Falcon Heavy Cross-Feed

[vigleik]

Is that assuming just M1d's 70% planned throttling?

Hmmm...if that's true, 1/2mt doesnt seem like a lot of lost payload on a 50mt-ish LV.  52.5mt instead of 53mt? 
To save the extra cost of designing and building a crossfeed system?

Dunno...doesn't seem like a bad trade if that's even close to accurate...

This is assuming modemeagle's simulator is accurate, I don't know exactly what assumptions he used. My estimate is simply based on the small difference in residual fuel for each stage.

I'm not actually a rocket scientist, but my gut feeling is that you lose much more than 0.5t. The fact that S1 staging happens at a much lower altitude (114.5km versus 149.2km) seems odd, maybe that's a clue.

According to the simulation it seems that the upper stage doesn't care so much about the staging altitude. But if that's true, then, in the cross-feed scenario, we should be able to take advantage of that by adjusting the pitch. Does that make sense?

[MP99]

Not sure if this question has already been answered, as I've not read all the pages on this thread, but I was wondering the reasons for doing crossfeed, rather than simply throttling down the central core during ascent to preserve it's fuel, and then after booster separationthere is still fuel left in the core.  I guess this would lead to higher staging, as the boosters aren't drainging their propellant into the central core, but wouldn't it accomplish roughly the same thing?

or not?
And if not, why not?

Well, you do start off with the same prop in the three first stage tanks, but if you throttle down the core, you reduce the thrust when the vehicle is heaviest. That increases gravity losses (but does assume the vehicles' structure can take all the thrust).

Also, if speculation is correct that the outriggers feed twelve engines each (their own, plus 3x core engines), then the outriggers will drain 4x faster than the core. At outrigger burnout, the core should have at least 75% of it's prop load remaining.

If you were to do the same via throttling the core, you'd need to throttle down to 25% (and lose a lot of T/W). M1Ds seem to throttle only down to 70%.

Which leads me to my 2nd question, would it be cheaper/easier to develop  M1d with that deep of throttling?  Or the extra complexity of crossfeed?

I don't know, just curious. 

modemeagle's FH simulations above show a liftoff T/W of 1.320.

If you throttled the nine central core engines to 25% at liftoff, then T/W would drop to 0.99, ie the vehicle just wouldn't lift off the ground at all!

That throttling to 25% was rather arbitrary, but it makes the point. DIVH throttles its central core, but doesn't throttle until well after liftoff, and nowhere near 25%. From first principles I'd assume similar restrictions on an FH that just used core throttling instead of cross-feed.

However, that does raise an interesting question - SpaceX quote over 40t for the non-crossfed config. Does that assume a DIVH-like central-core-throttled profile (which drops the outriggers before core burnout, just not as early as cross-feed). The all-three-cores-throttled-the-same profile should have less payload, but avoids a staging event. The three possible profiles would be:-

53t  full FH with crossfeed
??t  FH with throttling instead of crossfeed
??t  FH with all three cores throttled same (no outrigger separation required)

cheers, Martin

[ArbitraryConstant]

I agree that the difference is smaller than expected, but it's there. The residual fuel for all three stages is less in the throttle down scenario. My BOE calculation shows this to correspond to approximately a 25m/s difference in delta V, or a 500kg difference in payload, if you want to keep the residual fuel constant. (I don't have exact numbers so this is a rough estimate only.)

Are you taking gravity losses into account? That seems low.

If you throttled the nine central core engines to 25% at liftoff, then T/W would drop to 0.99, ie the vehicle just wouldn't lift off the ground at all!

That seems like pretty significant gravity losses.

[Idiomatic]

500kg loss seems extremely low. First, you aren't getting the most out of your engines by throttling down, this causes gravity losses. Second, you are carrying two boosters significantly further than you would be normally. Pure waste, they are like half the dry weight of the whole craft, and 2/3rds of the drag.

[modemeagle]

I updated the sheet in my previous post. 
http://forum.nasaspaceflight.com/index.php?topic=28424.msg925279#msg925279
Changes made:
1.  Added calculations to adjust ISP to account for any throttling at any altitude.
2.  Added another sheet to compare no cross feed.
3.  Adjusted payload to leave ~ 300 m/s residual in SII so the caparison is more apples to apples.
4.  Added residual delta-v to output sheet.

