Author Topic: Comprehensive Falcon Family Performance  (Read 14716 times)

Offline IRobot

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Re: Comprehensive Falcon Family Performance
« Reply #20 on: 02/21/2018 10:10 AM »
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 (recovery x3)$90M23.5318.118.006.663.653.123.17
Falcon 9 (expendable)$92M24.9922.808.307.744.253.654.02




If the numbers are correct, then FH 3x recovery makes no sense, as you can fly an expendable F9 with less risks.

Edit: could only make sense for a central core recovery for inspection, but not for all flights.
« Last Edit: 02/21/2018 10:12 AM by IRobot »

Offline speedevil

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Re: Comprehensive Falcon Family Performance
« Reply #21 on: 02/21/2018 10:13 AM »
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.

The spreadsheet - or at least more of the methodology needs spelled out.

I did rough numbers, and if you assume that the '10% less' number originates from a lower velocity at MECO, at least at LEO and GEO, the loss is about the same for the first stage velocity, at around 250m/s.

Offline sevenperforce

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Re: Comprehensive Falcon Family Performance
« Reply #22 on: 02/21/2018 11:50 AM »

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.
Wow, I'm an idiot.

So basically SpaceX's pricing is not actually straightforward.
« Last Edit: 02/21/2018 12:19 PM by sevenperforce »

Offline sevenperforce

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Re: Comprehensive Falcon Family Performance
« Reply #23 on: 02/21/2018 12:19 PM »
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)
Well, let's start with a benchmark that we know. FH expendable is advertised at 3.5 tonnes to Pluto, which requires around 8.2 km/s beyond LEO. A Falcon upper stage masses 4 tonnes and carries 107.5 tonnes of propellant, so m0/m1 = 15.33. At an isp of 345 seconds, that means the upper stage packs a total of 9.23 km/s.

If SpaceX's figure is to be believed, then, staging for an expendable max-payload Pluto mission occurs at LEO-1.03 km/s, or an absolute staging velocity of 6.77 km/s. If that 3.5-tonne Pluto payload was swapped out for a half-tonne IDA, then the upper stage would still have 78.1 tonnes of propellant remaining at orbital insertion.

Of course, the core is lifting slightly less mass with the IDA in place of the Pluto package, so we should expect slightly more velocity at staging, meaning more propellant remaining at SECO. The core throttledown profile is probably going to be tuned to each mission and payload, so estimating how the side boosters factor in will be difficult.

Quote
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.
Well, 6.77 km/s would already be achieved in an expendable flight with a payload of 3.5 tonnes. With an even lower payload, you could likely reach a higher staging velocity and still have enough propellant for booster recovery.

Offline Mader Levap

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Re: Comprehensive Falcon Family Performance
« Reply #24 on: 02/21/2018 12:25 PM »
This whole mess does not add up for very simple reason: those are prices for customer, not cost for SpaceX.

Things like "FH with middle core expended costs only 5 mln $ more" show it is fools' errand to try "what is true cost" kremlinology based on price alone. SpaceX can and will set up prices so certain behaviours are incentivized and other penalized. For example, they want reward customers for using FH fully reusable over F9 expendable.
Be successful.  Then tell the haters to (BLEEP) off. - deruch
...and if you have failure, tell it anyway.

Offline sevenperforce

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Re: Comprehensive Falcon Family Performance
« Reply #25 on: 02/21/2018 12:35 PM »
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)
Numbers for fully-recoverable FH are based on the advertised limit of 8 tonnes to GTO.

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)
Yes, that's precisely what was meant, and that's what I worked from.

He may have meant 10% performance loss to LEO, or he may have meant 10% performance loss to GTO. We don't know. That's why I said that those particular numbers are less certain.

If the numbers are correct, then FH 3x recovery makes no sense, as you can fly an expendable F9 with less risks.

Edit: could only make sense for a central core recovery for inspection, but not for all flights.
But a Falcon Heavy with three-core recovery is cheaper.

The numbers surprised me, too, but they're spelled out pretty clearly. The SpaceX pricing page says that Falcon 9 is available at the base price for up to 5.5 tonnes to GTO, but can deliver up to 8.03 tonnes to GTO expendable. It says that FH is available at the base price for up to 8 tonnes to GTO, but can deliver up to 26.7 tonnes to GTO expendable.

This whole mess does not add up for very simple reason: those are prices for customer, not cost for SpaceX.

Things like "FH with middle core expended costs only 5 mln $ more" show it is fools' errand to try "what is true cost" kremlinology based on price alone. SpaceX can and will set up prices so certain behaviours are incentivized and other penalized. For example, they want reward customers for using FH fully reusable over F9 expendable.
Yeah, you're right. Hence pricing FHxR3 lower than F9E.

