Page 264 - Aircraft Stuctures for Engineering Student

8.4 Symmetric manoeuvre loads 245

The loads are in static equilibrium since the aircraft is in a steady, unaccelerated,
level fight condition. Thus for vertical equilibrium
L+P- w=o (8.7)

for horizontal equilibrium
T-D=O
and taking moments about the aircraft’s centre of gravity in the plane of symmetry

La - Db - Tc - Mo -PI = 0 (8.9)
For a given aircraft weight, speed and altitude, Eqs (8.7), (8.8) and (8.9) may be solved
for the unknown lift, drag and tail loads. However, other parameters in these
equations, such as Mo, depend upon the wing incidence a which in turn is a function
of the required wing lift so that, in practice, a method of successive approximation is
found to be the most convenient means of solution.
As a first approximation we assume that the tail load P is small compared with the
wing lift L so that, from Eq. (8.7), L M W. From aerodynamic theory with the usual
notation

Hence
+pv2sc, M w (8.10)

Equation (8.10) gives the approximate lift coefficient CL and thus (from CL - a
curves established by wind tunnel tests) the wing incidence a. The drag load D follows
(knowing V and a) and hence we obtain the required engine thrust T from Eq. (8.8).
Also Mo, a, b, c and I may be calculated (again since V and a are known) and Eq. (8.9)
solved for P. As a second approximation this value of P is substituted in Eq. (8.7) to
obtain a more accurate value for L and the procedure is repeated. Usually three
approximations are sufficient to produce reasonably accurate values.
In most cases P, D and T are small compared with the lift and aircraft weight.
Therefore, from Eq. (8.7) L M W and substitution in Eq. (8.9) gives, neglecting D
and T

(8.11)

We see from Eq. (8.1 1) that if a is large then P will most likely be positive. In other
words the tail load acts upwards when the centre of gravity of the aircraft is far aft.
When a is small or negative, that is, a forward centre of gravity, then P will probably
be negative and act downwards.

8.4.2 General case of a symmetric manoeuvre
l*-llll_-----s._~_-~ _YI ._I_Y_-_..-_-*I,_I_Y_LIY.I-Ylli
In a rapid pull-out from a dive a downward load is applied to the tailplane, causing the
aircraft to pitch nose upwards. The downward load is achieved by a backward
movement of the control column, thereby applying negative incidence to the elevators,