The Horse-power of the Petrol Motor.
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Extracts from and Discussion on Mr. F. W. Lanchester's Paper.
The paper by Mr. F. W. Lanchester, in spite of its extremely scientific character, attracted a good audience to the last meeting of the Institution of Automobile Engineers, held on April loth, when Colonel Crompton occupied the chair. The author's reading of the paper, with explanatory additions and references to the appendices, was an admirably clear and explicit statement of the application of the dimensional theory to the petrol engine problem, and notwithstanding the intricate nature of the subject, implying the possession of not a little special knowledge clearly to follow the argument of the author, Mr. Lanchester succeeded in holding the interested attention of his audience for nearly one hour and a half. In order that the meeting should not break up without allowing some opportunity for discussion, the proceedings were prolonged until a somewhat late hour. As will be seen from the report of the discussion which appears below, authorities like Professor Unwin, Professor Callendar, Mr. Dugalcl Clerk and Professor Sharp referred in terms of admiration to the beautiful working out of the theory by Mr. Lanchester. The only person to attempt any serious criticism was Mr. Russell Clarke,who suggested that Mr. Lanchester had built up his mathematical edifice upon an unsound foundation, but it should be noted that Colonel Crompton was also inclined to criticise the author's mathematics. That the paper will be a noteworthy addition to the transactions of the Institution, admits of no doubt ; and it is not unlikely, as one speaker predicted, to take rank as a classic. As we are unable to give publicity to so hyper technical a paper, and one of purely engineering interest, we Only give the concluding remarks of the author, and the discussion which followed the reading. We shall, however, be happy to obtain a revised copy of the paper, for any reader who may wish to possess one.
Too many of our readers are commercial vehick users to justify the allotment of more of our space to the subject.
THE RATING RULE.
One of the principal collateral objects of the paper is the investigation of the rating rule, a somewhat vexed question amongst those concerned with the practical trial of motor vehicles and the organising of competitions.
The difficulty of framing a rating rule is not a matter peculiar to the automobile, it is a problem of no less difficulty in the yachting world, and the experience of yacht rating is instructive and, though not immediately to the point, there is much that is analogous in the two dissimilar sets of conditions. • In the early days of yacht racing, when boats were built for actual utility, for cruising or pleasure purposes, the framing of 8. rating rule, to appropriately handicap the laiger craft, pre' Seated no difficulty. The similarity of purpose resulted in a general similarity of form, and almost any measurement properly employed would serve as a basis. When, however, owners commenced to have boats built specially for racing, at the expense of other sea-going qualities, designers were not slow to take advantage of any weak points in the system of measurement, and the shape of the hull became fearfully and wonderfully distorted, and every new rating rule that is invented results in some new variety of distortion.
The same conditions obtain with certain variations in the case of the automobile. It is the manufacturer that wants to win races and competitions instead of the owner, and it is the manefacturer who tries to cheat the rating rule ; the conditions are otherwise very similar,
It is highly undesirable that the design of the petrol car should be pulled about by changing fashions in the way of rating rules, and it, therefore, behoves all automobile engineers and designers to thresh this matter out once and for all : it is not a matter in which perfection is attainable; any rating rule whatsoever is an addition to the conditions of the problun of automobile design, and as such must result in distortion ; all that can be secured by intelligent forethought is that the rating rule is of such a nature that the distortion is of a beneficial kind, or at least that it shall be harmless.
The question of the effect of a rating rule in producing distor. tion in design was touched upon, and the pcssihility of undesirable kinds of distortion has been pointed out. The employment of the cylinder measurements as a basis tends to make the designer give very free ingress and egress to the mixture and exhaust gases, a most desirable feature as tending to a reduction of petrol consumption.
It was proved on the hypothesis assumed that :— (1) The h.p. rating rule must obey the L2 law—that is to say, most be based on a quantity of the dimensions =
(2) That if based upon the two linear quantities, diameter D and Stroke S, it must be of the form De. St-, where the appropriate value of a deduced from mechanical considerations is. from 1.5 to about 1.6.
Departures from (1) lead to distortion in the direction of an increase or decrease, as the case may be, in the number of cylinders ; where the index is in excess of 2 it pays to increase the number of cylinders to the highest possible limit, and vice versa.
Departures from condition (2) lead to a distortion in the proportions of bore and stroke. When the value of n is increased it pays to build long-stroke engines ; when the value of n is decreased the short-stroke engine has the advantage. So long as the value of a is chosen between the limits given, it is doubtful whether a designer could obtain any material advantage byadopting extreme proportions. Taking everything into account, the simpler form of expression appears the more desirable, i.e.:— H.P. varies as D. ee D.1,/-S or
THE H.P. CONSTANT.
The author then went on to discuss the question of the constant C which will be appropriate to the. conditions, so that
H.P. = C. e/ DS S.
The expression, up to this point, is independent of the cycle. of the engine, in fact it might apply to a steam or other fluid pressure engine, the constant C being adjusted to suit.
