## 842 General case of a symmetric manoeuvre

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,

or horizontal tail if the latter is all-moving. If the manoeuvre is carried out rapidly the forward speed of the aircraft remains practically constant so that increases in lift and drag result from the increase in wing incidence only. Since the lift is now greater than that required to balance the aircraft weight the aircraft experiences an upward acceleration normal to its flight path. This normal acceleration combined with the aircraft's speed in the dive results in the curved flight path shown in Fig. 8.9. As the drag load builds up with an increase of incidence the forward speed of the aircraft falls since the thrust is assumed to remain constant during the manoeuvre. It is usual, as we observed in the discussion of the flight envelope, to describe the manoeuvres of an aircraft in terms of a manoeuvring load factor n. For steady level flight n = 1, giving 1 g flight, although in fact the acceleration is zero. What is implied in this method of description is that the inertia force on the aircraft in the level flight condition is 1.0 times its weight. It follows that the vertical inertia force on an aircraft carrying out an ng manoeuvre is nW. We may therefore replace the dynamic conditions of the accelerated motion by an equivalent set of static conditions in which the applied loads are in equilibrium with the inertia forces. Thus, in Fig. 8.9, n is the manoeuvre load factor while / is a similar factor giving the horizontal inertia force. Note that the actual normal acceleration in this particular case is (n — l)g.

For vertical equilibrium of the aircraft, we have, referring to Fig. 8.9 where the aircraft is shown at the lowest point of the pull-out

For horizontal equilibrium

and for pitching moment equilibrium about the aircraft's centre of gravity

Equation (8.14) contains no terms representing the effect of pitching acceleration of the aircraft; this is assumed to be negligible at this stage.

Again the method of successive approximation is found to be most convenient for the solution of Eqs (8.12), (8.13) and (8.14). There is, however, a difference to the procedure described for the steady level flight case. The engine thrust T is no longer directly related to the drag D as the latter changes during the manoeuvre. Generally, the thrust is regarded as remaining constant and equal to the value appropriate to conditions before the manoeuvre began.

### Example 8.3

The curves CD, a and CMiCG for a light aircraft are shown in Fig. 8.10(a). The aircraft weight is 8000 N, its wing area 14.5 m2 and its mean chord 1.35 m. Determine the lift, drag, tail load and forward inertia force for a symmetric manoeuvre corresponding to h = 4.5 and a speed of 60m/s. Assume that engine-off conditions apply and that the air density is 1.223 kg/m2. Figure 8.10(b) shows the relevant aircraft dimensions.

As a first approximation we neglect the tail load P. Therefore, from Eq. (8.12), since T = 0, we have

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