Maximum angle of climb
Figure 7.11 shows the forces acting on an aircraft in a steady climb. If the climb is steady then there can be no net force acting on the aircraft either along the flightpath, or at right angles to it. If we consider the forces acting along the flightpath we can see (Fig. 7.11) that the sine of the climb angle is given by the difference between thrust and drag divided by the aircraft weight. Thus to operate at the maximum angle of climb possible we need the biggest possible value of thrust minus drag.
If the thrust minus the drag is equal to the weight we have a vertical climb, e. g. the Harrier (Fig. 7.12). If thrust minus drag is greater than the weight then the aircraft will be in an accelerating, rather than a steady climb.
If, however the difference between thrust and drag is less than the aircraft weight, some lift must still be provided by the wings. To be able to climb at all the aircraft must be operating at a height at which the engine is capable of producing more thrust than the drag of the aircraft.
If, for instance, the aircraft is flying straight and level initially we can plot the now familiar variation of drag with flying speed. Let us suppose that the
Fig. 7.13 Climbing flight
Increased throttle setting gives excess of thrust over drag for climb Best climb angle is obtained when thrust minus drag is maximum
aircraft is operating at point A on this curve. An increase in throttle setting will give an available thrust-minus-drag difference for climb as shown (Fig. 7.13). If we know the engine characteristics at the new throttle setting we can optimise the airspeed to give the best possible thrust/drag difference.
Here we must turn our attention to the type of powerplant being used once again. If we are dealing with a turbo-jet and thrust will not vary very much with speed in the operating range we are considering. All we need to do therefore is to gratefully accept the maximum thrust that the engine will give and fly at the speed which produces the least amount of drag (point A in Fig. 7.14).
If we are using a piston engine/propeller combination, we have already seen that the thrust falls with increasing speed and so we must reach a compromise between the requirements of airframe and powerplant and operate at a speed somewhat lower than the minimum drag speed in order to achieve the maximum angle of climb (Fig. 7.15).
At this point a word of caution is necessary. We have estimated the best climbing angle using the drag curves derived for straight and level flight. When the aircraft is climbing examination of the forces normal to the flightpath (Fig. 7.11) shows that the lift developed by the wing will be reduced by a factor equal to the cosine of the climb angle and is thus no longer equal to the aircraft weight. Our drag curve will therefore need to be modified and this, in turn, may change the best speed for climb.
A large number of aircraft, such as civil airliners and military transport aircraft, are not required to indulge in particularly violent manouevres. Although the rate of climb might be quite high, because the forward speed is also high, the angle of climb is frequently not very great. In such cases our original approximation will not be too far from the truth.