In the case of the Otto cycle, at present almost universal,. where D and S are given in inches C may be taken as .4, giving an ordinary maximum b.h.p. value. For other forms of internal combustion engine appropriate values of C may be obtained based upon the cylinder pressures ordinarily attained in the particular cycle employed and the frequency of the impulses. He did not think it was expedient to attempt to run steam cars, and those propelled by the internal combustion engine, in one class, especially in hill-climbing contests, and though the proposed rating rule may be applied to the steam car, the constant being made proportional to the boiler pressure, such rating should be only employed for the purpose of comparison with other steam cars.
The constant should be looked upon as a quantity liable to to meet new conditions such as might arise from developments either in design or in the cycle. It is evident that. even if no departure be made from the Otto cycle, it may be found possible to greatly enhance the power obtainable from a given size or rating of cylinder by some artificial means, such as that proposed by Daimler in one of his very early patents, i.e., super-compression by surfeiting the cylinder at the end of the suction stroke. Under these conditions, some check may have to be applied by the responsible authorities, which will take the form of a schedule or tariff prescribing appropriate constants.
It is well known that certain compact forms of combustion space tend to higher mean pressures and greater economy, and without doubt such forms will give an advantage to competitors who adopt them. So long as no corresponding disadvantage exists such variations should be encouraged rather than otherwise, for that which tends towards higher mean pressure for a given composition of charge also tends to higher thermal efficiency. If, however, it should be found by experience that in the race for high pressures some undesirable forms of valve gear come into vogue, such as might be found to possess grave disadvantages in the hands of the public, it might be necessary to adopt special legislation, by scheduling a special value of constant.
The above is given as an example of the manner in which a rating rule of correct form may be adapted to meet all contingencies ; it is not a very likely example but one that illustrates the point. Tf the rating rule is not of the correct form, no reasonable alteration of the constant will make it serve.
SOME UNACCOUNTED FACTORS.
In view of the doubt that at present exists as to the extent of the influence of size of cylinder on mean pressure, and the fact that on the most reliable information at present available, the magnitude of this influence is small, it is dubious whether anything material is gained by introducing this factor into the rating expression. It would seem safer, at least for the time being, to accept the L2 law implicitly.
Another unaccounted factor is that introduced from considerations of mechanical efficiency. In general, we are accustomed to expect the mechanical efficiency of a large engine to be better than that of one of small size ; it is doubtful whether this is well founded. It is quite probable that the higher efficiency of a large engine is an actual fact, but that this is in part due to the greater care in design and construction that is bestowed on works of importance. On the other hand, there is every probability of a real effect of sensible magnitude, owing to the viscosity of the lubricant, and that of the working fluid. This, for engines, geometrically similar will be detrimental to the efficiency of the engine of smaller size, and for engines of different D/S ratio, it will be more detrimental to the efficiency of the engine of relatively short stroke.
Under all circumstances, the short stroke engine is at some slight disadvantage on the score of mechanical efficiency, for its main crank bearings and connecting rod heads consume about the same energy per revolution for a given revolution speed as a longer stroke engine of the same cylinder diameter. This is probably the reason why the stroke is proportionately so much longer in the gas engine, where economy is the all-important factor, and weight is of secondary importance.
The Author's Assumption Criticised.
Mr. Russell Clarke in opening the discussion said that Mr. Lanchester's paper gave one more to think about than any recent contribution to the transactions of a technical society. At the same time he was bound to say that he felt very doubtful about certain assumptions made by the author at the outset of his argument, and of course, unless these assumptions were shown to be correct a large portion of the results arrived at fell to the ground. He feared that Mr. Lanchester had made assumptions in assigning dimensions to various quantities, and then used those dimensions as a means of solving his equation. By exceedingly ingenious reasoning he had arrived at certain results, with which in the main he (Mr. Clarke) agreed. One result was that the h.p. varied as the square root of the linear dimensions. That was very largely correct, and it also agreed with the rating rule formula of the Automobile Club which was that the horse-power was determined by the square of the diameter of the piston, multiplied by the number of cylinders and multiplied by a co-efficient which varies between certain defined limits. Personally, he was not quite sure if it were not a preferable plan to boldly attack the problem by the assumption of a definite piston velocity rather than to try and avoid mathematical difficulties as Mr. Lanchester had done. With regard to the stress problem there was nothing in the author's paper to show how that was taken. He was very anxious to hear how it could possibly be argued that the assumptions of the character indicated were justifiable. Passing from that point to the rest of the paper he would say at once that he found it extremely valuable and interesting. All that was said on the subject of least weight applied perfectly well whether his criticisms were correct or not, if one assumed the L2 law, but that law could be arrived at in a more straightforward way by assuming a definite piston velocity. That gave something to go upon, and assumptions were made which were understood. He had read the paper with a certain amount of care and was not at all sure that the mathematical work had not been somewhat stamped. Application to Aerial Navigation Research.
