Page 48 - Aerodynamics for Engineering Students

r Basic concepts and definitions 31

Fig. 1.10

then

M,=M,-(Lcosa+Dsina)(a-x)

Converting to coefficient form by dividing by $pVSc gives
cM, = cM, - (cL cos a + CD sin a) (- - -) (1.46)
a
x
c c
With this equation it is easy to calculate CM~, for any value of x/c. As a particular
case, if the known pitching moment coefficient is that about the leading edge, CM~,
then a = 0, and Eqn (1.46) becomes

X
CM, = CM, + - (CL COS a + CD sin a) (1.47)
C

Aerodynamic centre
If the pitching moment coefficient at each point along the chord is calculated for each
of several values of CL, one very special point is found for which CM is virtually
constant, independent of the lift coefficient. This point is the aerodynamic centre.
For incidences up to 10 degrees or so it is a fixed point close to, but not in general on,
the chord line, between 23% and 25% of the chord behind the leading edge.
For a flat or curved plate in inviscid, incompressible flow the aerodynamic centre is
theoretically exactly one quarter of the chord behind the leading edge; but thickness
of the section, and viscosity of the fluid, tend to place it a few per cent further
forward as indicated above, while compressibility tends to move it backwards. For a
thin aerofoil of infinite aspect ratio in supersonic flow the aerodynamic centre is
theoretically at 50% chord.
Knowledge of how the pitching moment coefficient about a point distance a
behind the leading edge varies with CL may be used to find the position of the
aerodynamic centre behind the leading edge, and also the value of the pitching
moment coefficient there, CM,. Let the position of the aerodynamic centre be a
distance XAC behind the leading edge. Then, with Eqn (1.46) slightly rearranged,