Payload estimate for allowing routine re-entry

[LouScheffer]

Here's an estimate of how much less satellite mass would be required to make the re-entry burn routine.

According the SpaceX webcast, SES-9 was going about 2325 m/s at booster cutoff, about Mach 6.8.  There was a 17 second re-entry burn.  Each engine needs 270kg/sec, so that's 13.7t of fuel used.  Assuming an empty mass of 29t, 3t of fuel for the suicide slam, and a vacuum ISP of 311, then the delta v for the re-entry burn was 311*9.8*ln((32+13.7)/32) = 1086 m/s.  So the rocket was re-entering at about 2325 - 1086 = 1239 m/s, or about Mach 3.6 .  This is clearly marginal since Musk stated they did not expect it to survive re-entry. In practice, maybe it did or maybe it didn't.  It's not clear if the failure to restart one engine was a result of damage, too little fuel, or some other problem.

So how much margin do they need to make it work?  Given that it survived at all at Mach 3.6, Mach 2 should be OK with almost 6 times less peak heating and 3x less heating total. To get this they need to reduce the re-entry speed by about 550 m/s or so. Reserving more fuel for re-entry helps in two ways - booster cutoff will happen slightly earlier at a lower speed, and there is more fuel for the re-entry burn.  Since (from the point of view of the first stage) about 2/3 of the mass is shed at MECO (about 125t second stage, versus about 60t booster plus fuel), the second delta-V will be about 3x the first.  So about 137 m/s less at cutoff and a 412 m/s bigger re-entry burn.  A more careful calculation using the rocket equation give 121 m/s less boost and 429 m/s more burn.

So now the second stage has to provide 121 m/s more.  Assuming 111t fuel, 348 ISP, 5t empty,  5.3t SES-9, we get 348*9.8*ln(121.3/10.3) = 8410 m/s.  If we need 8530 m/s instead, that implies a 4900 kg or less payload.  For GTO payloads of this mass or less, SpaceX should  have all the margin needed to do a hot re-entry.

[MarekCyzio]

1. What if you assume MACH 2.5 as safe speed? How does it change satellite's weight?
2. Do these numbers assume all GTO satellites will be deployed to orbit similar to SES-9? Is this a valid assumption?
3. Do these numbers assume 3 engine landing burn? Is there any way to recalculate this using single engine burn?

[Doesitfloat]

Couple years ago we were looking at the dry weight if stage 1 and the consensus was about 20t.  You use 30t. While I concede it gained some weight with legs and fins, I doubt it was 10 tons.  If your stage went on a diet to say 25t what difference would that make?

[AncientU]

Thanks for the calculations, LouS.
Do you see 4,900 as clearly achievable and the margin between 4,900 and 5,300 'work required, but not impossible'?
Seems 5,300 is top of range that will be attempted, for now at least.

[livingjw]

Mach 3 - 3.5 should survive a reentry. SpaceX would have pushed both max reentry heat flux and minimum landing burn time. The high end of the former and the low end of the latter.

[LouScheffer]

1. What if you assume MACH 2.5 as safe speed? How does it change satellite's weight?

It allows about 100kg more (5030 kg by my estimate)

2. Do these numbers assume all GTO satellites will be deployed to orbit similar to SES-9? Is this a valid assumption?

Yes.  This is a fair but not perfect assumption.  SES-9 went to a GEO-1775 m/s orbit.  That's just a little better than a standard transfer orbit from the cape, which is GEO-1800 m/s.  SpaceX could add about 100 kg and still make a minimal GTO.

3. Do these numbers assume 3 engine landing burn? Is there any way to recalculate this using single engine burn?

Yes, they assume a suicide slam as used on SES-9.  Subtract about another 300 kg payload to allow a regular, single-engine landing burn.  So a 4600 kg payload allows a safe re-entry and a regular landing.

[cambrianera]

Couple years ago we were looking at the dry weight if stage 1 and the consensus was about 20t.  You use 30t. While I concede it gained some weight with legs and fins, I doubt it was 10 tons.  If your stage went on a diet to say 25t what difference would that make?

Here you can find why.
http://forum.nasaspaceflight.com/index.php?topic=37304.msg1358917#msg1358917
Number stated was approximate, and not clear if considering landing fuel or not; nevertheless it is the best number we have.

[LouScheffer]

Couple years ago we were looking at the dry weight if stage 1 and the consensus was about 20t.  You use 30t. While I concede it gained some weight with legs and fins, I doubt it was 10 tons.  If your stage went on a diet to say 25t what difference would that make?

If the stage goes on a 25t diet (hopefully not a crash diet), then the calculated performance allows a slightly higher payload - perhaps 5000 kg with a safe re-entry and a suicide slam, or 4700 kg with a safe re-entry and a "normal" landing.

