Spin Stability

"Topics in Advanced Model Rocketry", Chapter 2 by Gordon Mandell. He calls it roll stabilization, by the way. His is not a trivial explanation, but it can be understood without any math (although he does refer to some very significant equations to establish his assertions.)

I'll try to summarize, but you should go find a copy of this book.

Spin stabilization doesn't induce positive stability in a statically unstable rocket--the rocket will still be unstable. Instead, there are a few things at work that may keep an unstable rocket nonetheless flying straight:

- Spinning suppresses the growth rate of instability. The proof of this requires looking at the equations. For model rockets, with a flight duration of a few seconds, a fast enough roll rate may be enough to keep the instability from affecting the flight path.

- Spinning creates a high angular momentum, and subsequent additional angular disturbances add only a small change to the momentum vector. The initial size of the yaw or pitch rotation resulting from a disturbance will be less for a spinning rocket than a non-spinning rocket. (It's still possible to rotate a gyro off axis, it just takes a lot more force than if it wasn't spinning.) This is sort of the gyro effect you asked about, although "conservation of angular momentum" is misleading. Angular momentum can be changed through a force on the rocket/gyro.

- Spinning turns all disturbances due to imperfections in the rocket into "sinusoidal forcing at the roll frequency". In other words, a crimped body tube, for instance, will not cause an arcing trajectory if the rocket is spinning. However you will instead get yaw-roll coupling, resulting in a "corkscrew" flight.

The magnitude of these effects depends on the roll rate--the faster the spin the less the effect of disturbances on a rocket. In other words, a statically unstable rocket that isn't spinning fast enough won't fly straight. For example, the yaw-roll coupling I mentioned above could grow large enough to send a slowly spinning rocket off course. (Unfortunately, with yaw-roll coupling a very high roll frequency, while helping to keep the rocket on course, could tear the rocket apart.)

Thanks Steve, both for the reference and the summary. I see Apogee has the book, it's a tad expensive for me at $70 but sounds like it has a wealth of information.

Ted Mahler NAR 18184

Let me know if you didn't get the file I sent. Copyuright isn't an issue. We don't adhere to NAR guideleines. (Badges?! We don't need no stinking badges!) We have done spin-stabilized rockets, though, for many years.

Ted,

I sent you a high schoolers report on spin stabilization off chat, let me know if you got it.

Got it! I haven't read it yet but will! I actually came across this in my Google searches but all the links to it were dead or incomplete.

Thanks! Ted Mahler NAR 18184

Please post it to alt.binaries.models.rockets, or put it at a long lived location and post fresh links.

Alan

Done, check out abmr. I am also looking for a site to host it...

Erik Gates

Erik found a host! This document can be found at

Darrell

Thanks, I was able to get it from that site, and it has not propagated through ABMR yet. This report is well written, although it is padded out with a lot of historical material. It shows that deflected spin tabs do decrease altitude ("paddle wheel effect"?), at least for the rocket tested which had no need to be spun.

Alan

There is a great deal of literature available on this topic. I'm reluctant to suggest papers that may not be readily available to you, or that may not be appropriate for your 4th graders.

Spin stability works best when the spinning is done about the principle inertial axis, the one with the largest moment of inertia. Thus, spin stability words best with saucer like rockets, and some well designed space probes. You can spin a more typical rocket about the roll axis, and it will appear stable for a time but eventually it will try to transfer the angular momentum to spinning about the principle axis, e.g. an end over end flat spin.

Perhaps the best know case is the Explorer satellite launched on the Juno/Redsone vehicle. You can see the bucket full of Recruit motors and satellite spinning atop the nose before launch. This is actuality a two stage satellite boost package. The first stage has a rather large moment of inertia, while the final satellite stage has a small rocket like moment of inertia. To make matters worse, the satellite had flexible whip antennae that helped transfer the spin from the roll axis to the principle axis much quicker than expected.

Within the atmosphere, spinning is used quite effectively on bullets and artillery shells. The spinning is not strictly stable, but projectiles are fairly rigid, symmetrical, have a higher relative moment of roll inertial compared to sounding rockets. The flight times tend to be low, before the rounds begin to tumble, but it greatly improves range and accuracy.

For unguided rockets, fins are preferred for static stability. Even so, spin is desired to minimize dispersion. There can be some confusion calling these rockets spin stabilized. Generally, you want the highest roll rate at launch, to even out thrust misalignments, and somewhat less spin rate at max q. This can be sometimes be achieved with a spinning launch table, or a riffled launch tube. Sometimes, small rocket spin motors are used. Most commonly, the fins are simply canted to roll the rocket.

Dispersion is not as sexy a topic as altitude, but the tighter you control flight dispersion, the higher altitudes you can fly to within a given launch site, be it White Sands, or the school yard.

Using canted fins (or spin tabs) is difficult because you don't get the roll rate where you want it the most. So, you tend to want to use maximum amount of fin cant to spin up the rocket as quickly as possible. This can also result in an increase in drag. There is usually a maximum roll rate that will drive the rocket unstable, so you want to stay well below that. There is also a resonant roll-yaw coupling roll rate that should be avoided. Typically, sounding rockets are designed to fly through the resonant coupling rate quickly, before bad things start to happens. Many sounding rockets are spin balanced, and have fin cant angles tuned for particular missions.

For sport rockets, the roll you get through typical assembly, say a fin misaligned 0.5 deg. is probably good. Some rockets with some asymmetry, or clustering and staging, should have a bit more deliberate roll rate built in.

The easy answer is duh. The fin size required for static stability will have ample "roll power" to spin a typical rocket, and you need not increase fin size just to induce roll. There will be very little lag between the steady state roll rate and the dynamic roll rate as speed changes.

The optimum spin rate, or optimum fin cant angle, depends on your choice of optimality and your particular rocket. In many cases the optimal fin cant angle is zero with fins sized for one caliber static margin.l However, I've done some studies that suggests the two calibers of stability is optimal for a dual egglofter. You might look at an old Estes Cineroc carrier and decide that those barn door fins are way too big. After designing your "higher performance" Cineroc vehicle, and reviewing the resulting film, you will understand the reason for the "oversized" fins, damping.

Alan

Alan Jones wrote: > ... There is > usually a maximum roll rate that will drive the rocket unstable

This is interesting, and doesn't seem to agree with Mandell's analysis of spin stabilization. From what I read, the higher the roll rate the less the rocket will be perturbed from a straight flight path.

You could do some more reading, beyond the MR literature.