Author Topic: Reuse business case  (Read 136197 times)

Offline joek

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Re: Reuse business case
« Reply #20 on: 04/25/2015 09:34 AM »
I agree that item P (which I believe for Spacex is a 30% reduction in mass to orbit penalty for reuse) is appropriate to consider if what is being transported something like propellant, in other words if Spacex is being paid $x for each kg to orbit. However this calculation is not currently applicable to Spacex from a business perspective in my opinion because that is not how they are paid.

It is not how anyone in the launch business is paid.  Nevertheless, when attempting to do  apples-to-apples comparisons, you need to agree on the apples; in this case $/kg, a commonly used metric.  Or more properly in this case an abstraction of $/kg represented by the reuse index I.  That is inherently limited, but likely the best we can hope for at the moment (point #5 in post above) without actual cost data.

To determine which approach is most cost effective, you must also know the actual costs to translate I into $, and thus into $/kg.  You also need to know the reuse performance penalty for a payload of a given mass (i.e., the market requirement).  As you suggest, for some that will be zero (#6 and plots for scenario 1-x and 2-x in post above).

All of that applies to both SpaceX and ULA.  Although you might disagree with some of the assumptions or parameters, there is nothing peculiar or specific in the model to SpaceX or ULA.  Just be aware of the model's limitations and that caution is warranted.

For example, see plot Vulcan-A and Vulcan-B in the figure.  Vulcan-B appears to be preferable.  However, what if the reason is that the engine price increased in absolute terms and as a percentage of recoverable costs--with a consequent increase in launch costs?  That would not be good if your competitors costs have not increased.

Quote
I also agree with Lar that K should likely be closer to .7 not .4, I think the cost of the 1st stage is closer to 70% of the launch costs, not 40% of the launch costs.

From Musk lays out plans for reusability of the Falcon 9 rocket:
Quote
Musk believes that the most revolutionary aspect of the new Falcon 9 is the potential reuse of the first stage “which is almost three-quarters of the cost of the rocket.”

Cost of rocket is not the same as cost of launch.  While a k] of 0.4 for scenario 1 may be low, it is probably much closer than 0.7.

Quote
I also assume that while the .9 rate exponent may be appropriate for typical aerospace manufacturing, this number may not be the appropriate rate exponent for Spacex. Maybe someone could come up with another number for Spacex (considering the commonality of the upper stage, general manufacturing process and the fact Spacex might need the extra stages anyways for its small sat/mars projects) and then run all of these numbers and see how it looks.

See SpaceX-B plot in figure below; rate exponent rF = 1.0, which is as good as it gets (unless someone can make a case for rf > 1).  The difference is relatively small, although it does shift the minimum reuse point left a few launches..

Offline clongton

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Re: Reuse business case
« Reply #21 on: 04/25/2015 10:59 AM »
Do I correctly assume that scenario 1 is based on ULA's estimate of recovering the entire Vulcan booster stage?

Based on his quotes above, I think it's pretty clear scenario 1 was meant to track SpaceX recovering its entire first stage.

I disagree. If it were clear I wouldn't have asked the question. Using the 30% "penalty" could just as easily been applied to the Vulcan. Just because he said Ms Shotwell said the Falcon uses 30% doesn't mean he switched at that point to discussing the Falcon and not the Vulcan.  It is also possible that he simply used that data point for the Vulcan.

Else, why did he not say "Here's a comparison of Vulcan pod recovery v.s. Falcon stage recovery"? Right. He did not say that. ISTM that his spreadsheet, unless qualified otherwise, is discussing 2 different recovery modes for the Vulcan. But it's not clear. Hence my question.
« Last Edit: 04/25/2015 11:01 AM by clongton »
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Offline muomega0

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Re: Reuse business case
« Reply #22 on: 04/25/2015 02:28 PM »
Life Cycle Cost per Pound of Payload for Multiple Launchers not individual launchers

One of the key figures of merit when discussing reuse or LV pricing in general is Life Cycle Cost per Pound of Payload--scroll down to the plot shown at bottom of the link.  So once this is determined per LV, the integrated, multiple LV solution is then required.   If you take a close look at the plot, when the annual metric tonnes allocated to the individual LV decreases, the price increases per LV size (vertical).  How the annual metric tonnes are distributed is important to each LV, as well as size(s) and number of LV(s) and variants.