[LouScheffer]

Thanks for the calculations, LouS.
Do you see 4,900 as clearly achievable and the margin between 4,900 and 5,300 'work required, but not impossible'?
Seems 5,300 is top of range that will be attempted, for now at least.

Well, the 4900 figure had a safe re-entry, but still a suicide slam.  Getting rid of the slam completely costs about another 300 kg.  So I'd say 4600 kg should be clearly achievable - safe re-entry and already-proven landing.  5300 kg seems very marginal, though worth a try.   If I had to guess, after the system is characterized and all the bugs worked out, I'd say 5000 kg or less, they will expect to recover.  5001-5300 kg, they'll try, but not with high expectations.  5301-6500 kg, pure expendable - don't bother to send the barge.

[envy887]

Thanks for the calculations, LouS.
Do you see 4,900 as clearly achievable and the margin between 4,900 and 5,300 'work required, but not impossible'?
Seems 5,300 is top of range that will be attempted, for now at least.

Well, the 4900 figure had a safe re-entry, but still a suicide slam.  Getting rid of the slam completely costs about another 300 kg.  So I'd say 4600 kg should be clearly achievable - safe re-entry and already-proven landing.  5300 kg seems very marginal, though worth a try.   If I had to guess, after the system is characterized and all the bugs worked out, I'd say 5000 kg or less, they will expect to recover.  5001-5300 kg, they'll try, but not with high expectations.  5301-6500 kg, pure expendable - don't bother to send the barge.

Or (hopefully) do send the barge, because the other two cores are landing at home. 

[nadreck]

Thanks for the calculations, LouS.
Do you see 4,900 as clearly achievable and the margin between 4,900 and 5,300 'work required, but not impossible'?
Seems 5,300 is top of range that will be attempted, for now at least.

Well, the 4900 figure had a safe re-entry, but still a suicide slam.  Getting rid of the slam completely costs about another 300 kg.  So I'd say 4600 kg should be clearly achievable - safe re-entry and already-proven landing.  5300 kg seems very marginal, though worth a try.   If I had to guess, after the system is characterized and all the bugs worked out, I'd say 5000 kg or less, they will expect to recover.  5001-5300 kg, they'll try, but not with high expectations.  5301-6500 kg, pure expendable - don't bother to send the barge.

Or (hopefully) do send the barge, because the other two cores are landing at home. 

Actually I believe all 3 can go home up to 7t and from 7 to 10 the barge goes out for the centre core

[MarekCyzio]

Yes, they assume a suicide slam as used on SES-9.  Subtract about another 300 kg payload to allow a regular, single-engine landing burn.  So a 4600 kg payload allows a safe re-entry and a regular landing.

So it looks like SpaceX will try to master 3 engine landing as it gives significant mass increase compared to any other approach. It will be interesting to see what they decided to do for JCSAT-14.

[MarekCyzio]

Or (hopefully) do send the barge, because the other two cores are landing at home. 

There is no place to land two cores. And it does not look like SpaceX is builiding Landing Zone 2 - we have not seen any environmental studies yet.

[Kabloona]

Yes, they assume a suicide slam as used on SES-9.  Subtract about another 300 kg payload to allow a regular, single-engine landing burn.  So a 4600 kg payload allows a safe re-entry and a regular landing.

So it looks like SpaceX will try to master 3 engine landing as it gives significant mass increase compared to any other approach. It will be interesting to see what they decided to do for JCSAT-14.

JCSAT-14 mass has not been published yet that I know of, but based on data from Gunter's Space Page, I estimate it at 4300 kg, which would make it a comfortable single-engine landing burn.

[Lar]

Or (hopefully) do send the barge, because the other two cores are landing at home. 

There is no place to land two cores. And it does not look like SpaceX is builiding Landing Zone 2 - we have not seen any environmental studies yet.

We hear very conflicting things on this ... and discussion of whether there will be more places to land is off topic for this thread.

Could we adjourn that to https://forum.nasaspaceflight.com/index.php?topic=36513 (the eastern range landing zone thread)? I'll reply there.

[Dmitry_V_home]

Gentlemen, somebody can comment on new figures on the website SpaceX?
http://www.spacex.com/about/capabilities

[Zed_Noir]

Gentlemen, somebody can comment on new figures on the website SpaceX?
http://www.spacex.com/about/capabilities

Thanks for the info, Dimtry.

