Author Topic: Comprehensive Falcon Family Performance  (Read 14223 times)

Offline sevenperforce

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Comprehensive Falcon Family Performance
« on: 02/20/2018 04:19 PM »
Elon recently let slip on Twitter that flying Falcon Heavy with parallel booster recovery only (expendable core) represents a 10% performance loss over fully-expendable but would only run about $95M. With this figure, and the numbers already published by SpaceX, I was able to put together a pretty comprehensive table of Falcon family performance to virtually any destination. Took a lot of spreadsheet work, but it all came out pretty well.

VehiclePrice (USD)LEO (tanker only)LEO (payload)GTO (2.27km/s)TLI (2.73km/s)LLO (4.04km/s)GEO (4.33km/s)TMI (4.30km/s)
Falcon Heavy (expendable)$150M96.9163.8026.7025.1716.6815.2216.80
Falcon Heavy (recovery x2)$95M87.2257.4224.0322.6515.0113.7015.12
Falcon Heavy (recovery x3)$90M23.5318.118.006.663.653.123.17
Falcon 9 (expendable)$92M24.9922.808.307.744.253.654.02
Falcon 9 (ASDS recovery)$62M17.0413.305.504.502.141.711.75
Falcon 9 (RTLS recovery)<$62M11.749.413.512.700.850.520.56

RTLS performance values were estimated by carefully comparing staging velocities for RTLS missions to staging velocities for ASDS missions; this is likely an underestimate of RTLS capabilities because SpaceX has probably not pushed RTLS to its limits in missions to date.

Falcon Heavy with three-core recovery may also be underestimated for LEO performance, since Falcon Heavy's TWR is so much higher than Falcon 9's, but it should be accurate for BLEO destinations.

LLO and GEO delivery assume extended restart capability for the MVac and do not account for propellant boil-off; this must be adjusted for.

LEO tanker performance assumes that the payload is nothing but an International Docking Adapter (mass: 526 kg), so that it could be docked to a vehicle waiting in LEO for an ejection burn.

ASDS performance above assumes no boostback burn and maximum downrange ASDS position. For ASDS payloads below the maximum payload, SpaceX sends the ASDS only part of the way out and uses the extra margin for a boostback burn to save money and time.

Offline yokem55

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Re: Comprehensive Falcon Family Performance
« Reply #1 on: 02/20/2018 05:00 PM »
That Falcon Heavy 8 MT figure for three core recovery feels like it's been sand bagged a bit. It represents a 70+% loss in performance over fully expendable or expending just the core.

Offline speedevil

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Re: Comprehensive Falcon Family Performance
« Reply #2 on: 02/20/2018 05:09 PM »
That Falcon Heavy 8 MT figure for three core recovery feels like it's been sand bagged a bit. It represents a 70+% loss in performance over fully expendable or expending just the core.

If that is true, the recovery figure to LEO must also be wrong, as it's about right from the rocket equation.

What velocities are being assumed for FH centre core staging - some preliminary work I did on this indicated that you needed quite a lot of propellant remaining in the centre core to get it down to the hottest recovery velocities we've seen.

If we assume 57 tons to LEO recovering two is right, and 18 recovering three is also right, and that we can assume trajectory till BECO is the same, the difference in the centre cores velocity before sep must be the same as the additional second stage velocity required.

57+111+3t,347s->60 = 3571m/s.
?->347s->18+3t = 3571m/s
Gives 59 tons initial stage mass in the second case, 38 tons of fuel, not 111.

111+3+18t, 347s, 59t = 2688m/s.

This seems a very, very implausible number.
I'm probably doing something wrong.
« Last Edit: 02/20/2018 06:11 PM by speedevil »

Offline sevenperforce

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Re: Comprehensive Falcon Family Performance
« Reply #3 on: 02/20/2018 05:40 PM »
That Falcon Heavy 8 MT figure for three core recovery feels like it's been sand bagged a bit. It represents a 70+% loss in performance over fully expendable or expending just the core.
If it's a sandbag, it's not much of one. Three-core recovery requires RTLS on the side boosters and a very long braking burn (either boostback or longer entry burn) on the core, while two-core recovery represents dual ASDS landings for the side boosters but at a generally more benign speed than we've seen with Falcon 9. It's a huge difference.

The quoted payload drop of 10% represents a side-booster staging velocity of 230 m/s lower than if the side boosters were expended. Reserving those 230 m/s of stack dV on the boosters represents a LOT more dV for the naked boosters themselves. In contrast, the amount of propellant the center core needs to brake itself is much higher.