The model is only a start as pointed out by many above.  Thanks for posting the model, the explanation of the model and its limitations, and all the comments.  $/kg can only work if you consider the complete, consolidated fleet of LVs (how to determine the cost of 6,000kg of propellant launched a year ago by a different competitor otherwise in the gas n go architecture?)

The additional data required:
o Average annual metric tonnes is a key figure of merit (10 launches of 15 or 30 mT?)
o number of launch vehicles and providers (SLS, Delta, Atlas, Falcon, FH, Vulcan, and variants)
o payload capacity (s) of launch vehicles required (the size of payloads)
o how the payloads are distributed to the LV(s)
o development costs
o distribution of payload costs ($B satellite vs $/gal prop vs crew (no solids?),  IOW:  Class type)
o reliability of reuse helps determine cost of payload
o architecture (LEO depot?)
o the LV design options (if one can fill up on orbit, why have so many LV variants?)

One study examines the costs of reuse for Individual LVs, and the integrated study is required for multiple LVs. 

The solution will shift if/when one considers a larger market of separate Class D payload:  propellant,  but the current space policy is to keep everything separate.   Shifting HLV $ to payload/missions is a key consideration for reuse unless some other major market develops.
« Last Edit: 04/25/2015 07:53 PM by muomega0 »

Offline woods170

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Re: Reuse business case
« Reply #23 on: 04/25/2015 07:31 PM »
Lot's of interesting posts here but I worry about the total lack of credibility-analysis of the spreadsheet itself.
Half of the parameters used are either estimates, guesstimates or assumptions.
With that much uncertainty I personally would not give any credibility to any of the results of calculations based on this spreadsheet.

Offline John-H

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Re: Reuse business case
« Reply #24 on: 04/26/2015 12:11 AM »
Lot's of interesting posts here but I worry about the total lack of credibility-analysis of the spreadsheet itself.
Half of the parameters used are either estimates, guesstimates or assumptions.
With that much uncertainty I personally would not give any credibility to any of the results of calculations based on this spreadsheet.

There are a lot of assumptions here, but no more than any business plan that extends out more than a couple of years. Most of the parameters seem reasonable guesses at this stage.

I can say one thing with 100% certainty: None of the predictions by any of the parties will be valid 5 years from now. :)

John

Offline falconeer

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Re: Reuse business case
« Reply #25 on: 04/26/2015 03:21 AM »
It's not valid to include fixed costs as part of k because the model assumes k is fixed even if the number of launches changes.  Since the model is a $/kg to orbit, putting fixed costs in k implies you are comparing $/kg to orbit on the same number of flights, not the same number of kg to orbit.

The $/kg model assumes something like propellant to a depot, where the number of kg is fixed.  For example, if you lose 50% performance for re-use, you would have twice as many flights, and by having fixed costs in k that assumes your fixed costs double also.

The model only makes sense if k includes only marginal costs, not fixed costs.

The conclusions of the model are badly skewed by this error.

As far as I understand, your analysis is spot on. 'k' needs to marginal costs only (i.e. manufacturing, direct labor, propellant, transportation, per-flight range costs, etc...) for both Vulcan and F9. It should not include ANY fixed costs, as that would completely invalidate the analysis.

Unlike most of the other parameters, 'k' and 'p' have a huge effect on minimum flight rate.

Keeping 'p' at 1.43 (1/0.7), and the other parameters at their default values provided by Dr.Sowers,

@ k=0.4, break even @ 10 flights
@ k=0.5, break even @ 5 flights
@ k=0.6, break even @ 4 flights
@ k=0.7, break even @ 3 flights

As you can see, just the jump from k=0.4 to k=0.5 halves the required flight rate!

Using k=0.7 for F9 (and default parameters), you get:
- 3 flights to break even
- 33% cost reduction @ 10 flights.

Using k=0.6*0.65=0.39 for Vulcan (0.6 due to upper/lower stage cost ratio), and default parameters, you get:
-2 flights to break even
-26% cost reduction @ 10 flights

The two scenarios intersect at roughly 6 flights. So if one expected >6 reused flights, boostback seems to be the winner here.

I believe these numbers are the closest apples vs. apples comparison of the reuse modes in this model. If we could get clarification from both SpaceX and Dr.Sowers re: k-values (with only marginal costs) that would improve accuracy.

PS. Thanks again to Dr.Sowers for engaging with us!






