# Why can Falcon Heavy bring 4.2 times as much mass to Mars than F9, but only 2.7 times as much to LEO?

In Wikipedia's article SpaceX Falcon-Heavy the section titled Capabilities has a table comparing maximum payload masses to Falcon 9 for different payload destination. The current numbers there are shown below.

There is probably some fundamental, easy to grasp reason why Heavy can bring 4.2 times as much mass to Mars than F9, but only 3.2 times as much to GTO and only 2.7 times as much to LEO, but I don't know what that would be.

Payload            Falcon Heavy   Falcon 9    Ratio
LEO (28,5°)          63,800 kg   22,800 kg    2.68
GTO (27°)            26,700 kg    8,300 kg    3.22
GTO (27°) Reusable    8,000 kg    5,500 kg    1.45  -  does not apply here
Mars                 16,800 kg    4,020 kg    4.18
Pluto                 3,500 kg      - -


below: rough plot of ratio versus "altitude" of the three (presumably non-reusable) data points, just to show there is a trend.

below: Artist conception of a Falcon Heavy, from here.

• Mostly Falcon needs a better upper stage for planetary missions. Which implies the opposite of what you are suggesting but I am guessing they might imply a stretched upper stage for Mars missions, thus more propellant for more delta-V. Atlas V kicks Falcon's butt on planetary mission performance since RL-10's 460+ ISP is way better than Mvac's 311. ANd this is where ISP really matters. – geoffc Jul 28 '17 at 15:57
• @geoffc I'm not suggesting anything beyond arithmetic division. – uhoh Jul 28 '17 at 16:19
• I am not sure there is enough detailed technical information available for the public at this stage to answer this. I have skimmed through their pages and a lot of things are vague at best. I dont even get a proper number for the dry mass of a F9 first stage, not even to speak of the modified stage they are using as core in the F9H. My guess would be in reusability. It might just be that the nubers for F9H to mars are in fully expendable mode, so they need not to save fuel for the return. – Polygnome Jul 28 '17 at 16:37
• @Polygnome The numbers on the Capabilities page are for fully expendable vehicles. I'm guessing that's where the difference comes from. – DylanSp Jul 28 '17 at 18:58
• It would be very difficult to model the delta-v of Falcon 9 without any statistics, it isn't even on Falcon 9's user manual, you can certainly make assumptions on the mass, but the deviation would be quite off. – Raze Jul 31 '17 at 3:01

The final stage of a rocket has to lift not just the payload but also itself. So lets look not at the payload mass alone but at the total mass lifted to the final orbit.

According to http://www.spaceflightinsider.com/hangar/falcon/ the empty mass of the second stage is 3,900 kg. Lets add that the numbers in the table.

If we add the mass of the final stage to the numbers in your table we get.

Payload + 2nd stage Falcon Heavy   Falcon 9    Ratio
LEO (28,5°)          67.700 kg   26,700 kg    2.54
GTO (27°)            30,600 kg   12,200 kg    2.50
Mars                 20,700 kg    7,920 kg    2.61


Near enough the same.

• Very nicely done! Just as I suspected; "There is probably some fundamental, easy to grasp reason..." This is much easier to understand than the "impedance matching" answer. – uhoh Feb 7 '18 at 2:53

All else being equal (e.g. propellant choice), higher-energy trajectories favor a rocket with more stages.

One thought experiment that can help you understand this is to consider two missions launched on identical rockets, the first to LEO and the second to an interplanetary trajectory. Both missions have payloads sized to "max out" the capacity of the launch vehicle. Obviously the second payload will have to be much lighter than the first, but notice that the second payload is therefore a much smaller fraction of the dry mass of the upper stage. Recall that the upper stage must end up on the same trajectory as the payload, so that second mission is less "efficient" because most of the work the upper stage does is just accelerating its own mass rather than the payload.

If you were constrained to the same overall vehicle mass, you'd be better off with a smaller second stage and adding a third stage. That way the upper stage mass will be better matched to the payload mass, so less of the work it does will be wasted. It's almost like impedance-matched power transfer.

So how does this relate to the Falcon Heavy? Essentially the addition of the extra boosters make the system into a 3-stage rocket. The center core is throttled down during first-stage flight, so it still has quite a bit of propellant remaining when the side boosters empty themselves and separate. The center core burns for a while longer (effectively 2nd-stage flight, because you've thrown away the dead mass of the empty side boosters), then it too separates and the upper stage takes over. This means that the upper stage of the Heavy is responsible for a smaller fraction of the overall energy delivered (or the velocity added) compared to the upper stage of the F9. So for the reasons described earlier, the Heavy as a vehicle is more efficient at delivering payloads to high energy trajectories than the F9.

• "...the Heavy as a vehicle is more efficient at delivering payloads to high energy trajectories than the F9." I've asked why the FH/F9 is 4.2 to mars but 2.7 to LEO, a double-ratio. So maybe a better way to explain would be to address why FH is "only" 2.7 times better than F9 to LEO - why the same gain of 4.2 over F9 is not available to low orbits. I'm better with math than paragraphs of analogies, I was hoping this would fall directly out of Tsiolkovsky's rocket equation. Thanks! – uhoh Aug 1 '17 at 6:27
• Unfortunately Tsiolkovsky's equation applies only to one stage at a time, and this question is fundamentally related to the impact of staging. But you should be able to derive a simple model via repeated application of that equation and some consideration of thrust levels and gravity loss. Made-up numbers should be sufficient to show the principle. If I get time I'll try to extend my answer to more directly address the way you put it in your comment. Briefly, the tradeoff of having more stages is lower thrust on the upper stage and therefore more gravity loss for heavy payloads. – pericynthion Aug 1 '17 at 20:38
• This answer seems to be much easier to understand, as well as numerically conclusive. – uhoh Feb 7 '18 at 2:52

Moving around once in orbit is a lot easier than getting something into orbit. The only issue with this is bringing either another stage or even just a larger stage into orbit first to allow for fuel amounts to get to mars. The extra 40 tons to LEO of the Falcon Heavy allows for it to get this extra stage/ larger stage to orbit which it can then use to get to Mars. For the Falcon 9 to get something to Mars it would also need this extra/larger stage to get to orbit however the lifting capability of only 9 Merlin engines would result in an extremely inefficient launch to orbit due to the first stage burning so much extra fuel to get the extra/larger stage to orbit. This would result in the extra/larger stage using up more of it's own fuel getting to orbit and therefore would have less net force left to push the payload to Mars.

• On the contrary, adding an upper stage to the F9 would considerably improve its performance in delivering payloads to interplanetary trajectories. – pericynthion Aug 1 '17 at 4:31