Ballpark comparison of a hypothetical Falcon 'Quad' Heavy with cross feeds

Question

This engineering question got me wondering. If cross feed technology were sufficiently developed, and stresses could be managed (these are big if's, and there are more I'm sure), how would these various configurations roughly compare?

Are there numbers out there, or could someone ballpark them, or tell me a simple way to ballpark the missing values?

The first two are copied from Wikipedia's Falcon Heavy. They are tons to LEO. They also agree with the numbers in this Reddit which is probably not independent, but that table also gives the third number as well.

F9 FT:      22.8
FH:         54.4
FH w/cf:    64.5 
FQH:         ?
FQH w/cf:    ?

In my very unofficial acronyms, FQH = 'Falcon Quad Heavy' - four F9-like boosters, and w/cf = 'with cross feed'.

Cross feed for FQH might have boosters 1 and 3 feeding into 2 and 4, and dropping off first, while boosters 2 and 4 are also simultaneously feeding the core. It's a mess of engineering - I'm not proposing it as a real solution - it's more of a best possible (or best imaginable) upper limit.

edit: I'm starting to rethink this question; The potential benefit of the "FQH" might be better realized by optimizing throttling and even staggering engine starts. In other words, maybe this is more difficult to even "ballpark" than I first realized.

Answer 1

Do you know KSP? It simulates unrealistic perfect crossfeed capability which allows for Asparagus staging - a very effective technique in the simulation (look at some videos, I remember one showing a rocked with stage separation ocurring each 3 seconds or such all the way to orbit).

The problem with it is that fueling of 1 F9 booster takes roughly 30 minutes and using that fuel through engines only a bit more than 150s (based on MECO times of GTO launches where the remaining fuel was minimal). For the crossfeed to work optimaly in quad or more side boosters configuration, you need to "refuel" the "inner" boosters with a flow roughly 4 times bigger than during fueling (for quad, n-fold more for each additional "layer" of boosters). You soon find out that the pipes get quite wide and the pumps very heavy.

But to the question - I don't have exact numbers, but my understanding is that without crossfeeed you are looking at a problem with quickly diminishing returns. You either have too much thrust and lose to drag (or lose the vehicle), or you throttle down (or turn off) the "inner" engines and lose to gravity:

• if you just lower the thrust of all or some engines, you will get almost drained fuel tanks after separation.
• if you disable some engines and start them later to preserve fuel in "inner" boosters, you turned the thing into normal 3-(or-more)-stages rocket, just with small stages on the side instead of bigger one at the bottom.

With super-crossfeed you can model the entire situation a bit simpler:

• FH w/cf turns to a fully fuelled F9 after side booster separation but with all the height and velocity already imparted by the boosters. You are effectively air launching F9 (but with the advantage of not needing to change velocity from horizontal to vertical). To get the numbers you need to compute the delta-v of two cores of propelant with thrust of 3 cores (but it will have to throttle down for Max-Q etc.) and payload of full F9. You can then add the delta-v of "normal" F9 to get the ability of entire stack.
• FQH w/cf - analogically, you are air-launching FH, you just now have fuel of 2 boosters to feed 5 sets of engines (= 45 Merlins) so the staging will happen sooner.

My "launch-math" is not good enough to provide any reasonable estimates for actual numbers unfortunatelly. I just know from my KSP tests that the difference between no crossfeed and full crossfeed is really substantial - where without crossfeed the rocket did not even get out off the atmosphere, the crossfeed variant was able to get straight up to escape velocity.