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The Airscrew. The Rankine-Froude theorems on propulsion by the sternward projection of a stream of the surrounding fluid by the use of a screw-propeller, or other means, are well known. These state that the highest efficiency is attained by the projection of the greatest amount of fluid at the lowest speed, and indicate the use of propellers of the greatest practicable diameter. The only waste considered is the kinetic energy imparted to the fluid. An upper limit of efficiency is thus determined in terms of the diameter and the thrust of the propeller and the speed of motion. The design of marine screws proceeds mainly upon empirical lines based upon experience. The early airscrews were designed by a similar process of trial and error.

F. W. Lanchester (Aerodynamics, 1892), regarding the airscrew blade as a twisted aeroplane wing rotating about one tip as it ad- vances through the air, assumed that the total reaction may be ob- tained by integrating the forces which would act upon elements at successive radii if these were elements of a complete wing. This method of treatment, which was also advanced by Drzewiecki, has provided the basis of airscrew design. As first applied, the theory was incomplete, chiefly because it ignored the fact that the blades in following each other act on disturbed air. For example, if the number of blades be increased, the theory indicates no fall in the efficiency, and reactions directly proportional to the number of blades, which experiment showed to be untrue. Moreover, the effi- ciency so calculated might exceed that given by the Rankine-Froude theorems. It was therefore sought to combine the two aspects of the action of the airscrew in one theory, and the further theorem of Froude that the stream has reached half the final velocity at the propeller disc appeared to provide a means of estimating the degree of disturbance of the air in which the blade acts. It is generally agreed that the original theory is over-corrected by this modification. The blade element under consideration is itself partly causing the acceleration of the stream, and this acceleration is the total and not merely the initial disturbance of flow in the neighbourhood of the element. Figures for the reaction on the elements were obtained by testing a small wing of the same section in a wind produced artifi- cially in a " wind tunnel." This wing produces a disturbance of flow equivalent in an airscrew to an acceleration.

It was found in practice that the assumption of an arbitrary ac- celeration less than one-half of the final acceleration made it pos- sible by the use of the theory of Lanchester to predict the aerody- namic performance of an airscrew with a valuable accuracy. The com- bined theory leads to two important conclusions, completely verified by experience. Firstly, the efficiency increases with increasing ratio of the pitch at which the screw operates to its diameter up to an optimum value seldom employed in practice. Secondly, for given thrust and speed the diameter must be so large that it acts upon a sufficient mass of air per unit of time to attain a satisfactory effi- ciency. The latter brings the theory into conformity with the law of Rankine and Froude. The former in practice brings the airscrew designer into conflict with the designer of aeroplane motors. Higher crankshaft speeds are required to produce a light-weight internal-combustion engine than are demanded by this condition for high airscrew efficiency. This has resulted in a large number of aeroplane engines being arranged to drive the airscrew through a reduction gear. The point at which gearing becomes desirable in practice is not easily determined. It depends upon a number of factors. Among these are a small loss of energy in the gears, added weight and cost, various practical reasons for dispensing with addi- tional mechanism if this is not of sufficient value and the adverse effects of the greater torque of the slower running airscrew upon the control of the aeroplane, which must be offset against the gain in airscrew efficiency. In this question is also involved the considera- tion of the strength of the airscrew to resist the stresses due to ro- tation. This imposes a limit upon diameter, decreasing as the speed of rotation is increased, which may result in a further reduction of efficiency for the high-speed airscrew.

During the war large aeroplanes were built for which single en- gines of the required power were not available. In so far as two en- gines were sufficient, these were placed on either side of the main body of the aeroplane, each driving a separate airscrew. It became necessary ultimately to install four engines in a few aeroplanes and these were placed in pairs driving two pairs of airscrews in tandem. The design of the rear propeller in this arrangement involves an estimate of the rate at which air is supplied to it by the screw in front. With the same limitation of diameter the efficiency of pro- pulsion attainable is approximately the same as if the two engines were coupled and drove a single airscrew of the same diameter, but is less than would be obtained by the use of four separate systems of propulsion. The tandem system is preferred for reasons of com- pactness and the difficulties of control attendant upon the use of a number of lines of thrust.

