Falcon Heavy Cross-Feed

[Robotbeat]

3rd stage mean Isp is WAY off. Much higher than 311s for the Vacuum-optimized Merlin.

[meekGee]

I have a question for the experts.

If the side core tanks are somewhat (10%?) taller than the center core tanks, the pressure at their bottoms will be higher.  A cross-connect will transfer propellant from them into the main tank, keeping it full - until the levels match.

This will allow the center core engines to work off of the side core tanks for the beginning of the flight, when you need all engines.

Once the level equalize, you can shut down (throttle down?) the center engines (3?  maybe 9?) and only relight them later after side core separation.

The nice thing about this is that you don't need to feed engines from other cores - just do tank-to-tank transfer.

Is this being done on some rockets?  if not, why not?

[MP99]

It's not that complicated. Just treat the F9H as a three stage rocket and using the basic rocket equation.

1st Stage Starting Mass = Falcon Heavy published Launch Mass + 53 tons
1st Stage Ending Mass = Launch Mass - Fuel of 2 x Side boosters
1st Stage Mean Isp = 293 secs -- (275 + 311) / 2
1st Stage Starting Velocity = 0

This "combined" stage also consumes some of the core prop, so subtract this also from the ending mass. This does mean the "combined" stage / high thrust phase lasts longer.

This means "2nd stage" also starts with less prop.

2nd Stage Starting Mass = Falcon 9 1.1 published Mass + 53 tons

Also, would F9 v1.1's published mass include it's payload (about 40t difference)?

cheers, Martin

[modemeagle]

It's not that complicated. Just treat the F9H as a three stage rocket and using the basic rocket equation.

1st Stage Starting Mass = Falcon Heavy published Launch Mass + 53 tons
1st Stage Ending Mass = Launch Mass - Fuel of 2 x Side boosters
1st Stage Mean Isp = 293 secs -- (275 + 311) / 2
1st Stage Starting Velocity = 0

This "combined" stage also consumes some of the core prop, so subtract this also from the ending mass. This does mean the "combined" stage / high thrust phase lasts longer.

This means "2nd stage" also starts with less prop.

2nd Stage Starting Mass = Falcon 9 1.1 published Mass + 53 tons

Also, would F9 v1.1's published mass include it's payload (about 40t difference)?

cheers, Martin

I questioned this once and was quickly corrected that the published lift off mass includes max LEO payload.

[dwightlooi]

I have a question for the experts.

If the side core tanks are somewhat (10%?) taller than the center core tanks, the pressure at their bottoms will be higher.  A cross-connect will transfer propellant from them into the main tank, keeping it full - until the levels match.

This will allow the center core engines to work off of the side core tanks for the beginning of the flight, when you need all engines.

Once the level equalize, you can shut down (throttle down?) the center engines (3?  maybe 9?) and only relight them later after side core separation.

The nice thing about this is that you don't need to feed engines from other cores - just do tank-to-tank transfer.

Is this being done on some rockets?  if not, why not?

That doesn't really work because that 10% taller tankage shared between will only amount to 6~7% the burn time of the side boosters. Basically, you'll have crossfeed only for 10~12 seconds. That isn't worth much, and certainly won't get you from 36 metric tons for a non-crossfed F9H to the 53 metric tons advertized.

[vigleik]

I used your numbers and the single stage rocket equation, 3 times, and got these numbers. Delta V at BECO = 2702.326619, additional Delta V at MECO = 3788.807724 and additional Delta V at S-2 Burn-out = 2774.079887 for a total Delta V of the 53 tonne payload and S-2 dry of 9265.21423. If you'd like to do a check of those numbers, feel free to tell me your findings.

The problem though, is still in this application of the rocket equation. Wikipedia states without equivocation that the correct formulation of the rocket equation with cross-feed is Delta V = Isp * g ln(3MR^2/MR+2). I asked before if anyone could derive this formulation, so far with no takers. I've Googled it and found 2 derivations, neither of which I could follow, but with results that are clearly not the same as the single stage rocket equation.

The point is that the Triamese rocket equation results in much higher Delta V values than results from using the single stage rocket equation. This is the case even though with the Triamese rocket, there are only two stages, with the second stage being correctly treated with the single stage rocket equation.

Using your numbers and the Triamese rocket equation gives Stage 2 plus payload burn-out velocity of 12471.88613 m/s. This discrepency between the two approaches crys for resolution and I am not satisfied by saying that Wikipedia is known to have errors.