Updated performance figures from the SpaceX website

F9     28800 kg   to   LEO
          8300 kg   to   GTO
          4020 kg   to   MTO

FH    54400 kg   to   LEO
        22200 kg   to   GTO
        13600 kg   to   MTO

Wow, the F9 have the same lift as the Delta IV Heavy with the RS-68A to LEO in the expandable mode. Does this mean that the Delta IV Heavy can be dispense with for polar missions out of VAFB?

[LouScheffer]

Gentlemen, somebody can comment on new figures on the website SpaceX?
http://www.spacex.com/about/capabilities

Wow - 8300 kg to GTO.  I did not see that coming.

5500 kg recoverable makes sense.  They almost recovered SES-9 at 5300.  With a slightly less aggressive GTO, 5500 seems doable.

But 8300 kg is a lot.  We know that SES-9 had a 17 second re-entry, and a roughly 6 second landing, both with 3 engines.  So an expendable could have perhaps 8 more seconds of 9-engine booster burn.  We know that near cutoff the booster is accelerating at 4-5 Gs, so that's maybe 350 m/s more for expendable.

But with a 121t starting mass (after fairing jettison), a 5t empty mass, and a 348 ISP, going from 5.5t to 8.3t means 800 m/s less.  That's too much to reach GTO with only 350 m/s more from the first stage.  A lower empy mass for the second stage only makes this discrepancy worse.

So I'm guessing it's the trajectory.  It must be that ANY recoverable trajectory, not just RLTS, involves more initial lofting, perhaps to get the first stage out out of the atmosphere so it can turn around.  If SpaceX is not recovering, the first stage goes more horizontal and builds up more orbital velocity, and stages at a lower altitude.  This reduces the gravity and pitch losses. 

[Rebel44]

Gentlemen, somebody can comment on new figures on the website SpaceX?
http://www.spacex.com/about/capabilities

Wow - 8300 kg to GTO.  I did not see that coming.

5500 kg recoverable makes sense.  They almost recovered SES-9 at 5300.  With a slightly less aggressive GTO, 5500 seems doable.

But 8300 kg is a lot.  We know that SES-9 had a 17 second re-entry, and a roughly 6 second landing, both with 3 engines.  So an expendable could have perhaps 8 more seconds of 9-engine booster burn.  We know that near cutoff the booster is accelerating at 4-5 Gs, so that's maybe 350 m/s more for expendable.

But with a 121t starting mass (after fairing jettison), a 5t empty mass, and a 348 ISP, going from 5.5t to 8.3t means 800 m/s less.  That's too much to reach GTO with only 350 m/s more from the first stage.  A lower empy mass for the second stage only makes this discrepancy worse.

So I'm guessing it's the trajectory.  It must be that ANY recoverable trajectory, not just RLTS, involves more initial lofting, perhaps to get the first stage out out of the atmosphere so it can turn around.  If SpaceX is not recovering, the first stage goes more horizontal and builds up more orbital velocity, and stages at a lower altitude.  This reduces the gravity and pitch losses.

Based on updated numbers at SX website, Merlin engines are again getting more powerful - so less gravity losses during whole flight should help somewhat (and maybe other improvements).

[woods170]

Gentlemen, somebody can comment on new figures on the website SpaceX?
http://www.spacex.com/about/capabilities

Wow - 8300 kg to GTO.  I did not see that coming.

5500 kg recoverable makes sense.  They almost recovered SES-9 at 5300.  With a slightly less aggressive GTO, 5500 seems doable.

But 8300 kg is a lot.  We know that SES-9 had a 17 second re-entry, and a roughly 6 second landing, both with 3 engines.  So an expendable could have perhaps 8 more seconds of 9-engine booster burn.  We know that near cutoff the booster is accelerating at 4-5 Gs, so that's maybe 350 m/s more for expendable.

But with a 121t starting mass (after fairing jettison), a 5t empty mass, and a 348 ISP, going from 5.5t to 8.3t means 800 m/s less.  That's too much to reach GTO with only 350 m/s more from the first stage.  A lower empy mass for the second stage only makes this discrepancy worse.

So I'm guessing it's the trajectory.  It must be that ANY recoverable trajectory, not just RLTS, involves more initial lofting, perhaps to get the first stage out out of the atmosphere so it can turn around.  If SpaceX is not recovering, the first stage goes more horizontal and builds up more orbital velocity, and stages at a lower altitude.  This reduces the gravity and pitch losses.

Based on updated numbers at SX website, Merlin engines are again getting more powerful - so less gravity losses during whole flight should help somewhat (and maybe other improvements).

It has been suspected for a long time that SpaceX sandbagged the initial performance numbers of Merlin 1D and Falcon 9. The new performance figures seem to confirm this: now that SpaceX has a good number of missions of both the 1.1 and the FT under it's belt they likely have more confidence in the final performance figures.