Off Topic > General Discussion
Recent Claim by Musk concerning hot 2nd stage start
bknight:
In a recent interview Musk has stated that a hot start of the second stage while still attached to the first stage will "conservatively result in 10% more payload into LEO. Is this correct?
https://twitter.com/i/spaces/1OyJAVEdkMaxb
Note this is a 49 minute interview and there were sound issues for the first 16:30 . Skip ahead, if you are listening.
Now I realize that shutting down the first stage and letting the vehicles separate prior to second stage results in the second stage decelerating until it begins to accelerated again. So hot starting will result in more payload to LEO, but 10%? SpaceX is installing an extension to the inner stage and beefing up the first stage to prevent damage to the first stage.
smartcooky:
Not sure of the engineering calculations, but it sound reasonable. The payload only comprises a relatively small percentage of the second stage mass. Here are some figures for Falcon 9, non-expended
Empty Mass:... 3900 kg
Propellant:.... 92,670 kg
Payload:....... 22,800 kg
--------
Total.... ..... 119370 kg
The payload is 19% of the total mass of the second stage at firing
Increase the mass of the payload by 10% = 25080 Kg
Empty Mass:... 3900 kg
Propellant:.... 92,670 kg
Payload:....... 25,080 kg
--------
Total.... ..... 121650 kg
The payload is now 21% of the second stage at firing
So in reality, there is only a 2% increase in mass to orbit
(provided my back-of-the-envelope math is correct)
ETA: Of course, this is very simplified. I have take no account of the reduction in overall mass as the propellant is burned, but it doesn't seem unreasonable to me that firing the second stage engine a few seconds early, and before it has a chance to start to decelerate might allow a couple of additional % points of mass to LEO.
bknight:
Well I created a velocity spreadsheet for A11 with the help of BobB a few years ago and the numbers seem more like your 2% that 10%. And remember he said conservative 10%. I posted part of the spreadsheet in CQ, and I have shut it down currently and will be back tomorrow and post it here.
smartcooky:
Fair enough, and if Musk is making exaggerated claims, well, it wouldn't be the first time, would it?
I'm just pointing out that a 10% increase in payload is a significantly less than that in overall second stage mass. Remember that the second stage goes all the way to orbit with the payload, and in the case of Falcon 9 and Falcon Heavy, carries some extra fuel for a de-orbit burn.
Also, any mass you can strip from the second stage can go to payload. For example, when Rocketlab's Electron made its first flight six years ago, it had a maximum payload to LEO of 225kg. This has gone up to 300 KG, because in the intervening six years, the lithium polymer batteries they use to drive the fuel pumps have gotten smaller and lighter while still delivering the same capacity.
In the case of Falcon 9, with a "hot start" on the second stage, the fact that it will be traveling at a higher velocity might mean it needs to carry less fuel... which equals less mass. I just had a quick look at a Starlink launch - at MECO (2m33s) the whole stack is traveling at 8184 km/h, and drops to 8057 km/h at the moment of stage separation. When SES happens, the second stage does not get back up to 8187 km/h until 2m 49s.
PS: Its worth noting that the Russians have used hot staging on their rockets since the late 1050s. India and China also use it.
bknight:
--- Quote from: smartcooky on June 26, 2023, 07:01:13 AM ---Fair enough, and if Musk is making exaggerated claims, well, it wouldn't be the first time, would it?
I'm just pointing out that a 10% increase in payload is a significantly less than that in overall second stage mass. Remember that the second stage goes all the way to orbit with the payload, and in the case of Falcon 9 and Falcon Heavy, carries some extra fuel for a de-orbit burn.
Also, any mass you can strip from the second stage can go to payload. For example, when Rocketlab's Electron made its first flight six years ago, it had a maximum payload to LEO of 225kg. This has gone up to 300 KG, because in the intervening six years, the lithium polymer batteries they use to drive the fuel pumps have gotten smaller and lighter while still delivering the same capacity.