Remember, just like the Shilling's calculations this is not exact. The guidance SpaceX uses will not be the same guidance I use.

[dudealus]

I find the small difference very suprising as well. Ow well, maybe it is true . Though what stands out for me as well are the G-loads in the non crossfeed versions, they seem rather harsh... Maybe the difference would be alot bigger if you would constrain all 3 versions to 4 G's?

[modemeagle]

I find the small difference very suprising as well. Ow well, maybe it is true . Though what stands out for me as well are the G-loads in the non crossfeed versions, they seem rather harsh... Maybe the difference would be alot bigger if you would constrain all 3 versions to 4 G's?

The throttle point was set to 6.5g and peaked at 6.928 3.0 seconds after min throttle was hit.  The second stage may be a little heavier on the real one which would prevent the spike in acceleration at the end of the booster phase.

To lower the acceleration I would have to cut engines which will lead to higher gravity losses.  If SpaceX is limiting the rocket to a lower acceleration then this may be why their non cross feed is lower then mine.  Waiting for a falcon heavy user manual for answers.

[dudealus]

Sounds about right. Didn't really know what kind of G-loads are usual in launch vehicles, so looked it up for Atlas V (max 4.8 ), Delta 4 (6.0) and Falcon 9 B2 (6.0 max). So I would suggest setting the throttle point at 6g, they aren't throttling down the Falcon 9 for nothing i guess

[vigleik]

I think I understand now. Let's assume the drag losses are the same for all the flight profiles we consider, and let's ignore the fact that the high g-forces we see in some profiles might not be acceptable. Then there are two considerations:

1. Gravity loss. We want to spend the fuel as quickly as possible to minimise gravity loss. Hence the no cross-feed flight profile has the lowest gravity loss, while full cross-feed has the highest gravity loss.

2. Staging. The no cross-feed flight profile does not take advantage of the "third stage", while full cross-feed takes maximal advantage.

Now consider varying the amount of cross-feed, between the two scenarios. As we increase the amount of cross-feed the gravity loss increases while the advantage of staging increases. Consider payload to LEO as a function of the amount of cross-feed used. This will almost certainly be a concave function. I thought the maximum would be at maximum cross-feed, but it's clear from the numbers that the maximum is going to be somewhere in the middle.

Also, if we can use any amount of cross-feed we want then it's always better to use that than to throttle down. To be specific, use as much cross-feed as required to leave the core with the same amount of fuel at BECO as with the throttle down. Then we get the same benefit from staging, but because the thrust is higher the gravity loss will be lower.

Some additional points:
(a) If cross-feed is not available, then throttle-down might still make sense, sacrificing some gravity loss for advantage of staging.

(b) If the dry weight of the boosters is higher, the benefit from staging is higher. This will tilt the balance towards more cross-feed.

(c) If we need to throttle down to limit the g-forces, that tilts the balance towards more cross-feed as well.

(d) If we're going to try to reuse the boosters, that tilts the balance towards more cross-feed, both because of (b) and for the obvious reason.

[modemeagle]

I think I understand now. Let's assume the drag losses are the same for all the flight profiles we consider, and let's ignore the fact that the high g-forces we see in some profiles might not be acceptable. Then there are two considerations:

1. Gravity loss. We want to spend the fuel as quickly as possible to minimise gravity loss. Hence the no cross-feed flight profile has the lowest gravity loss, while full cross-feed has the highest gravity loss.

2. Staging. The no cross-feed flight profile does not take advantage of the "third stage", while full cross-feed takes maximal advantage.

Now consider varying the amount of cross-feed, between the two scenarios. As we increase the amount of cross-feed the gravity loss increases while the advantage of staging increases. Consider payload to LEO as a function of the amount of cross-feed used. This will almost certainly be a concave function. I thought the maximum would be at maximum cross-feed, but it's clear from the numbers that the maximum is going to be somewhere in the middle.

Also, if we can use any amount of cross-feed we want then it's always better to use that than to throttle down. To be specific, use as much cross-feed as required to leave the core with the same amount of fuel at BECO as with the throttle down. Then we get the same benefit from staging, but because the thrust is higher the gravity loss will be lower.

