So if your rocket is flying slow, and has very small fins, the Reynolds number might be so low that the fin will be very ineffective (because the Coefficient of Lift will be smaller). And if your rocket starts to stray from a vertical path, the model will cant much further over before the AOA is high enough to force a larger Coefficient of Lift. This will then start to bring the rocket back to vertical, but now the induced drag really starts to increase as does profile drag; because the side of the rocket is exposed to the airflow. This makes it highly desirable to have a fin that has a high Coefficient of Lift, so the model quickly restores to the correct flight path when the AOA is still small.

If you look around for data, you will find that the Coefficient of Lift is determined by the airfoil of the fin, not its shape. We will now see that the wrong shape can make the situation even worse.

So if your rocket is flying slow, and has very small fins, the Reynolds number might be so low that the fin will be very ineffective (because the Coefficient of Lift will be smaller). And if your rocket starts to stray from a vertical path, the model will cant much further over before the AOA is high enough to force a larger Coefficient of Lift. This will then start to bring the rocket back to vertical, but now the induced drag really starts to increase as does profile drag; because the side of the rocket is exposed to the airflow. This makes it highly desirable to have a fin that has a high Coefficient of Lift, so the model quickly restores to the correct flight path when the AOA is still small.

If you look around for data, you will find that the Coefficient of Lift is determined by the airfoil of the fin, not its shape. We will now see that the wrong shape can make the situation even worse.

The most efficient part of the fin is at the tips; where the airflow is nice and smooth because it is outside the turbulence caused by air flowing over the nose of the rocket. On elliptical fins, and on other shapes where the tip is reduced because of tapering, the Reynolds Number is even further reduced - remember that Reynolds Number is a function of the chord length of the fin. So, because the Reynolds Number at the tip is lower, the tip is less effective at creating lift to restore the rocket to vertical if it should be disturbed. To compensate for this, you'll have to increase the size of the fin, which defeats the purpose of trying to make the model as small as possible to help reduce both weight and profile drag.

Another problem associated with tapered fin shapes is that the airfoil shape typically changes too. Why is this? Because the thickness as a percent of the chord length increases unless the fin thickness get progressively thinner toward the tip of the fin. Even people that sand an airfoil into the fin rarely make the tips thin compared to the root to keep a constant airfoil. This is because they are already starting with a thin fin, and it would be difficult and time consuming to sand the fin so thin that you could see through it. Well... this fatter airfoil makes the problem associated with low Reynolds Numbers worse! The tip of the fin is even less effective at creating a restoring force if it should become disturbed.

So we now see that the elliptical fin or the highly tapered fin may not be the optimum for lowest drag. These fins will require the model be further deflected before the forces acting on the fins are large enough to cause them to be effective in straightening out the flight of the rocket. And while the rocket is deflected, the nose and body tube are presenting a lot of side area to the on-rushing airflow; so the drag can be huge.

It would be better to use a shape that is more effective at low Reynolds Numbers, and that is easy to make without the hassle of thinning the thickness of the fin toward the tip. The better solution would seem to indicate that a rectangular or parallelogram would yield lower overall drag.

And there is a huge advantage to the rectangular shaped fin; you can cut and sand one long strip of balsa wood. Then you can just section it into the individual fins. All the fins now have the identical airfoil shape! This helps reduce the drag forces on a fin that might otherwise be non-identical with the others on the model.

There you have it. The best shape for a small competition model is a rectangle or the parallelogram. And it just happens to be the easiest fin to make!

References:

"Problems Reduce Benefits of Elliptical Fins" By Bob Parks. Journal of the International Spacemodeling Society. September 1993 (Volume 1, Number 5). pg 4.

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