SpaceX Falcon Heavy Discussion (Thread 6)

[Kabloona]

Keep in mind that the dry mass calculated from LSP numbers will include residuals to allow the some performance reserve to meet LSP margins. SpaceX's published figures are probably for a burn to depletion. I think that better explains the ~1,000 kg difference between this method and other methods for backing out the mass of the upper stage.

Isn't that 1,000 kg difference what Lou was referring to in the para quoted below, ie the difference between his calculations for dry (4.5t) and dry + residuals (5.5t) ?

The second stage starts at 109 tonnes + payload, and ends at 5537 kg + payload.   The 5537 kg includes the dry mass, the residuals, and the payload adapter.  Both of these are consistent with earlier estimates.  Musk talked about the first stage lifting 125 tonnes, which could be 109 (stage) + 12 (payload) + 4 (fairing).  Also, the stage has about 100 tonnes of fuel, so 1% residuals would be 1 tonne, so the dry mass would be about 4.5t.   So all is consistent.

Or are you saying other methods get 3.5t dry?

[envy887]

Keep in mind that the dry mass calculated from LSP numbers will include residuals to allow the some performance reserve to meet LSP margins. SpaceX's published figures are probably for a burn to depletion. I think that better explains the ~1,000 kg difference between this method and other methods for backing out the mass of the upper stage.

Isn't that 1,000 kg difference what Lou was referring to in the para quoted below, ie the difference between his calculations for dry (4.5t) and dry + residuals (5.5t) ?

Yes. I was just clarifying how the LSP margins lead to a performance different than SpaceX's published figures..

Or are you saying other methods get 3.5t dry?

No.

[Kabloona]

OK, thank you for the clarification.

[OneSpeed]

I put this in a spreadsheet where you enter the apogee of the injection burn (166 km for the NASA numbers)

From the NASA launch vehicle performance comments: 160 km (86 nmi) park orbit perigee altitude. This increases your average error to 4.33m/s.

Also, the stage has about 100 tonnes of fuel, so 1% residuals would be 1 tonne, so the dry mass would be about 4.5t.

From the comments: 3-sigma guidance reserves. 3σ is 99.7%, so the NASA estimate of ullage is roughly your suggested 100 tonnes x 0.003 = 0.3mT. Plugging 4.5 + 0.3 = 4.8mT into your spreadsheet further increases your average error to -250.34m/s.

If I take your 4.5mT S2 dry mass estimate and plug it into my spreadsheet, which references only the NASA data and physics, then the S2 dry mass estimate becomes 4.8mT. The total payload to LEO for C3 from 0 to 100 ranges between 51 and 44 mT to LEO. The corresponding mass at launch would range from 1,421 to 1407 mT, so for an effective Isp of 291.15, 9500 to 9893 m/s. That gives 393 / 14 = 28m/s/mT, higher than your suggested range.

With a 160km parking orbit, your error is now minimised at about 5.52mT empty+residuals+adapter, giving a dry mass of 5.22mT. Plugging this value into my spreadsheet ranges between 53 and 50mT to LEO, giving for an effective Isp of 294.55, 9500 to 9640 m/s. That gives 140 / 14 = 10m/s/mT, at the bottom of your suggested range.

You may want to recalculate your booster estimates, but I suspect we are headed towards a 5.0mT S2 dry mass figure. I'm still surprised how low the payload to LEO figures are.

[LouScheffer]

I put this in a spreadsheet where you enter the apogee of the injection burn (166 km for the NASA numbers)

From the NASA launch vehicle performance comments: 160 km (86 nmi) park orbit perigee altitude. This increases your average error to 4.33m/s.

No, if you change one parameter you need to re-optimize all the others.   Try:
Altitude   160000   meters   
Booster supplies (0 payload)   5180.5   m/s
Booster penalty    0.01600   m/s per kg
stage 2 initial mass (no payload)   108000   kg
ISP   348   
empty+residuals+adapter   5532.8   kg

And you will see an error of less than 1.45 m/s.

Also, the stage has about 100 tonnes of fuel, so 1% residuals would be 1 tonne, so the dry mass would be about 4.5t.

From the comments: 3-sigma guidance reserves. 3σ is 99.7%, so the NASA estimate of ullage is roughly your suggested 100 tonnes x 0.003 = 0.3mT. Plugging 4.5 + 0.3 = 4.8mT into your spreadsheet further increases your average error to -250.34m/s.