Recall that an expendable Falcon 9 bills at $92M, while a triple-core-recovery FH is $2M cheaper. If triple recovery FH could deliver more payload than an expendable Falcon 9, it would surely cost more.

Offline Nomadd

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Re: Comprehensive Falcon Family Performance
« Reply #4 on: 02/20/2018 07:38 PM »
 I think people might be giving these prices a little too much credibility. How can expended side boosters raise the price $55 million, but an expended core only $5 million?

Offline Semmel

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Re: Comprehensive Falcon Family Performance
« Reply #5 on: 02/20/2018 07:39 PM »
If it's a sandbag, it's not much of one. Three-core recovery requires RTLS on the side boosters and a very long braking burn (either boostback or longer entry burn) on the core, while two-core recovery represents dual ASDS landings for the side boosters but at a generally more benign speed than we've seen with Falcon 9. It's a huge difference.

Hmm, side booster landings on the drone ships should be faster reenty than single stick F9 because the increased T/W ratio makes it go faster (even with throttled centre core). The burn time of the side boosters should be identical, hence the velocity should be higher for FH.

Recall that an expendable Falcon 9 bills at $92M, while a triple-core-recovery FH is $2M cheaper. If triple recovery FH could deliver more payload than an expendable Falcon 9, it would surely cost more.

Not necessarily true. Recovered boosters have value in them selfs. A throw away F9 could cost more than a recoverable FH, even if F9 would throw less than FH.

Offline kdhilliard

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Re: Comprehensive Falcon Family Performance
« Reply #6 on: 02/20/2018 07:58 PM »
I think people might be giving these prices a little too much credibility. How can expended side boosters raise the price $55 million, but an expended core only $5 million?

An expended core and twin ASDS recoveries.  Agreed.  However $95 million makes more sense based on Chris G.'s FH reusable price, though I don't understand how he came up with such a precise figure.  From our 2018-02-09 feature article, Falcon Heavy success paves the way for open access to space beyond Earth:
Quote
But perhaps most surprising was a statement made by Mr. Musk the day before Falcon Heavy’s first launch.  During that teleconference, Mr. Musk stated that the overall price for a Falcon Heavy could reduce significantly once Falcon Heavy flies in its fully reusable configuration – essentially lowering its price to just $62 million dollars or the price of a regular, brand new Falcon 9.

Teleconference transcript here
Quote
Well, you know Falcon Heavy is essentially, from a cost standpoint, it's Falcon 9 plus two side boosters. And we expect to recover all three cores, or at least two of the three cores on every flight. Now this is a development flight, so who knows what'll happen on this flight. But being able to reuse those rocket booster cores means that the expendable portion of the Falcon Heavy flight is the same as a Falcon 9 flight. On Falcon 9 we expend the upper stage. We are in the process of recovering the fairing, we're getting better and better at recovering the fairing. So we expect to recover the fairing and the booster, the first stage of Falcon 9. Like I said, only the second stage will be expended. And what's interesting is for Falcon Heavy, it's the same amount that's expended, just the upper stage. So it means we're able to offer heavy, arguably super heavy lift, nearing super heavy lift capability for not much more than the cost of a Falcon 9.

I suspect that the $95 million price was likewise based on high hopes for ease of block 5 reusability.

Offline sevenperforce

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Re: Comprehensive Falcon Family Performance
« Reply #7 on: 02/20/2018 08:28 PM »
I think people might be giving these prices a little too much credibility. How can expended side boosters raise the price $55 million, but an expended core only $5 million?
I try to take everything Elon says with a grain of salt, but pricing information seems like one of those things he wouldn't just make up.

Falcon 9's base price is $62M. Sacrificing the core is a $30M markup, to $92M.

Falcon Heavy's base price is $90M. Sacrificing all three cores is a $30M x 3 markup, to $150M. Tracking so far.

Elon said on Twitter that 2-core recovery "really just costs a little more than expending a Falcon 9", so a $3M markup to $95M. But this would suggest that adding two recoverable boosters would only cost $3M more, in which case we would expect the base price of Falcon Heavy (with triple recovery) to be just $65M.

If it's a sandbag, it's not much of one. Three-core recovery requires RTLS on the side boosters and a very long braking burn (either boostback or longer entry burn) on the core, while two-core recovery represents dual ASDS landings for the side boosters but at a generally more benign speed than we've seen with Falcon 9. It's a huge difference.

Hmm, side booster landings on the drone ships should be faster reenty than single stick F9 because the increased T/W ratio makes it go faster (even with throttled centre core). The burn time of the side boosters should be identical, hence the velocity should be higher for FH.
It depends. Single-stick has to throttle the core down at Max-Q and again as the TWR climbs relatively high, meaning a longer burn time, while the Falcon Heavy can do all the downthrottling with the core and get a more rapid side booster burnout. So the burn time isn't necessarily exactly the same.