The triamese rocket equation from wikipedia only works with zero payload. If M is the wet mass and m is the dry mass of each core and you treat it as a two stage rocket you get a mass fraction of 3M/(M+2m) for the first stage and M/m for the second stage. From that you can derive the triamese rocket equation by adding logs.

Since the payload is not zero, you have to treat it as a three stage system. There's really no way around it.

[aero]

Hey all you experts, why do you think the FH has a second stage? Run your numbers without the second stage. Looks to me like the boosted core stage can reach orbit by itself.

[modemeagle]

Hey all you experts, why do you think the FH has a second stage? Run your numbers without the second stage. Looks to me like the boosted core stage can reach orbit by itself.

My simulation get 13.125 tonnes to orbit not using a 2nd stage with 7.15% residual fuel in SI.  Does not make sense to spend 3 cores for the same payload of F9V1.1.

[aero]

Hey all you experts, why do you think the FH has a second stage? Run your numbers without the second stage. Looks to me like the boosted core stage can reach orbit by itself.

My simulation get 13.125 tonnes to orbit not using a 2nd stage with 7.15% residual fuel in SI.  Does not make sense to spend 3 cores for the same payload of F9V1.1.

The way I'm doing it, using your numbers, I get Delta V at MECO of 8.847 km/s with 53 tonne payload. That may not be enough velocity, but it is arguable.

All I did was zero out the wet mass of the second stage in the calculations I posted before using the normal version of the rocket equation.

[modemeagle]

Hey all you experts, why do you think the FH has a second stage? Run your numbers without the second stage. Looks to me like the boosted core stage can reach orbit by itself.

My simulation get 13.125 tonnes to orbit not using a 2nd stage with 7.15% residual fuel in SI.  Does not make sense to spend 3 cores for the same payload of F9V1.1.

The way I'm doing it, using your numbers, I get Delta V at MECO of 8.847 km/s with 53 tonne payload. That may not be enough velocity, but it is arguable.

All I did was zero out the wet mass of the second stage in the calculations I posted before using the normal version of the rocket equation.

You could probably get close to 30 tonnes (using the calculation spreadsheet I posted earlier), but the guidance system better be very good.  Mine is not very responsive to accurate insertion at very high acceleration (between 3.5 and 6 g)

[aero]

I used your numbers and the single stage rocket equation, 3 times, and got these numbers. Delta V at BECO = 2702.326619, additional Delta V at MECO = 3788.807724 and additional Delta V at S-2 Burn-out = 2774.079887 for a total Delta V of the 53 tonne payload and S-2 dry of 9265.21423. If you'd like to do a check of those numbers, feel free to tell me your findings.

The problem though, is still in this application of the rocket equation. Wikipedia states without equivocation that the correct formulation of the rocket equation with cross-feed is Delta V = Isp * g ln(3MR^2/MR+2). I asked before if anyone could derive this formulation, so far with no takers. I've Googled it and found 2 derivations, neither of which I could follow, but with results that are clearly not the same as the single stage rocket equation.

The point is that the Triamese rocket equation results in much higher Delta V values than results from using the single stage rocket equation. This is the case even though with the Triamese rocket, there are only two stages, with the second stage being correctly treated with the single stage rocket equation.

Using your numbers and the Triamese rocket equation gives Stage 2 plus payload burn-out velocity of 12471.88613 m/s. This discrepency between the two approaches crys for resolution and I am not satisfied by saying that Wikipedia is known to have errors.

The triamese rocket equation from wikipedia only works with zero payload. If M is the wet mass and m is the dry mass of each core and you treat it as a two stage rocket you get a mass fraction of 3M/(M+2m) for the first stage and M/m for the second stage. From that you can derive the triamese rocket equation by adding logs.

Since the payload is not zero, you have to treat it as a three stage system. There's really no way around it.

OK, that was simple enough. Thanks. Note that in the Wikipedia equation, there is a missing "(" in the denominator. The correction gives

Delta V = Ve * ln ( 3MR^2/(MR + 2))

As for lack of payload, you're right, this equation doesn't have the payload term. I'll look into it farther. I have discovered other forms of the rocket equation so maybe I can figure something out. Its good to realize that this equation is just a re-casting of the original for a specific purpose.

[Jason1701]

Hey all you experts, why do you think the FH has a second stage? Run your numbers without the second stage. Looks to me like the boosted core stage can reach orbit by itself.

It would burn out 5 minutes into flight and something else would have to provide circularization.

