Technical Publication #16
of Fin Shape is Best?
By Tim Van
I'm often asked the question of which fin shape is best for small
competition rockets. What I'm about to tell you about this may shock
Many people have been told that the elliptical fin shape has the
lowest induced drag. While that may be true for full size airplanes,
it may not be necessarily true for small model rockets. The reason
is buried in the very technical subject about something called the
fin's "Reynolds Number." I'll try to describe this without getting
too technical, because I want even young modelers to understand this
(I've seen too many science fair projects with the subject being
'optimum fin shapes' -- which you won't find in my book: 69 Simple
Science Fair Projects with Model Rockets: Aeronautics).
There are two types of drag on a rocket; induced drag, and
profile drag. Induced drag only occurs when the fin creates lift. So
if the rocket is flying along nice-and-stable, the fins don't have
to create any lift forces to straighten out the flight path of the
rocket. Hence, the induced drag on the rocket may be near zero.
Therefore, it is highly likely that your rocket will have the same
induced drag forces no matter what shape fin you use - because
typically a model flies straight and true and the induced drag in
the rocket is very, very small.
Profile drag on the other hand, is always present. It is a
combination of friction drag and pressure drag. The profile drag
force is determined by a number of factors, including the surface
finish on the fin, airfoil used, area of the fin, the length of the
fin chord, and the speed at which the rocket travels. The last two
factors are also used with other parameters to determine the
Reynolds Number for the rocket.
The Reynolds Number is often used to determine the Coefficient of
Lift of the fin at various angle of attacks (AOA). You can see from
the figure below, that the higher the Reynolds Number, the higher
the fins Coefficient of Lift. Therefore, it will be more efficient
at creating a restoring force to correct the path of a rocket.
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
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
Changing the Airfoil on the fin
affects performance too!
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
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
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!
"Problems Reduce Benefits of Elliptical Fins" By Bob Parks.
Journal of the International Spacemodeling Society. September 1993
(Volume 1, Number 5). pg 4.
Permission is granted to reprint this article in club
newsletters. Please give proper credit, and include a link to the
Apogee Components web site: http://www.apogeerockets.com/
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while doing initial research for his science fair project.
Little did we know the extent of what you would contribute to
his learning." -- Susan M. Laue
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