Operationally, I do wonder what will give the best performance in a core-expended FH launch. Do they only throttle the core down briefly for Max-Q and gee-loading, and simply cut the side boosters off when their reserves drop to what they need for entry and ASDS landing, or do they throttle the core down gradually throughout the flight to reserve more propellant at side booster MECO?

I suppose the same question applies to a three-core-recovery FH. Even if they burned all the boosters at full throttle from start to finish, they'd need to MECO the side boosters first, to reserve enough propellant for RTLS boostback, while the core could continue to fire for a few seconds. Would this give higher performance than differentially throttling the core?

Not that it matters for number-crunching. I'm sure SpaceX has already determined what the highest performance is, since that's what they are quoting.


Offline hkultala

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Re: Comprehensive Falcon Family Performance
« Reply #8 on: 02/20/2018 08:38 PM »
LEO tanker performance assumes that the payload is nothing but an International Docking Adapter (mass: 526 kg), so that it could be docked to a vehicle waiting in LEO for an ejection burn.

umm.. I don't undestand what you mean by this. Fuel remaining in the tank after reaching the orbit with this?


Offline sevenperforce

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Re: Comprehensive Falcon Family Performance
« Reply #9 on: 02/20/2018 08:49 PM »
LEO tanker performance assumes that the payload is nothing but an International Docking Adapter (mass: 526 kg), so that it could be docked to a vehicle waiting in LEO for an ejection burn.

umm.. I don't undestand what you mean by this. Fuel remaining in the tank after reaching the orbit with this?
Right. Elon has talked about orbital propellant transfer, and while this is very unlikely for the Falcon upper stage, I've also seen mission proposals where an empty upper stage is sent into orbit to dock with another vehicle and perform a burn BLEO. So I threw in one column where you'd merely be figuring out how much propellant you'd have left over.

Offline speedevil

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Re: Comprehensive Falcon Family Performance
« Reply #10 on: 02/20/2018 09:01 PM »
Right. Elon has talked about orbital propellant transfer, and while this is very unlikely for the Falcon upper stage, I've also seen mission proposals where an empty upper stage is sent into orbit to dock with another vehicle and perform a burn BLEO. So I threw in one column where you'd merely be figuring out how much propellant you'd have left over.

Does LEO tanker include the fact that it doesn't need a fairing, which must save a fair bit of weight and drag.

I note that the price of FH all recovered + f9 recovered, with F9 launching a payload, and FH launching expendable is the same, and the capability to high energy orbits doing this is also comparable.

Is the 'tanker' mass including or excluding the stage?

Capability with FH expendable as tanker goes up really quite a lot.

I note my 'F9 moon lander' thread. https://forum.nasaspaceflight.com/index.php?topic=45010.0 which goes into some of the sillier possibilities if refuelling works as more than just connecting partially expended stages to your payload.
« Last Edit: 02/20/2018 09:24 PM by speedevil »

Offline sevenperforce

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Re: Comprehensive Falcon Family Performance
« Reply #11 on: 02/20/2018 09:33 PM »
Does LEO tanker include the fact that it doesn't need a fairing, which must save a fair bit of weight and drag.

I note that the price of FH all recovered + f9 recovered, with F9 launching a payload, and FH launching expendable is the same, and the capability to high energy orbits doing this is also comparable.

Is the 'tanker' mass including or excluding the stage?

Capability with FH expendable as tanker goes up really quite a lot.

I note my 'F9 moon lander' thread. https://forum.nasaspaceflight.com/index.php?topic=45010.0
Flying as a tanker (really, flying as a separately-launched BLEO kick stage) would still require SOME kind of cover over the docking adapter, so that their aero model doesn't get weird. Rather than building a completely new fairing, they'd probably just put on a regular clamshell. Other option is to cover it with the nosecone from the Dragon 1.

The "tanker" column lists only the mass of the propellant after orbital insertion, expected in a nominal 185 x 185 km 28.5 degree parking orbit. The true mass will be 4 tonnes more.

Offline speedevil

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Re: Comprehensive Falcon Family Performance
« Reply #12 on: 02/20/2018 09:47 PM »
Rather than building a completely new fairing, they'd probably just put on a regular clamshell. Other option is to cover it with the nosecone from the Dragon 1.

I think I was assuming the booster fairings would fit, but I guess the attachments are rather different, and there is no provision for them to come off.

