Page 47 - Aerodynamics for Engineering Students

30 Aerodynamics for Engineering Students

surface has the opposite effect. With the pressure distribution as sketched, the effect
on the upper surface is the larger, and there is a resultant upwards force on the
section, that is the lift.
As incidence is increased from zero the following points are noted:
(i) the pressure reduction on the upper surface increases both in intensity and extent
until, at large incidence, it actually encroaches on a small part of the front lower
surface;
(ii) the stagnation point moves progressively further back on the lower surface, and
the increased pressure on the lower surface covers a greater proportion of the
surface. The pressure reduction on the lower surface is simultaneously decreased
in both intensity and extent.
The large negative values of C, reached on the upper surface at high incidences, e.g.
15 degrees, are also noteworthy. In some cases values of -6 or -7 are found. This
corresponds to local flow speeds of nearly three times the speed of the undisturbed
stream.
From the foregoing, the following conclusions may be drawn:
(i) at low incidence the lift is generated by the difference between the pressure
reductions on the upper and lower surfaces;
(ii) at higher incidences the lift is partly due to pressure reduction on the upper
surface and partly due to pressure increase on the lower surface.

At angles of incidence around 18" or 20" the pressure reduction on the upper
surface suddenly collapses and what little lift remains is due principally to the
pressure increase on the lower surface. A picture drawn for one small negative
incidence (for this aerofoil section, about -4") would show equal suction effects on
the upper and lower surfaces, and the section would give no lift. At more negative
incidences the lift would be negative.
The relationship between the pressure distribution and the drag of an aerofoil
section is discussed later (Section 1.5.5).

1.5.4 Pitching moment

The pitching moment on a wing may be estimated experimentally by two principal
methods: direct measurement on a balance, or by pressure plotting, as described in
Section 1.5.6. In either case, the pitching moment coefficient is measured about some
definite point on the aerofoil chord, while for some particular purpose it may be
desirable to know the pitching moment coefficient about some other point on the chord.
To convert from one reference point to the other is a simple application of statics.
Suppose, for example, the lift and drag are known, as also is the pitching moment
Ma about a point distance a from the leading edge, and it is desired to find the
pitching moment Mx about a different point, distance x behind the leading edge. The
situation is then as shown in Fig. 1 .lo. Figure 1 .loa represents the known conditions,
and Fig. 1.10b the unknown conditions. These represent two alternative ways of
looking at the same physical system, and must therefore give identical effects on the
aerofoil.
Obviously, then, L = L and D = D.
Taking moments in each case about the leading edge:
MLE = Ma -La cosa - Da sin0 = Mx - Lx cosa - Dx sina