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The crossfeed system is not yet realized for Falcon Heavy. Instead, the central booster will throttle down after liftoff and resume "full thrust after side boosters separate".

Why would one do that instead of keeping it at 100%? (Except of course around the point of maximum aerodynamic pressure.)

Isn't it like "the sooner the thrust, the better"?

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    $\begingroup$ That way the center core will be out of fuel at the same time as the side boosters. You then get a two stage rocket instead of 2.5. And too much thrust means higher aerodynamic losses (and probably higher/sooner max q?). $\endgroup$ – jkavalik Feb 5 '18 at 7:39
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    $\begingroup$ Going too fast too soon has its disadvantages, especially due to drag. Drag doesn't increase linearly with speed so by waiting till the atmosphere is thinner, fuel becomes more efficient per mass up to a point. $\endgroup$ – Dragongeek Feb 5 '18 at 9:40
  • $\begingroup$ @jkavalik They do have a 2.5 stage rocket. Note that to avoid that they would have to throttle back the side boosters! The thing is the side boosters went back to the cape and thus required a boostback burn. The core went for the droneship, no boostback burn. Thus it could burn longer. $\endgroup$ – Loren Pechtel Feb 7 '18 at 5:52
  • $\begingroup$ @LorenPechtel according to some graphics and what I think I saw on the webcast there was a partial boostback of the center core. Still true that less propellant is needed there. $\endgroup$ – jkavalik Feb 7 '18 at 6:02
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Because you wind up getting more total ΔV out of the deal, which is what matters. By reserving some propellant in the center core when the outer cores stage, you suddenly get a lot more ΔV out of that remaining propellant because you're not pushing as much mass uphill.

The Falcon upper stage is relatively wimpy when it comes to ΔV (it's why an Atlas can put a heavier payload into GTO/GEO than F9, even though the situation is reversed for LEO), so you want to maximize the ΔV you get out of the booster.

Edit

Tsiolkovsky ideal rocket equation1:

$$\Delta V = \ln{\left(\frac{Mass_{initial}}{Mass_{final}}\right)} I_{sp} g$$

To compute the total ΔV for a multi-stage rocket, compute the ΔV for each stage separately and sum the results.

Per Spaceflight 101, F9 dry mass is ~25,600 kg and prop mass is ~395,700 kg, and the M1D specific impulse at sea level is ~282 s (those numbers are out of date with respect to the latest Falcon cores and don't account for additional dry mass of the FH center core, but should be good enough to illustrate the point). We'll also use their numbers for the upper stage - assuming a 2000 kg payload, that should come out to 98,570 kg. And the ideal rocket equation doesn't take losses from aero or gravity drag into account, so these numbers won't reflect actual performance, but again, this is mostly for illustration purposes.

So we have two scenarios. In the first scenario, we burn all three first stage cores to depletion and drop them all at the same time:

Burn #      Start Mass (kg)   End Mass (kg)    Delta V (m/s)
------      ---------         --------         -------
     1        1362470           175370            5666

In the second scenario, we burn the center core at 80%, such that when the outer cores are depleted, there's still 20% propellant left in the center core. We drop the outer cores and keep burning the remaining propellant in the center core:

Burn #      Start Mass (kg)   End Mass (kg)    Delta V (m/s)
------      ---------         --------         -------
     1        1362470           254510            4637
     2         203310           124170            1363

Giving us a total ΔV of (very) roughly 6000 m/s. So by throttling back the center core by 20%, we gain an additional 340 or so m/s ΔV.