The aeroplane propeller, unlike the propeller of ship or airship, is required to transmit the full power of the engine at different speeds of flight, both when the craft is flying level at full speed, and when it is flying slow in order to climb. The airscrew cannot be designed to discharge both functions in the most efficient manner possible in each case. This was of little consequence in the early days of flight when the range of flying speed was small ; but as the range was in- creased, some attention was paid to the design of airscrews of vari-

able pitch. These have been experimented with, notably at the Royal Aircraft Establishment, with some success; but they have not been used so far in service. If any device for preventing the loss of engine power with increasing height by an initial compression of the charge to ground-level density should come into use, the variable airscrew would become necessary. Such devices are, however, still in an experimental stage.

The number of blades in an airscrew is commonly two. but four blades have been extensively used. The two-bladed airscrew has an advantage in convenience for storing and transport. The use of more blades reduces vibration due to errors in blade angles, and eliminates gyroscopic vibration when the aeroplane is turning, and vibration due to aerodynamic causes both when the axis of rotation is inclined to the line of flight and when the aeroplane is turning. Airscrews have been almost universally made of timber, which should be continuous through the boss from blade tip to blade tip. This has prevented the use of three blades. In deciding the number of blades, two or four, the designer is largely guided by the blade area required, which depends upon the speed of motion of the blade and the power transmitted. Thus a slow-running airscrew has conveniently four blades, whereas for a high-speed screw two blades are preferred. A four-bladed high-speed screw might require such narrow blades that in order to resist the bending due to the thrust they would be so thick as to reduce the efficiency seriously.

At the speed of flight of an aeroplane the changes of pressure of the air flowing past the wings amount only to a small fraction of the atmospheric pressure. The blade tips of airscrews, however, commonly reach speeds of 800 ft. per second, approaching the veloc- ity of sound in air. It follows that while the wings may be regarded as operating in a fluid of constant density, the compressibility of the air rriay have important effects in the case of the airscrew. With increase of blade speed effects must be anticipated similar to the phenomenon of cavitation experienced with marine screws. Such effects in a gas may, however, occur gradually with increasing speed. Experiments with small model wings in a wind tunnel in America showed a fall in lift and increase in resistance at speeds in the neighbourhood of 6po ft. per second at large angles, and it is clear that the distribution of low pressure over the upper surface cannot continue indefinitely. It appears, however, that airscrews so far designed have been free from any marked effect of this nature. The efficiency estimated has been attained in practice, although designers to a certain extent miscalculated the power required to drive airscrews as the speed of the blade tips was increased. The error cannot, however, be ascribed to the effects of compressibility owing to uncertainty as to many other factors involved. On the whole the method of aerodynamic analysis led to sufficiently accurate design.

The screw-propeller as a mechanism for the transmission of power is convenient and efficient. In the airscrew narrower blades can be used than in the marine propeller, and efficiencies as high as 85 % have been attained with airscrews of high pitch and large diameter, smaller fast-running airscrews giving efficiencies of 75 per cent.

FORWARD SPEED

FIG. 153. Variation of Thrust at constant Torque. FIG. 15. Variation of Thrust, Torque and Effi- ciency of an Airscrew with forward speed at constant rate of revolution.

Owing to the light weight and high tensile strength of timber for its weight, the designer has found in wood his most convenient material. African walnut has proved the best timber when the stresses are most severe. Honduras mahogany is satisfactory for most purposes. Spruce and poplar have also been used, but are not suitable for higher powers and speeds. The screw is constructed of planks, or laminations, about an inch thick, glued together and cut to shape. The grain of the wood should be straight and run as far as possible along the blade. The method of construction secures a good approximation to this requirement. Timber has the advan- tage of large hysteresis and consequent power of damping vibra- tions. The Wright brothers' airscrews were made of spruce cut from a single piece of timber. An interesting design appeared in 1913 in the " Garuda " airscrew, of laminated wood construction with the blades tilted forward so that to a large extent stresses due to rotation neutralized those due to thrust. The forward tilt was obtained by bending the laminations during manufacture, a rather questionable practice. This method of balancing stresses has not