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 investigation into tyre power loss, including a formula and analysis on a test drum.
| Identifier | ExFiles\Box 158\2\ scan0032 | |
| Date | 5th June 1939 | |
| - 2 - BY/B.4/G.5.6.39. An approximate mathematical investigation, assuming the surface of road contact to be an ellipse, shows that the power loss is of the form E = (k m W^1.5 V^3) / (p^1.5 r^1.75 r1^0.25) where E = work dissipated per second. m = mass of tyre tread per unit area of periphery. W = total load on wheel. p = inflation pressure. r = radius of tyre tread in side view. r1 = radius of cross section, (assumed circular), of tyre. V = linear velocity of wheel centre. k = a constant. The value of large diameter wheels with light treads, inflated to high pressures and carrying light loads is thus clearly demonstrated, when maximum speeds are to be attained. It will be observed that, with a given inflation pressure, the power loss increases more rapidly than the weight W, varying as the 1.5th power of W. (2) On test drum. As each element of the tyre tread arrives at A its vertical velocity (= ω.AC) is not merely brought to zero, but is reversed in direction, being given the upward velocity of the corresponding point on the drum (= Ω.AC) Thus the total change of velocity is (ω + Ω). AC. The consequent change of momentum of the tyre elements requires a mutual torque between tyre and drum, resisting the motion of each, and causing an energy loss in the case of each which has to be made up from outside. [Image of a wheel on a test drum, labeled 'Wheel', 'Drum', 'Fig 2', and showing various forces and radii such as 'ω', 'r', 'Ω', 'R', and points 'A', 'B', 'C', 'D', 'E'.] | ||