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).
Explanation of the 'K' formula for measuring engine capacity and performance, using a bicycle as an initial example.
| Identifier | ExFiles\Box 37\1\ scan 072 | |
| Date | 4th March 1920 guessed | |
| ONE often wonders that the usefulness of the “K” formula, originally given in The Autocar of June 22nd, 1912, in an article by Mr. J.{Mr Johnson W.M.} W. Roebuck, Whit. Ex., Roy.{Sir Henry Royce} Ex., etc., is not more widely recognised. The average motorist will grant its applications for the designer and the expert, but does not realise that even for the ordinary man it is a ready means of roughly forecasting the performance of a strange car in comparison with that of one already known. This is of service in buying a car, since the K of half a dozen cars under consideration may be compared with the K of the car now in use, a performance of which in one’s own district is known. Cars with an equal K should perform similarly; and with certain reservations that will be dealt with later this is, broadly speaking, true. The motorist judged the ability of cars to do certain work by their horse-power formerly: he is now arriving at a comparison of cubic capacities of engines, and knows that gear ratio and total weight enter into the matter somewhere, but has no clear comprehension of where performance is affected by these varying factors. It is at this point that what is known as the “K” formula steps in. K, what it is and what it can do. Briefly, K is a measure of the engine capacity available for driving unit weight unit distance, and automatically adjusts for differing weights and gear ratios. It outlines an answer to a question frequently put, as to whether a modern light car or a standard 15.9 h.p. car is the livelier. Everyone knows the 15.9 h.p. car has the more powerful engine, but does its extra weight and the necessarily more robust chassis more than counterbalance that extra power? In other words, and still colloquially, which car has the more power in reserve? The K of a Man on a Bicycle. To get a clear idea of what K means, let us construct a K formula for a man riding a bicycle. We will assume his maximum push on the pedals is a force of 100 lb. with each leg. Making two pushes per crank revolution, his push per crank revolution is 200 lb. His back wheel is driven round three times for every crank revolution, so that the pounds push per back wheel revolution is 200/3 lb. A back wheel of 28in. diameter covers 88in. of road per revolution. Therefore, the man can push 200 / (3 x 88) lb. per inch of road travelled. We have now to consider the total weight which is pushed. If the man weigh ten stone and the bicycle 30 lb. we have a total weight of 170 lb. If we divide the fraction just mentioned by this we shall get the pounds push per inch of read travelled per lb. weight pushed. The whole sum is 200 / (3 x 88 x 170) = 0.0045. Let us suppose, now, that the weight of another bicycle be 35 lbs., but the other factors remain the same. K alters instantly to 0.0043. It would be the simplest sum in elementary algebra to find what extra pressure on the pedals was needed to give the same K with the heavier bicycle, i.e., how much stronger the man would need to be, or with the same man what gear would have to be used; but this is the road that designers travel, and we need do no more than peep down it. Writing this down as a formula we should express it K = PG / IW' where P = lb. pressure available per crank revolution, G = gear ratio (1 to 3 in the above example, hence 3 appearing below), I = inches travelled per road wheel revolution, and W = weight in lbs. How K is applied to Cars. In a way precisely similar K for cars is written K = MG / TQ, where M = a measure of engine power presently to be explained, G = gear ratio, T = tyre diameter, and Q = weight. M, the measure of the engine power, or, to speak more correctly, of the work the engine ought to be able to do, is reckoned as cubic capacity. Very much as we might say the amount of alcohol in a cask of beer could be reckoned by the cubic capacity of the cask, so we say the amount of work an engine can do can be measured by the cubic capacity of its cylinders. In other words, every cubic centimetre ought to do a definite amount of work; any increase in capacity should bring about a proportionate increase in the amount of work that can be got out of the engine. Actually, engines vary, as is well-known, and the limitations in this respect with regard to K will be dealt with shortly; for the present we will continue our exposition of the formula. Now the volumes of cylinders are as the squares of their diameters multiplied by their lengths. The volume is π/4 D²S; but for purposes of comparison we can omit π/4. Similarly, when comparing the sizes of wheels we may omit π. It is obvious that if the circumference of a wheel is twice that of another wheel, the diameter of the first must be twice that of the second. | ||