Falcon Heavy Cross-Feed

[go4mars]

What boost-back phase?

The boost-back phase after separation of course! 

Yes I realize that there will be a few years of practice launches using expendible versions. I doubt they are designing with obviously non-reusable solutions for important components on the first few iterations though.   But you would know better than I. 


What boost-back phase? 
For example:

These quotes, in the context of this article, makes it pretty clear imo.
http://www.popularmechanics.com/science/space/rockets/elon-musk-on-spacexs-reusable-rocket-plans-6653023

"Falcon Heavy is particularly amenable to reuse of the first stage—the two outer cores in particular, because they separate at a much lower velocity than the center one, being dropped off early in the flight."  -Elon


"Multiple flights per day for first stage and side boosters," -Elon

[Liryc]

Hi everyone,

not sure if that's the right place to ask.. but I'll give it a try.

I'm trying to figure out the mechanical system used for Falcon's quick-disconnect ssystem...
In this page we can se the cryogenic plug disconnects when the launcher lifts-off...

But when I look at other cryogenic feeding lines (like European or some in the US (Delta IV Heavy)) they open shortly before lauch.
This seems to be quite constraintful as you have to get back up there to reconnect the line if launch is aborted after separation..

Any idea on how it's beeing made ?
Why don't we do it on all our launchers ?

Thanks !
Cyril

[Jim]

But when I look at other cryogenic feeding lines (like European or some in the US (Delta IV Heavy)) they open shortly before lauch.

No, Atlas and Delta disconnect fill and drain lines at liftoff and not before.

Atlas only disconnects a He purge line before liftoff

[Liryc]

Ok, thanks for the correction.
I'll try to find some info on it.

[fatjohn1408]

Cool thread, learned that alot I took for granted about this subject was horribly wrong.

Most interesting post in the thread is this one, why aren't there more replies? Is this not feasible and superior to all other configurations proposed?

I have my own theory of how cross-feed works, made from the little info we have.

Spacex's website says that FH's mass and thrust at lift off is 1,400 mt and 3,800,000 lbf (1,724 mtf) (22 Merlin-1D at full thrust is the absolute minimum to elevate 1,400 mt).

It also says: "Propellant cross-feeding leaves the center core still carrying the majority of its propellant after the side boosters separate".

Can't find where I saw it but I remember to have read about a 90% propellant remaining in the core tanks right after boosters cut off.

In the video looks like all 27 engines are started at the same time, and we know that a Merlin-1D can only be throttled down to a 70% of its nominal thrust.

Easy to calculate that even with 3 engines at 70% more than a 10% of the core fuel would be gone when the booster tanks reach the empty mark.

So, I think it could be like this: Feed valves are set as Jim depicted. Before lift-off the core tanks valves are closed and all 9 core engines are fed from both booster tanks.

This mode lasts until the booster tanks are near 10%, when the core tanks valves are switch to open, and the valves that communicate core turbopumps and booster tanks are closed.

After that core and boosters keep burning exclusively its own fuel until the booster tanks are depleted, triggering separation.

P.E. And no, three engines are not enough to keep FH in flight after separation.

[Idiomatic]

Explosive bolts could possibly be skipped simply because SpaceX has a history of doing so. There are a number of events where normally explosive bolts would be used and SpaceX has chosen not to. (I still think they will go explosive though)

[dwightlooi]

I really don't know where the only whole concept of side boosters feeding 3 additional engines each came from. I wasn't able to find any SpaceX references to it formally or informally. The only thing that seems to pop up is Musk saying that because they have a large number of small engines, it is possible for an engine to be individually connected to and draw propellants from adjacent engine(s). And, that this makes crossfeeding easier to accomplish -- presumably because same interconnects and small valves are more easier to deal wit that huge pipes and gigantic valves.

The math that adds up to 53 metric tons to 7.8km/s with an Isp of ~310 secs dictates that the FH will probably run all its engines from the side boosters until moments before separation. The only reason the center core is not 100% full at separation is probably from the fact that you CANNOT ever have a propellant switch over at separation, it'll have to happen before that. The logical thing to do will be for the vehicle to switch from drawing fuel solely from the side boosters to three unconnected boosters each feeding their own 9 engines during the last 10~15 seconds of the side booster burn. It'll probably be a rotary valve rather than two on-off valves doing the work with each connection. There will be zero transient shock in the fluid because the transition is gradual and every bit of flow reduction from the side tanks is exactly matched by a flow increase from the center tank at all times.

