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Comparisons - expend./reusable,heavy/light,theory/practice

Posted by: Ekkehard Augustin - Thu Mar 30, 2006 8:38 am
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Comparisons - expend./reusable,heavy/light,theory/practice 
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Post    Posted on: Mon May 08, 2006 11:16 am
In between I seem to have found one part of the function:

Each expendable rocket has one launch only. After that launch all its equipment - engine(s), (tank(s) etc. - is lost.

Since each engine, tank etc. in a series of homgenous engines or tanks can have its own failures, errors etc. they all need to be tested separately. This can be done prior to launch by a test.

But this means that at least some systems are run two times - one time to test them and another time at launch. And there are systems going to work at higher altitudes only which only can be tested under simulated conditions - this doesn't guarantee that they will work at launch/flight really.

So the systems of expendable rockets will be run twice per launch.

For reusable rockets this will or might be different - and in the longer run after a certain number of launches it will be different really: Each launch of a reusable rocket in principle is a test for its next launch also. Systems that have to be run at higher altitudes are tested really at that altitude if looked at under this perspective and the data of each flight can be gathered and evaluated.

So in the reusability case the systems will be run only one time per launch plus the test(s) before the first launch.

Since this seems to mean to assume an ideal world the reality will be that the number and duration of tests will depnd on the number of launches already done.

This means that the function will be of negative slope, its independant variable will be the number of launches already done and the dependent variable will be a vector of the number of tests to be done, the number of systems to be tested, the duration of test(s) and so on. The vector might be expressed by a key number perhaps - I have to think about it.

At the moment I consider this to be one part of the function - I will think about this also. But this part I will try to look for a equation for.



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Post    Posted on: Wed May 10, 2006 2:13 pm
Because I realised just in the last few moments - there is function describing a partcular connection between time and the heavy/light-aspect:

To lift heavy weights requires more propellant than to lift light weights. Since more time is required to fill larger amounts of propellant into the tanks of a vehicle than to fill smaller amounts of propellant into the tanks of a vehicle light payloads and/or light lift vehicles require less time from "notice" or decision to launch than heavy payloads and/or heavy vehicles.

This is of meaning for FerrisValyns launch-on-demand-idea - he is right regarding that idea and the function means that the lighter a vehicle the better it is to use for launch-on-demand and the lighter a payload the better it can be launched on demand.

I am not going yet to consider the theory/practice-aspect - but according to Air Launch LLC's website QuickReach will be able or is designed to be able to be launched including payload within 24 hourse of notice. This fits into FerrisValyn's idea as well as it can be concluded from the function which at first glance simply is a linear function of the weight - but this I still should think about.



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Post    Posted on: Sat May 13, 2006 8:32 am
I will turn back to the function(s) for the expendable/reusable-aspect later.

A valid comparison requires that some "partS2 of functions are to be made constants:

1. The velocity to be achieved has be made a constant. So V in the Ziolkovsky-formular is a constant here - I will call it Kv here.

2. The material the vehicles are made of will have to be assumed to be the same for all vehicles.

I am going to think about more such requirements but these two I consider to be very important - they ensure that all the vehicles have to achieve the same velocity and are made of the same material. This means that there are two condiations they all have to fit into - two rules like in competitions.

...



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Post    Posted on: Fri May 19, 2006 7:52 am
The previous post means that the equation

e^(v/ve) = Mv/Ml

is going to be used here as e^(Kv/ve) = Mv/Ml.

But this is insufficient here - the term "Heavy Lift" doesn't mean something monolithic and unstructured but something separated into a payload and a vehicle including engines, tanks and so on.

Because of this Ml needs to be modified into Mlp + Mlv where Mlp is the mass of the payload and Mlv the mass of the vehicle.

Since I in an earlier post already said that regarding exponentiality of or in the equation I am speaking about the connection between ve and volume of tank(s) - a connection established by the density etc. of the propellant providing only one concrete value or perhaps a small range of values of ve - the tank(s) also need to be made explicit: Mlv = Mlt + Mlr with v = vehicle, t = tank(s) and r = remainder.