Offline hkultala

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Re: Comprehensive Falcon Family Performance
« Reply #26 on: 02/21/2018 01:18 PM »
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)
Numbers for fully-recoverable FH are based on the advertised limit of 8 tonnes to GTO.

Advertized limit for $90 million price tag. Not advertised limit of fully reusable.

The price point has been put up to the web page 5.5.2016. Back then they had no operational block 5 engines, and the number is probably based on block 3 engines, not block 5 engines.

5.5.2016 (and much later also) the maximum payload of FH was listed as 55400 kg. As the maximum payload has increased by 15% since, probably also the reusable payload has increased by about similar amount (but probably even more, as there have been also other advances that help especially reusable payload, like 3-engine landing burn, and the better T/W also helps reusable payload more, as the side boosters run out of fuel faster, after moving shorter horizontal distance, so less flyback distance).

So now they have updated their maximum payload number for block 5 engines, but their pricing number is still based on the block 3 reusable payload.

So, if you want to base your FH GTO performance on the FH adverticed pricing numbers, use at least 9.2 tonnes to GTO instead.
« Last Edit: 02/21/2018 01:26 PM by hkultala »

Offline sevenperforce

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Re: Comprehensive Falcon Family Performance
« Reply #27 on: 02/21/2018 01:30 PM »
The spreadsheet - or at least more of the methodology needs spelled out.

I did rough numbers, and if you assume that the '10% less' number originates from a lower velocity at MECO, at least at LEO and GEO, the loss is about the same for the first stage velocity, at around 250m/s.
The methodology was fairly straightforward. If you take the advertised payloads for Falcon Heavy expendable, you can trivially determine the total dV on the upper stage at staging for each given payload. For example, a 3.5-tonne payload (to Pluto) packs 9.23 km/s, a 16.8-tonne payload (to Mars) packs 6.15 km/s, and a 26.7-tonne payload (to GTO) packs 5.09 km/s. We also know the excess residual dV each stage has; transfer to Pluto costs 8.2 km/s, transfer to Mars costs 4.3 km/s, and GTO costs 2.27 km/s.

If you plot the total stage dV against the excess residual dV, you get a perfectly straight line. The line crosses the y-axis at 3.212 km/s total dV, 0 km/s excess residual dV...and sure enough, you get 3.2 km/s of total dV when the upper stage has 63.8 tonnes of payload, corresponding to the maximum advertised LEO payload.

This allows you to estimate residual dV for any possible payload...or, inversely, the maximum payload for any given destination. It should be quite accurate for any payloads between 64 tonnes and 3.5 tonnes, though extrapolating out to payloads under 3 tonnes may be a bad idea since the curve should start to curve toward an absolute ceiling.

The same method was used to determine the payloads for Falcon 9 expendable.

For ASDS recovery (and for 3-core recovery), I determined what gap in staging velocity would yield the advertised payload drop. For example, we know that ASDS recovery tops out at 5.5 tonnes to GTO. From the expendable Falcon 9 performance curve, a 5.5-tonne payload would have 3.52 km/s of residual dV, 1.25 km/s more than needed for GTO. So we can estimate that an ASDS recovery F9 would need to stage 1.25 km/s slower than an expendable F9, and I calculated the performance curve for F9 ASDS accordingly.

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)
Numbers for fully-recoverable FH are based on the advertised limit of 8 tonnes to GTO.

Advertized limit for $90 million price tag. Not advertised limit of fully reusable.
Well, Elon said that two-core recovery is $95M and expendable is $150M, so the only other option is three-core recovery.

Quote
The price point has been put up to the web page 5.5.2016. Back then they had no operational block 5 engines, and the number is probably based on block 3 engines, not block 5 engines.

5.5.2016 (and much later also) the maximum payload of FH was listed as 55400 kg. As the maximum payload has increased by 15% since, probably also the reusable payload has increased by about similar amount (but probably even more, as there have been also other advances that help especially reusable payload, like 3-engine landing burn, and the better T/W also helps reusable payload more, as the side boosters run out of fuel faster, after moving shorter horizontal distance, so less flyback distance).

So now they have updated their maximum payload number for block 5 engines, but their pricing number is still based on the block 3 reusable payload.

So, if you want to base your FH GTO performance on the FH adverticed pricing numbers, use at least 9.2 tonnes to GTO instead.
I can certainly accept that the FHRx3 payload to GTO has increased, but what's the basis for the 9.2-tonne number?