Offline RedLineTrain

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Re: Reuse business case
« Reply #26 on: 04/26/2015 04:55 PM »
Lot's of interesting posts here but I worry about the total lack of credibility-analysis of the spreadsheet itself.
Half of the parameters used are either estimates, guesstimates or assumptions.

The model is very sensitive to p.  Keeping all else as given, taking a 25% payload hit instead of a 30% hit results in payback in 5 launches rather than 10.  A 35% hit results in payback in 91 launches.

While reasonable for Dr. Sowers to use this 30% number (it is from Shotwell), I have always thought of this as a sandbagged figure, even when returning to launch site.  It would be nice to see some analysis.  It might also be a number that could move downward over time.
« Last Edit: 04/26/2015 06:08 PM by RedLineTrain »

Offline The Amazing Catstronaut

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Re: Reuse business case
« Reply #27 on: 04/26/2015 08:06 PM »
Are refurbishment costs being factored here?

Edit: That's unknown (or at best, speculative) information from both parties, right now. Another unknown which messes with the method.
« Last Edit: 04/26/2015 08:08 PM by The Amazing Catstronaut »
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Online MikeAtkinson

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Re: Reuse business case
« Reply #28 on: 04/26/2015 11:09 PM »
There are several strategies used to adapt launch vehicles to different payload masses and destination orbits:

1. Use different second stages or a 3rd (kick) stage
2. Dual launch, mix and match satellites (Ariane 5/6)
3. single and tri-core (F9/FH)
4. Add boosters to the 1st stage (e.g. Vulcan)

The reusability business case needs to be investigated for each strategy separately, comparing different strategies is difficult because so many other factors change.

Different second stages / 3rd stage

It is difficult to make the business case for a reusable 1st stage. For any given payload a larger and more capable  (and hence more expensive) second stage is needed. As the exponential part of the rocket equation really kicks in at the needed delta-v for the second stage to GTO and similar orbits, it is unlikely the savings on the first stage would be much more than the added cost of the second stage. Adding a 3rd stage adds cost and risk (another separation event, more engine starts) and is probably not worth it either.

Dual launch, mix and match satellites

Assuming a 30% payload reduction, if the launcher is kept the same size then the smaller satellite would no longer fit. Dual launch would become single launch for the majority of satellites, only two small satellites could ride share, there has not been enough small satellites for efficient ride sharing.

If the launcher were made 30% larger, then the same satellites could ride share as the expendable launcher, but costs (as an expendable) would be 30% more. Reuse would reduce this by some factor, but for a launcher like Ariane 5 where a significant proportion of the costs are in the solid boosters, just reusing the core stage is probably not worth it. Ariane 6 looks like it will have solid first stage and that makes reuse problematic at the best of time.

This explains why reuse has not been on the agenda for Ariane 5 and probably won't be for Ariane 6.


Single and tri-core

For a pure single-core / tri-core launcher system, with no added solid boosters and a common upper stage, reuse makes sense if the cost of reuse is < 1/3 the cost of a new core and the cost of integrating and using the extra boosters on the tri-core version is a small proportion of the total cost. If these conditions are met, any payload which can be launched with an expendable version can be launched cheaper with the reusable version. Some payloads have to be transferred from the single-core to the tri-core but the launch cost is still less.

There are no (or at least very few) payloads that need the full expendable capacity of the heavy version, it is not worth considering reusability for those payloads (which are likely to be very expensive anyway).

Payloads that are too heavy for the single stick version, would still fly on the heavy version, just at lower cost.

Payloads that can fly on the reusable single stick (including probably most, if not all, LEO payloads that tend to be volume limited), continue to do so just at lower cost. This would include Delta-II and Soyuz class payloads.

That leaves payloads that are too heavy for the reusable single stick. Some proportion of those can fly on the heavy at lower cost. If the cost of stage reuse is low, then that proportion could be 100%. If the cost of reuse is higher or if the overhead of using a tri-core is high, then this proportion could be 0%. These are likely to be a relatively small proportion of the entire payloads (though a bigger proportion in value terms). Using down range recovery with a 15% payload loss means that a proportion (30-50%) of these payloads can still be launched on the single-core, but with added reuse costs, whether to use a single-core or heavy launch for these payloads is a decision that can be made when the costs of the various options are known.

