Page 244 - Aerodynamics for Engineering Students

Finite wing theory 227

Ground
level

-roe s’ ys’- -ro

Fig. 5.18

Total change in drag AD, across the span is the integral of Eqn (5.20) from -s‘ to s‘ (or twice
that from 0 to s’). Therefore

From the geometry, Y! = 4h2 + (s‘ + JJ)~ and r; = 4h2 + (s’ - v)~. Making these substitutions
and evaluating the integral

With W = pvrom i.e. and s‘ = (7r/4)s (assuming elliptic distribution):

and substituting the values given
AD, = 1390 N
A simpler approach is to assume that mid-span conditions are typical of the whole wing.
With this the case

S’
Q1 = Q2 = 8 = arccos
VFTm
and the change in drag is to be 1524N (a difference of about 10% from the first answer).

5.4 Vortex sheets

To estimate the influence of the near wake on the aerodynamic characteristics of
a lifting wing it is useful to investigate the ‘hypothetical’ bound vortex in greater
detail. For this the wing is replaced for the purposes of analysis by a sheet of vortex