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The basic idea of staged rocketry is to get rid of the mass of empty tanks et cetera as soon as possible during launch, isn't it? So you would ideally want to drop them one at a time as soon as they are emptied.

AFAIK, Delta IV Heavy does, and Falcon Heavy and Angara are planned to, drop their common booster side cores both at once (with Angara planning up to 6 strap on common cores, I don't know if they will drop 2 at a time or all 6 at once). But why not drop just one at a time?

One argument for simultaneous separation might be to maintain symmetry and stability. But at least naively, if the rocket rotates 90 degrees so that the three cores are on top of each other, then removing one of them should not create any asymmetry.

Also, while SpaceX plans to reuse its boosters, Delta IV Heavy does not. SpaceX needs boosters on their side cores in order to soft land them. But why does Delta IV Heavy have rocket engines on its side cores? Engines which are dropped when there's fuel left in the central core. Why not fix all rocket engines to the central core and just use drop tanks on the side?

For Atlas V, Ariane 5, Proton, SLS the empty weight of the smallish side boosters might be too little to care too much about. But it must be very different with rockets using 3 or more similarly sized cores in a bundle.

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If all 3 boosters of Delta IV Heavy exhaust simultaneously, then all the three of them should separate simultaneously. But the center one keeps on burning for a while. It's not a 1st stage of three cores, it's 2+1 a first/second stage. Also, I read on SpaceX website spacex.com/falcon-heavy that the Falcon Heavy will have a "PROPELLANT CROSS-FEED SYSTEM ... where Propellant feeds from the side boosters to the center core so that the center core retains a significant amount of fuel after the boosters separate" But if so, why don't they empty and drop only one at a time? –  LocalFluff Jul 11 at 13:06
    
What do you mean by "rotates 90 degrees"? Are you talking about literally having the rocket aiming sideways, or do you mean "put the boosters on top of each other, and only use one at a time"? Because the second of those is just normal serial staging; the former would result in either firing a rocket into another rocket or the whole craft going sideways. –  cpast Jul 19 at 21:16

3 Answers 3

Your assumption that rotating the rocket removes asymmetry is incorrect.
The total thrust of the rocket can be visualized as a vector. This vector should point at the center of gravity of the rocket. If it doesn't, the thrust will change the direction of the rocket. It's easy to see that a rocket with 1 booster will not have its thrust vector pointing at its CoG.

Edit: If you rotate the rocket as you describe, the direction change will be "up" or "down". Either way the rocket will try to fly in a circle. Throttling won't help keep the rocket on course, unless you throttle the booster engines to 0, and then why bother keeping the booster around?
As @TildalWave says in the comments, you might be able to compensate by gimballing the engines but then you lose some performance.

The rocket body must be aligned with its velocity vector at all times. If it gets out of alignment (i.e. it slews or sideslips), drag rises enormously and the rocket is at risk of breaking up. If you drop one booster, you get asymmetric thrust and drag, both of which will try to slew the rocket around. You'd have to time your nozzle gimballing perfectly to survive. Dropping both boosters is a much simpler and less risky maneuver: you just have to make sure the separation charges fire simultaneously.

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Might be worth taking into account that the CoG of a rocket changes. –  Mehrdad Jul 11 at 21:39
    
Strictly technically, throttleable or gimballed engines could compensate for a few meters lateral CoG change with thrust vectoring at the expense of slightly lower performance, possible higher vibration (exhausts could cross resulting in a back-propagating shock wave), and somewhat longer reaction time and/or diminished attitude control range. Bigger problem with such configuration would be less than optimal T/W ratio, if cores are exhausted serially instead of in parallel. To the point it might not even make it off the ground with one booster core being dead weight until the other burns out. –  Noordung Jul 12 at 1:45
    
In the Up case (having dropped the upper booster), the vector would point upward from Earth' gravity. One throttles the engines to keep the climb rate constant. Why would that case be unstable? –  LocalFluff Jul 12 at 5:01

Consider the amount of thrust the various cited side boosters provide.