For reuse to be fully effective for this strategy, cost of reuse of the core has to be small. Ideally whole core should be recovered whole at the launch site and reused with minimal processing.

This explains why SpaceX are so interested in RTLS of the entire stage and will probably reserve drone ship landings for only a couple of of launches a year.


Add boosters to the 1st stage

For any given payload the cost of reuse has to be compensated by adding solid rocket boosters. SMART needs 0.5 of a booster on average, while downrange recovery of the entire stage (15%) would need 1-2 boosters and RTLS would need 2-3 boosters.

The largest satellites and the most demanding trajectories could not use whole core recovery as the number of solid boosters is already at the limit.

This explains why ULA are looking at SMART for reuse for Valcan, no spreadsheet required :-)


Discussion

The SMART strategy gives bigger reductions (in percent of the total launch cost) for small payloads, for large payloads the cost of the solid boosters is significant and so limits the percentage reduction. Over the entire payload range the reduction in cost in $ terms will be similar.

For Falcon low mass payloads have a large reduction in percentage terms, medium payloads (at the top end of the F9 expendable range) have little or perhaps no reduction and high end payloads a large reduction as 3 cores are now reused. These medium payloads are a large percentage of the current market in both numbers and value. F9R is probably adequate for LEO launches, if launching LEO constellations becomes the dominant reason for launch then the F9 reuse strategy is very effective.

The big unknown is reuse cost. Falcon first stage might need a complete refurbishment and the long term costs of running the drone ship could be high, alternatively the first stage might just need an inspection and a quick clean and RTLS makes the drone ship almost redundant. Similarly the cost of recovery and reuse for SMART is unknown, ULA probably have some idea of the order of magnitude, but this early in the design not much more than that.

Using RTLS most cores will be recovered, just an occasional core will be lost due to failures in the return flight or engine recovery. A few cores will be recovered downrange and perhaps 30% of these will fail due to adverse weather. If SpaceX are launching their LEO satellite constellation we can expect about 2 recovery failure per year (50+ launches) or a recovery rate of 96%

SMART will recover the engines further downrange than the F9 cores where weather conditions are likely to be slightly worse on average. It is hard to estimate recovery percentage, but lets guess at 70%.

The effect of reuse on production rates is hard to quantify. SpaceX are limited to 40 cores/year at Hawthorne, which is 10 F9 and 10 FH. Reuse would allow them to increase the number of Falcon flights without relocating from Hawthorne, as the upper stage also uses Merlin engines increasing to 50+ flights per year for their LEO constellation reuse would not lead to a drop in Merlin production and a replacement of cores with upper stages on the production lines using much the same tooling. ULA will have to size production for their expected launch rate and reuse rate, hard to say what that might be at the moment, I believe ULA are basing their calculations on 15-20 per year, with about 10 launches the break even point.

Any economic case has to consider the price which can be charged. That is a large subject and deserves a post on its own.

Offline MarekCyzio

Re: Reuse business case
« Reply #29 on: 04/27/2015 02:15 PM »
I played with the numbers dr. Sowers provided and it seems to me that under slightly different assumptions Falcon 9 reuse becomes viable only after 5 flights. I changed two parameters:
- rF - based on other posts in SpaceX treads, it is not always true that mass production reduces unit costs. This is why SpaceX is planning to recover payload covers - increasing their production rate would increase the cost instead of decreasing it.
- RR_ratio - SpaceX goal is to make rockets as reusable as planes, so I assumed 0.01. I think it makes sense - if the booster costs $20M, refurbishment cost of $200K sounds reasonable

To make things even more interesting, if we assume rF being 1.1 (that would mean expanding production is expensive) makes F9 reuse viable only after 4 launches.

Offline Malderi

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Re: Reuse business case
« Reply #30 on: 04/27/2015 05:11 PM »
I played with the numbers dr. Sowers provided and it seems to me that under slightly different assumptions Falcon 9 reuse becomes viable only after 5 flights. I changed two parameters:
- rF - based on other posts in SpaceX treads, it is not always true that mass production reduces unit costs. This is why SpaceX is planning to recover payload covers - increasing their production rate would increase the cost instead of decreasing it.
- RR_ratio - SpaceX goal is to make rockets as reusable as planes, so I assumed 0.01. I think it makes sense - if the booster costs $20M, refurbishment cost of $200K sounds reasonable

To make things even more interesting, if we assume rF being 1.1 (that would mean expanding production is expensive) makes F9 reuse viable only after 4 launches.

