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Cost of a TSpace CXV launch
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Moderator
Joined: Thu Jun 03, 2004 11:23 am
Posts: 3745 Location: Hamburg, Germany 
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 fullscale booster is 19.57541292 times that of the Drop Test Article and since I take the DTAweight of 2018 lbs as the weight of the surface material here I get a fullscale 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 DARPAbooster. 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 nonpropellantmaterial of the booster. Dipl.Volkswirt (bdvb) Augustin (Political Economist) 
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Moon Mission Member
Joined: Mon Nov 01, 2004 6:15 pm
Posts: 1233 Location: London, England 
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. _________________ A journey of a thousand miles begins with a single step. 
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Moderator
Joined: Thu Jun 03, 2004 11:23 am
Posts: 3745 Location: Hamburg, Germany 
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. Dipl.Volkswirt (bdvb) Augustin (Political Economist) 
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Moderator
Joined: Thu Jun 03, 2004 11:23 am
Posts: 3745 Location: Hamburg, Germany 
In between I am making use of the information that the booster of the 1000lbsDARPApayload will cost less than 5 million dollars.
I remember that I would have to use the Ziolkovskyformular 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 Ziolkovskyformular 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 DARPAbooster 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 CXVbooster 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 CXVbooster 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 DARPAbooster at which the result for the CXVbooster achieves 20 million dollars I divided the surface of the CXVbooster 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 CXVbooster 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 CXVflights 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 CXVbooster 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... ... Dipl.Volkswirt (bdvb) Augustin (Political Economist) 
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Joined: Thu Jun 03, 2004 11:23 am
Posts: 3745 Location: Hamburg, Germany 
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 DARPAbooster 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 CXVbooster 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 CXVflights and increasing advantages of recovery and refurbishing  The costs of the DARPAbooster explicitly will be less than 5 million  and the more the costs are below that number the less the costs of the CXVbooster will be  The volume of the DARPAbooster really will be significantly less than calculated because of the exponentiality of the Ziolkovskyformular  The booster has the VAPAKtechnology 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 nonbooster, nonpropellant and nonvehicle costs have to be included some way.  The payloads  CXV or DARPApayload  plus their boosters have to be carried to some altitude by airplanes. So those flightcosts of the CXV which don't have been considered in this thread yet will include propellantcosts of the airplane. These costs have an upper boundary already known from the Accumulationindetailthread. 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 CXVflights 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 Accumulationindetailthread. 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. Dipl.Volkswirt (bdvb) Augustin (Political Economist) 
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Moderator
Joined: Thu Jun 03, 2004 11:23 am
Posts: 3745 Location: Hamburg, Germany 
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. Dipl.Volkswirt (bdvb) Augustin (Political Economist) 
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Space Station Commander
Joined: Wed Mar 09, 2005 1:25 am
Posts: 891 
The current Popular Science mag has a bit on t/Space this monthI haven't read it but there are some more details.

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Moderator
Joined: Thu Jun 03, 2004 11:23 am
Posts: 3745 Location: Hamburg, Germany 
There is an approach which might provide more insights:
The CXV has been concepted for NASA  as a competitor in the cancelled flyoffs 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. Dipl.Volkswirt (bdvb) Augustin (Political Economist) 
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Moon Mission Member
Joined: Mon Nov 01, 2004 6:15 pm
Posts: 1233 Location: London, England 
The attached article on TSpace 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 _________________ A journey of a thousand miles begins with a single step. 
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Moderator
Joined: Thu Jun 03, 2004 11:23 am
Posts: 3745 Location: Hamburg, Germany 
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 Regarding reusability I already considered the booster to be expendable but could imagine that the SS3 would use a reusable booster  if at all. Dipl.Volkswirt (bdvb) Augustin (Political Economist) 
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Moon Mission Member
Joined: Mon Nov 01, 2004 6:15 pm
Posts: 1233 Location: London, England 
Ekkehard Augustin wrote: Since I haven't read the article yet I am wondering what's menat by Quote: both of its rocket stages 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 deorbit 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. _________________ A journey of a thousand miles begins with a single step. 
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Moderator
Joined: Thu Jun 03, 2004 11:23 am
Posts: 3745 Location: Hamburg, Germany 
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. ... Dipl.Volkswirt (bdvb) Augustin (Political Economist) 
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Moderator
Joined: Thu Jun 03, 2004 11:23 am
Posts: 3745 Location: Hamburg, Germany 
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 NASAflights per year. The result is the number of years until amortization and payoff. 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 payoff, turnaroundtime etc. it's still not possible to get better insights into the booster costs but the approach is more simmilar to that in the accumulationindetailthread 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 accumualtionindetailthread. This menas that the costs will be far less if the vehicle has the lifetime of SS2 and the booster would be made reusable. Dipl.Volkswirt (bdvb) Augustin (Political Economist) 
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Joined: Thu Jun 03, 2004 11:23 am
Posts: 3745 Location: Hamburg, Germany 
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 Soyuzlaunch is estimated to cost 65 million dollars. Since the Soyuz is expendable these costs are variable costs completely and the total costs of all Soyuzflights 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 breakevenpoint. Given the informations available this the point here where the CXV begins to be cheaper than the Soyut. I get the breakevenpoint as follows. The flight costs of the  reusable  CXV are number of flights * (propellant costs + variable boostercosts + remainder variable costs) + vehicleinvestment + boosterinvestment The flight costs of sveral Soyuzflights in total are number of flights * launch costs Setting these both equal results in the equation number of flights * (propellant costs + variable boostercosts + remainder variable costs) + vehicleinvestment + boosterinvestment = number of flights * launch costs 1. modifiactaion: Divison by number of flights: propellant costs + variable boostercosts + remainder variable costs + (vehicleinvestment + boosterinvestment)/number of flights = launch costs 2. modification subtraction of the varaibale costs of the CXV: (vehicleinvestment + boosterinvestment)/number of flights = launch costs  propellant costs  variable boostercosts  remainder variable costs 3. modification Multiplication by number of flights and in parallel division by "launch costs  ...  remainder variable costs": (vehicleinvestment + boosterinvestment)/(launch costs  propellant costs  variable boostercosts  remainder variable costs) = number of flights vehicleinvetsment 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 Soyuzfligths 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. Dipl.Volkswirt (bdvb) Augustin (Political Economist) 
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Moderator
Joined: Thu Jun 03, 2004 11:23 am
Posts: 3745 Location: Hamburg, Germany 
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 Dipl.Volkswirt (bdvb) Augustin (Political Economist) 
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