Efficiency

Now the efficiency of a propeller is the ratio of the useful work given out by the propeller to the work put into it by the engine. Mechanical work done is measured by the force multiplied by the distance moved, and so when either the force or the distance is zero, the useful work done is zero, and the efficiency nil. Thus when the propeller moves forward in each revolution a distance equal to the experimental pitch, the fact that there is no thrust means that there is no efficiency. Also, when there is no forward speed, there is no distance moved, no work done and therefore no efficiency. Between these two extremes are the normal conditions of flight.

It might be thought that the object of the propeller is to give the maximum thrust (T) with the minimum torque (Q), i. e. to give the maximum T/Q ratio. However, Figs 4.6 and 4.7 show that in order to get a high value of T/Q, two things are required – a high value of L/D and the optimum helix angle, which is theoretically around 45 degrees. The high value of T/D is fairly easy, and is an old problem; what is needed is a good aerofoil section, set at near the correct small angle to the relative air flow, and this means twisting the blade, as already explained.

The provision of the optimum helix angle is more difficult, as this would require matching the rotational speed to the forward speed. In practice, this is impractical, and the propeller is normally run at near constant speed, as described later. In any case, the optimum helix angle can only be obtained at one position along the blade, since the blade is twisted. However, the tip of the propeller is moving faster than the inboard sections, and thus tends to produce a high proportion of the thrust, so it is the angle of the tip that is most important. With fixed pitch propellers, a compromise on the pitch angle has to be made between high efficiency cruising, and high thrust for take-off.

Under conditions of maximum efficiency the advance per revolution is usually considerably less than the experimental pitch. The experimental pitch is sometimes called the ideal pitch, while the advance per revolution is the actual practical pitch. The difference between the two is called the slip, and is usually expressed as a percentage.

The calculation of propeller efficiency is quite straightforward. For example, if the total drag of an aeroplane at 65 m/s is 4.22 kN and the power developed by the engine when the aeroplane is flying at this speed is 336 kW, then –

Work given to propeller per second = 336 000 joules

Work done by propeller per second = 4220 X 65

= 274 300 joules

So efficiency of the propeller = Work got out/Work put in X 100 per cent

= (274 300/336 000) X 100 per cent

= 81.6 per cent

This represents the approximate value of the efficiency obtainable from a good propeller, although in some instances it may rise as high as 85 or even 90 per cent. The best efficiency is obtained when the slip is of the order of 30 per cent.

For those who prefer to examine this question in terms of mathematical symbols the efficiency of a propeller can be deduced as follows –

Tet v = forward velocity in m/s

T = thrust of propeller in newtons n = revolutions per second of engine Q = torque exerted by engine in N-m

Work done by thrust T at v metres per second = Tv joules per second, or watts

Work given by engine = 2nQ joules per rev

= 2miQ joules per second, or watts Efficiency of propeller = (Tv/2imQ) X 100 per cent