I don't think their refurbishment costs will be anywhere near $200k. Probably several million at least, just in operations labor costs. Unless you're literally landing right back on your launch pad, you've got a lot of people involved in safing and moving it back and everything.

Offline Rocket Surgeon

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Re: Reuse business case
« Reply #31 on: 04/28/2015 01:26 AM »
Dr. Sowers: I love the explanation of the spreadsheet (thanks for sharing the sheet and your exposition) but I was unclear as to the k values (k is "the fraction of the total cost of the expendable launch service represented by the production cost of the hardware to be reused." which is C(B)/ C(B) + C(~B) )

You stated for the SpaceX scenario 1 case that you are using .4 for k ("based on internet chatter" :) ) and that ULA is <.3 but in the ULA scenario 2 case you state k at .18

Could you clarify that? Are you saying that if ULA did a flyback booster you'd have a .3 or less but with the SMART proposal it's .18 or ???

Also if I understand k, it's the fraction of the total cost of the vehicle that is recovered because that part of the vehicle is reused... internet chatter on NSF seems to use .7 as the fraction of an F9 cost based on Elon saying the first stage is 70% of the cost.

Thanks for shedding light!

The booster is <0.3 of our total cost.  The engines, which we are recovering via SMART reuse are 0.18 of the total cost.  I don't think 0.7 can possibly be relative to the total cost including fixed cost and overhead.  It might be relative to the total production cost.  If you use that with some reasonable assumption about other non-hardware costs, 0.4 is appropriate. 

I have a detailed understanding of our cost structure.  I know how much is pads and factory and engineering and management and all those things other than pure hardware.  Even though I don't have any insight into details of SpX, I know they have more as many pads as we do, a factory like we do, a test site we don't have, more employees, etc.  All that has to be accounted for in the cost.

It's not valid to include fixed costs as part of k because the model assumes k is fixed even if the number of launches changes.  Since the model is a $/kg to orbit, putting fixed costs in k implies you are comparing $/kg to orbit on the same number of flights, not the same number of kg to orbit.

The $/kg model assumes something like propellant to a depot, where the number of kg is fixed.  For example, if you lose 50% performance for re-use, you would have twice as many flights, and by having fixed costs in k that assumes your fixed costs double also.

The model only makes sense if k includes only marginal costs, not fixed costs.

The conclusions of the model are badly skewed by this error.

This would only be the case if there was a massive increase in launch rates, at a rate of 10 launches per year, which is with in the current capabilities and launch demands of both of these companies, assuming the fixed costs don't change from their current ratios is fairly reasonable.
However, if launch rates increase dramatically, then we would see a shift in K, becoming larger as the fixed costs are spread out more.

Discussion:
An interesting spread sheet, and I always love taking these things out to their limits to test them...kind of depressing to see that 100 reuses only reduces costs by 80-90%... but I guess by that point this model would no longer be valid.

One interesting implication of this that I worry about for the ULA is the fact that the Falcon 9 is essentially operating at the top of the curve already. i.e. n=1, Reuse Index =1.516. Based on that, the Falcon 9 could already be considered overpriced/under-performing for reusability with the loss of performance going to their testing, at least for LEO launches, and for future GTO launches once upgraded to the v1.2. Therefore, while the ULA method may actually be more effective at reducing costs (all things being equal and the assumptions in this spreadsheet being accurate), they are still going to be massively behind the 8-ball, as with only 3 reuses, the SpaceX price drops to ~$45 million, and averaging that over 10 launches. The Vulcan doing the same only averages at $88 million, almost double. Of course performance does need to be considered there, but I doubt the Vulcan is going to be able to lift twice as much as the Falcon 9 in its base configuration.

Online TrevorMonty

Re: Reuse business case
« Reply #32 on: 04/28/2015 04:13 AM »
You need to be comparing $/kg to GTO not actual launch cost for fair comparison.
 F9R will be  approx $11,000/kg ie <4t at $45m.
F9E will be $11,000/kg ie 6t at $65m
Vulcan ACES version will be approx $11,000/kg ie 8t at $90m  (Dimitry's estimate for core without SRB).

Given both LVs are same $/kg it comes down preferred vendor and payload mass.

