Page 62 - Aerodynamics for Engineering Students

Basic concepts and definitions 45

Fig. 1.23 Typical lift curves for sections of moderate thickness and various cambers

zero camber, it is seen to consist of a straight line passing through the origin, curving
over at the higher values of CL, reaching a maximum value of C,, at an incidence of
as, known as the stalling point. After the stalling point, the lift coefficient decreases,
tending to level off at some lower value for higher incidences. The slope of
the straight portion of the curve is called the two-dimensional lift-curve slope,
(dCL/da), or a,. Its theoretical value for a thin section (strictly a curved or flat
plate) is 27r per radian (see Section 4.4.1). For a section of finite thickness in air, a
more accurate empirical value is
(zJm 1.87r ( 1 +0.8- :> (1.66)

dCL
=

The value of C,, is a very important characteristic of the aerofoil since it determines
the minimum speed at which an aeroplane can fly. A typical value for the type of
aerofoil section mentioned is about 1.5. The corresponding value of as would be
around 18".
Curves (b) and (c) in Fig. 1.23 are for sections that have the same thickness
distribution but that are cambered, (c) being more cambered than (b). The effect of
camber is merely to reduce the incidence at which a given lift coefficient is produced,
i.e. to shift the whole lift curve somewhat to the left, with negligible change in the
value of the lift-curve slope, or in the shape of the curve. This shift of the curve is
measured by the incidence at which the lift coefficient is zero. This is the no-lift
incidence, denoted by 00, and a typical value is -3". The same reduction occurs in a,.
Thus a cambered section has the same value of CL as does its thickness distribu-
tion, but this occurs at a smaller incidence.
Modern, thin, sharp-nosed sections display a slightly different characteristic to the
above, as shown in Fig. 1.24. In this case, the lift curve has two approximately
straight portions, of different slopes. The slope of the lower portion is almost the
same as that for a thicker section but, at a moderate incidence, the slope takes a
different, smaller value, leading to a smaller value of CL, typically of the order of
unity. This change in the lift-curve slope is due to a change in the type of flow near
the nose of the aerofoil.