Some additional points:
(a) If cross-feed is not available, then throttle-down might still make sense, sacrificing some gravity loss for advantage of staging.

(b) If the dry weight of the boosters is higher, the benefit from staging is higher. This will tilt the balance towards more cross-feed.

(c) If we need to throttle down to limit the g-forces, that tilts the balance towards more cross-feed as well.

(d) If we're going to try to reuse the boosters, that tilts the balance towards more cross-feed, both because of (b) and for the obvious reason.

Very good observations.  I originally found cross feeding 6 gave me the best performance.  I am going to run the sim doing zero through 9 and will post that for comparison.

I left the sim in 9 since it would reach orbit with 300 m/s residual which should be a decent margin.  I would like to hear from anybody, even in a PM, as to what kind of margin a real launcher would normally have.

EDIT:  I updated my sheet again to include cross feed between 1 and 8 engines.  Interesting to see what the best result was.

[ArbitraryConstant]

1. Gravity loss. We want to spend the fuel as quickly as possible to minimise gravity loss. Hence the no cross-feed flight profile has the lowest gravity loss, while full cross-feed has the highest gravity loss.

I assume you're saying this because the total fuel of the first stage + boosters is expended faster with 27 engines the whole time rather than 9 for part of the time. But aren't you also carrying the boosters for longer and to higher altitude? More seconds carrying the boosters means more total impulse received from gravity. I guess taking longer to relieve the vehicle of fuel loss does that.

But force times time is linear, the difference in kinetic energy received by the boosters is squared.

huh

Not that intuitive I guess. Rocket science, lol.

[Idiomatic]

"Not that intuitive I guess"

Imagine you launched both versions at the same time.

1. Both versions fire all engines at max expending the same amount of fuel.

2. At some point, the boosters will drop off of the core. At this point the crossfeed one will have 1 core and one tank of fuel. The non-crossfeed will have 3 cores and one tank of fuel spread across them. Non-crossfeed will be spending fuel 3 times faster and accelerating faster now but weigh more and have more drag (which wouldn't matter much at 50km or so with negligible atmosphere). Crossfeed will now weigh less but it will be accelerating slower and spend more time being effected by gravity.

The dry:launch weight ratio for the boosters is supposedly 30:1. So they add a few percentage points of mass to the rocket which includes a fully fueled core, 2nd stage, payload.

That said, a rocket cannot be launched like this. 7G is too much even for cargo. 4G is tops for people though F9 should be doing all the HSF missions afaik. Crossfeed keeps acceleration fairly even without being a large loss in efficiency like throttling down. As well, crossfeed should? show larger gains in BEO targets.

[Jim]

That said, a rocket cannot be launched like this. 7G is too much even for cargo. 4G is tops for people though F9 should be doing all the HSF missions afaik.

Huh?  Where are those requirements documented?

[Idiomatic]

That said, a rocket cannot be launched like this. 7G is too much even for cargo. 4G is tops for people though F9 should be doing all the HSF missions afaik.

Huh?  Where are those requirements documented?

Err... the Saturn V shut off engines to keep under 4g. The shuttle limited to 3. I don't think that SpaceX will be pushing any frontiers in the field of making astronauts unsafe. NASA would not let them anyways.

[Jim]

That said, a rocket cannot be launched like this. 7G is too much even for cargo. 4G is tops for people though F9 should be doing all the HSF missions afaik.

Huh?  Where are those requirements documented?

Err... the Saturn V shut off engines to keep under 4g. The shuttle limited to 3. I don't think that SpaceX will be pushing any frontiers in the field of making astronauts unsafe. NASA would not let them anyways.

Err... what?
Don't need to stutter here.  Either base conjecture on facts or don't make them.
You are making assumptions not based on reality.
Shuttle environments are not applicable.
This isn't a Saturn V
ELV's routine have 6's or more, so why is that too much for cargo?
Who says 6g's isn't safe for crew?  Gemini loads were higher.

Again, where are those requirements documented?
Here is where they are documented:
NASA-STD-3001, VOLUME 2

And one data point which negates your line of reasons.  7.5g's is allowed for 300 seconds, basically the whole ride into orbit.

[kirghizstan]

That said, a rocket cannot be launched like this. 7G is too much even for cargo. 4G is tops for people though F9 should be doing all the HSF missions afaik.