This argument confuses two very different statistical concepts.  99.7% is the percentage of the trials that are within the bounds, but does not say what those bounds are.  This depends on the variation of the rocket from trial to trial.  Say we had a rocket that was quite variable performance, say a standard deviation of 3% in ISP.  Then we would need to reserve 9% of the fuel (3 sigma) to make sure would could complete the mission 99.7% of the time, and an average mission would have 9% of the fuel left. 

Historically, reserving 1% of fuel for performance variation is a typical number, though only SpaceX (and other folks sworn to keeping it proprietary) know for sure.  0.3% would be a very low figure - see, for example, the "Propellant Budget" section of this presentation on rocket design.

And indeed plugging 4.8t into the spreadsheet gives a big error.   This implies that 4.8 tonnes is not a good estimate for the end-of-burn mass.  If end-of-burn mass was 4.8t, you'd get much bigger speeds than NASA quotes. 5.5t gives a much better match to the quoted performance.

[OneSpeed]

Yep, that makes sense, I've updated my spreadsheet (hoping not to change it again at least until they start attaching S2 recovery hardware).

[Lar]

For raw data I went to the NASA LSP web site, and typed in C3 from 0 to 100 by 10, and recorded the FH payload for each C3.

I love this analysis but I thought I read somewhere that it was asserted that the LSP numbers were off?

Edit: Apparently they were fixed. See this post

https://forum.nasaspaceflight.com/index.php?topic=42637.msg1852550

[Robotbeat]

For raw data I went to the NASA LSP web site, and typed in C3 from 0 to 100 by 10, and recorded the FH payload for each C3.

I love this analysis but I thought I read somewhere that it was asserted that the LSP numbers were off?

Edit: Apparently they were fixed. See this post

https://forum.nasaspaceflight.com/index.php?topic=42637.msg1852550

They were fixed, but the LSP numbers are still on the conservative side. They are contracted numbers, not what FH can likely actually do. And it certainly doesn't include any stretching, which would help a lot, has been discussed, and wouldn't be that hard. (Of course, other relatively easy upgrades to other ELVs also aren't included, so this isn't any kind of bias, I'm just pointing out that it might be tough to reverse engineer FH this way.)

[OneSpeed]

They were fixed, but the LSP numbers are still on the conservative side. They are contracted numbers, not what FH can likely actually do.

That would help to explain the low mass to LEO figures for FH, but by way of comparison, here is a spreadsheet for Delta IV Heavy. Parker Solar Probe was 2,849kg to C3=59km²/s², just below the LSP 3000kg payload to C3=60. So sandbagged perhaps, but not by much.

[Comga]

They were fixed, but the LSP numbers are still on the conservative side.
They are contracted numbers, not what FH can likely actually do.

That would help to explain the low mass to LEO figures for FH, but by way of comparison, here is a spreadsheet for Delta IV Heavy. Parker Solar Probe was 2,849kg to C3=59km²/s², just below the LSP 3000kg payload to C3=60. So sandbagged perhaps, but not by much.

That the Parker Solar Probe achieved 97% of the energy with 95% of the rated mass doesn’t say anything about capacity beyond what is stated, any “sandbagging”.  It just says that the ratings were sufficiently conservative for the program to work to them, as Robotbeat says.

[LouScheffer]

[...] by way of comparison, here is a spreadsheet for Delta IV Heavy. Parker Solar Probe was 2,849kg to C3=59km²/s², just below the LSP 3000kg payload to C3=60. So sandbagged perhaps, but not by much.

Repeating the analysis for D4H is an excellent idea.  I went the the LSP web site and got the following numbers:
C3 kg
0 10185
10 8460
20 6995
30 5755
40 4700
50 3790
60 3000
70 2315
80 1710
90 1180
100 705

Then took the starting mass from Wikipedia (30700 kg), optimized as above and got:

Booster supplies (0 payload)   6864.4   m/s
Booster penalty                            0.04184   m/s per kg
stage 2 initial mass (no payload)   30700   kg
ISP                                           462   
empty+residuals+adapter       4591.2   kg

And once again achieved an excellent fit (less than 1 m/s out of 12,000).  Again this is consistent with what we know.  Booster contribution is much higher than F9 or even F9H expendable.  And Wikipedia has the empty mass as 3480 kg, so about 1000 kg of residuals + adapter. 

The "booster penalty" is much larger at 41.8 m/s per 1000 kg of payload.  In real life this is probably a combination of the real booster penalty, plus increased gravity loss for the second stage.  At this level of modelling, there is no way to distinguish the two.  All you see is the sum, and you can't tell which stage contributes how much.