[aero]

Hey all you experts, why do you think the FH has a second stage? Run your numbers without the second stage. Looks to me like the boosted core stage can reach orbit by itself.

It would burn out 5 minutes into flight and something else would have to provide circularization.

Right, and that's true no matter how much excess delta V the three boosters generate. What does it take to circularize 53 tonnes of payload? A full second stage or something less? Maybe a restart of one of the core engines?

[meekGee]

I have a question for the experts.

If the side core tanks are somewhat (10%?) taller than the center core tanks, the pressure at their bottoms will be higher.  A cross-connect will transfer propellant from them into the main tank, keeping it full - until the levels match.

This will allow the center core engines to work off of the side core tanks for the beginning of the flight, when you need all engines.

Once the level equalize, you can shut down (throttle down?) the center engines (3?  maybe 9?) and only relight them later after side core separation.

The nice thing about this is that you don't need to feed engines from other cores - just do tank-to-tank transfer.

Is this being done on some rockets?  if not, why not?

That doesn't really work because that 10% taller tankage shared between will only amount to 6~7% the burn time of the side boosters. Basically, you'll have crossfeed only for 10~12 seconds. That isn't worth much, and certainly won't get you from 36 metric tons for a non-crossfed F9H to the 53 metric tons advertized.

Some of this can be solved.  Extend the outer tanks while shortening the center core.  Same total propellant, same total thrust, but now maybe 40% difference in height.  So now you have free propellant transfer to the center core until about 25% of your propellant is depleted, at which point you can shut down the center core.

Now you're flying on two side cores, and not depleting the center core.  Finally, you drop the side cores, relight the center core, and finish the first stage burn.

The downside of this scheme, aside from the extra ignition step, is that you sacrifice thrust, and so IIUC will suffer more gravity losses.

The upside is that you made the x-feed simpler.

It could be that this is just not a good enough trade and so was never used.

[aero]

How did they do the cross feed on the space shuttle? H2 from the external tank to the engines was like cross feed.

The main problem IMO is proving reliability, but triply redundant cross feed pipes seems foolish. If one fuel or oxidizer pipe breaks, it's LOM, no matter how many good pipes you have. Design it to make use of the existing turbopumps with highly reliable valves. Would turning a valve from one source of fuel to the other cause any engine transient problems?

[dwightlooi]

Some of this can be solved.  Extend the outer tanks while shortening the center core.  Same total propellant, same total thrust, but now maybe 40% difference in height.  So now you have free propellant transfer to the center core until about 25% of your propellant is depleted, at which point you can shut down the center core.

Now you're flying on two side cores, and not depleting the center core.  Finally, you drop the side cores, relight the center core, and finish the first stage burn.

The downside of this scheme, aside from the extra ignition step, is that you sacrifice thrust, and so IIUC will suffer more gravity losses.

The upside is that you made the x-feed simpler.

It could be that this is just not a good enough trade and so was never used.

If the tanks are simply connected with NO VALVING you won't be able to shut down the center engines and preserve the center booster fuel supply -- because they are all connected!

If you have valving, then it'll be better to simply switch the center engines' fuel supply between the center and side tanks.

[Jorge]

How did they do the cross feed on the space shuttle? H2...

and O2

... from the external tank to the engines was like cross feed.

Critical distinction: on the shuttle, MECO was prior to ET sep, so ET sep was not performed under acceleration, nor did they have to restart engines after ET sep.

[Jim]

http://forum.nasaspaceflight.com/index.php?topic=28424.msg876160#msg876160

[meekGee]

If the tanks are simply connected with NO VALVING you won't be able to shut down the center engines and preserve the center booster fuel supply -- because they are all connected!

If you have valving, then it'll be better to simply switch the center engines' fuel supply between the center and side tanks.

Yes I was not implying no valving...  Was trying to separate the x-feed valving from the engine block, since the x-connect can be higher.  But I think at the end the complexity savings are not that great, so nevermind.

[aero]

If the tanks are simply connected with NO VALVING you won't be able to shut down the center engines and preserve the center booster fuel supply -- because they are all connected!

If you have valving, then it'll be better to simply switch the center engines' fuel supply between the center and side tanks.

Yes I was not implying no valving...  Was trying to separate the x-feed valving from the engine block, since the x-connect can be higher.  But I think at the end the complexity savings are not that great, so nevermind.

A point. Cross feed, tank to tank requires two pipes and two valves. Cross feed tank to engine requires a number (nine?) pipes and valves. There is a mass and complexity trade in there somewhere, not to mention space for pipe runs.