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 examination of tyre energy loss, comparing drum and flat road performance, and analysing dynamical losses at high speeds.
| Identifier | ExFiles\Box 158\2\ scan0033 | |
| Date | 5th June 1939 | |
| - 3 - BY/B.4/G.5.6.39. Mathematical examination gives in this case the result :- Energy loss per sec. on drum ---------------------------- = (1 + r/R)^1.75 " " " " " flat road Thus we see that if the drum radius R is only equal to the tyre radius r, then the tractive resistance or energy loss per second on the drum will be (1 + 1/1)^1.75 = 3.36 times that on a flat road at the same speed. (3) Dynamical Losses at High Speeds. (Standing wave or bulge). [Diagram labeled Fig. 3 showing a cross-section of a tyre with points A, B, C, O and vectors V, Y, YY] At the rear end B of the road contact area the tyre tread elements which are at rest at B are required to have the velocity corresponding to the tyre tread an instant later. At high speeds this sudden change of velocity represents a very high acceleration, and would require an extremely large force acting on the tread elements at B, supplied by the tyre tread just above here which is leaving the ground. As a result the tyre tread leaving the ground bulges out as shown, taking such a shape that the lifting forces on the tread elements, due to the stretched out shape of the bulge, equal the acceleration forces on the elements, reduced as they are by the fact that the elements only rise from the ground to the bulge outline instead of to the normal tread circle. The effect of the bulge, by displacing the tyre inertiaforce Y to the rear of B as shown, is to increase the rolling resistance couple at a rate greater than the square of the speed. The bulge effect will be accentuated on the test drum because the change of vertical velocity is so much greater at the point B than it is on the road. The bulge effect also, will be worse with a heavy tread and with a low inflation pressure, which increases the distance C B, as well as reducing the virtual stiffness of the casing. | ||