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).
Mathematical development of the law of speed scale contraction relating to tyre diameter and road speed.
| Identifier | ExFiles\Box 59\2\ Scan123 | |
| Date | 23th March 1931 guessed | |
| -3- (2) The development of the mathematical application of the law of speed scale contraction. For the purpose of developing the law of scale contraction :- Let Do be the effective driving wheel tyre diameter at normal inflation and dead slow road speed and D that at any road speed S. The effect of centrifugal force is that D is increased slightly and progressively as the speed increases. The acting forces are proportional to the square of S. Owing to the form of the tyre it cannot, however, be said that the increment in tyre diameter resulting from speed will also be proportional to S², it being clear that the tyre more easily deflects in the early stages than in the later. It is therefore probably approximately true to say that the increment of tyre diameter is proportional to the speed i.e. to S and not to S². Thus we may write :- D = Do + aS (a being a constant) we have D/Do = 1 + a/Do .S and Do/D = 1 - a/Do .S (approximately by Binomial Theorem) whence 1/D = 1/Do - a/Do² .S The road wheel revolutions per mile :- R = K/D (where K is some constant) = K/Do - aK/Do² .S = Ro{C. C. Rose - Export Manager} - bS{A J. Barnes - Assistant Manager} where Ro{C. C. Rose - Export Manager} is the dead slow wheel revolutions per mile and b another constant. | ||