  1. Does not take aerodynamic drag or gravity losses into account

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  • $\begingroup$ This still seems counter-intuitive because the unused propellant in the center core is "pushed uphill". How do I calculate/estimate ΔV? $\endgroup$ – Everyday Astronaut Feb 6 '18 at 20:41
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    $\begingroup$ Most of it is mass differentials. A single engine with a lot of fuel in open space is far more efficient than lots of big heavy engines with the same fuel. The factors in the equations are mass, thrust and the intended dV, your dV is static, you need X dV to get where you're going. The mass/Thrust ratio bears some resemblance to the old Cube-Squared law of biology, if you have three times the mass, you need much more than three times the thrust to push it at the same impulse. Essentially, an ideal spacecraft is a huge fuel tank and a tiny engine with infinite time to get where it wants to go $\endgroup$ – Ruadhan2300 Feb 7 '18 at 14:47
  • $\begingroup$ @derwodamaso: see my edit. Tried to use realistic numbers. $\endgroup$ – John Bode Feb 7 '18 at 17:24
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The idea behind cross feed is to allow for a staging like event.

The center core runs off fuel from the side boosters, so when they are empty and expended, the center core is still full of fuel to be the second stage. The press kit was released and it looks like this only buys the center core stage 35 seconds of extra flight time. That surprised me, I expected more.

F-H Flight timeline

Without cross feed, you get something similar by throttling down the center core so it can run after stage separation for some period of time. That is, you can drop the side cores, and still run the center core, to get the benefit of full thrust for longer without the extra mass of the side core. (Which is a very poor definition of the value of staging).

Put another way, it turns it into an additional stage instead of just a more power first stage. Albeit, only for 35 extra seconds.

SpaceX gave up on cross feed, most assume, because it was way harder than they expected, and as the performance of Falcon 9 grew, no customer needed it.

The original Falcon 9 1.0 with a Merlin 1C had about 10,000kg payload to LEO. The updated Falcon 9 1.1 with Merlin 1D has about 13,000kg payload to LEO. The currently flying Block 3 Falcon 9 1.2 Full Thrust has a payload of 23,000kg to LEO. (I used all the possible names in that one, see what I did?). The soon to be flying Block 5 (in theory) is expected to have a further 10% boost in performance.

The first Falcon Heavy is using two Block 3's that were previously flown as the side boosters and a new center booster.

Future Falcon Heavy missions are expected to use Block 5 cores, with all the extra performance.

Thus they were able to recover virtually all the performance cross feed offered, just by the growth in performance as the Falcon 9 design matured. Remember Falcon Heavy was announced in 2011 and these have been very evolutionary years at SpaceX for the Falcon 9 booster.

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    $\begingroup$ The falcon heavy has no cross-feed capability. This was originally planned but it was found to be too difficult to do and is not included in the current design. $\endgroup$ – Dragongeek Feb 5 '18 at 9:37
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    $\begingroup$ @Dragongeek Updated to clarify. $\endgroup$ – geoffc Feb 5 '18 at 12:58
  • $\begingroup$ @JCRM Better now? $\endgroup$ – geoffc Feb 5 '18 at 15:56
  • $\begingroup$ Much better, I can see why someone might still choose not to up-vote it but I don't understand the downvotes. $\endgroup$ – JCRM Feb 5 '18 at 16:11
  • $\begingroup$ @jcrm I assume it is personal, and deeply formed. You get used to it. Assume the worst and you will be pleasantly surprised more often. $\endgroup$ – geoffc Feb 5 '18 at 16:12
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"The more thrust, the better" isn't true in all cases. The two main reasons are g-loading and atmospheric drag.

During the first stage burn, a single-stick Falcon 9 will have the thrust of one first stage accelerating the weight of the first stage, second stage, and payload. By throttling down slightly towards the end of the first-stage run, the maximum acceleration (and thus the strain on the payload and payload adapter) is capped at (I think) 6g.

With the three-core Falcon Heavy, the thrust is tripled but the weight is less-than-tripled -- there's still only one second stage and one payload. All other things being equal, this would increase the acceleration (particularly toward the end of the burn, when the first stage and boosters will be nearly empty and thus quite light).

Instead, by reducing the thrust and fuel consumption rate of the core stage, it acts as a "ballast", limiting the maximum acceleration of the stack so the payload isn't crushed.

Atmospheric drag is the other consideration; going too fast in dense air (i.e. at low altitude) wastes energy. For a high thrust rocket like FH, it can be more efficient to save a little oomph for later.

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