Of course I will have a look of the impact of engines and nozzles on ve later.

So the following is got now:

Ml = Mlp + Mlt + Mlr

e^(Kv/ve) = Mv/(Mlp + Mlt + Mlr)

Since the former Ml is included in Mv this also needs to be modified - it is Mve + Mlp + Mlt + Mlr where ve is the exhaust velocity representing the propellant. I want to avoid any mentioning of the propellant here since it might cause complexity and because I consider such mentioning to be proceeding to far this moment.

e^(Kv/ve) = (Mve + Mlp + Mlt + Mlr)/(Mlp + Mlt + Mlr)

...



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Post    Posted on: Mon May 22, 2006 5:08 am
One additional complication, is that the density & ISP (effectively exhaust velocity) of the fuel and the thrust to weight ratio of the engines ( also dependant on the fuel selected), ALL effect the total velocity change required to make orbit.

There is no single final velocity in the rocket equation, that fits all vehicles:

Vt = Vo + Vd + Vg. (t=total, o=orbital, d=drag loss & g=gravity loss)

Aerodynamic drag loss increases with low density becuase the vehicle is bigger. Gravity loss increases with high ISP because the weight of fuel is not burned off as fast, and with low thrust to weight ratio because it takes longer. So LOX/LH2, which is the most efficient fuel in regular use, requires a higher deltaV to make orbit, offsetting some of its advantages.


I've recently looked at SSTO tri-propellant vehicles, where there are 3 fuel tanks. One for LOX, one for LH2 and one for a higher density, lower ISP fuel like kerosene. The vehicle is much smaller, reducing drag losses. The high density fuel is burned off first giving high thrust and reducing the weight quickly. At altitude the LH2 is burned, giving high ISP.

The overall effect is a vehicle with average ISP approaching 400 & average propellant density about .8 (water = 1). Another advantage is the LOX/Kerosene engine nozzles can be optimized for low altitude, and the LOX\LH2 for vacuum.

One might think that carrying 2 types of engine would be a weight burden, but with SSTO much more thrust and more engines are required at liftoff than at orbital insertion anyway. I would think 4 LOX/Kerosene & 1 LOX/LH2 engines would be reasonable. Or maybe more smaller LOX/Kerosene engines for VTVL, to avoid deep throttling.

The Russians designed one engine that used both fuels in 2 modes, for the MAKS spaceplane, but that seems overly complicated.


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Post    Posted on: Mon May 22, 2006 6:27 am
Ekkehard, it seems to me that this is one area where there are multiple solution sets, there is not one correct answer. Although there are very many wrong answers. The technology choice and number of launches during the vehicle's operational lifetime, determines whether ELV or RLV is the way to go.

Two Extremes:

1) If the cost per kg of an empty rocket (excluding payload) is of the same order of magnitude as the cost per kg of it's propellants, then the empty rocket should itself be considered as a variable cost item and ELV is the way to go.

2) If the cost to recover & service a rocket after a mission is comparable to the total cost of propellants for one mission, AND if the development cost of the vehicle divided by the number of vehicles and by the expected number of missions per vehicle, plus the build cost of the vehicle divided by the expected number of missions per vehicle, is also comparable to the total cost of propellants for one mission, then RLV is the way to go.

In between these two extremes lies the problem. And, I suspect, all existing launch vehicles.


Size is not as important as you might think in quick response. Except to get the rocket physically to a particular launch location. Big rockets can be filled just as fast using bigger hoses. And boil-off of cryogenic propellants is a lot slower. What happened to Falcon 1's first attempts, wouldn't necessarily effect a larger rocket.


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Post    Posted on: Mon May 22, 2006 6:53 am
Hello, WannabeSpaceCadet,

your answers seem to go to some degree to the direction I have in mind.

In particular the fact that you suppose multiple solutions sets to be there is an argument against preferences of HLLVs over the others as well as reverse.

