Dimples On Model Aircraft Could Greatly Extend Range
On Wed, 05 Nov 2008 00:10:29 -0800, bbrought wrote:
On Nov 4, 9:04Â*pm, Bret Cahill wrote:
Have they tried dimples on radio controlled aircraft? Â* 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. Â*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.
Now THATS what Usenet should be like! Thanks for an interesting,
informative post.
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