POWER REQUIRED FOR FLIGHT - AEROPLANE OR AIRPLANE When an aeroplane of conventional design and normal propor tions is flying horizontally (in air of a given density) the power 'Angle of the chord to the longitudinal axis of the aeroplane. The chord of the wing sections in fig. 2 is indicated by a straight line.
of the engine is disposed of in the following ways : (a) About 25% is lost owing to the inefficiency of the air screw.
(b) From 30% to 45% is used in overcoming the resistance of the air to the passage of the body, including the engine itself, the undercarriage and the exposed part of the wing structure, etc.
(c) From 45% to 3o% is similarly absorbed by the resistance of the wings.
The choice between the alternative figures in (b) and (c) depends on the speed of flight, the former corresponding to low, and the latter to high speeds. The resistance of the parts included in (a) varies practically as the square of the speed of flight, and the corresponding power therefore as the cube. The resistance of the wings (c) may be further subdivided as follows : (c. .r) From a third to three-quarters is due to the equivalent of friction of the air on the surface of the wings (the profile drag). This varies as the square of the speed, and the power as the cube. If the area of the wing is changed, the profile drag changes in pro portion. Each wing section has a typical coefficient of profile drag, and, apart from maximum lift, this is in fact nearly all that distinguishes one section from another.
(c. 2) From two-thirds to a quarter is due directly to the action of the wings as generators of a lifting force (the induced drag of Prandtl; see AERODYNAMICS). This varies inversely as the square of the speed, and the power therefore inversely as the speed. It does not depend on the shape of the wing section, or on the area of the wings, but (for a given lifting force, i.e., weight) only on their overall width or span, being inversely proportional to the square of the span. This induced resistance is the essential fea ture in which transport by aircraft heavier than air differs from all other methods, for in no other is it necessary to expend energy in order to sustain the vehicle. About 8% of the fuel used by a normal aeroplane is used in this way (fig. 5).
This division of the resistance of the wings into two parts—one of which increases with the speed of flight, while the other de creases, the former dependent (broadly speaking) only on the section and shape of the wings, the latter independent of these factors and governed by the extent to which the span of the wings allows the aeroplane to "grip" the air (see AIRSCREW)-was originally suggested by F. W. Lanchester. It lay dormant for some years, largely because there was not forthcoming any ade quate theory by means of which it would be given quantitative expression in terms of the dimensions of the wings. This expres sion has been rendered possible by the work of L. Prandtl of Gottingen and his collaborators, with great advantage to the technique of aeroplane design. Its chief merit is that it enables a designer to examine the economics of wing proportions without continual resort to model experiments. It has been abundantly verified by comparison with experiments.
In normal flying conditions, as opposed to the special conditions characteristic of arising from and alighting on the ground, the speed of an aeroplane may vary from I•2 to 3.5 times its stalling speed. The upper of these two figures can be raised by the pro vision of more power. At its top speed the engine is working at its full power, which is not an economical condition from the point of view either of the life of the engine or of fuel consumed per ton-mile. The most economical speed, taking into consideration all the various factors, is at about 6o% to 75% of maximum power. The diagrams in fig. 5 show the way in which the power required for flight depends on the speed. The maximum brake horse-power of the engine has been taken to be ioo and the mini mum speed 5om. per hour. These diagrams illustrate the rapid rise of power required with the speed of flight. For such an aero plane the most economical speed would be about 75m.p.h., requir ing about so brake horse-power.
If the engine throttle is fully opened at the lower of the two speeds considered above, the aeroplane will climb. The angle of climb for modern commercial aeroplanes is from i in i o tor in 15. For high-powered war machines it may rise tor in 6, or more. When the engine is cut off the aeroplane will lose altitude, its path being inclined downwards at a corresponding angle, and the necessary power will be supplied by gravity. The angle of de scent for a modern aeroplane is from i in 6 to 1 in 8. Thus a passenger in an aeroplane will not in general be subjected to greater changes of inclination of the direction of motion than one who travels by road.