Page 56 - Aerodynamics for Engineering Students

Basic concepts and definitions 39

Fig. 1.18 Normal pressure force on an element of aerofoil surface

so that
SZ, = -puSx per unit span
Similarly, for the lower surface

SZe =p& per unit span
We now add these two contributions and integrate with respect to x between x = 0
and x = c to get

Z = -Lcpudx + LCpcdx

But we can always subtract a constant pressure from both pu and pe without altering
the value of Z, so we can write

where px is the pressure in the free stream (we could equally well use any other
constant pressure, e.g. the stagnation pressure in the free stream).
Equation (1.58) can readily be converted into coefficient form. Recalling that the
aerofoil section is of unit span, the area S = 1 x c = cy so we obtain

[(Pu - P~) (Pe - prn)ldx
-
Remembering that (l/c)dx = d(x/c) and that the definition of pressure coefficient is

we see that

(1.59a)