In principle, the airflow seems not to be a problem, as S2 of course is gone when all the boosters are doing anything aero.
« Last Edit: 02/20/2018 09:54 PM by speedevil »

Offline sevenperforce

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Re: Comprehensive Falcon Family Performance
« Reply #13 on: 02/20/2018 09:57 PM »
Rather than building a completely new fairing, they'd probably just put on a regular clamshell. Other option is to cover it with the nosecone from the Dragon 1.

I think I was assuming the booster fairings would fit, but I guess the attachments are rather different, and there is no provision for them to come off.

In principle, the airflow seems not to be a problem, as S2 of course is gone when all the boosters are doing anything aero.
Yes, I was thinking standard booster fairings. The IDA can fit in the trunk of a Dragon 1 so surely it can be bolted to the PAF under a standard recoverable fairing.

Airflow for boosters is all backwards, so that's a little different.

Offline hkultala

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Re: Comprehensive Falcon Family Performance
« Reply #14 on: 02/20/2018 10:08 PM »
LEO tanker performance assumes that the payload is nothing but an International Docking Adapter (mass: 526 kg), so that it could be docked to a vehicle waiting in LEO for an ejection burn.

umm.. I don't undestand what you mean by this. Fuel remaining in the tank after reaching the orbit with this?
Right. Elon has talked about orbital propellant transfer, and while this is very unlikely for the Falcon upper stage, I've also seen mission proposals where an empty upper stage is sent into orbit to dock with another vehicle and perform a burn BLEO. So I threw in one column where you'd merely be figuring out how much propellant you'd have left over.

Then those numbers look like they have something badly wrong.

first, the principle. We know that the second stage is undersized for FH. It would make sense to spend MORE fuel for 2nd stage burn, not less.


Then some calculations:

Expendable FH:

F9/FH second stage + your adapter is ~4.5 tonnes, and has about 107500 tonnes of propellant.

With 97 tonnes of fuel remaining, this means that the second stage would give it only ~328 m/s of delta-v.

So the core would need to go to almost orbital velocity (with a 112-tonne 2nd stage as a payload)


FH with reusable side boosters:

With 87 tonnes of fuel remaining, this means that the second stage would give it only about 673 m/s of delta-v

And with your reusable side boosters, the core would have to reach ~6.8km/s of staging velocity (in addition to the gravity losses).


These don't seem like reasonable staging velocities, no way the boosters and core are capable of this.



« Last Edit: 02/21/2018 07:51 AM by hkultala »

Offline Nomadd

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Re: Comprehensive Falcon Family Performance
« Reply #15 on: 02/20/2018 10:43 PM »

Falcon Heavy's base price is $90M. Sacrificing all three cores is a $30M x 3 markup, to $150M. Tracking so far.

That's some interesting math there.

Offline hkultala

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Re: Comprehensive Falcon Family Performance
« Reply #16 on: 02/21/2018 08:26 AM »
Numbers for fully recoverable FH seem to be considerably lower in this than the NASA database.

(which itself probably has too low numbers, based on old FH model)
« Last Edit: 02/21/2018 09:31 AM by hkultala »

Offline guckyfan

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Re: Comprehensive Falcon Family Performance
« Reply #17 on: 02/21/2018 08:27 AM »
Falcon Heavy (recovery x3)   3.17t to TMI

3.17t to TMI seems way low. When Red Dragon was still on Elon once mentioned that they may be able to send it off to Mars while recovering all 3 cores. Though that was maybe not likely the performance needs to be a lot closer to 10t to even consider it.

Offline MATTBLAK

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Re: Comprehensive Falcon Family Performance
« Reply #18 on: 02/21/2018 08:51 AM »
The mass of the empty second stage and engine, plus the payload adaptor and Tesla should bring us closer to the answer.
« Last Edit: 02/21/2018 11:36 AM by MATTBLAK »
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Offline hkultala

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Re: Comprehensive Falcon Family Performance
« Reply #19 on: 02/21/2018 09:27 AM »
Elon recently let slip on Twitter that flying Falcon Heavy with parallel booster recovery only (expendable core) represents a 10% performance loss over fully-expendable but would only run about $95M.

When he said it, he obviously meant it's about 10% performance loss is to SOME orbit. (probably LEO maximum payload).

For other orbits, the difference is different, and probably much greater for high energy trajectories.

And he may even have meant barge landing instead of RTLS of the side boosters in this number. (construction/buying another barge to atlantic was just announced)




This payload table is simply FULL or errors, inconsistent numbers based on incorrect assumptions.

« Last Edit: 02/21/2018 09:37 AM by hkultala »

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