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From the Rolls-Royce experimental archive: a quarter of a million communications from Rolls-Royce, 1906 to 1960's. Documents from the Sir Henry Royce Memorial Foundation (SHRMF).
Technical analysis of increasing fan power with speed, discussing propeller and blade design.

Identifier  ExFiles\Box 181\M8\  img013
Date  1st December 1919
  
-2- Contd.

(2) Rate of increase of power with speed.

The speed of the car and the speed of the fan increase at the same rate. It therefore follows that the power absorbed by the fan will increase as the cube of the speed of the fan, and the efficiency of the fan will remain constant.

To make the power increase at any less rate involves either :-

(i) Making the speed of the fan increase at a slower rate than the speed of the car, in which case the power could be made to decrease near to zero at high speeds.

(ii) Using a variable pitch propeller.

The twist is approximately proportional to n². Hence if there is any twist at all it will get greater as the speed goes up, this keeping down the power absorbed. It is quite impossible by this means to prevent the power increasing to some considerable extent since the thrust must increase if the blade twist is to increase. This decreasing pitch effect is dangerous in a wooden screw since the blades tend to split. It can be obtained in your present type of construction if you sweep back the blades opposite to the direction of rotation and make them of thin gauge steel. I doubt whether aluminium thick enough for general strength would be sufficiently flexible. The twisting effect and also the efficiency would be greater if you rounded off the tip on the leading edge.

With the blade angles I have recommended the efficiency would increase slightly as the blade twisted, or alternatively, as the belt slipped (within limits).

If you have any facilities for doing so it would be interesting to try three amounts of sweep-back and to measure the power absorbed at various speeds in still air over as wide a range as possible.

I should add that if the back pressure in the bonnet amounts up at high speed this makes matters worse, since K in the expression Torque = PKq n²D⁵ will increase and the power will increase at a greater rate than the cube of the speed.

I regret that I cannot make any more definite recommendations.

I could design a wooden screw which would within limits tend to increase its efficiency as the belt slipped but I should not care to make it such as to twist under load.
Yours faithfully,
(sgd) H.C. Watts.
  
  


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