In the case of Falcon 9, with a "hot start" on the second stage, the fact that it will be traveling at a higher velocity might mean it needs to carry less fuel... which equals less mass. I just had a quick look at a Starlink launch - at MECO (2m33s) the whole stack is traveling at 8184 km/h, and drops to 8057 km/h at the moment of stage separation. When SES happens, the second stage does not get back up to 8187 km/h until 2m 49s.
PS: Its worth noting that the Russians have used hot staging on their rockets since the late 1050s. India and China also use it.
--- End quote ---
That observation (16 sec) seems a bit slow, but your eye not mine, just saying.
Vehicle Mass Acceleration Space-fixed velocity
Time Dry Fuel Total Flow Thrust ISP Throttle Pitch g Horz. Vert. Load Horz. Vert. Total f
(s) (kg) (kg) (kg) (kg/s) (N) (s) (%) (deg) (m/s2) (m/s2) (m/s2) (g) (m/s) (m/s) (m/s) (deg)
161.63 242186 577266 819452 10716.83 27808451 304.0 100% 70.14 9.650 31.632 2.716 3.46 2339.6 673.1 2434.5 16.05
162.00 242186 575284 817470 0.00 0 0.0 0% 70.25 9.650 -0.285 -8.807 0.00 2345.4 671.9 2439.7 15.99
162.11 242186 575284 817470 0.00 0 0.0 0% 70.28 9.649 -0.284 -8.807 0.00 2345.3 671.0 2439.4 15.97
162.30 242153 575284 817470 0.00 0 0.0 0% 70.34 9.649 -0.283 -8.807 0.00 2345.3 669.3 2438.9 15.93
163.00 109139 550330 817470 0.00 0 0.0 0% 70.55 9.648 -0.268 -8.801 0.00 2345.1 663.1 2437.1 15.79
164.00 108963 550330 816857 1225.45 5104333 427.7 100% 70.84 9.646 5.639 -6.746 0.63 2347.8 655.4 2437.5 15.60
165.00 108786 549105 815631 1225.45 5104333 427.7 100% 71.14 9.644 5.662 -6.767 0.64 2353.4 648.6 2441.2 15.41
165.61 108678 548357 814884 1225.45 5104333 427.7 100% 70.82 9.643 5.658 -6.727 0.64 2356.9 644.5 2443.4 15.29
166.00 108678 547879 814406 1225.45 5104333 427.7 100% 70.61 9.642 5.656 -6.702 0.64 2359.1 641.9 2444.9 15.22
167.00 108678 546654 813181 1225.45 5104333 427.7 100% 70.08 9.640 5.649 -6.638 0.64 2364.7 635.2 2448.6 15.04
168.00 108678 545428 811955 1225.45 5104333 427.7 100% 69.55 9.638 5.641 -6.574 0.64 2370.4 628.6 2452.3 14.85
169.00 108678 544203 810730 1225.45 5104333 427.7 100% 69.03 9.636 5.632 -6.510 0.64 2376.0 622.1 2456.1 14.67
170.00 108678 542977 809504 1225.45 5104333 427.7 100% 68.50 9.634 5.623 -6.446 0.64 2381.7 615.6 2459.9 14.49
171.00 108678 541752 808279 1225.45 5104333 427.7 100% 67.97 9.632 5.613 -6.382 0.64 2387.3 609.2 2463.8 14.31
172.00 108678 540526 807053 1225.45 5104333 427.7 100% 67.44 9.631 5.603 -6.318 0.64 2392.9 602.8 2467.6 14.14
173.00 108678 539301 805828 1225.45 5104333 427.7 100% 66.91 9.629 5.592 -6.255 0.64 2398.5 596.5 2471.5 13.97
174.00 108678 538076 804602 1225.45 5104333 427.7 100% 66.38 9.627 5.580 -6.191 0.65 2404.1 590.3 2475.5 13.80
175.00 108678 536850 803377 1225.45 5104333 427.7 100% 65.86 9.625 5.568 -6.127 0.65 2409.6 584.1 2479.4 13.63
176.00 108678 535625 802152 1225.45 5104333 427.7 100% 65.33 9.624 5.555 -6.064 0.65 2415.2 578.0 2483.4 13.46
