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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).
Article from 'The Autocar' magazine discussing the principles and conditions for ideal motor car acceleration.

Identifier  ExFiles\Box 113\2\  scan0003
Date  14th September 1912
  
THE AUTOCAR, September 14th, 1912. 491

The Acceleration of a Motor Car.

one-third; this should not cause slipping if the clutch is let in gently, but with sudden starting the momentary acceleration may rise high enough to cause slipping to begin, and once begun it is liable to continue.
Ideal Acceleration.—Ideal acceleration would require to conform to the following conditions: It should at any moment absorb the full output of which the engine is capable, i.e., the horse-power exerted should be constant, and it should be graduated so that the acceleration does not increase or decrease faster than a certain rate.
It may be said at once that neither of these conditions can be fulfilled by the motor car as at present made. Material alterations would be necessary. To yield a constant horse-power throughout the starting period—and when hill-climbing—it would require to be fitted with an infinitely variable gear box; instead of there being three torque curves, as in fig. 1, there would be only one, viz., the rectangular hyperbola, which would be the envelope of an infinite number of such curves. The limit to the vertical height to which such a hyperbolic torque curve could usefully be taken would be the limiting torque at which the rear road wheels would slip.
The curve corresponding to these conditions is that shown at A B C in fig. 7. Modification is needed even in this curve, however, if the acceleration is to be graduated with time. To provide for the acceleration not growing faster than a certain number of feet per second per second in a second it is necessary to replace the vertical line O A with the parabolic arc shown dotted.
To conform to these ideals the car would probably need either electric or hydraulic transmission. Both of these have been shown to be capable of giving a hyperbolic torque curve, and the former has been found able to give a graduated acceleration. Any successful application of them should therefore find a wide use both on road and rail.
  
  


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