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 discussing the theory and graphical representation of motor car acceleration.
| Identifier | ExFiles\Box 113\2\ scan0001 | |
| Date | 14th September 1912 | |
| THE AUTOCAR, September 14th, 1912. 489 The Acceleration of a Motor Car.* By H.{Arthur M. Hanbury - Head Complaints} E.{Mr Elliott - Chief Engineer} Wimperis, M.A. THE acceleration of any given motor car at any moment depends primarily upon two factors—(1) the engine torque; (2) the gear ratio in use. The former is governed by the total cubic capacity of the cylinders of the engine, and the latter by the gear box ratio corresponding to the gear in use at the moment. The proportionality of torque to cylinder volumes is based upon the experimentally ascertained fact that the mean pressure is not appreciably affected by cylinder dimensions in any four-stroke petrol engine as usually built. Given this constancy of mean pressure, it follows that the mean torque must depend upon the product of cylinder area by crank throw, i.e., upon D² L, the cylinder displacement. An interesting corollary to this is the deduction that for any given gear ratio on a given car the torque curve against car speed will be identical for all engines of equal volume which may be fitted to the car. A graphical construction affords the readiest way of tracing the relationship between acceleration, torque, and gear ratio. Thus in fig. 1, A B is the torque curve on top gear, C D the torque curve on second gear, and E F that on bottom gear (taking the case of a three-gear car). These torque curves are plotted with car speed horizontally and pounds per ton of equivalent tractive effort vertically. A definition of the vertical co-ordinate would be that it is the number of pounds of tractive effort per ton weight of vehicle at the road wheels equivalent to the engine torque at that speed. On the same diagram, and to precisely the same scale, it is possible to plot the curve G H, representing at each speed the total resistance to motion, including the friction of any internal gearing between the clutch and the road wheels. Now, at the point K two of these curves cross, showing that at that point the tractive effort due to the engine is exactly balanced by the resistance to motion. This point therefore gives the speed—some 32 m.p.h.—at which the car would travel with throttle open on a level road. The effect of climbing a gradient is to increase the resistance to motion by an amount proportional to the gradient, and the resistance curve G H rises, keeping parallel to itself, by this amount, so that the point K moves in to the left, showing that the steady speed will be less. At the speed O S the resistance is only M S, whereas the engine effort is equal to L S; the excess force L M produces acceleration if the road be level, or a combination of acceleration and hill-climbing ability if the road be rising. When the road is level the whole of M produces acceleration, and the amount of that acceleration can be directly scaled off by the length of L M (1ft. per second per second is very nearly equivalent to 70 lb. per ton). The relationship between the three torque curves shown in fig. 1 is very simple. A B is the torque curve on top gear plotted directly from a bench test diagram. C D is the same curve compressed horizontally and expanded vertically. The ratio of this compression and expansion is the ratio of the engine revolutions per minute at any given car speed when on top gear to the engine revolutions per minute at the same car speed when on second gear. It will be readily seen that corresponding points on the torque curves will lie on the same rectangular hyperbola, and this gives an easy graphical construction for drawing the curves E F and C D when A B is given and the gear ratios of each gear are known. The rectangular hyperbola which just touches each of these curves touches them at the points of maximum horse-power. Each of the torque curves thus obtained requires, properly, its own resistance curve, since the frictional loss between clutch and road wheels will depend upon which of the gear wheel combinations in the gear box is in use—most of the gear box friction arises from the churning up of the grease or oil in use, is not sensitive to the amount of torque transmitted, but rises rapidly with speed. There should, therefore, be three resistance curves, each a little higher than the last. But it is found to be far simpler to keep to the one resistance curve and to lower the curves E F and C D by the amount of this extra friction. This convention greatly simplifies the diagram. Thus, on bottom gear, the maximum possible acceleration can be directly scaled from the length N P. In this manner it is possible to predict the acceleration on each gear at any car speed, and from the figures so obtained to make a graph of predicted acceleration on a car speed base. When such a graph has been obtained it is sometimes desired to convert it into one based on time instead of on car speed. To do this we must plot on the car speed base the reciprocal of the acceleration and measure the area between this curve and the horizontal axis; these areas will give the time in seconds corresponding to each acceleration value, and the acceleration and time graph can then be constructed. The exactitude of this procedure follows from the relationships— ∫ 1/a . dv = ∫ dv/v̇ = ∫ dt The curves in fig. 1 have been drawn to represent to scale the case of a 15 h.p. (R.A.C. rating) touring car with hood and screen in use. From this we will proceed to predict the acceleration-time graph. The first difficulty that arises lies in the fact that the car does not start with the engine in gear and the curve E N F does not meet the vertical axis. For reasons explained later this is met by drawing the dotted line T N and treating it as a part of the bottom gear torque curve. The acceleration speed graph shown by the firm line in fig. 2 is obtained from fig. 1 by direct scaling, as already explained. The dotted curve gives the reciprocal of the acceleration, and the shaded area measures the time taken from rest to attain an acceleration equal to A C. The acceleration-time graph thus predicted is shown in figs. 3 and 4, allowing an interval of one second to effect the gear changes from bottom to second and from second to top. The distinction between figs. 3 and 4 is that in the former the driver is assumed to change gear at 2,000 r.p.m., and in the latter at 1,600 r.p.m.; also that in the former the gear box friction has not been allowed for, whilst in the second it has. It will be seen from fig. 2 that the maximum possible acceleration is about 1.1ft. per second per second on top gear, 3.0ft. per second per second on second gear, and 7.0ft. per second on bottom gear. Experimental Measurements.—The above is a simple method of predicting the acceleration of a motor car; it remains to describe how this acceleration can be experimentally measured, Fig. 1. — Motor car torque and resistance curves. Fig. 2. — Method of predicting the acceleration time graph. * Paper read before the British Association at Dundee by Mr. H.{Arthur M. Hanbury - Head Complaints} E.{Mr Elliott - Chief Engineer} Wimperis, M.A., inventor of the Wimperis accelerometer. | ||