the CXV-booster by multiplying the 5 million dollars by 376.4186656 m^2/187.4565571 m^2 which results in 10,301,128.44 dollars as the upper boundary of the costs of the surface of the CXV-booster which has a radius of 2.1 m.

I have done an alternative calculation too because the previous one is a special case. To look for the lower boundary of the DARPA-booster at which the result for the CXV-booster achieves 20 million dollars I divided the surface of the CXV-booster by 20,000,000 dollars/5 million dollars and got 96.55070361 m^2. To get still a volume of 46.4714402 m^3 the DARPA booster would have to have a radius of between 0.49 m and 0.564189 (I have been playing with alternative numbers to get these numbers) and a lentgh of around 46,47153633 m.

This means that the CXV booster could be at the upper boundary only if its radius would be around 0,5 m too.

From this it follows that the CXV-booster will be the cheaper the larger the radius is up to a certain point.

I find this "approach" weak - I am not that content with it because

- it seems to be mathematical inconsequent,
- doesn't provide functions and
- is not a consistent economical approach.

Perhaps I look for the mathematical functions any time later - but methods of Economics should be used here.

On the other hand I am missing data and so I think that nothing better is possible currently.

I have used formulars for surface and volume to be found at Wikipedia.

Currently it seems that the cost structure of CXV-flights is around 50% variable costs - propellant + booster and around 50% fix costs - the CXV itself - at the current state of calculations.

But this is not correct - I am looking at it further and will post something about it later.

What's interesting at the end of this post is that the CXV-booster without the propellant might cost several million dollars which is much in relation to the costs of the propellant. It would be commercially advantageous to make the booster recoverable and refurbishable - this could result in high drops of flight costs down under 15 million dollars.

That t/Space seems to not work on recoverability of the booster will have to do with the goal - they want to be able to have ready a working CXV + booster until 2008 because it is a project for NASA. This is a deadline and a constraint.

Scaled Composites and Virgin Galactic on the other hand have announced an orbital SS3 if SS2 is a success. The two have no such a deadline and constraint - and may be thinking of a recoverable booster! This may be enabling them to achieve large reductions of flight costs...

...



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Post    Posted on: Thu Sep 15, 2005 11:09 am
1. Some remark on additional weaknesses of the "approach"

There are weaknesses to be seen in the data I got as results.

- The length of the DARPA-booster of between 45 meters and 60 meters seems to be insane and extreme and should be expected to be less. This in turn would mean that the costs of the CXV-booster would be more than the around 10 million dollars calculated resulting in a significantly higher share of the variable costs in the costs structure of CXV-flights and increasing advantages of recovery and refurbishing
- The costs of the DARPA-booster explicitly will be less than 5 million - and the more the costs are below that number the less the costs of the CXV-booster will be
- The volume of the DARPA-booster really will be significantly less than calculated because of the exponentiality of the Ziolkovsky-formular
- The booster has the VAPAK-technology inside the costs of which I don't know no data about. So the structure of the costs of the booster - without the propellant - is unknown: I do not know the shares of VAPAK and surface each. VAPAK may be nearly fix in comparison to the surface and may be the larger portion of the costs of the booster.



2. Completing the considerations

Assumed the costs calculated in the previous posts are nearly correct the non-booster, non-propellant and non-vehicle costs have to be included some way.

- The payloads - CXV or DARPA-payload - plus their boosters have to be carried to some altitude by airplanes. So those flight-costs of the CXV which don't have been considered in this thread yet will include propellant-costs of the airplane.

These costs have an upper boundary already known from the Accumulation-in-detail-thread. The calculations there result in variable costs of between 21,000 dollars and 121,000 dollars per flight. These include the propellant costs of the mothership. So these of their own will be less than those both numbers. They are variable costs too.

So obviously the propellant costs of CXV-flights will be less than 500,000 dollars if the calculations in this thread are not too wrong.

Next the required airplane itself means fixed costs. Again I refer to the Accumulation-in-detail-thread. There 100 millions dollars for infrastructure have been used and an article under www.xprizenews.com has been quoted which asked if the motherships for Virgin Galactic will be the motherships for the CXV too. If that is really the case then these investments will have to be depreciated and the depreciations are a portion of the fixed costs of the flights.

At this point it is of menaing that the issue "less than 5 million dollars" depends on 20 flights according to one of the earlier listed links. Then the airplane has to be depreciated over 20 flights too - which will result in 1 million dollars per flight at least perhaps.

The depreciation of the CXV over 20 flights would be at 20 million dollars. Since the flight costs are said to be 20 million the number of flights calculated will be significantly larger than 20 and the depreciation of the airplane will be less also - but the larger number of flights may mean more motherships too...

This thread remains interesting for a long time I suppose because there are a lot of infomrational gaps have to be filled.



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Post    Posted on: Mon Sep 19, 2005 11:44 am
Please compare the weight of one human - 176.37 lbs or 80 kilograms in case of a human of 1.80 meters height - to the weight of the CXV of 8,100 lbs.

