Page 240 - Aerodynamics for Engineering Students

Finite wing theory 223

Thus
lift
r02s' = area under general distribution = -
PV
Hence
total lift
s' - (5.16)
s 2spvro
2s' is the distance between the trailing vortex core centres. From Eqn (5.47a) (see
page 246) it follows that
L = pV2'2S22rA1

and substituting also
7r
I?,-, = 4sVCA, sin n -
2
s' - pV222rA1
-
-
s 2p V24s2C A, sin n 5
7r
-
-
- A1
4 [AI - A3 + A5 -AT.. .]
For the general case then:
(5.17)

For the simpler elliptic distribution (see Section 5.5.3 below):

A3 = A5 = A7 = 0

(5.18)

In the absence of other information it is usual to assume that the separation of the
trailing vortices is given by the elliptic case.

5.3.1 Formation flying effects
Aircraft flying in close proximity experience mutual interference effects and good
estimates of these influences are obtained by replacing each aircraft in the formation
by its equivalent simplified horseshoe vortex.
Consider the problem shown in Fig. 5.15 where three identical aircraft are flying in
a vee formation at a forward speed V in the same horizontal plane. The total mutual
interference is the sum of (i) that of the followers on the leader (l), (ii) that of the
leader and follower (2) on (3): and (iii) that of leader and follower (3) on (2). (ii) and
(iii) are identical.
(i) The leader is flying in a flow regime that has additional vertical flow com-
ponents induced by the following vortices. Upward components appear from
the bound vortices a2c2, a3c3, trailing vortices c2d2, a3b3 and downward