177.00 108678 534399 800926 1225.45 5104333 427.7 100% 64.80 9.622 5.541 -6.001 0.65 2420.7 572.0 2487.4 13.29
178.00 108678 533174 799701 1225.45 5104333 427.7 100% 64.27 9.620 5.527 -5.937 0.65 2426.3 566.0 2491.4 13.13
179.00 108678 531948 798475 1225.45 5104333 427.7 100% 63.74 9.618 5.512 -5.874 0.65 2431.8 560.1 2495.5 12.97
180.00 108678 530723 797250 1225.45 5104333 427.7 100% 63.21 9.617 5.497 -5.811 0.65 2437.3 554.3 2499.5 12.81
181.00 108678 529497 796024 1225.45 5104333 427.7 100% 62.68 9.615 5.481 -5.748 0.65 2442.8 548.5 2503.6 12.66
182.00 108678 528272 794799 1225.45 5104333 427.7 100% 62.16 9.614 5.465 -5.685 0.65 2448.3 542.8 2507.7 12.50
183.00 108678 527046 793573 1225.45 5104333 427.7 100% 61.63 9.612 5.448 -5.622 0.66 2453.7 537.1 2511.8 12.35
184.00 108678 525821 792348 1225.45 5104333 427.7 100% 61.10 9.610 5.430 -5.560 0.66 2459.2 531.6 2516.0 12.20
185.00 108678 524596 791123 1225.45 5104333 427.7 100% 60.57 9.609 5.412 -5.497 0.66 2464.6 526.0 2520.1 12.05
186.00 108678 523370 789897 1225.45 5104333 427.7 100% 60.60 9.607 5.425 -5.489 0.66 2470.0 520.5 2524.3 11.90
187.00 108678 522145 788672 1225.45 5104333 427.7 100% 60.63 9.606 5.437 -5.482 0.66 2475.4 515.0 2528.4 11.75
188.00 108678 520919 787446 1225.45 5104333 427.7 100% 60.66 9.604 5.450 -5.474 0.66 2480.9 509.6 2532.7 11.61
189.00 108678 519694 786221 1225.45 5104333 427.7 100% 60.69 9.603 5.462 -5.466 0.66 2486.3 504.1 2536.9 11.46
190.00 108678 518468 784995 1225.45 5104333 427.7 100% 60.73 9.601 5.475 -5.459 0.66 2491.8 498.6 2541.2 11.32
191.00 108678 517243 783770 1225.45 5104333 427.7 100% 60.76 9.600 5.487 -5.451 0.66 2497.3 493.2 2545.5 11.17
192.00 108678 516017 782544 1225.45 5104333 427.7 100% 60.79 9.598 5.500 -5.444 0.66 2502.8 487.7 2549.9 11.03
192.30 108678 515650 782177 1225.45 5104333 427.7 100% 60.80 9.598 5.504 -5.441 0.67 2504.4 486.1 2551.2 10.98
Pasting spreadsheets to forums is not good. Anyway this in A11 and the velocities are space fixed.
For reference:
161.63 OESC S1
162.3 Stage separation.
164 ESC S2.
You can see the acceleration drops from 2.76 m/s at OESC to Earth's gravity. That continues for ~ 2 sec. Then S2 ESC. In this scenario the total velocity meets/exceeds first stage total velocity in ~3.5 sec. 161.63-165. Note most of the acceleration is going into horizontal velocity also Earth's gravity effect is diminishing. I realize that the trajectories will be different so a one to one comparison is not valid.
Note that the speadsheet averages every one second(or one row) but it is a close approximation. BobB's sheet and mine are very similar, he helped a lot and I give him credit for sticking with me during the development.
Note also the total velocity never decreases, just slows from the vertical gravity effect, horizontal was only slowed by the atmosphere.
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