Online envy887

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Re: Comprehensive Falcon Family Performance
« Reply #28 on: 02/21/2018 01:51 PM »
NASA LSP updated didn't update the numbers for FH in the last couple weeks, but they still don't match SpaceX's website. I wonder if SpaceX is assuming MRS and LSP is applying some margins?
« Last Edit: 02/21/2018 04:00 PM by envy887 »

Online ugordan

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Re: Comprehensive Falcon Family Performance
« Reply #29 on: 02/21/2018 01:55 PM »
NASA LSP updated the numbers for FH in the last couple weeks

They don't look updated to me and those two graphs look identical to me?

Offline hkultala

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Re: Comprehensive Falcon Family Performance
« Reply #30 on: 02/21/2018 02:14 PM »
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)
Numbers for fully-recoverable FH are based on the advertised limit of 8 tonnes to GTO.

Advertized limit for $90 million price tag. Not advertised limit of fully reusable.
Well, Elon said that two-core recovery is $95M and expendable is $150M, so the only other option is three-core recovery.

Yes, but for OLD version of FH and maybe with some extra margins for just to be sure they can reach it if some problems would arrive. (either development problems or accident-like problems)

For example, a margin to be able to lose one engine from a side booster and still be able to do everything like planned.

Quote
Quote
The price point has been put up to the web page 5.5.2016. Back then they had no operational block 5 engines, and the number is probably based on block 3 engines, not block 5 engines.

5.5.2016 (and much later also) the maximum payload of FH was listed as 55400 kg. As the maximum payload has increased by 15% since, probably also the reusable payload has increased by about similar amount (but probably even more, as there have been also other advances that help especially reusable payload, like 3-engine landing burn, and the better T/W also helps reusable payload more, as the side boosters run out of fuel faster, after moving shorter horizontal distance, so less flyback distance).

So now they have updated their maximum payload number for block 5 engines, but their pricing number is still based on the block 3 reusable payload.

So, if you want to base your FH GTO performance on the FH adverticed pricing numbers, use at least 9.2 tonnes to GTO instead.
I can certainly accept that the FHRx3 payload to GTO has increased, but what's the basis for the 9.2-tonne number?

Linear extrapolation from the maximum LEO payload increase between 5.5.2016(block 3) and current (block 5)

63.8 / 54.4   = 1.15
1.15 * 8 = 9.2

Extrapolation from expendable GTO capacities gives even bigger increase

26.7 /22.2 = 1.20
1.20 * 8 = 9.6

And extrapolation from expendable TMI capacities even more.

16.8 / 13.6 = 1.235

1.235 * 8 = 9.9


The payload size and stage2 delta-v for 3-S1 recoverable is closest to the TMI of the expendable, so from these 3 numbers we should use that as our basis.

So actually the payload of FHR to GTO should be in the range of ~10 tonnes. (if the original 8 tonnes was to full capacity of block 3)
« Last Edit: 02/21/2018 02:30 PM by hkultala »

Offline IRobot

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Re: Comprehensive Falcon Family Performance
« Reply #31 on: 02/21/2018 03:49 PM »
If the numbers are correct, then FH 3x recovery makes no sense, as you can fly an expendable F9 with less risks.

Edit: could only make sense for a central core recovery for inspection, but not for all flights.
But a Falcon Heavy with three-core recovery is cheaper.
They are very similar prices, so an expendable F9 has less risk and no recovery costs.

Online envy887

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Re: Comprehensive Falcon Family Performance
« Reply #32 on: 02/21/2018 03:55 PM »
NASA LSP updated the numbers for FH in the last couple weeks

They don't look updated to me and those two graphs look identical to me?

Whoops. I was reading the c3=12 line on one and the c3=0 line on the other. They are the same.

Online envy887

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Re: Comprehensive Falcon Family Performance
« Reply #33 on: 02/21/2018 04:00 PM »
If the numbers are correct, then FH 3x recovery makes no sense, as you can fly an expendable F9 with less risks.

Edit: could only make sense for a central core recovery for inspection, but not for all flights.
But a Falcon Heavy with three-core recovery is cheaper.
They are very similar prices, so an expendable F9 has less risk and no recovery costs.

Price isn't everything. If the lead time for an expendable F9 is 6 months longer because of a slower production rate, and your satellite earns $20M per month, then you just lost $122 million.

IMO those prices won't be similar for long, as SpaceX can probably make about three times as much profit on a FHR as on F9E.

Offline sevenperforce

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Re: Comprehensive Falcon Family Performance
« Reply #34 on: 02/21/2018 04:21 PM »
I can certainly accept that the FHRx3 payload to GTO has increased, but what's the basis for the 9.2-tonne number?

Linear extrapolation from the maximum LEO payload increase between 5.5.2016(block 3) and current (block 5)

63.8 / 54.4   = 1.15
1.15 * 8 = 9.2

Extrapolation from expendable GTO capacities gives even bigger increase

26.7 /22.2 = 1.20
1.20 * 8 = 9.6

And extrapolation from expendable TMI capacities even more.