You refer to concrete propellants (LOX and LH2) - its to early to do so in my eyes - the current step and stage should be exploited to some degree first. For example comparisons require more terms to be set constant in the detailed formular I listed.

The complication you added I also know about - but for this it's also to early. They are steps to the theory/practice-aspect the other two aspects aren't sufficiently prepared for yet.

But both of your answers mean that some judgements in the Heavy Lift-thread and some subjective/personal claims are injustified.

I will continue to keep away costs, units of money and Economics from this thread - but I find it very good that you added the separation of V into its details. I will think about how to incorporate it - V is a constant in between called Kv...



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Post    Posted on: Mon May 29, 2006 10:57 am
The equation e^(Kv/ve) = (Mve + Mlp + Mlt + Mlr)/(Mlp + Mlt + Mlr) needs to be modified a bit by introducing more constants.

Expendable rockts/vehicles as well as reusable ones have standardized or not changeable capacities meaning that the the non-payload-weight of the not-fueled rocket/vehicle is constant. So Mlt and Mlr should be constants to enable comparisons - both are identifying properties of rockets and vehicles.

So Mlt is to replaced by Klt and Mlr by Klr. Mlp - mass of the payload - I keep variable at present because it is not required that the weight capacity is completely used. But this may change later.

So the reuqired version of the equation at present is e^(Kv/ve) = (Mve + Mlp + Klt + Klr)/(Mlp + Klt + Klr).

So the only variables left are ve, Mve and Mlp now.

...



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Post    Posted on: Tue Jun 06, 2006 11:23 am
Now for the modified Ziolkovsky-formular the following is valid:

1. If Mlp is given and thus fixed then the higher ve the less Mve or the less ve the higher Mve. So ve might be a criterion to choose a vehicle for a payload of given and thus fixed weight.

2. If Mve is given and thus fixed then the higher ve the higher Mve. I didn't use derivations but had a look to the right half of the equation - an increase of Mlp results in a larger increase of the term to divide by than of the term divided which includes Mve. So ve might be a criterion to choose what payloads to carry by a vehicle.

Please note here - if Mlp is given the choice of the vehicle would be done by ve but if Mve is given the choice of the payload is done by ve. These are views at it from different or even opposite directions. And the first view is the view from the payload. At present it is not possible to conclude links or connections between ve and Mve. This requires more which will be considered later.

The expendability/reusability-function says that the higher the number of launches of a vehicle the less the number, duration. intensity etc. of tests.

Next there is the function linking time to heavy/light. If ve is given and thus fixed then the higher the weight the more time is required - the weight here is Mve + Mlp. So this means that the time available is a criterion which vehicle to choose or what a payload to launch. This provides flexibility, suggests multiple launches of parts of a larger object/structure and more.

So there are some technological criterions are found to choose a vehicle or a payload - ve, number, duration or intensity etc. of tests required and time available. Although at least one criterion might speak for HLLV the others might speak for light lift vehicles.

But this still is incomplete and I am still thinking about and looking for formulars for expendability/reusability and for linking time to heavy/light.



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Post    Posted on: Mon Jun 12, 2006 10:40 am
Before I go on there is one aspect I didn't worl out that clearly yet.

There are concepts of reusability using parachutes or retrorockets. Parachutes and - more - retrorockets (may) mean higher Klr or/and Klt (remainder and tanks). This menas even higher Mve to launch that rocket - and then to this the weight of the payload has to be added.

This might limit the capacity of reusable rockets/vehicles. I still don't want to discuss practzice/reality now and I will not discuss the economical side of rockets here - but my approaches to look into the economical properties of rockets in the Financial Barriers section seems to indicate that a non-reusable HLLV can't beat a reusable non-HLLV if the launch rate exceeds a critical value.

So at this point it is to be suspected that from a certain capacity on reusability isn't possible no more - it may be that HLLV can be expendable only while non-HLLV can be both reusable and expendable. And then there is a certain probability that HLLV is disadvantageous compared to reusable non-HLLVs because of the amount of hardware.