The last 5~10 seconds will see essentially three independent F9 cores with no crossflow. At separation, flow would have stopped a while ago and the interconnecting pipes would have been purged so it'll be a dry separation. When the side boosters go MECO and fall away the center booster will have consumed about 5~10% of its fuel only from the fact that it had been operating with partial to no cross flow during the last 15 seconds prior to separation.

[SpacexULA]

Elon Mentioned it in one of 1000 videos.. heck if I remember which one.

[Jim]

I really don't know where the only whole concept of side boosters feeding 3 additional engines each came from. I wasn't able to find any SpaceX references to it formally or informally. The only thing that seems to pop up is Musk saying that because they have a large number of small engines, it is possible for an engine to be individually connected to and draw propellants from adjacent engine(s). And, that this makes crossfeeding easier to accomplish -- presumably because same interconnects and small valves are more easier to deal wit that huge pipes and gigantic valves.

The math that adds up to 53 metric tons to 7.8km/s with an Isp of ~310 secs dictates that the FH will probably run all its engines from the side boosters until moments before separation. The only reason the center core is not 100% full at separation is probably from the fact that you CANNOT ever have a propellant switch over at separation, it'll have to happen before that. The logical thing to do will be for the vehicle to switch from drawing fuel solely from the side boosters to three unconnected boosters each feeding their own 9 engines during the last 10~15 seconds of the side booster burn. It'll probably be a rotary valve rather than two on-off valves doing the work with each connection. There will be zero transient shock in the fluid because the transition is gradual and every bit of flow reduction from the side tanks is exactly matched by a flow increase from the center tank at all times.

The last 5~10 seconds will see essentially three independent F9 cores with no crossflow. At separation, flow would have stopped a while ago and the interconnecting pipes would have been purged so it'll be a dry separation. When the side boosters go MECO and fall away the center booster will have consumed about 5~10% of its fuel only from the fact that it had been operating with partial to no cross flow during the last 15 seconds prior to separation.

Purging the lines for dry separation is not needed, see heritage Atlas
Same goes for rotary valves

[modemeagle]

Here is how I handle cross feed with my simulation (not SpaceX approved)

1.  cross feed is 6 of 9 engines
Elon said during a Q&A that each side feeds the engines on that side, not sure whether it means 2,4,6 or 8 cross feeding.  In the past I found better payload with 6 vs all 9, I will run the numbers again and will edit if I find differently.
2.  cross feed ends when booster propellant mass reaches 5% (3.30 seconds before booster MECO)
3.  booster MECO is at 1.2 seconds of propellant remaining

When SpaceX releases the real numbers then I will adjust my simulation accordingly.

[kirghizstan]

Here is how I handle cross feed with my simulation (not SpaceX approved)

1.  cross feed is 6 of 9 engines
Elon said during a Q&A that each side feeds the engines on that side, not sure whether it means 2,4,6 or 8 cross feeding.  In the past I found better payload with 6 vs all 9, I will run the numbers again and will edit if I find differently.
2.  cross feed ends when booster propellant mass reaches 5% (3.30 seconds before booster MECO)
3.  booster MECO is at 1.2 seconds of propellant remaining

When SpaceX releases the real numbers then I will adjust my simulation accordingly.

Assuming f9 v1.1 what about cross feeding 8, what is the performance of that?

[modemeagle]

Here is how I handle cross feed with my simulation (not SpaceX approved)

1.  cross feed is 6 of 9 engines
Elon said during a Q&A that each side feeds the engines on that side, not sure whether it means 2,4,6 or 8 cross feeding.  In the past I found better payload with 6 vs all 9, I will run the numbers again and will edit if I find differently.
2.  cross feed ends when booster propellant mass reaches 5% (3.30 seconds before booster MECO)
3.  booster MECO is at 1.2 seconds of propellant remaining

When SpaceX releases the real numbers then I will adjust my simulation accordingly.

Assuming f9 v1.1 what about cross feeding 8, what is the performance of that?