Falcon 9 Heavy: 9 Merlin 1Ds at 155Klbs each = 1.4 Mlbs thrust Delta 4 Heavy: 1 RS-68 ~ 600Klbs thrust Araine 5: P230 solid 1.45 Mlbs thrust Angara: RD-191 on a URM ~432 KLbs thrust

These are not minor numbers (Conceded my point is less valid on Angara and D4-H)

If you generate a thrust instability of 1.4 million lbs on anything, it is not going to end well.

However since the paired side boosters typically ignite at the same time, burn at the same rate, using identical components, they burn out at the same time.

The core may be throttled down (D-4H and probably Angara in the future, only a single URM model has launched sub orbital so far) or use cross feed (F9-H maybe) in the case of identical core modules. It may be a different setup entirely (Ariane 5, Vulcain main engine vs solids) when the center core and strapons are totally different.

One of the Atlas models with lots of smaller GEM solid strapons would air ignite some of the strapons once they reached a certain speed/altitude and had dropped others to get performance benefits.

A second question you asked was, why engines in the side cores. That is sort of the question of why is everything not like Proton. Proton looks like it has a center core, and a bunch of smaller strapons, but the strapons have engines using fuel from the center core. And they do not separate.

In the case of F-9H and D-4H carrying all those extra engines to orbit would be a big weight penalty, defeating the porpoise of staging. The extra side cores are not so much as a bigger stage 1, rather they are a stage 1 (side cores) and stage 1+ or 2 (center core).

The original Atlas did the opposite. It had three engines, and would drop the two side engines as staging, but keep the shared tankage (Ballon tanks, very lightweight).

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Just to clarify the statement about the Russian Proton booster -- the central core has no engines, but is just tanks for the hypergolic fuels. All 6 engines are in the outboard "strap ons" (which do not separate). –  Phil Perry Jul 11 at 17:17
    
@PhilPerry Oops. backwards. Thanks. –  geoffc Jul 11 at 18:08

All rockets need to keep the center of thrust (Ct) beneath the Center of Mass (Cm).

Let's assume for the moment a 2-booster rocket stack; the rocket and the boosters all produce thrust of 500 Tons-thrust. the left booster is 3m from centerline, and the right also 3m from centerline. The center of thrust can be figured multiplying the thrust by the distance from centerline for each thruster (getting the thrust moment), and then dividing by the total thrust of the system

Likewise, the center of mass can be figured by taking the mass times the distance from reference centerline, then dividing by total mass. Let's assume each booster is mass 50T, as is the 1st stage, and the upper stage is 25T, and the payload 25T.

(Every aircraft pilot is supposed to do similar calculations for loadout prior to takeoff...)

Case 1: all three going.
Left Booster 500TT @ -3m, moment -1500
Right Booster 500TT @ +3m, moment +1500
stage 1: 500TT @ 0m, moment 0
Total Moment 0
center of thrust 0 (= Moment/ThrustTotal = 0/1500)

Center of mass, case 1
LB 50T x -3m moment=-150
RB 50T x +3m moment=+150
S1 50T x 0m moment=0
S2 25T x 0m moment=0
PL 25T x 0m moment=0
Total Moment = 0 (=150-150+0+0+0) Center of mass = 0 (= Moment/TotalMass = 0/200)

Case 2: Only the left going, right dropped
Left Booster 500TT @ -3m, moment -1500
stage 1: 500TT @ 0m, moment 0
Total Moment -1500
center of thrust -1.5m (= Moment/ThrustTotal = -1500/1000)

Center of mass, case 1
LB 50T x -3m moment=-150
S1 50T x 0m moment=0
S2 25T x 0m moment=0
PL 25T x 0m moment=0
Total Moment = -150 (=-150+0+0+0) Center of mass = -1 (= Moment/TotalMass = -150/150)

Note that in case 2, the Ct and Cm do not match; this will force a spin to the right, since the center of thrust is left of the center of mass. (The actual rate of spin will be determined by how far UP the stack the center of mass is. These calcs can be done in 3D.)

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But what if the rocket turns 90 degrees so that we have Upper and Lower boosters instead of left and right? The moment after having dropped the Lower booster while keeping the Upper booster, should be in the same direction as the gravity the rocket already struggles against. –  LocalFluff Jul 12 at 4:52
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@LocalFluff: Then your rocket's pointing the wrong way. (It's also still unbalanced, so now you have two problems.) –  user2357112 Jul 12 at 6:45

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