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).
The arguments for applying the law of speed scale contraction to speedometers, both with and without mile counters.
Identifier | ExFiles\Box 59\2\ Scan127 | |
Date | 23th March 1931 guessed | |
-7- (3) The argument for the application of the law of speed scale contraction to the case of a speedometer without mile counter portion. Consider, in the first instance, the drive ratio of such an instrument to the road wheels to be such that the speed indications are correct at very slow speeds (i.e. mathematically at infinitely slow speeds). The speed indications at higher and higher speeds will then fall away from their corresponding correct speeds according to a parabolic law and no speed indication will be actually correct but all of them more or less low. We can now, by increasing the drive gear ratio slightly, increase all the indications in such a way as to make the indication be quite correct at some one speed which is open to our choice. Below this speed the indications will be high by relatively slight amounts and above this speed the indications will be low by amounts greater (as a result of the parabolic law) than the amount by which the lower speeds are high. If our range of speed were 0 to 90 miles per hour and we in this way arranged for correct speed to be indicated at 60 miles per hour, this would appear to be reasonably correct, for on the basis of the times of running at all speeds being equal, the speed indications would then average out to correctness. More particularly, however, it would prevent the speed readings at high speeds being too much low. By contracting the scale according to our law the speed indication could be made correct at every speed, but in view of the fact that average correctness without contraction can be secured as above, and further that the resulting error is not great, the advantage of speed scale contraction, though existent, would be comparatively small. (4) The further argument for the application of this law of speed scale contraction to a speedometer which combines the function of mile counter with that of speed indicator. Consider an instrument with an internally exactly correct relation between the mile counter portion and the speed indications ( the instrument is considered to be at some one temperature say 35°C.). Consider further that the drive of this instrument in relation to the road wheels is such that at very slow speeds | ||