Throttle bucket and Max-Q

[LouScheffer]

I always thought the throttle bucket was to reduce stress at Max-Q.

But the throttle bucket is (usually) finished well before Max-Q, on all but the crew missions.  For the crew missions, the throttle down starts before trans-sonic, and throttles back up after Max-Q.  On all other missions, the vast majority, (both regular fairing and CRS cargo) the throttle up happens well before Max-Q.

For example, on the most recent StarLink (4-27) the bucket is 50-61 seconds, and supersonic at 55 seconds, and Max-Q at 71 seconds. So back to full power well before Max-Q.

Numerical calculations back this up.   Consider the stress on the interstage.  At Max-Q, it's accelerating the second stage (about 120t) at 1 G, hence about 2.4MN compression stress.  The Max-Q dynamic pressure is about 30-40 kPa.  The frontal area of the fairing (5.2 meter diameter) is about 21.2 m^2.  Even at a Cd of 1 (and the fairing is much more streamlined than that) that's a force of 859 kN.   So a total stress on the interstage of 3.25 MN.  But the stress is much worse just before first stage burnout, when the rocket is accelerating at 3 Gs, where the stress is 4.8 MN.  So Max-Q is not the highest stress.

On the other hand, all flights - Starlink, Commercial resupply, and crew - stay throttled down while passing through the sound barrier.  So the conclusion is the throttle bucket is for the sound barrier, not Max-Q. 

It's not even clear that Max-Q is maximum stress.  Stress = Cd x dynamic pressure, but Cd also varies with speed, often peaking at about the sound barrier.

So what's the limiting piece of hardware?  It's not the fairing, since even fairing-less missions (CRS) have the bucket.  It's likely not the second stage, since even at Max-Q,  it should still be in tension (3.7 meter diameter pressurized to 3 bar is 3.2 MN tension).  The same argument for the interstage given above also applies to the first stage LOX tank.   So maybe the first stage fuel tank walls are the weak point?  (These are most likely to be in compression due to accelerating the LOX tank + aero forces.)

So does anyone know what the throttle bucket is for, and where the limiting factor is in the design?

[Alexphysics]

You don't need to throttle up after Max Q, you can throttle up before and be okay. I've actually tinkered with this on Flight Club many times and discovered myself that you can easily just throttle up a few seconds before Max Q and the value of that Max Q doesn't really go considerably high. As you go through that period of Max Q what happens if you throttle up before that is that it lasts a bit longer but it doesn't have time for the Q to increase considerably because you've done it close enough that you're already reaching the peak of the curve, but you're up there for longer.

For crewed missions they may not want that high Q to happen for a prolonged period of time, specially if you think of an abort scenario. So they do the throttle afterwards instead, whereas fairing missions most likely don't need the throttle up to be that late anyways.

[sdsds]

Excellent question. Did your analysis consider vibratory loads?

[r8ix]

Just in terms of speed v. atmospheric density, actual "Max" Q happens on the way down to landing...

[meekGee]

I think it's a "self-defeating" question.

Ignoring vibrations, the load is composed of inertial and aerodynamic forces.  One is a function of acceleration (and thus thrust) the other a function of speed and air density.

Without a throttle-down, it would have peaked at a certain point in the trajectory.

But once you apply the mitigation everything shifts to later in the trajectory.

There still is a max-Q point, but it occurs later, and with lower values.

So which point is it that you think you're restoring thrust relative to?  The hypothetical max-Q that never happened, or the new one that almost by definition happens after you throttle up?

I think they're marking the actual max-Q  and so it makes sense that it occurs after throttle up.

[John-H]

Without the throttle bucket, where would the max Q be? It would be lower and stronger, but would it be significantly more dangerous?

John

[LouScheffer]

Some more notes:

RocketLab's Electron does exactly the same, throttle down for trans-sonic but not Max-Q.  See, for example "Look Ma no hands", which has a thrust bucket from 60-70 seconds.  Transonic is at +62 seconds, but MaxQ is at +78 seconds, well after throttle up.  This plot, too, is mislabeled with no bucket at MaxQ.