In short - there is a function linking weight to reusability/expendability that has negative slope. If his function is taken reverse that weight is negatively linked to reusability/expendability - and there are other functions not to be considered yet or here linked positively to reusability/expendability. This results in a clear preference for medium lift and light weight lift.

I will proceed later - the positively linking functions will be considered later also.



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Post    Posted on: Fri Jun 16, 2006 8:18 pm
We've tried the reusability route--and the complexity and front end costs of an RLV speak against it as compared to comparitively simple HLLVs.


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Post    Posted on: Mon Jun 19, 2006 10:46 am
Any function between ve and Mve isn't introduced here yet. To look for that function seems to require a look onto the propellants since these are providing the ve.

But that look is one step from theory to practice and it still is a little bit too early for that step.

So this moment it is still required to assume that there is a link/connection between ve and Mve that allows for variations even if the propellant of the mass Mve is left unchanged. For example it can be supposed in this theoretical step that the properties of the engine(s), the nozzle etc. has an impact on ve.

So the function could have positive, negative or zero slope - or different local slopes also!

There seems to be something missing here - which may be due to the original purpose of the Ziolkovsky-formular: to calculate what amount of a known propellant is required by a known engine and rocket/vehicle.

Looking at the formulars of theory it seems that it would be advantageous if the function between ve and Mve would be of negative slope - this would mean that Klt could be set to a low value for all rockets and vehicles. Klt limits the maximum amount of propellant that can be used - which might be interesting in the thread about standardization in another section.



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Post    Posted on: Tue Jun 20, 2006 10:49 pm
Valid points. Here is a paper (prieview only, sadly) that you may find of interest:

http://pdf.aiaa.org/preview/1995/PV1995_3816.pdf

It shouldn't be hard to track that down. CaLV is certainly a step in the direction. Remember, Buran-T was to be a winged version on Energiya. I can see a winged HLLV evolving out of CaLV as well.

Winged Saturns were being considered, after all:
http://www.up-ship.com/apr/apr.htm

Buran-T
http://www.buran.ru/htm/mtkkmain.htm
http://pdf.aiaa.org/preview/1995/PV1995_3816.pdf
http://www.ceebd.co.uk/ceebd/molniy75.htm


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Post    Posted on: Mon Jun 26, 2006 10:38 am
In between I found out that there ve is positively linked to the pressure inside the burning chamber - this is an additional function of positive slope. The way the pressure is got is a property of the "r" in Klr. That way may have an impact on the value of Klr - but that's a constant and so the impact would have to be considered later.

So there is an additional function - but it is of no meaning yet because of the constants.



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Post    Posted on: Mon Jul 03, 2006 12:03 pm
table replaced by the correct version

Up to now I seem to have found the following functions of the Theory-aspect:

Ziolkovsky: e^(Kv/ve) = (Mve + Mlp + Klt + Klr)/(Mlp + Klt + Klr)

1. mofification: e^(Kv/ve) * (Mlp + Klt + Klr) = (Mve + Mlp + Klt + Klr)
2. modification: e^(Kv/ve) * (Mlp + Klt + Klr) - (Klt + Klr) = (Mve + Mlp)
3. modification: e^(Kv/ve) * Mlp + (e^(Kv/ve) - 1) * (Klt + Klr) = (Mve + Mlp)
4. modification: (e^(Kv/ve) - 1) * (Klt + Klr) = (Mve + Mlp) - e^(Kv/ve) * Mlp
5. modification: (e^(Kv/ve) - 1) * (Klt + Klr) = Mve + (1 - e^(Kv/ve)) * Mlp
6. modification: depends on the choice if Mve or Mlp or ve should be kept constant for decisions

The slope too depends on the choice - let's call this function f then the slope is f'.

expendability/reusability: g(number of launches)
g' is negative - which means negative slope

linked to number, duration, intensity etc. of tests.

heavy/light: h(time)
h' is positive - positive slope

expendability/reusability B: i(weight)
i' is negative - negative slope

ve: j(Mve)
j' unknown in this general version

ve B: k(chamber pressure)
k' is positive - positive slope

remainder of vehicle/rocket: l(Klr)
l' unknown to me presently - I suppose it to be very complex

That's the state of what I said at the point where I get a step closer to practice now - real practice still needs to wait.