The result of the comparison is that an increase in the number of persons carried by the CXV wouldn't have significant impacts on the flight costs. The CXV would have to be larger and thus more expensive in total - but the flight costs per passenger would decrease.

So the potential orbital SS3 Scaled Composites and Virgin Galactic have been speaking of very short may be designed for more than 4 - 6 persons/passengers - close to 10 perhaps.

This may result in low costs to orbit if the booster is much cheaper than the upper boundary calculated in this thread or if the booster is recoverable. There really economies of scale may be behind the idea of the potential orbital SS3.



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Post    Posted on: Wed Sep 21, 2005 8:44 pm
The current Popular Science mag has a bit on t/Space this month--I haven't read it but there are some more details.


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Post    Posted on: Sun Sep 25, 2005 3:39 pm
There is an approach which might provide more insights:

The CXV has been concepted for NASA - as a competitor in the cancelled fly-offs of 2008.

Since NASA is a governmental agency it is not going for profits. It simply has a budget only. So the costs of the CXV have to fit into that budget - precisely the total costs of all its flights during its lifetime can't be larger than the budget.

So the application of the budget will tell more abou the CXV perhaps. I am going to look for a possible approach.



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Post    Posted on: Mon Sep 26, 2005 11:58 am
The attached article on T-Space says on the 3rd page that both of its rocket stages are not reusable. If this is correct then this obviously means that their replacement costs will have to be factored into every CXV launch.

http://www.popsci.com/popsci/aviationsp ... drcrd.html

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Post    Posted on: Mon Sep 26, 2005 3:21 pm
Hello, Andy,

Thank You Very Much for that hint.

IO haven't read it yet but I will have to in order to take it into account as I go on in trying to analyze the CXV launch costs.

Since I haven't read the article yet I am wondering what's menat by
Quote:
both of its rocket stages
- did I overlook something? The past informations were talking about an airplane, one booster and the CXV itself only. Ass understood them at least.

Regarding reusability I already considered the booster to be expendable but could imagine that the SS3 would use a reusable booster - if at all.



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Post    Posted on: Mon Sep 26, 2005 5:24 pm
Ekkehard Augustin wrote:
Since I haven't read the article yet I am wondering what's menat by
Quote:
both of its rocket stages
- did I overlook something? The past informations were talking about an airplane, one booster and the CXV itself only. Ass understood them at least.

Regarding reusability I already considered the booster to be expendable but could imagine that the SS3 would use a reusable booster - if at all.


The VLA carries the CXV stack which comprises a first stage booster, an upper orbital insertion stage and the CXV itself. As I understand it the CXV's engines are used only for orbital manouvres and a de-orbit burn, not to get it into orbit.

The VLA doesn't really act as a stage it is used more for allowing ease of launch and safety reasons rather than the altitude/velocity it imparts to the CXV to get it into orbit.

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Post    Posted on: Wed Sep 28, 2005 10:43 am
Hello, Andy,

sounds as if I didn't miss something. There was an article supposing that Virgin Galactic's motherships may be identical to the VLA - if that wasn't a misunderstanding.

...



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Post    Posted on: Sat Oct 01, 2005 9:37 am
To make use of budgets I am going to use the following equations (or functions) here:

I. flight costs = propellant costs + booster costs + remainder variable costs + fixed costs/number of flights
Because only the complete flights costs (t/Space), the investment into the vehicle (t/Space) and the upper boundary of propellant costs (whonos) are known this is modified first to

II. flight costs = propellant coists + booster costs + remainder variable costs + (vehicle costs + fixed booster costs)/number of flights
Thus next has to be modified to

III. flight costs - propellant costs - remainder variable costs - booster costs = (vehicle costs + fixed booster costs)/number of flights
In this post I later need the number of flights - so a final modification is required:

IV. number of flights = (vehicle costs + fixed booster costs)/(flight costs - propellant costs - booster costs - remainder variable costs)

Into IV the investment into the vehicle of 400,000,000 is inserted as vehicle costs, the flight costs published are 20,000,000 and the propellant costs whonos calculated as ...



Code:
vehicle     fixed costs   flight     prop.   var. costs   rem.    num.      remark
costs       booster       costs      costs   booster      var.    of        about
                                                          costs   flights   booster

400000000   - / -         20000000   76202   - / -        0       21        unknown
400000000    5000000      20000000   76202   - / -        0       21        reusable
400000000   10000000      20000000   76202   - / -        0       21        reusable
400000000   10301128      20000000   76202   - / -        0       21        reusable
400000000   15000000      20000000   76202   - / -        0       21        reusable
400000000   - / -         20000000   76202    5000000     0       28        expend.
400000000   - / -         20000000   76202   10000000     0       42        expend.
400000000   - / -         20000000   76202   10301128     0       43        expend.
400000000   - / -         20000000   76202   15000000     0       85        expend.




