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If you made a '2nd stage to orbit and return' vehicle capable of sitting atop the reusable Falcon Heavy 1st stage, how heavy could it be, and to what height and speed could the 1st stage push it in a trajectory directly upwards1?

Elon Musk is quoted in the article linked above:

Falcon 9 will do satellites up to roughly 3.5 tonnes, with full reusability of the boost stage, and Falcon Heavy will do satellites up to 7 tonnes with full reusability of the all three boost stages …

That suggests the mass it can push in fully reusable mode is '7 tonnes + the mass of the 2nd stage'. Unfortunately I can't locate a mass for the 2nd stage! As to the figures for altitude & velocity at time of separation, I'm not having any luck.

  1. Originally I was after a trajectory that would give the greatest time between separating from the first stage and the payload hitting a high before falling back to the atmosphere (with its associated drag) in order to allow the '2nd stage' enough time to reach orbital velocity (presuming it has a relatively low acceleration rate). But I'm thinking those figures are simply not available. So.. I'd happily accept the numbers for an actual mission profile instead.
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    $\begingroup$ Velocity at separation is approximately 1.8-2.0km/s. $\endgroup$
    – marked-down
    Apr 21, 2015 at 9:22
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    $\begingroup$ That 7 tonnes is delivered to a GTO orbit, which is much higher and harder than LEO. To LEO they estimate in the 50 metric tonne range, which is about 100,000 lbs. $\endgroup$
    – geoffc
    Apr 21, 2015 at 11:45
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    $\begingroup$ www.spacelaunchreport.com estimates the second stage to be 6000kg mass + 93000kg fuel. $\endgroup$
    – user8406
    Apr 21, 2015 at 12:31
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    $\begingroup$ @AndrewThompson Yep. F-H is a kick ass launcher design, now actually launch it SpaceX!!! Come on, launch in 2015, just for me, please. Now if the Merlin 1D-V based upper stage was more efficient (ISP wise) then payload to higher orbits would be better. Thrust is king in the first stage, ISP is king everywhere else. $\endgroup$
    – geoffc
    Apr 22, 2015 at 0:50
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    $\begingroup$ "...a trajectory directly upwards?" Are you really asking for a straight-up vertical flight, i.e. non-orbital, and ending in a straight-down high speed reentry? $\endgroup$
    – Russell Borogove
    Apr 27, 2015 at 3:54

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If I understand your question correctly, what you actually want to know is, if you replaced the FH disposable second stage and payload with a combined get-into-low-orbit-and-return vehicle, what could the size of that vehicle be.

So that's just FH's second stage mass (~101 tons) plus LEO payload mass (~53 tons), for a total of ~154 tons. Quite a bit more than an STS orbiter!

Plugging Spaceflight101's numbers for the Falcon Heavy into the rocket equation, and assuming it's using the planned fuel crossfeed system, the boosters provide 2387m/s ∆v, the core 3647m/s, and the second stage 3364m/s, for a total of 9398m/s. Orbital speed is about 7.7km/s, so subtracting out the second stage leaves you with 4.3km/s at core burnout. I'm not sure what sort of trajectory FH would normally fly, but you'd probably be above 175km at that point, effectively in vacuum for purposes of engine efficiency.

(Lose about 1.1km/s (or cut the payload by 20 tons) if they wind up not doing fuel crossfeed.)

So for your orbit-and-return vehicle, you've got a mass budget of 154 tons, and you probably want 4000m/s of ∆v for orbit and deorbit -- more if you're thinking about a powered landing back on Earth. Put a NTR with an ISP of 800 seconds on it and you'd need about 40% propellant fraction, 62 tons of LH2. It'd be bulky as hell!

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    $\begingroup$ Much less than an STS orbiter + fueled external tank. $\endgroup$
    – pericynthion
    Apr 27, 2015 at 18:37
  • $\begingroup$ How accurately do you want to know it, and why? $\endgroup$
    – Russell Borogove
    Apr 28, 2015 at 0:43
  • $\begingroup$ 2km/s is the number for F9R (single core, with some fuel held back for landing); I think it's got to be substantially higher for Falcon Heavy with fuel crossfeed, because at the point of booster separation, it's a fully fueled F9R starting three minutes into the air (it's more like a 3-stage rocket than a 2-stage rocket). My wild-ass guess (not within 10%, and coming with no warranty) is 5km/s at 175km. $\endgroup$
    – Russell Borogove
    Apr 28, 2015 at 0:58
  • $\begingroup$ Note also that if your nuclear-powered upper stage reusable spacecraft is much lighter than 154 tons, you'll be going faster and higher at 1st stage cutoff than if you were at the limit. NERVA was supposed to be 330kN thrust, about half a Merlin 1D; Timberwind 75 would do the trick nicely (and is plenty powerful even in atmosphere). $\endgroup$
    – Russell Borogove
    Apr 28, 2015 at 1:15
  • $\begingroup$ Worked out the numbers a little more carefully for you. $\endgroup$
    – Russell Borogove
    Apr 28, 2015 at 22:19

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