This is the FH with the F9V1.1 core.
8 gives you 6.39% residual vs 7.42% with 6.
9 gives 5.62%

[MP99]

Here is how I handle cross feed with my simulation (not SpaceX approved)
...
2.  cross feed ends when booster propellant mass reaches 5% (3.30 seconds before booster MECO)

3.  booster MECO is at 1.2 seconds of propellant remaining

Booster MECO = BECO?



ISTM the two boosters won't hit their cutoffs at exactly the same point, due to natural variations between engines. Obviously, simplest is to cutoff both when the faster-burning booster reaches it's limit, and I'd think this would have a pretty small hit to performance.

However, I understand the single-stick F9 uses mixture ratio management to ensure one propellant isn't exhausted before the other - I believe there was a callout to that effect on F9 #003 launch. It would seem to be a natural extension to try to coordinate exhaustion of the two boosters - ie BECO when the slower-consuming booster hits it's limit. There seem to be two obvious ways to achieve that:-

1) Minor throttle back on the side that is consuming faster (perhaps just on a single engine, given this is likely to be pretty small). This takes a small hit on T/W, but the vehicle will remain in balance as the boosters empty at the same rate. Any engine on the vehicle centre-line could be throttled - whichever trims out the net thrust best, ie minimises engine array gimballing. Booster outboard engine if that booster is the "hotter", or the cross-fed core engine if thrust is similar but consumption is higher.

2) The side that is consuming faster switches off cross-feed slightly earlier. Maximises T/W, but the cores would have a growing mass & T/W imbalance until the first booster ends cross-feed, with the imbalance timed to zero out just as the second booster cuts it's cross-feed.

Both have the same burn time - ie until the slower-consuming booster is drained instead of the faster.

cheers, Martin

[modemeagle]

Here is how I handle cross feed with my simulation (not SpaceX approved)
...
2.  cross feed ends when booster propellant mass reaches 5% (3.30 seconds before booster MECO)

3.  booster MECO is at 1.2 seconds of propellant remaining

Booster MECO = BECO?



ISTM the two boosters won't hit their cutoffs at exactly the same point, due to natural variations between engines. Obviously, simplest is to cutoff both when the faster-burning booster reaches it's limit, and I'd think this would have a pretty small hit to performance.

However, I understand the single-stick F9 uses mixture ratio management to ensure one propellant isn't exhausted before the other - I believe there was a callout to that effect on F9 #003 launch. It would seem to be a natural extension to try to coordinate exhaustion of the two boosters - ie BECO when the slower-consuming booster hits it's limit. There seem to be two obvious ways to achieve that:-

1) Minor throttle back on the side that is consuming faster (perhaps just on a single engine, given this is likely to be pretty small). This takes a small hit on T/W, but the vehicle will remain in balance as the boosters empty at the same rate. Any engine on the vehicle centre-line could be throttled - whichever trims out the net thrust best, ie minimises engine array gimballing. Booster outboard engine if that booster is the "hotter", or the cross-fed core engine if thrust is similar but consumption is higher.

2) The side that is consuming faster switches off cross-feed slightly earlier. Maximises T/W, but the cores would have a growing mass & T/W imbalance until the first booster ends cross-feed, with the imbalance timed to zero out just as the second booster cuts it's cross-feed.

Both have the same burn time - ie until the slower-consuming booster is drained instead of the faster.

cheers, Martin

3.  Regulation of flow rates during cross feed to make sure each booster is emptying at the same rate. (minimum performance loss)

4.  Early BECO. When one booster is depleted, both are shutdown and jettisoned. (some performance loss)

[MP99]

Here is how I handle cross feed with my simulation (not SpaceX approved)
...
2.  cross feed ends when booster propellant mass reaches 5% (3.30 seconds before booster MECO)

3.  booster MECO is at 1.2 seconds of propellant remaining

Booster MECO = BECO?



ISTM the two boosters won't hit their cutoffs at exactly the same point, due to natural variations between engines. Obviously, simplest is to cutoff both when the faster-burning booster reaches it's limit, and I'd think this would have a pretty small hit to performance.

