GENERAL POINTS ARISING FROM THE FROUDE EQUATION

The inflow factor is large if the increase of flow velocity produced by the propeller is large. If, for example, v, the flow speed increment added by the propeller to the slipstream, is equal to the flight speed, so that the speed of the slipstream behind the aeroplane becomes V + 2V = 3V, the ratio of v/V is 1.0 and the Froude efficiency equals 0.5. If the inflow factor is smaller, an increase in efficiency results: if v is only one tenth of V so that the

slipstream velocity aft is V + (1/5 X V) or 1.2V, the ideal efficiency is 0.909. A given thrust can be obtained either by using a propeller of large diameter driven at a low rate, to produce a small pressure difference spread over a large disc area, or by a small propeller turning faster, creating a larger pressure difference spread over a smaller disc. The large diameter propeller, as the above examples show, would be much more efficient This point applies quite generally for model aeroplanes.

With full-sized aircraft propellers and helicopter rotors, a limitation to propeller diameter is set by the tip speed of the blades. If this approaches the speed of sound, efficiency falls off, quite apart from the high stresses and noise produced. Model propellers rarely enter such regions although it is possible for them to do so. There are other obvious limits for models and all aeroplanes to the practical diameter of a propeller. Ground clearance and undercarriage length usually prevent the use of the most efficient propeller diameter when the engine power is great

With model internal combustion engines, which are rarely geared down, rates o. rotation at maximum power are high and it is important, in competition flying, that the engine should run at its maximum power r. p.m. when required. A large diameter propeller will not develop more thrust than a small one, if it overloads the engine and prevents it reaching its best r. p.m. But it follows that if two engines of equal maximum power output are available and one runs at a lower r. p.m. than the other, more thrust will be obtained from a larger propeller on the slower engine. A crucial point here is the diameter to pitch ratio, of which more appears below.

The inflow factor also depends on the flight velocity. It is large if V is small and vice versa. If V is zero, as when die aeroplane is standing on the ground with engine running, no matter how much velocity the slipstream has, the propeller efficiency is zero. As the aircraft speeds up, efficiency increases. A limit is set to the attainable (level flight) speed of a model aeroplane by the total drag which will increase as the model accelerates until it comes to equal the thrust The rate of climb is subject to equivalent restrictions. If the drag is reduced by some aerodynamic improvement the potential will not be fully realised unless the propeller is changed to one which reaches its maximum efficiency at a higher speed. Every change to the aircraft requires a change to the propeller, if the best performance is to be attained.

On the other hand, if a propeller is designed very exactly to reach its peak efficiency at a particular flight attitude, speed and power, it will, at all other times, be working ‘off design’ and will be less efficient In particular, take-off performance, when propeller efficiency is bound to be low because V is small, will suffer if a high speed propeller is used. Racers need to take off smartly and accelerate to their best speed quickly. With simple propellers, some compromise has to be struck. With aerobatic models a propeller which has a narrow peak of efficiency will perform badly, because the airspeed varies constantly during the aerial pattern flying. In a vertical climb, V is low, yet the climb must be maintained. Yet rapid acceleration and high entry speed is needed for some manoeuvres. A propeller with a wide tolerance is required. The same applies, though with less urgency, to sport flying models generally.