16.8 / 13.6 = 1.235

1.235 * 8 = 9.9


The payload size and stage2 delta-v for 3-S1 recoverable is closest to the TMI of the expendable, so from these 3 numbers we should use that as our basis.

So actually the payload of FHR to GTO should be in the range of ~10 tonnes. (if the original 8 tonnes was to full capacity of block 3)
Interesting. Originally, I had tried to calculate F9's ASDS performance based on the observed MECO velocities, and came up with a much higher number than 5.5 tonnes. Do you know if the F9 reusable performance has gone up as well?

I'm not sure if linear extrapolation is the best approach, especially since LEO and BLEO capabilities are going to be wildly divergent since kerolox is low-isp, high-thrust.

Here's an approach that might be a little more promising. A 54.4-tonne payload on the 4-tonne upper stage would have 3530 m/s of dV on the upper stage. In contrast, a 63.8-tonne payload would have 3212 m/s of dV. Since neither the MVac isp nor the propellant load on the upper stage has changed from Block 3 to Block 5, this means Block 5 FHe must stage 318 m/s higher than Block 3 FHe to improve the payload capability by this much.

How does this equate to FHR3? Well, a higher staging velocity means more propellant needs to be reserved on the core for a longer boostback or entry burn, but improvements in landing burns and glide ratio have probably counterbalanced this. So if Block 3 FHR could do 8 tonnes to GTO, Block 5 FHR would be able to send an 8-tonne payload to GTO with 318 m/s of dV left in the tank.

Modifying my payload predictor curve to meet this performance (specifically, 8 tonnes to LEO+2.588 km/s) brings us to a Falcon Heavy capability of 21.2 tonnes to LEO, 9.44 tonnes to GTO, 3.94 tonnes to Mars, 7.9 tonnes to the moon, 3.88 tonnes direct to GEO, 4.49 tonnes to lunar orbit, and 27.6 tonnes of residuals when flown to LEO with only an IDA.

Offline sevenperforce

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Re: Comprehensive Falcon Family Performance
« Reply #35 on: 02/21/2018 04:42 PM »
For reference, if you do the same math with the other performance increases, you're looking at a 423 m/s staging velocity increase for the GTO-class payloads on FH expendable, and a 480 m/s staging velocity increase for the TMI-class payloads on FH expendable. However, the tyranny of the rocket equation says that if you're staging much earlier for FHR3, you're not going to see quite as much of a jump, so sticking with those lower figures is probably a safe bet.

That's interesting. FHR3 outperforms F9E for all payloads except TMI and LEO.

Offline intrepidpursuit

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Re: Comprehensive Falcon Family Performance
« Reply #36 on: 02/22/2018 06:49 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 posted about this in great detail in in this thread. Essentially, it all makes sense if you subscribe the premise that SpaceX make way more margin on recovered flights than expendable. There is no pressure on them to go lower in price right now and they have a big investment to pay off. So keep the expendable flights sustainable, but make bank to pay for BFR on recovery.

As long as it is cheaper to use a fully reusable FH than an expendable F9 and no one is making payloads that require an expendable FH, they make a huge margin while being the cheapest and most capable provider in the industry.

Online envy887

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Re: Comprehensive Falcon Family Performance
« Reply #37 on: 02/23/2018 03:16 AM »
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?

SpaceX can charge whatever price they want. An expended F9 could be $6 billion per flight and reused FH 3 for a nickel. Who says it has to make sense?

Offline Stan-1967

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Re: Comprehensive Falcon Family Performance
« Reply #38 on: 02/23/2018 03:33 AM »
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?

SpaceX likely has different amortization rates for side boosters vs. the center core.  The price for FH probably assumes just a few re-uses of the core, and perhaps only a single use for the average FH mission.  Block 5 side cores are supposed to give 10 re-uses without refurbishment, so if you prematurely expend an asset that is supposed to be on your books generating revenue, you would want to recover that cost & revenue if they were going to be expended. 

The condition of re-used side cores is a place where buying launches from SpaceX is going to more analogous to going to a used car lot.  They will, by necessity, assert that all previous flown boosters are the same.  However behind the scenes, they will know which are aging rapidly, and which ones are true cherries.  This will leave plenty negotiating room to whittle away at that $55M premium to expend the side cores if it makes the difference in winning a launch.

Offline Nomadd

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Re: Comprehensive Falcon Family Performance
« Reply #39 on: 02/24/2018 07:23 AM »
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?

SpaceX can charge whatever price they want. An expended F9 could be $6 billion per flight and reused FH 3 for a nickel. Who says it has to make sense?
The people who pay the bill.

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