However, I understand the single-stick F9 uses mixture ratio management to ensure one propellant isn't exhausted before the other - I believe there was a callout to that effect on F9 #003 launch. It would seem to be a natural extension to try to coordinate exhaustion of the two boosters - ie BECO when the slower-consuming booster hits it's limit. There seem to be two obvious ways to achieve that:-

1) Minor throttle back on the side that is consuming faster (perhaps just on a single engine, given this is likely to be pretty small). This takes a small hit on T/W, but the vehicle will remain in balance as the boosters empty at the same rate. Any engine on the vehicle centre-line could be throttled - whichever trims out the net thrust best, ie minimises engine array gimballing. Booster outboard engine if that booster is the "hotter", or the cross-fed core engine if thrust is similar but consumption is higher.

2) The side that is consuming faster switches off cross-feed slightly earlier. Maximises T/W, but the cores would have a growing mass & T/W imbalance until the first booster ends cross-feed, with the imbalance timed to zero out just as the second booster cuts it's cross-feed.

Both have the same burn time - ie until the slower-consuming booster is drained instead of the faster.

cheers, Martin

3.  Regulation of flow rates during cross feed to make sure each booster is emptying at the same rate. (minimum performance loss)

(3) is a subset of my (1), presuming the cross-fed engines are independent of the core as expected. Cutting flow rate on one cross-feed will throttle at least one of the core engines. But the thrust may be better balanced by throttling an outside engine on the booster instead of a core engine.

4.  Early BECO. When one booster is depleted, both are shutdown and jettisoned. (some performance loss)

Obviously, simplest is to cutoff both when the faster-burning booster reaches it's limit, and I'd think this would have a pretty small hit to performance.

cheers, Martin

[aero]

This is not directly speculation on how SpaceX is building their crossfeed system, but rather points to the losses resulting from suboptimal crossfeed implementations.

Can anyone point to the dirivation of the rocket equation for a triamese rocket? That is the Falcon Heavy configuration, and Wikipedia says this.

Bimese & Triamese (Crossfeed)
 
Two or three similar stages are stacked side by side, and burn in parallel. Using crossfeed, the fuel tanks of the orbital stage are kept full, while the tank(s) in the booster stage(s) are used to run engines in the booster stage(s) and orbital stage. Once the boosters run dry, they are ejected, and (typically) glide back to a landing. The advantage to this is that the mass ratios of the individual stages is vastly reduced due to the way cross feed modifies the rocket equation. Isp*g*ln(2MR^2/MR+1) & Isp*g*ln(3MR^2/MR+2) respectively. With hydrogen engines, a triamese only needs an MR of 5, as opposed to an MR of 10 for a single stage equivalent vehicle.
 
A criticism of this approach is that designing separate orbiter and boosters, or a single vehicle that could do both, would compromise performance, safety, and possible cost savings. Compromising maximum performance to reduce cargo cost however, is the POINT of the triamese approach. Stacking two or three winged vehicles can also be challenging. Optimistically, the lower mass ratios would translate to lower overall R&D costs, even if two different stage designs. While many aerospace designs have successfully been modified far beyond the original designers intentions (Boeing's 747 is perhaps the best example) the slow and painful birth of the F-35 family demonstrates that it is not always a guarantee of such flexibility.
 
Crossfeed is to be an important part of SpaceX's Falcon Heavy - and one of the main reasons it will be able to lift ~5 times as much cargo to orbit as the standard Falcon 9.

http://en.wikipedia.org/wiki/Reusable_launch_system

I ran a spreadsheet on the FH using the Delta V equation above and derived some really large excess capacity for the vehicle. I know speculation is that FH will only achieve something like 40 to 50 tonnes to LEO, but my spreadsheet gave well over 53 tonnes using 9.8 km/s as the total required Delta V. Of course, that was for an expendable FH.

[MP99]

This is not directly speculation on how SpaceX is building their crossfeed system, but rather points to the losses resulting from suboptimal crossfeed implementations.

Can anyone point to the dirivation of the rocket equation for a triamese rocket? That is the Falcon Heavy configuration, and Wikipedia says this.