Huh?  Where are those requirements documented?

Err... the Saturn V shut off engines to keep under 4g. The shuttle limited to 3. I don't think that SpaceX will be pushing any frontiers in the field of making astronauts unsafe. NASA would not let them anyways.

Err... what?
Don't need to stutter here.  Either base conjecture on facts or don't make them.
You are making assumptions not based on reality.
Shuttle environments are not applicable.
This isn't a Saturn V
ELV's routine have 6's or more, so why is that too much for cargo?
Who says 6g's isn't safe for crew?  Gemini loads were higher.

Again, where are those requirements documented?
Here is where they are documented:
NASA-STD-3001, VOLUME 2

And one data point which negates your line of reasons.  7.5g's is allowed for 300 seconds, basically the whole ride into orbit.

5g at launch and almost 6 during second stage for gemini if i remember correctly

[dudealus]

@Jim, as you seem to have the most experience in this. Are most payloads built to cope with those kind of forces? I just imagined 6 g's was the maximum normal (off course you could get higher if your launch vehicle and payload can cope with it) as the user manuals of multiple launchers stated it as their max loads. I have no idea what most payloads are calculated on though, maybe you can clarify it a bit? thanks

[Idiomatic]

I stand corrected. Though I'm now confused as to why the g-forces were limited previously......... You'd think a billion dollar device wouldn't be giving up capability unless it were required.

[Downix]

Not sure if this question has already been answered, as I've not read all the pages on this thread, but I was wondering the reasons for doing crossfeed, rather than simply throttling down the central core during ascent to preserve it's fuel, and then after booster separationthere is still fuel left in the core.  I guess this would lead to higher staging, as the boosters aren't drainging their propellant into the central core, but wouldn't it accomplish roughly the same thing?

or not?
And if not, why not?

Well, you do start off with the same prop in the three first stage tanks, but if you throttle down the core, you reduce the thrust when the vehicle is heaviest. That increases gravity losses (but does assume the vehicles' structure can take all the thrust).

Also, if speculation is correct that the outriggers feed twelve engines each (their own, plus 3x core engines), then the outriggers will drain 4x faster than the core. At outrigger burnout, the core should have at least 75% of it's prop load remaining.

If you were to do the same via throttling the core, you'd need to throttle down to 25% (and lose a lot of T/W). M1Ds seem to throttle only down to 70%.

Which leads me to my 2nd question, would it be cheaper/easier to develop  M1d with that deep of throttling?  Or the extra complexity of crossfeed?

I don't know, just curious. 

modemeagle's FH simulations above show a liftoff T/W of 1.320.

If you throttled the nine central core engines to 25% at liftoff, then T/W would drop to 0.99, ie the vehicle just wouldn't lift off the ground at all!

That throttling to 25% was rather arbitrary, but it makes the point. DIVH throttles its central core, but doesn't throttle until well after liftoff, and nowhere near 25%. From first principles I'd assume similar restrictions on an FH that just used core throttling instead of cross-feed.

However, that does raise an interesting question - SpaceX quote over 40t for the non-crossfed config. Does that assume a DIVH-like central-core-throttled profile (which drops the outriggers before core burnout, just not as early as cross-feed). The all-three-cores-throttled-the-same profile should have less payload, but avoids a staging event. The three possible profiles would be:-

53t  full FH with crossfeed
??t  FH with throttling instead of crossfeed
??t  FH with all three cores throttled same (no outrigger separation required)

cheers, Martin

I did some calculations:

With separate core throttling: 31 metric tons
WIthout separate core throttling: 27 metric tons

[aero]

Did you take into account the loss of efficiency resulting from throttling the engines below their optimum (design) thrust level? Actually, throttled engines seem to perform quite well with less than 10% loss in Isp over a wide range of thrust. Above 80% thrust, Isp increases to 100% of the nominal value, but between ~30% to ~80% throttle, ~10% reduction in Isp seems to be typical. Thrust can be increased to compensate by throttling up, but fuel consumption would increase. Also, throttleable engines seem to be noteably more massive than the fixed thrust counterpart. Of course, 1% of engine weight is only 5 added kg  so maybe the added mass wouldn't be much in absolute terms.

Do a Google search on "rocket engine throttling," or something like that, there are a lot of references.