Steering Torque needed for rocket stabilization

Okay all you aerodynamics and physics minds.

I am looking for a Fermi estimate (within an order of magnitude) of the torque/moment range that would be needed for an active stabilization for a high power rocket (lets say a 6" 10' 3FNC). Assume the fins are aligned so any correction needed would be to overcome weathercocking.

So does anyone have a method or an idea of how much torque can weathercocking forces impart to the rocket? Again order of magnitude estimates are all thats needed. (SI N-M or english oz-in units are fine)

The instantaneous force on the rocket under boost is the thrust so the non-vertical component should be proportional to sin alpha squared, where alpha is the degrees off vertical.

The natural lever arm is the distance between the CP and the CG. If I assume that you use balanced forward canards located forward of the CG, the minimum corrective torque should be roughly proportional to maximum thrust x sin alpha ^2 x (d (cp-cg))/(d (canard-cg)).

Faster responding canards should require the least correcting torque since the torque is proportional to the sin squared of the angle.

An Eagle Tree Guardian would be an interest test control system.

Bob

To counteract weathercocking (keep the rocket vertical) I think I need to counteract the moment caused by the rocket having a non-zero angle of attack with the relative wind. The AOA I can estimate by assuming various wind and rocket velocities. Estimating the distribution of lift over the rocket airframe and fins is what I am looking for help on.
Also I am contemplating doing this without canards. But that is discussion for another thread. :wink:

The non-zero angle of attack is alpha, and the effective leverarm is the distance from CG to CP.........

You can perform the correction by attaching servos to the fins, but the packaging is more complicated because the motor tube is in the way so you have to have a linkage from the servo to the fins. You can also gimbal the motor but this too is complicated and only provides correction when the motor is thrusting.

The advantage of the canards is that all your electronics can be in one bay, and the bay can be interchangeable with your other rockets with the same airframe diameter.....and you have active control through apogee.

Bob

I am doing the math to see if I can do the correction with reaction wheels. One system I have on paper can generate 11 in-oz of corrective torque, I need to estimate if that is enough for an otherwise "well behaved" rocket.

It will depend on what phase of flight you want to correct on, how fast you are traveling, and at what altitude. Your torque force will also depend on how fast you need to make the correction.

If you are trying to combat weather cocking you probably want to do that in the first phase (thrust) portion of your flight, since the error from the initial weather cocking will propagate throughout the rest of the flight and higher angles of attack require more force to correct. Since you motor is involved there will be a much more significant level of forces to correct. You could use a very short duration motor burn, which will remove the motor thrust from the equation, but now you are traveling mach or higher at a very low altitude. Which means your aerodynamic forces are going to be larger. Great if you are controlling it with flight surfaces, not so great if you are trying to use reaction wheels. So you are going to be working against your thrust and Speed, which will determine how long of duration you have to make your correction, and how much torque you will need.

I would hazard a guess that for a 6" 10' tall rocket with an M or N in it 0.05208 ft*lbs is not nearly enough to make a significant difference in the first phase of flight. At a high apogee that reaction wheel very well could make a decent sized change. I think by the time you get a reaction wheel large enough to have enough force to make a significant guidance input it will weigh a rather obscene amount.

I know you are trying to find a simple number for torque so you can make an easy comparison, but that torque number is going to follow a few different curves over time, depending on what you do.

I think a better question for you to be asking for your reaction wheel problem isn't how big of a wheel do I need to do X. More I have X reaction wheel, now where can I best apply it over the course of the flight. Since I think the performance of your reaction wheel is going to be the constraining factor.

Xrain said:

It will depend on what phase of flight you want to correct on, how fast you are traveling, and at what altitude. Your torque force will also depend on how fast you need to make the correction.

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Xrain, thanks for the thoughtful response.

Here is my thinking, I am looking for relatively small corrections. Large rockets seem to naturally fly pretty straight in light to moderate winds due to their large moments of inertia, they do not like to rotate very fast. I would use reaction wheels already spinning at around 10K rpm before launch. This would add (maybe significant) angular momentum to the rocket so the first phase of the flight may not have that much deviation to correct. Then use the reaction wheels for rather small corrections.

That is my thinking anyways. In other words, design the rocket and open loop performance to fly pretty damn straight without and active correction, then apply a little.

jderimig said:

So does anyone have a method or an idea of how much torque can weathercocking forces impart to the rocket? Again order of magnitude estimates are all thats needed. (SI N-M or english oz-in units are fine)

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Rocksim can do this easily. Just plot "Torque".

Interesting idea!

So to figure out if you are even in the right ball park i'd just calculate the moments of intertia for the rocket and the wheel to start with.

Ignore air, friction and everything else, calculate the moment of intertia for the rocket, and the moment of intertia of your wheel, then see how many rotations of your wheel it will take to rotate the rocket 180 degrees. If you get something like 100,000 rotations of the wheel; well, there is a good chance all you will be doing is flying a quickly spinning wheel. If the rotations is in the thousands or less then there exists a much better chance for you to be able to do some control actions on your rocket.

Next you can calculate how much kinetic energy you have in your wheel. I would have the starting rpm on your wheel be set halfway of its total energy level, if it can spin 15k rpm then its center point energy level would be somewhere around 13k rpm (remember v is squared). That way you have an equal level of energy available in either direction for your control.

These should get you at least give you a good enough idea on the feasibility of the system to see if it is worth looking deeper.

From here you can start to get some better resolution on the system. To get some numbers on the applied torque from weather cocking, take a look at a similarly sized rocket that you know weather cocked. Ideally you should have a video of it. Take a look how much the angle changed, and how long it took for it to make that change. From there with some guesstimations on speed to get the aerodynamic forces, and the inertia you can get the torque that it applied. This should give you a average torque value that is in the ball park to see how much you will have to compensate for.

Alternatively go peek around through some old NASA technical papers. There has been a lot of study into passively guided rockets, so there is probably some paper floating around on weather cocking that can give you some sort of formula. I know there is one for fin flutter, that gave an empirical formula for calculating the likelihood of flutter taking place.

If you want to get a much better idea than that you will probably have to build a simulation for your system. That way you can plug is some reasonably good calculations for the aerodynamic factors, inertia, lever arms, as well as the rotational elements of your gyro. Then this can give you a good enough evaluation of your system to move on to putting it into hardware.

Or if that sounds like not much fun, take the guesstimates that you had and just go right to hardware.

The rocket is set up to be a stable system with the CG ahead of the CP. The greater the speed, the greater stabilization force. In the subsonic realm, aerodynamic forces generally are a function of the square of the airspeed neglecting Reynolds numbers effects. This stabilization will resist changes in rocket orientation - including corrections that are intended.

In the transonic range, the stability will increase due to CP shift rearwards on the fins from the quarter MAC to more like half. Plus there are likely CP shifts due to the nosecone and tube themselves but I haven't studied up on that. Up towards M3 though stability should be back in the ballpark of subsonic as the CP is moving forwards as speed increases in the supersonic range. Continuing faster, stability decreases.

Stability also decreases as the rocket yaws. A stable rocket may not be stable at a moderate yaw angle. There can also be yaw->roll coupling, particularly with an odd number of fins or in the presense of roll.

An actively stabilized rocket may require less reaction torque if it is inherently less stable.

Keep in mind that a control system has time lag on response. A bad combination of time lag and control authority can result in bad things...

Gerald

UhClem said:

Rocksim can do this easily. Just plot "Torque".

Click to expand...

Hmm, you are correct!

View attachment 177258

Perhaps I should spend more time looking at everything that rocksim will do...