For LEO missions F9 maybe cheaper per kg but ACES is more versatile with endurance measured in days and multiple restarts. These features would be ideal for constellation deployment.
« Last Edit: 04/28/2015 04:26 AM by TrevorMonty »

Offline ChrisWilson68

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Re: Reuse business case
« Reply #33 on: 04/28/2015 04:26 AM »
Dr. Sowers: I love the explanation of the spreadsheet (thanks for sharing the sheet and your exposition) but I was unclear as to the k values (k is "the fraction of the total cost of the expendable launch service represented by the production cost of the hardware to be reused." which is C(B)/ C(B) + C(~B) )

You stated for the SpaceX scenario 1 case that you are using .4 for k ("based on internet chatter" :) ) and that ULA is <.3 but in the ULA scenario 2 case you state k at .18

Could you clarify that? Are you saying that if ULA did a flyback booster you'd have a .3 or less but with the SMART proposal it's .18 or ???

Also if I understand k, it's the fraction of the total cost of the vehicle that is recovered because that part of the vehicle is reused... internet chatter on NSF seems to use .7 as the fraction of an F9 cost based on Elon saying the first stage is 70% of the cost.

Thanks for shedding light!

The booster is <0.3 of our total cost.  The engines, which we are recovering via SMART reuse are 0.18 of the total cost.  I don't think 0.7 can possibly be relative to the total cost including fixed cost and overhead.  It might be relative to the total production cost.  If you use that with some reasonable assumption about other non-hardware costs, 0.4 is appropriate. 

I have a detailed understanding of our cost structure.  I know how much is pads and factory and engineering and management and all those things other than pure hardware.  Even though I don't have any insight into details of SpX, I know they have more as many pads as we do, a factory like we do, a test site we don't have, more employees, etc.  All that has to be accounted for in the cost.

It's not valid to include fixed costs as part of k because the model assumes k is fixed even if the number of launches changes.  Since the model is a $/kg to orbit, putting fixed costs in k implies you are comparing $/kg to orbit on the same number of flights, not the same number of kg to orbit.

The $/kg model assumes something like propellant to a depot, where the number of kg is fixed.  For example, if you lose 50% performance for re-use, you would have twice as many flights, and by having fixed costs in k that assumes your fixed costs double also.

The model only makes sense if k includes only marginal costs, not fixed costs.

The conclusions of the model are badly skewed by this error.

This would only be the case if there was a massive increase in launch rates, at a rate of 10 launches per year, which is with in the current capabilities and launch demands of both of these companies, assuming the fixed costs don't change from their current ratios is fairly reasonable.
However, if launch rates increase dramatically, then we would see a shift in K, becoming larger as the fixed costs are spread out more.

No, you completely misunderstood my point.

Nearly everything we discuss on these boards is a matter of opinion.  This is not.  This is one of those rare cases where it's a matter of objective fact.

The model presented is incorrect if k includes fixed costs.  There's no dependence on "massive increase in launch rates".

The whole basis of the model is to compare re-use against no-re-use and see which is cheaper for each number of launches.  This is then used to determine how many launches are needed before re-use makes economic sense.

The model is based on the idea of $/kg, so if you lose performance, you need to do more flights to make up for it.  But it's using the same k for the re-use case (with more flights) as for the non-reuse case (with fewer flights.  That cannot be correct if k includes fixed costs.

The model is highly sensitive to changes is k, as mentioned in other posts.  Whether k is 0.4 or 0.7 makes an enormous difference in where the breakeven point is for re-use.

Fixed costs are an enormous portion of the costs for launch service providers.  So k with them and k without them is very different.

Fixed costs should be left out of this model entirely, because they are the same whether there is reuse or not.  It's only marginal costs that matter for the purposes of determining which is cheaper, reuse or no reuse.

Offline ChrisWilson68

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Re: Reuse business case
« Reply #34 on: 04/28/2015 04:44 AM »
Here's an example to illustrate what I mean.  Suppose your annual fixed costs are $1 billion.  Suppose your marginal costs are $50 million per launch for hardware and $50 million per launch for non-hardware.  Suppose you are doing 10 launches a year and your vehicle has no re-use.  Then your fixed costs are amortized over 10 launches and it comes to $100 million in fixed costs per launch.  So total cost per launch is $200 million including fixed costs.  k is .25 ($50 million out of $200 million) if you consider fixed costs as part of your k.