Also, a quick model indicates it may well be the first stage fuel tank that is the limiting factor.  Assuming the fuel tank walls must support the LOX tank + payload, but the lox tank and interstage need only support the second stage and payload, then the max structural load of the LOX tank and the interstage occur at the end of the first stage firing, not near MaxQ.  However the max fuel tank load occurs during the peak of aerodynamic forces.  (Assumptions: total propellant = 400,000 kg, 310 lox and 90 kerosene, empty first stage = 30 t, second stage + payload = 120 t, pressurization = 3 bar, Cd = 1, aero forces approximated with a simple peak).  Because Cd also varies with Mach number, it seems likely that the max aero forces occur at trans-sonic, not at MaxQ.

[Jim]

1.  I always thought the throttle bucket was to reduce stress at Max-Q.

2.  But the throttle bucket is (usually) finished well before Max-Q, on all but the crew missions.  For the crew missions, the throttle down starts before trans-sonic, and throttles back up after Max-Q.  On all other missions, the vast majority, (both regular fairing and CRS cargo) the throttle up happens well before Max-Q.

3.  It's not even clear that Max-Q is maximum stress.

1. It is to reduce the actual Max q

2.  Because q is 1/2rhoV^2.   Max q exists because V=0 when the vehicle is on the pad and atmospheric density decreases to zero with altitude, there is a peak in between.  Magnitude and altitude of Max q is variable and a function of velocity.  Throttling is done so that the vehicle doesn't go too fast while low in the thicker part of the atmosphere. 
The vehicle can throttle back up before hitting Max q because it won't have an immediate effect on velocity, making the Max q higher.   It is an optimization program.

3.  It isn't, it is maximum aero loads on the airframe and fairing.  Angle of attack and shear winds play into it.


Need to look at a chart of thrust, velocity, and q vs time

[Jim]

Without the throttle bucket, where would the max Q be? It would be lower and stronger, but would it be significantly more dangerous?

John

Yes

[MP99]

Also, a quick model indicates it may well be the first stage fuel tank that is the limiting factor.  Assuming the fuel tank walls must support the LOX tank + payload, but the lox tank and interstage need only support the second stage and payload, then the max structural load of the LOX tank and the interstage occur at the end of the first stage firing, not near MaxQ.  However the max fuel tank load occurs during the peak of aerodynamic forces.

That always seemed to be the obvious reason why Booster & Starship switched the lox tank to be below the methane. (Edit: much shorter section of the tank walls needs to be strong enough to support the lox mass.) Also why that thrust beam just under the lox tank in the Shuttle (etc!) was so cunning.

I believe the "usual" reason for placing the heavier lox tank above the fuel is that it makes it easier to keep the rocket balanced - like a broomstick is easier to balance with head at the top instead of bottom. I wonder if Booster will just brute force it during landing with cold gas thrusters from the ullage, which will be easier with the lox tank at the bottom.

Cheers, Martin

[Jim]

Except hydrogen upperstages.   See Centaur, Delta and Saturn

[Robotbeat]

Also, a quick model indicates it may well be the first stage fuel tank that is the limiting factor.  Assuming the fuel tank walls must support the LOX tank + payload, but the lox tank and interstage need only support the second stage and payload, then the max structural load of the LOX tank and the interstage occur at the end of the first stage firing, not near MaxQ.  However the max fuel tank load occurs during the peak of aerodynamic forces.

That always seemed to be the obvious reason why Booster & Starship switched the lox tank to be below the methane. (Edit: much shorter section of the tank walls needs to be strong enough to support the lox mass.) Also why that thrust beam just under the lox tank in the Shuttle (etc!) was so cunning.

I believe the "usual" reason for placing the heavier lox tank above the fuel is that it makes it easier to keep the rocket balanced - like a broomstick is easier to balance with head at the top instead of bottom. I wonder if Booster will just brute force it during landing with cold gas thrusters from the ullage, which will be easier with the lox tank at the bottom.

Cheers, Martin

having the LOx tank below the fuel tank reduces degree of mixing in case of common dome failure.

[Twark_Main]

3.  It's not even clear that Max-Q is maximum stress.

3.  It isn't, it is maximum aero loads on the airframe and fairing.  Angle of attack and shear winds play into it.

Also changing C_d. That's the difference between max drag and max Q

[acsawdey]

Is it possible this is to do with a different (less lofted) trajectory for crew missions? The atmospheric density is not decreasing as rapidly so you have to stay in the throttle bucket longer to keep max-Q from going to high?