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Re: Airplane Drag



At 19:33 9/11/99 -0600, Jim Green wrote:
Can someone please write an expression for the frictional force on a smooth
aircraft as a function of airspeed....
I think it is something like f=kv^n where n=n(v), but it might be a series
of terms.

Aero engineers calculate lift drag and moment in standardized expressions
which at their simplest involve
1) a dynamic air pressure factor, namely 1/2 rho v^2
where v is true airspeed and rho is air density;
2) a coefficient of lift, drag or moment, and
3) a scaling factor that depends on some representative
aircraft quantity.

So you can find the force due to lift expressed as 1/2 rho V^2 S CL
where s is a gross wing area and CL is the lift coefficient associated
with a particular wing shape and angle of attack.

Similarly, the drag force which has to be countered by the thrust from
an engine or propeller, or a diluted gravitational force in sailplanes
can be given as 1/2 rho v^2 S Cd
where Cd is a coefficient of drag.

Drag on a wing may be divided into several contributions - skin friction,
form drag and compressibility drag, but the first two contributions are
associated with the boundary layer near the wing surface. This layer
is thin at the leading edge and gets thicker.

Its flow is laminar and damped while the local speed is increasing
with reducing pressure ( = Higher Reynold's number) but towards maximal
wing thickness the speed begins to decrease, the pressure recovers,
and surface waviness and protuberences encourage the transition from
laminar flow to turbulent flow in a thicker boundary
and with greater skin friction.


Thus the frictional drag on the plane increases with airspeed.
BUT
I am told by my pilot son that the frictional drag due to the extension of
the airplane's ailerons or flaps _decreases_ with increasing airspeed -- at
least at the normal extensions during landing.

Is this true?...
Jim Green

Jim's son may have in mind a graphical comparison of coefficient
of Lift and drag for a particular wing shape.
This generally exhibits a curve which is concave upwards:
for CL on the abscissa and Cd on the ordinate, you could expect a
curve which passes through these coordinates:
[-0.5,0.015], [0.2,0.01], [1.0,0.016]
for standard roughness and with Cd reduced by one third for
particular smooth surfaced wings.

This arises because near stall (lower value of v^2) a higher value
of CL is needed (obtained with increased angle of attack) and hence
a higher Cd obtains.

In particular wings, this drag coefficient reduction tends to
counter the V^2 increase up to a particular speed where the
Cd/CL bottoms out.

Reviewing a data table for various kinds of flaps (split, plain,
single slot, Fowler) I see that while they all greatly increase
the max CL, they all also increase Cd - so that as you sit in an
airplane on final descent, as the flaps are set down, the engine
note often increases to supply thrust needed to counter the
extra drag.

In summary, I cannot find conditions for which there is
reduced drag at increased airspeed for flaps and ailerons.

(General treatment after Maccabee, Light Aircraft
Design, Loughboro U.)



brian whatcott <inet@intellisys.net>
Altus OK