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I am designing a model rocket and am using 3 B6-4 Engines. Inevitably there will be perturbation of its trajectory by wind and engine/thrust inconsistencies. The way that I currently understand the Centre of mass (CM) and Centre of pressure (CP) in terms of correcting an altered trajectory, is that the lift acts through the CP to create a torque about the CM in the opposite direction to the torque that initially caused the rotation of the rocket.

So, say there is a constant clockwise torque of x Nm, I need to create a counterclockwise torque of (x + a) Nm. What should the value of a be? Is it a proportion of x? The value of a needs to be great enough that it sufficiently causes the rocket to right itself and overcome equilibrium, but it can't be large enough that it causes significant overcompensation (causing the rocket to pass vertical by its momentum).

Also, what sort of torque values are likely to be induced to the rocket from wind and engine/thrust inconsistencies. Are the fins or other mechanical attributes of a rocket realistically sufficient to create enough "counter-torque"? What about adjustable fins?

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is that the lift acts through the CP to create a torque about the CM in the opposite direction to the torque that initially caused the rotation of the rocket.

Not really lift (well it us, but), it's simpler.

Imagine a wind that blows at right angles to the fuselage. The magnitude of the force it causes is a function of the wind speed, the cross-sectional area and the fuselage shape (streamlining). For a first-order approximation, you can ignore the shaping, and assume the wind is less than the airspeed of the rocket, so the force becomes a function of cross-section. If you then integrate that force over the entire rocket, you'll find there's more force where the rocket is wider (the fins) and less where it's not (the fuselage and nose) and the net result is uneven. This can be reduced to two forces, a net sideways force and a torque.

When the rocket is aligned with the relative wind, then, as seen from the air's point of view, the rocket is completely symmetrical -its a circle with some very thin fins sticking out evenly around it. It's only when there's a sideways component -wind- that the "apparent shape" becomes non-symmetrical and there's a torque. And that only lasts until the rocket rotates into the apparent wind and becomes symmetrical to it.

but it can't be large enough that it causes significant overcompensation (causing the rocket to pass vertical by its momentum).

Rockets generally have very little rotation momentum compared to the force of their fins. It's an issue to consider, but generally speaking, if it's stable in the wind, it's stable.

I do need to point out that such a case is not, as you put it, because it's too stable. The fins always work to align the rocket with the wind, putting on too much fin will lower performance through drag and trajectory issues, but it won't make it less stable.

Also, what sort of torque values are likely to be induced to the rocket from wind and engine/thrust inconsistencies

In your example, this is much more important. When you have multiple engines in a cluster you have to consider stability in an engine-out condition. This might happen right off the rail if one of the igniters fails or simply takes too long, but it also happens at the end of firing if one engine is running a little hotter than the others.

For stability, you can consider the worst-case scenario. So if your engines are arranged in a triangle, for instance, you want to know what happens when one of the engines fails. This is simple vector decomposition - you have 2 x F(r) on one side of the triangle and 0 on the other, acting through the center of mass some distance forward of the engines. This will tell you the torque from the asymmetry.

Now the problem is calculating the torque from the fins. This varies widely based on the design of the fins. NARCON has some stuff on this, but it gets complex really fast. I recommend reading the section on the topic found here, although this is J class engines, not B's.

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  • $\begingroup$ Thanks for the elaborate answer! If I've understood correctly, my greatest concern in regards to stability is going to be compensating for thrust inconsistencies. Do you think that realistically, it is possible for fins to compensate for this? If not, am I better off investigating alternative solutions? $\endgroup$ Apr 9 '19 at 14:05
  • $\begingroup$ Once the rocket is up and running the fins should have plenty of force to fix this, but the problem is that its most likely to happen at launch due to a failed igniter, and thus the rocket won't be going very fast and the fins won't do much of anything. That said, with a cluster of B's the overall size is pretty small, so the torque won't be that high. Put some bigger than normal fins on it and extend the launch rail and you should be OK. Just don't try it with a couple of D's. $\endgroup$ Apr 10 '19 at 18:48
  • $\begingroup$ Oh PS, if you click the check mark at the top of this reply it will mark the thread answered. $\endgroup$ Apr 10 '19 at 18:48

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