Under www.bernd-leitenberger.de there is a table linking oxidators and propellants to Isp, average density and some additionaly numbers. I didn't copy that table because I wanted to select a few data and to sort them by Isp. So the tabel is modified to some degree and I also hope not to have hurted the Copyright Bernd Leitenberger claims - in which he is right given the lot of work he seems to have invested.

Here the table now:

Code:
Oxidator                  Propellant          Isp    Average
                                                     Density

Dinitrogen tetroxide      Lithium hydride     2441
Chlordifluoride           Cerosene            2530   1.41
Nitric acid               Lithium hydride     2549
Hydrogenperoxide 95 %     Lithium hydride     2559
Oxygen                    Lithium hydride     2569
Nitric acid               Cerosene            2630   1.35
Dinitrogen tetroxide      Polyethylene        2696
Dinitrogen tetroxide      Cerosene            2710   1.26
Nitric acid               ADMH                2710   1.25
Hydrogenperoxide 95 %     ADMH                2720   1.24
Oxygen                    Ethanol             2740   1.1
Hydrogenperoxide 95 %     Cerosene            2745
Hydrogenperoxide 95 %     Hydrazine           2760   1.26
Nitric acid               Hydrazine           2775   1.28
Dinitrogen tetroxide      ADMH                2804
Dinitrogen tetroxide      Aerozine 50         2820   1.2
Dinitrogen tetroxide      Hydrazine           2865   1.22
Oxygen                    Cerosene            2945   1.2
Oxygen                    ADMH                3010
Oxygen                    Hydrazine           3070   1.7
Fluorine                  Cerosene            3139
Hydrogenperoxide 95 %     Hydrogen            3187
Difluoroxide              Cerosene            3196
Hydrogenperoxide 95 %     Diborane            3246
Dinitrogen tetroxide      Hydrogen            3353
FLOX (Fluorine and LOX)   ADMH                3373
Oxygen                    Diborane            3374
Difluoroxide              Hydrazine           3383
Dinitrogen tetroxide      Beryllium hydride   3432
Difluoroxide              ADMH                3442
Fluorine                  Ammonia             3500   1.18
Fluorine                  Pentaborane         3530
FLOX (Fluorine and LOX)   Cerosene            3550
Fluorine                  Hydrazine           3560   1.31
Fluorine                  ADMH                3569
Fluorine                  Lithium hydride     3569
Difluoroxide              Diborane            3569
Oxygen                    Beryllium hydride   3628
Fluorine                  Diborane            3638
Hydrogenperoxide 95 %     Beryllium hydride   3667
Difluoroxide              Beryllium hydride   3746
Oxygen                    Hydrogen            3830   0.28
Fluorine                  Beryllium hydride   3863
Fluorine                  Hydrogen            4020   0.45
Difluoroxide              Hydrogen            4020


I inserted these data into an Excel spreadsheet and created a diagram. The fragments of the curve tell me that the curve is very wild - the slope is neither constantly positive nor constantly negative.

From the average density the volume and thus the surface of the tanks follows for each ve and oxidator-propellant-combination. The curve of the function between those combinations and their Isp and the volume/surface of the tanks is wild also - and this still holds if the weight of the tanks is considered and the material the tanks are made of is kept allways the same.

But the weight of the tank contributes to the required Mve.

So at this point I seem to have to give up the constant Klt because this is the weight of the tank(s). I have to think about that and so have a break again here.

But one important and essential point I have to remark here - the table above is one major link to the theoretical Cost-thread in the Financial Barriers section. It is going into it to some degree because the oxidators and propellants have a price their amounts have to be multiplied by - the table is part of the variable costs function. May be I will mention the cost function itself later here.



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