Bimese & Triamese (Crossfeed)
 
Two or three similar stages are stacked side by side, and burn in parallel. Using crossfeed, the fuel tanks of the orbital stage are kept full, while the tank(s) in the booster stage(s) are used to run engines in the booster stage(s) and orbital stage. Once the boosters run dry, they are ejected, and (typically) glide back to a landing. The advantage to this is that the mass ratios of the individual stages is vastly reduced due to the way cross feed modifies the rocket equation. Isp*g*ln(2MR^2/MR+1) & Isp*g*ln(3MR^2/MR+2) respectively. With hydrogen engines, a triamese only needs an MR of 5, as opposed to an MR of 10 for a single stage equivalent vehicle.
 
A criticism of this approach is that designing separate orbiter and boosters, or a single vehicle that could do both, would compromise performance, safety, and possible cost savings. Compromising maximum performance to reduce cargo cost however, is the POINT of the triamese approach. Stacking two or three winged vehicles can also be challenging. Optimistically, the lower mass ratios would translate to lower overall R&D costs, even if two different stage designs. While many aerospace designs have successfully been modified far beyond the original designers intentions (Boeing's 747 is perhaps the best example) the slow and painful birth of the F-35 family demonstrates that it is not always a guarantee of such flexibility.
 
Crossfeed is to be an important part of SpaceX's Falcon Heavy - and one of the main reasons it will be able to lift ~5 times as much cargo to orbit as the standard Falcon 9.

http://en.wikipedia.org/wiki/Reusable_launch_system

I ran a spreadsheet on the FH using the Delta V equation above and derived some really large excess capacity for the vehicle. I know speculation is that FH will only achieve something like 40 to 50 tonnes to LEO, but my spreadsheet gave well over 53 tonnes using 9.8 km/s as the total required Delta V. Of course, that was for an expendable FH.

FH is not complex to model. Can easily do it on Schillings, etc. [Edit 2: Actually, ISTR Schillings can model parallel core & boosters, but the principal below applies if you're modeling for yourself.]

Treat the boosters as first stage, just with the thrust of all 27 engines (instead of 18), [edit: and consuming booster prop plus whatever core prop is used].

Once the boosters are ejected, treat the core as a simple second stage with nine engines, and whatever core prop is left. One benefit - there's no gap in thrust between first & second stages, though [edit: my speculation] there may be a short throttle-back at staging.

Upper stage is a simple third stage.



There is only one mystery - what is the exact cross-feed scheme, and how much prop does that leave in the core at booster separation?

cheers, Martin

[modemeagle]

There is only one mystery - what is the exact cross-feed scheme, and how much prop does that leave in the core at booster separation?

cheers, Martin

We will probably first hear about how it's done when we hear about the 4 1/2 minute full duration core test.  The time they run it to will tell us how many engines are cross-fed.

My simulation only uses 9.1 km/s to get to orbit, just over 1.4 km/s for gravity losses, .116 km/s aero losses and 7.375 km/s for insertion (.409 km/s was free from the Earth's rotation).

Here is a quick sheet showing the math.

[aero]

There is only one mystery - what is the exact cross-feed scheme, and how much prop does that leave in the core at booster separation?

cheers, Martin

We will probably first hear about how it's done when we hear about the 4 1/2 minute full duration core test.  The time they run it to will tell us how many engines are cross-fed.

My simulation only uses 9.1 km/s to get to orbit, just over 1.4 km/s for gravity losses, .116 km/s aero losses and 7.375 km/s for insertion (.409 km/s was free from the Earth's rotation).

Here is a quick sheet showing the math.

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.

[dwightlooi]

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

2nd Stage Starting Mass = Falcon 9 1.1 published Mass + 53 tons
2nd Stage Ending Mass = Falcon 9 1.1 published Mass + 53 tons - Fuel of F1.1 core
2nd Stage Mean Isp = 311 secs
2nd Stage Starting Velocity = 1st stage burn out velocity

3rd Stage Starting Mass = F9 Upper Stage Mass + 53 tons
3rd Stage Ending Mass = F9 Upper Stage Mass + 53 tons - Fuel of Upper Stage
3rd Stage Mean Isp = 311 secs
3rd Stage Starting Velocity = 2nd stage burn out velocity

Total Gravity + Aerodynamic + staging losses = 15% (typical for orbital launch vehicles)

This all works out to about 7.8 km/s only when the core booster is practically full at staging.