[Robotbeat]

Gravity loss is a big difference. Also, one thing that is important for missions with a kick stage is burnout altitude. Delta IV upper stage is low thrust and thus takes longer (altitude) to deplete the stage, leaving the kick stage at a higher altitude (worse Oberth performance) than Falcon Heavy at burnout for the same C3.

[LouScheffer]

They were fixed, but the LSP numbers are still on the conservative side.

Above we have a model that matches LSP numbers almost perfectly, for C3 >= 0.  If we extrapolate this back to LEO (C3 = -61 km^2/sec^2), it says 52,500 kg to LEO, where SpaceX claims 63,800 kg.   Likewise, extrapolating back to GTO (C3 = -24.2) gives 24,100 kg, where SpaceX says 26,700 kg.

The GTO numbers are close enough to be understandable (maybe LSP does 3 sigma and SpaceX does burn to depletion) but the LEO number is very different. 

Of course the number of 52+ tonne payloads to LEO is pretty small (as in 0, currently) so the difference may be academic.

[Robotbeat]

It depends exactly how the margin is being done, it might not show up as distortion in the C3 curve.

[alexterrell]

Sorry if the answer is obvious...

It seems the boosters for Falcon Heavy are slightly different from those for Falcon 9.

Does that mean that Falcon Heavy will need its own dedicated Block 5 boosters?

With Falcon Heavy having a fairly low flight rate, would that mean SpaceX will build just three (and maybe a spare) Block 5 boosters?

Or are the block 5s planned to be interchangable?

[Cheapchips]

Sorry if the answer is obvious...

It seems the boosters for Falcon Heavy are slightly different from those for Falcon 9.

Does that mean that Falcon Heavy will need its own dedicated Block 5 boosters?

With Falcon Heavy having a fairly low flight rate, would that mean SpaceX will build just three (and maybe a spare) Block 5 boosters?

Or are the block 5s planned to be interchangable?

Standard B5's can be used for the outside boosters.  The centre core isn't standard.  It's a reinforced design to cope with the heavier stresses it's put under. 

Don't know if any of the planned FH launches are ditching the centre core.  If they're all a reusable flight profile then they could get away with only building one centre core to cover the next couple of years.

[Alexphysics]

Sorry if the answer is obvious...

It seems the boosters for Falcon Heavy are slightly different from those for Falcon 9.

Does that mean that Falcon Heavy will need its own dedicated Block 5 boosters?

With Falcon Heavy having a fairly low flight rate, would that mean SpaceX will build just three (and maybe a spare) Block 5 boosters?

Or are the block 5s planned to be interchangable?

Only the center core has to be specially built for FH, the sides can be reused from F9 boosters and viceversa, Elon says they just need to change the interstage for a nosecone and add the mounting hardware. The first Falcon Heavy already did something like this, the sides were reused from old F9 boosters. However it is worth noting that, although it's something possible to do, it doesn't mean every FH flight will reuse the sides, there is an Air Force mission, STP-2, that will fly early next year and that will use all new boosters.

[alexterrell]

Thanks for the answer. That makes it clearer.

Only the center core has to be specially built for FH, the sides can be reused from F9 boosters and viceversa, Elon says they just need to change the interstage for a nosecone and add the mounting hardware. The first Falcon Heavy already did something like this, the sides were reused from old F9 boosters. However it is worth noting that, although it's something possible to do, it doesn't mean every FH flight will reuse the sides, there is an Air Force mission, STP-2, that will fly early next year and that will use all new boosters.

The flights with all new boosters are of course the reason to build new boosters.

I suspect in the early days, with both F9 and FH, quite a few customers will demand new boosters, so SpaceX will build up aninventory of boosters, FH centre boosters, excess nose cones and mounting hardware.

Once the concept of "flight proven boosters" is "proven", then the inventory could run down.

Around 2022, if BFR is flying, SpaceX might be selling F9 and FH flights at real knock down prices.

[oiorionsbelt]

Around 2022, if BFR is flying, SpaceX might be selling F9 and FH flights at real knock down prices.

Or F9, FH pricing stays the same and BFR is cheaper.

[guckyfan]

Around 2022, if BFR is flying, SpaceX might be selling F9 and FH flights at real knock down prices.

That one point I don't agree with. They may not want to force the change to BFR but they also don't want to delay it. They have no reason to make Falcon cheap once they have the capacity to do things with BFR.