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Even though there are plenty of literature regarding the pitch control of launch vehicle, I couldn't find any regarding the roll autopilot. Is there any formula on how aerodynamic forces affect the roll of a launch vehicle? If no controller is used, to what value can the roll rate increase increase during the phase? Also what is considered as safe limit of the roll rate for the mission to be successful?. (The reports on Apollo mission states that they plan to abandon the mission if the roll rate increases to 20deg/s.)

nik
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  • One of the reasons why literature regarding roll control is scarce is that, for most rockets, the roll control problem is less challenging when compared to pitch and yaw and so most of the designer's effort and hence the literature is biased in favour of pitch and yaw control. – AJN Dec 14 '21 at 12:05
  • yep, What @AJN is saying.. Usually, for roll control to fail you need to be doing something actively wrong. Typically a roll-control mechanism that is malfunctioning. Whereas pitch and yaw control are things that want to go wrong, and you need to juggle multiple balls just right to keep them steady, or invest in a heavy an draggy tail aero assembly to keep orientation straight by brute force. – CuteKItty_pleaseStopBArking Dec 14 '21 at 14:37

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Roll in a launch vehicle is caused by asymmetric torque along its axis.

Either from aerodynamic causes, or from asymmetry in the thrust. (other internal factors like turbopump spinup can induce a momentary roll, but that stops as the internal change stabilizes. Internal causes cannot apply an indefinite sustained torque)

As either of these causes would tend to be constant and persistent, the roll will tend to get worse without active control to correct it.

As to why (uncontrolled) roll is bad:

  • it imposes unwanted and unplanned forces on the vehicle.
  • it complexifies the control of the vehicle. And directional sensing and control avionics must now act faster than the roll rate to have any chance of controlling the flight path. It can cause communications alignment problems. Even if it can handle the rate of change, it forces the avionics to work a lot harder to keep up.
  • in a liquid-fuelled rocket, the fuel and oxydizer might cetrifuge to the side to the tank, starving the fuel inlet to the propulsion.
  • gyroscopic effect of the rotating body will make any attitude changes require more force, and to head off on unexpected directions. (rotation movement is at 90 degrees to force applied!)

How to control roll:

  • identify and remove the root cause. This could be asymmetric fairing/body of the rocket, a bent fin or other aero element, a gas generator exhaust that is misaligned, off gimballing if you have multiple engines, (transient) inertia of spinning-up turbopumps, even swirl in the liquid tank as it drains or radial asymmetry in your nozzle flow
  • remove, reduce or balance these root caused where possible.
  • add a roll control system, and counter any remaining unwanted roll. This could be aero fins, or the directed exhaust of your gas generator, or pairs of engines gimballing, or dedicated roll control engines/thrusters, or RCS.

How much is too much:
Look to the negative effects that can occur above, and calculate what your control and mechanical systems can tolerate. This tolerance will wary wildly between different launch systems. Some launch system want to roll at a rate or several hundred rpm. Most prefer zero, which is of course not quite attainable. Your rocket will tell you what it can handle. In the case of the Apollo, the figure was 20 degrees per second, which is a mere 3.33 RPM!

CuteKItty_pleaseStopBArking
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  • Kitty Re: "swirl in the tank as it drains" I picture water spiraling down a sink drain, conserving angular momentum. But if it is conserving angular momentum as it swirls, how does it create roll? But wait... once all the fuel is drained, the momentum is gone. where did it go? Obviously, I'm confused. – Woody Dec 15 '21 at 03:55
  • @Woody if the outlet is asymmetrical, it is possible for a swirl to be self-amplifying, applying a small torque on the tank and a similar counter-torque in the drain pipe. Net torque on the whole structure is nil, but as the two forces are not aligned it does cause a torsion of the structure as a whole. Worse is if the "drain" that forms this swirl is the nozzle exit, as the counter-rotation is now in your exhaust, and not coupled to the vehicle. Liquids of gases exiting an aperture can carry quite a bit of rotational momentum around. – CuteKItty_pleaseStopBArking Dec 15 '21 at 06:57