Now suppose re-use costs you a 50% payload hit.  Then in the re-use case you need to do 20 launches.  Now, your $1 billion in fixed costs is $50 million per flight.  Now your k becomes .33 ($50 million out of $150 million) for the re-use case if you consider fixed costs as part of your k.

But the model assumes one k is applicable for both the re-use and non-reuse case.  That's not true here.

The fundamental problem is that fixed costs are divided by a different number of flights in the re-use and non-reuse case.

If you include fixed costs in your k, you're essentially treating them as marginal costs, because the model uses k in calculating the costs for the extra flights you have to fly to make up for the lower payload per flight because of re-use.  In this example, k can only be the same if fixed costs are $2 billion for the re-use case and $1 billion for the non-reuse case.

These problems go away if you remove the fixed costs from k.

Offline arachnitect

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Re: Reuse business case
« Reply #35 on: 04/28/2015 06:07 AM »
Here's an example to illustrate what I mean.  Suppose your annual fixed costs are $1 billion.  Suppose your marginal costs are $50 million per launch for hardware and $50 million per launch for non-hardware.  Suppose you are doing 10 launches a year and your vehicle has no re-use.  Then your fixed costs are amortized over 10 launches and it comes to $100 million in fixed costs per launch.  So total cost per launch is $200 million including fixed costs.  k is .25 ($50 million out of $200 million) if you consider fixed costs as part of your k.

Now suppose re-use costs you a 50% payload hit.  Then in the re-use case you need to do 20 launches.  Now, your $1 billion in fixed costs is $50 million per flight.  Now your k becomes .33 ($50 million out of $150 million) for the re-use case if you consider fixed costs as part of your k.

But the model assumes one k is applicable for both the re-use and non-reuse case.  That's not true here.

The fundamental problem is that fixed costs are divided by a different number of flights in the re-use and non-reuse case.

If you include fixed costs in your k, you're essentially treating them as marginal costs, because the model uses k in calculating the costs for the extra flights you have to fly to make up for the lower payload per flight because of re-use.  In this example, k can only be the same if fixed costs are $2 billion for the re-use case and $1 billion for the non-reuse case.

These problems go away if you remove the fixed costs from k.


I don't follow exactly. My understanding is that this model is built to address certain kinds of commercial payloads that must be discrete, yet can take advantage of marginal performance. If you are building a GSO commsat you have only one launch but you can use extra performance to buy more fuel, more antenna, more power, etc.

Offline Rocket Surgeon

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Re: Reuse business case
« Reply #36 on: 04/28/2015 06:15 AM »
Wow.. I've never had a post generate so much discussion before, awesome!

You need to be comparing $/kg to GTO not actual launch cost for fair comparison.
 F9R will be  approx $11,000/kg ie <4t at $45m.
F9E will be $11,000/kg ie 6t at $65m
Vulcan ACES version will be approx $11,000/kg ie 8t at $90m  (Dimitry's estimate for core without SRB).

Thanks for pointing out the GTO performances, completely forgot about that. This more than anything make me think that a Falcon Heavy of varying degrees of reuse will be the main competition for the Vulcan, not the Falcon 9.

Still think it's an interesting point, if you assume the same starting 'price', then the cost of the SpaceX method drops faster, and SpaceX is demonstrating that they can launch at an already lower cost, even at the top of the curve when it 'should' be more expensive. Even if a (mostly) reusable Falcon Heavy launches at $100 million and can only be reused 10 times, then they will be able to charge lower average prices. Also bare in mind that the Vulcan won't be trying re-usability for almost a decade. Where was SpaceX a decade ago? Then again, SpaceX may very well not exist in a decade... who knows, eh?


Here's an example to illustrate what I mean.  Suppose your annual fixed costs are $1 billion.  Suppose your marginal costs are $50 million per launch for hardware and $50 million per launch for non-hardware.  Suppose you are doing 10 launches a year and your vehicle has no re-use.  Then your fixed costs are amortized over 10 launches and it comes to $100 million in fixed costs per launch.  So total cost per launch is $200 million including fixed costs.  k is .25 ($50 million out of $200 million) if you consider fixed costs as part of your k.

Now suppose re-use costs you a 50% payload hit.  Then in the re-use case you need to do 20 launches.  Now, your $1 billion in fixed costs is $50 million per flight.  Now your k becomes .33 ($50 million out of $150 million) for the re-use case if you consider fixed costs as part of your k.

