Have they tried dimples on radio controlled aircraft? � The size and
speed could designed around the magic Reynolds number = 100,000 where
the coefficient of drag drops precipitously.

Dimpling could vastly extent the range of large and slow as well as
small and fast radio controlled aircraft.

A competitive cyclist is the right size and speed for Nre = 100,000 so
dimple suits can work. �Same for golf balls.

Nre = 100,000 for widebodies going 0.5 knots so dimples won't work
except on the runway.

From fluid mechanics the Reynolds number is the ratio of inertial
forces/viscous forces.

N re = Diameter X velocity X density of fluid/viscosity of fluid.

Bret Cahill

You have a fundamental misunderstanding of aerodynamics. There are
several mechanics that produce drag, and the two involved here are
pressure drag due to seperated flow and skin friction drag. First, on
a bluff body, such as a golf ball (and a cyclist for that matter), the
majority of the drag is pressure drag due to the flow seperating as it
cannot negotiate the steep adverse pressure gradient towards the rear
of the object. Pressure drag is much higher - sometimes one or more
orders of magnitude - than skin friction drag.

Skin friction drag comes from the shear inside the boundary layer,
where the airspeed drops from approximately the free-stream velocity
outside the boundary layer to zero where it actually touches the
surface. This comes in two forms - laminar and turbulent. The skin
friction drag due to a laminar boundary layer is once again much lower
than that due to a turbulent boundary layer.

The reason dimples work on a golf ball is due to the fact that a
turbulent boundary layer, although having more drag than a laminar
boundary layer, tends to stay attached through much steeper adverse
pressure gradients than laminar boundary layers. The dimples force the
flow to transition from laminar to turbulent, which means it stays
attached for longer and you therefore end up reducing the pressure
drag as a smaller region of flow eventually seperates. The drag
savings therefore is because there is less seperated flow, not because
a dimpled surface causes less skin friction than a smooth one. Many
bluff bodies can benefit from this.

When it comes to streamlined bodies, such as an airplane wing, the
situation is very different. When an airfoil is well designed (I'll
get back to low Reynolds number airfoils on which I have done quite a
bit of work over the years) the flow is almost completely attached at
the typical local angle of attack that the wing sees at speeds between
loiter and maximum speed, which is of course where the low drag
matters. Since there is virtually no seperated flow (there is usually
a tiny bit right at the trailing edge), there is no extra benefit to
be had from dimpling. In fact, if you dimple the whole wing you are
going to transition to a turbulent boundary layer early and you are
actually goint to increase the total drag.

Low Reynolds number airfoils are slightly different. The Reynolds
numbers of interest for small - not micro - UAVs is typically between
about 40,000 on tail surfaces to about 500,000 on the wing. At these
Reynolds numbers you sometimes get what is called a "seperation
bubble". While still laminar, the flow seperates, but then it
transitions to turbulent off the surface and then re-attach as a
turbulent boundary layer that remains attached all the way to the
trailing edge if properly designed. These seperation bubbles are
sometimes unavoidable, but good airfoil design can minimize their size
and therefore their drag. In some instances, a small strip can be used
to force the boundary layer to transition to turbulent just ahead of
the point where the flow would have seperated, to prevent the
formation of the seperation bubble. If well designed and placed, you
end up with a nice low drag laminar boundary layer over the forward
part of the airfoil, and then a higher drag turbulent boundary layer
towards the rear but without the seperation bubble. The overall drag
is usually only reduced over a small part of the flight envelope and
only if designed and placed properly - and it only really works at
Reynolds numbers below about 200,000. Again dimples would be too crude
to lead to an overall improvement, as you will once again end up with
a fully turbulent boundary layer while you could have benefitted from
keeping some of the flow laminar.

Finally, your equation:

N re = Diameter X velocity X density of fluid/viscosity of fluid.

That 100,000 you used is for Reynolds number based on diameter as in
your equation above, which is indeed valid for a sphere or cylinder.
However, a wing's Reynolds number is based on the local chord (it
changes along the span if the wing is tapered):

Re = chord X velocity X density of fluid / viscosity of fluid.

Because we are talking about a completely different situation on a
streamlined body such as a wing, that magic Reynolds number of 100,000
that you quoted for a sphere is simply not relevant.

I caught that in a post yesterday but I'm glad someone gave a more
detailed treatment. Usually I have to correct my errors myself.

Still there may be some situation where an airfoil might conflict with
a structure, either because of cost or other considerations.


Bret Cahill