It's not just fin area that matters, but semi-span. With a greater semi-span, you can do with a lot less fin area at the tradeoff of greater drag due to increased frontal area.

Warren

So what about a small semi-span with a long root edge? do they counter balance?

Check out these sites:

http://my.execpc.com/~culp/rockets/Barrowman.html

http://www.webcalc.net/calc/0225.php

http://www.apogeerockets.com/Education/rocket_stability.asp

Doug

I've never seen the formula, but if the fin semi-span is less than the airframe diameter, the root has to go up a LOT to counterbalance reductions in semi-span. It is NOT linear.

W

Thanks Doug. The rocket im building now it stable in Rocksim. Yet my SSSS was stable in rocksim but never flew straight, everytime it did cartwheeles. Im assuming its because i just didnt have enough stability from such small fins. My new set of fins have a span equal to the rockets. But this time my root is longer, almost 60% longer. So im curious to know beofre hand if that is enough.

Most, but not all, of the equations are based on a physics MIT graduate student named James Barowman who, with others, came up with them in the late 1960's. Estes an Centuri produced booklets with graphs for you to design you own. I still have my copies.

There is also the cardboard cutout method. Very conservative but if you're stranded on an island and you want to build a rocket and all you have is cardboard and scissors... But now there are programs, like Rocsim, to do it for you. However, Rocsim has their own method of calculating stability and in the general section of the design you can select which method to use.

Please note that these equations, like all the methods, are based on assumptions and will not fit every design. I haven't seen the assumptions that Rocsim uses but I'm sure they are there. A typical example about the Barrowman method is that the fins are "thin flat plates". The calculations do not work for a stick attached to a motor like a bottle rocket (which we know is stable). This is especially of concern for me when I have a camera cowling sticking off the side of the rocket. I still treat it as a fin but in case you wonder why my rockets have over sized fins... However, for most typical rocket designs they work great.

Now if you’re really into the math you may wish to check out “Topics in Advanced Model Rocketry” by Mandell, Caporaso and Bengen published from MIT Press in 1973. It has many of the equations and methods used by the simulation programs. It is available from Amazon and you also may be able to find it in your local library. It was my bible for rocketry unlike Stine’s Handbook...

Doug

Don't forget two things - the principle of moment arm in leverage and laminar flow. Air flow close to the airframe is different than airflow further out. Also, stubby fins in terms of semi-span relative to airframe diameter have less moment-arm for leverage to stablize a bird. I've long lived by one rule of thumb - semi-span should equal or exceed airframe diameter.

Warren

Thanks Doug. The rocket im building now it stable in Rocksim. Yet my SSSS was stable in rocksim but never flew straight, everytime it did cartwheeles. Im assuming its because i just didnt have enough stability from such small fins. My new set of fins have a span equal to the rockets. But this time my root is longer, almost 60% longer. So im curious to know beofre hand if that is enough.

Another cause of cartwheels that almost nobody ever talks about is a lateral mass offset. If the center of mass is a little bit away from the centerline, then the motor thrust will make your rocket pitch over. I had at least one rocket that had plenty of fin area to make it stable, but a mass offset caused it to cartwheel all the way to the ground. If your rocket will roll smoothly on a table with the fins hanging off the edge, it will fly o.k. But if it wants to settle to a particular orientation, watch out. Even if it has enough fins to be stable, there's a good chance it will take off at an angle or have some nasty coning.

I flew the same small-finned rocket twice, first without any correction to the CG. It took off at about a 30-40 degree flight angle, had some nasty coning and I was lucky to recover it. Then I flew it again with a counterbalance weight to center the CG, and it flew beautifully.

Excellent point Adrian. One thought that brings to mind is it seems to me that C-slot and moonburner motors more often than not "wobble" or "wiggle" or whatever in flight, particularly in minimum diameter rockets. Sometimes even when the rocket is flawlessly designed and constructed. Might that be the difference in mass off centerline as the motor burns?

Warren

Yes, you can really notice the mass offset in the Ellis G37 motors when you roll them, since they have an offset core.

Not to beat a dead horse here, but I think the c-slot combined with a medusa nozzle is a recipe for an erratic flight with a minimum diameter rocket. I can't tell you how many rockets I've seen this on - bullet straight with a K550, loopty loop with a J135. I think larger rockets, more fin area, more etc. can handle medusas and c-slots, but I won't do that on a minimum diameter rocket again.

This is why I used the M1450 (bates grains, single throat nozzle) on my M shot in July. Ed D (who has considerably more building skills than I) had some corkscrewing on his boost. You can bet your hat his fins were on straight, and that wobble was NOT his fault. This is a real challenge, and probably what haunts me most on doing an N altitude shot. (the price of those N1100s doesn't help, either!)

I wonder if anyone has messed around with a helical offset core? That would give it the same burn geometry (at least in 2D), but eliminate the weight imbalance. As long as it were a perfect helix, the core could be extracted (with effort 😉 ) or milled in after casting(?)

As long as there is a chamber at the bottom and a single nozzle, it should cancel out any inherent spin effects.

Just my uninformed L1 idea!
Ken

Another cause of cartwheels that almost nobody ever talks about is a lateral mass offset. If the center of mass is a little bit away from the centerline, then the motor thrust will make your rocket pitch over. I had at least one rocket that had plenty of fin area to make it stable, but a mass offset caused it to cartwheel all the way to the ground.

Sorry to disagree with you Adrian but that is not the case. I have flown many rockets with cameras hanging off the side and yes you may get very slight arcs in trajectory (no more than weather cocking does) but having the mass off center will not cause cartwheels.

Take a look at Freeze Frame. It had a 10 pound camera 3 inches lateral distance off of the centerline and it was stable. Another example is cluster where one motor doesn't light. The may have curved trajectories but if your rocket is doing cartwheels, it is likely unstable.

Remember another factor in stability is the airspeed of the rocket. Some rockets can be stable at low speeds but change out the motors to ones with higher thrust and you can go unstable even if the center of gravity hasn't changed.

Doug

Concerning the medusa nozzle...
Relaying statements from my dad, the medusa nozzle should not effect the flow of gases going through the nozzle. I have yet to find out any specific reason why the medusa nozzle is used, being more efficient or something of that nature. This being a opinionated statement, but a medusa nozzle is only useful for being cost effective. All the motors used with the medusa nozzle are the exact same. From the L motors to the M motors. The only difference is how many throats are boared out. Supposedly the gases should, even with a C-slot, be converged to the nozzle with a even flow, resulting in a normal burn. I would have to agree I have seen John fly a rocket with two different motors. One being a medusa nozzle like at balls and it corkscrewed, and one before with a bates bates/single nozzle where it was bullet straight. Its hard to tell what was the case, scientifically the medusa nozzle should work exactly like a bates grain, single throat nozzle motor. Reminder, all opinions 😆