Page 66 - Aerodynamics for Engineering Students

Basic concepts and definitions 49

curve
idealized case in which Coo is independent of lift coefficient, the C~,:(CL)~ for a
family of wings of various aspect ratios as is shown in Fig. 1.28.

Pitching moment coefficient
In Section 1.5.4 it was shown that

EX = constant
dCL
the value of the constant depending on the point of the aerofoil section about which
CM is measured. Thus a curve of CM against CL is theoretically as shown in Fig. 1.29.
Line (a) for which dCM/dCL fi - is for CM measured about the leading edge.
Line (c), for which the slope is zero, is for the case where CM is measured about the
aerodynamic centre. Line (b) would be obtained if CM were measured about a point
between the leading edge and the aerodynamic centre, while for (d) the reference
point is behind the aerodynamic centre. These curves are straight only for moderate
values of CL. As the lift coefficient approaches C,, , the CM against CL curve departs
from the straight line. The two possibilities are sketched in Fig. 1.30.
For curve (a) the pitching moment coefficient becomes more negative near the
stall, thus tending to decrease the incidence, and unstall the wing. This is known as
a stable break. Curve (b), on the other hand, shows that, near the stall, the pitching
moment coefficient becomes less negative. The tendency then is for the incidence to

Fig. 1.29 Variation of CM with CL for an aerofoil section, for four different reference points

0
CL

Fig. 1.30 The behaviour of the pitching moment coefficient in the region of the stalling point, showing
stable and unstable breaks