But the model assumes one k is applicable for both the re-use and non-reuse case.  That's not true here.

The fundamental problem is that fixed costs are divided by a different number of flights in the re-use and non-reuse case.

If you include fixed costs in your k, you're essentially treating them as marginal costs, because the model uses k in calculating the costs for the extra flights you have to fly to make up for the lower payload per flight because of re-use.  In this example, k can only be the same if fixed costs are $2 billion for the re-use case and $1 billion for the non-reuse case.

These problems go away if you remove the fixed costs from k.

I see what you're saying there and you're right. Is there an easy way to modify the spreadsheet to do that? and would it matter anyway? The spread sheet compares the different reuse methods and assumes roughly the same fixed costs, if you removed it, you change the slope of the graphs, but not the difference between them.
From my research at uni, on average 53% of the launch cost of a rocket is the actual rocket, with 47% being everything else... interestingly, if the first stage of the Falcon 9 is 70% of the rocket cost, then the first stage would make up 37.1% of the total launch cost... or roughly k = .4 ;)
Getting more precise in the specific difference between the Vulcan and the Falcon 9 would be impossible, as the Vulcan doesn't exists yet, and would undermine the comparison of the different methods, as you'd then be comparing a lot more than just that.

Cheers!
« Last Edit: 04/28/2015 06:16 AM by Rocket Surgeon »

Offline ChrisWilson68

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Re: Reuse business case
« Reply #37 on: 04/28/2015 06:27 AM »
I see what you're saying there and you're right. Is there an easy way to modify the spreadsheet to do that?

The spreadsheet is fine as long as k doesn't include fixed costs.  Leave out all fixed costs and it works fine.

and would it matter anyway?

Yes, it matters.  It's the difference between a 0.4 and a 0.7  for k, and we saw in the discussion above what a drastic difference there is between a 0.4 and 0.7 k for the SpaceX case plugged into the model.

The conclusion that partial reuse as proposed for Vulcan makes more economic sense than full first-stage re-use changes if you exclude the fixed costs from k.


Offline Rocket Surgeon

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Re: Reuse business case
« Reply #38 on: 04/28/2015 06:55 AM »
I see what you're saying there and you're right. Is there an easy way to modify the spreadsheet to do that?

The spreadsheet is fine as long as k doesn't include fixed costs.  Leave out all fixed costs and it works fine.

and would it matter anyway?

Yes, it matters.  It's the difference between a 0.4 and a 0.7  for k, and we saw in the discussion above what a drastic difference there is between a 0.4 and 0.7 k for the SpaceX case plugged into the model.

The conclusion that partial reuse as proposed for Vulcan makes more economic sense than full first-stage re-use changes if you exclude the fixed costs from k.

Ah, but the issue there is what do you use for the Vulcan number? Like I said, I see what your saying, but this spreadsheet isn't designed to compare Falcon 9 to Vulcan, its supposed to compare Boost-back recovery and Modular Recovery for Vulcan (though it uses SpaceX's numbers for the effects of a boost back recovery). The question this is used to ask is whether or not the Vulcan should boost back or use the modular recovery and the conclusion is that the Vulcan should use modular recovery as it pays back quicker, .... problem is in reality, the Falcon 9 is already a very different beast. Unless they have a much more in depth analysis than this spreadsheet (I sure hope they do) then the mistake is comparing apples-to-apples, we really have apples-to-oranges.

Offline The Amazing Catstronaut

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Re: Reuse business case
« Reply #39 on: 04/28/2015 08:33 AM »
The question this is used to ask is whether or not the Vulcan should boost back or use the modular recovery and the conclusion is that the Vulcan should use modular recovery as it pays back quicker, .... problem is in reality, the Falcon 9 is already a very different beast. Unless they have a much more in depth analysis than this spreadsheet (I sure hope they do) then the mistake is comparing apples-to-apples, we really have apples-to-oranges.

Agreed, I get the feeling that this is more of a justification as why ULA have gone this route with reusability - and for the Vulcan, it is the best route to take, than any evidence comparing economics tit-for-tat with F9 directly. Heck, since  nobody has access to all the numbers at work, it's going to take a good few years of both LVs working side by side for us to gain a comprehensive understanding of how the two LV's reusability methods pan out dime for dime. Prolepsis isn't all that reliable yet.
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