Based oon the numbers of flights I get the following required mimimum budget by the equation

budget = vehicle + fixed booster costs + number of flights * (propellant costs + variable booster costs + remainder variable costs)


Code:
number     budget       depre-     fixed costs   var. costs remark
of                      ciation    booster       booster    about
flights                                                     booster

21         401529873    19923798   - / -         - / -      unknown
21         401548996    19923798    5000000      - / -      reusable
21         401568120    19923798   10000000      - / -      reusable
21         401569272    19923798   10301128      - / -      reusable
21         401587243    19923798   15000000      - / -      resuable
28         537757287    14923798   - / -          5000000   expendable
42         816296562     9923798   - / -         10000000   expendable
43         842479102     9622670   - / -         10301128   expendable
85        1670690667     4923798   - / -         15000000   expendable


Where the booster was reusable I calculated the sum of the depreciations of the booster plus the vehicle only.



Ass can be seen by the tables the costs of the booster wouldn't be of that large mmeaning if it were reusable. But the booster is expendable and so its costs have a large impact on budget and costs.

The budgets calculated mustn't compared to NASA's budgets yet because they are calculated for the complete period until the vehicle is completely amortized and payed off. To get budgets which can be compared to NASA's budgets the number of flights has to be calculated by the expected number of NASA-flights per year. The result is the number of years until amortization and pay-off. The claculated budgets have to be divided by this number - the reuslt can be compared to NASA's budget and is the minimum required average annual budget.

Without infrmations about the lifetime of the CXV in number of flights, the time to pay-off, turn-around-time etc. it's still not possible to get better insights into the booster costs but the approach is more simmilar to that in the accumulation-in-detail-thread now. I will look for additional improvements.

I also still have to provide comparisons to Delta rockets etc.



Please note: The numbers of flights I got here are far below the number of flights I used in the accumualtion-in-detail-thread. This menas that the costs will be far less if the vehicle has the lifetime of SS2 and the booster would be made reusable.



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Post    Posted on: Sat Oct 08, 2005 11:25 am
I still don't have numbers by which I could provide the comparison to Delta $ -launches etc. mentions in the inital post.

But I am going to use a substitute here.

The article "X Prize veterans work on next space steps" ( msnbc.msn.com/id/9615023/ ) is quoting Dabid Gump having said that one Soyuz-launch is estimated to cost 65 million dollars.

Since the Soyuz is expendable these costs are variable costs completely and the total costs of all Soyuz-flights are got by mulitplication of the $65 million by the number of flights.

I currently don't know the total number of flights occurred upto now or per year but first it is more interesting to look for a break-even-point. Given the informations available this the point here where the CXV begins to be cheaper than the Soyut.

I get the break-even-point as follows.

The flight costs of the - reusable - CXV are

number of flights * (propellant costs + variable booster-costs + remainder variable costs) + vehicle-investment + booster-investment

The flight costs of sveral Soyuz-flights in total are

number of flights * launch costs

Setting these both equal results in the equation

number of flights * (propellant costs + variable booster-costs + remainder variable costs) + vehicle-investment + booster-investment = number of flights * launch costs

1. modifiactaion:

Divison by number of flights:

propellant costs + variable booster-costs + remainder variable costs + (vehicle-investment + booster-investment)/number of flights = launch costs



2. modification

subtraction of the varaibale costs of the CXV:

(vehicle-investment + booster-investment)/number of flights = launch costs - propellant costs - variable booster-costs - remainder variable costs



3. modification

Multiplication by number of flights and in parallel division by "launch costs - ... - remainder variable costs":


(vehicle-investment + booster-investment)/(launch costs - propellant costs - variable booster-costs - remainder variable costs) = number of flights

vehicle-invetsment is 400,000,000,
booster investment is 0,
launch costs are 65,000,000,
propellant costs are 76202,
variable booster costs are 10301128 and
remainder variable costs are 0.

These numbers I insert into the result of the third modification:

(400,000,000 - 0)/(65,000,000 - 76202 - 10301128 - 0) =
400,000,000/54622670 =
7,322966819

This means: If there are more than 7 flights then the CXV is cheaper than the Soyuz.

This alone doesn't have that much to do with the topic of this thread - but it includes the eseetial difference between the SOYUZ and the CXV:

The launch costs of the Soyuz are 65,000,000 and the Soyuz is expendable - meaning that for each launch a new Siyuz has to be produced, manufactured or how it should be called.

So the complete investment of the Soyuz is included in its launch costs - the vehcile itself is estimated to cost less than 65,000,000. But the CXV explicitly costs 400,000,000 which is much much more than the investment into one Soyuz. A portion of the variable costs of Soyuz-fligths has been converted into fixed costs - varaible costs are re´duced while fixed costs are significantly increased: economies of scale it seems (but this would desrve check and verification.

So far a first comparison of the CXV to an expendable vehilce.



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Post    Posted on: Fri Oct 14, 2005 12:22 pm
To improve the comparison I have made the following table comparing the physical data used in this thread. There may be economies of scale involved - but there are other reasons too:

Code:
System as a whole   Sojus (A)   Sojus (TM)    CXV
Total weight (kg)     5880         7250      3674
Length (m)             7,4         7,48      4,422
Diameter (m)           2,3         2,72      4,2




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