Professor H. I.. Callendar said it was a significant fact when one of the most scientific and leading designers adopted_ the theory of dimensions for working out a problem of this kind. All who had studied the subject knew what a useful tool the theory of dimensions had proved to the physicist, and it would. always give correct results provided that at the outset all the necessary factors were introduced. He believed Mr. Lanchester had fulfilled that condition. He not only had shown the relations of h.p. to linear dimensions but he had shown that the weight varied inversely to the linear dimensions. This latter was an exceedingly important point in the design not only of motors generally but particularly in the design of motors for flying machines, where the condition of minimum weight was so enormously important. Mr. Lanchester had shown how weight could be reduced by the use of a number of small units instead of a single big unit. If designers would fully realise the vital character of the weight problem, the advent of the flying machine would certainly be hastened, but up to, the present the majority of designers had appeared to absolutely ignore this fundamental principle. Personally he would like to have said a good deal more about the exceedingly interesting points raised at the end of the paper where Mr. Lanchester dealt with some unaccounted factors which might influence the rating rule, but inasmuch as he had promised to read a paper before their Institution on a closely-related subject at the next meeting, he would defer any further remarks until that time.
Dr. Hele-Shaw, F.R.S., did not know which to admire most, the courage of Mr. Lanchester in treating a mechanical engineering problem in the way he had or the frank admiss'ion of Mr. Russell Clarke that he could not follow Mr. Lanchester in his fundamental argument. However, Mr, Lanchester had quitesatisfied him personally, and members of the Institution ought to be grateful for the demonstration given as to the value of the dimensional theory. There were traces of genius evident in this research. It was exceedingly interesting to see that the Automobile Club formula was the same in principle as Mr. Lanchester's. which showed that engineers had in practice arrived at a fairly good basis for rating. He quite agreed with the author that a rating rule should be so drawn up as to lead. to the improvement of the engine, and not as in the case of yacht rating to the distortion of the design. It was only right that the designers doing the best work should reap the advantage by the use of high-class materials, higher piston speeds. could be attained and a reduction of weight effected, an object to be aimed at both in the touring and the racing car. It was gratifying to know that the rating rule of the Automobile Club. and the slight modifications suggested by Mr. Lanchester tended to the general improvement of the automobile.
Economy of the Large Engine.
'Mr. Dugald Clerk said that he was the more able to appreciate Mr. Lanchester's work as it related to a problem he was himself investigating. Personally he had been to some extent. 'responsible for the rating rule of the Automobile Club. No doubt, in some respects, the rating rule was wrong. It had', however, been arrived at from experience of a number of engines in actual practice. The conclusion reached was that even with variations in stroke and diameter, the engines might be taken' to run at a fairly constant piston speed. The mean pressure was
found by actual experiment, and the rule based on that investiga:Lion gave a close approximation to the truth. He personally proposed 2.4 as the divisor, but the Club adopted 2.5. It was satisfactory to find that the rule gave such general satisfaction. At the same time he believed it would be improved by some such modification as that suggested by the author, and certainly if a law could be stated on the subject of piston speed there would be ample justification for taking that into consideration in favour of the rule. Mr. Lanchester had attacked the whole problem in a bold and original way, taking a fundamental proposition and testing the general law, which was broadly true, under all kinds of variations of circumstances. In that way he had arrived at certain conclusions in relation to bore, stroke and weight, and had presented them in a series of beautiful formul. Mr. Lanchester referred at the end of the paper to some experiments which had been made by the Institution of Civil Engineers on three engines, pointing out that a difference in linear size of about 2i to 1 gave a difference of mean pressure of about 9 per cent. He agreed that the variation between the smallest engine and the largest engine, so far as economy was concerned, was exceedingly small. Undoubtedly there was greater economy in the large engine, and he hoped that when further experiments were made more definite -knowledge might he obtained. He hoped that something might be heard from Professor Callendar in his forthcoming paper on that subject, but in the light of existing knowledge it was well to leave it out of account in any formula. A further reason for leaving it out was that the dimensions of petrol engine cylinders varied so little.
A Classic Paper.
Professor Unwin found the paper exceedingly interesting and was inclined to think that the method adopted was entirely • satisfactory to the general solution of the problem Mr. Lanchester had before him.
Professor Archibald Sharp was of opinion that the paper would rank as a classic, and it should be quoted in all text books dealing with petrol motor problems. He could wish that the author had gone more fully into certain matters. In par
ticular, he desired more information as to the exact stress on particular parts of any type of engine which really determined the horse-power which could be obtained. In the one-cylinder -big flywheel type the stress factor would be the bursting stress of the flywheel rim, but with regard to the multiple-cylinder type he would have liked to have heard more as to what was the actual limiting factor in that case. Was it the size of the .port openings, or was it the stress in the connecting rod due to the high speed or the varying pressure on the crank pin or gudgeon pin? The paper had been somewhat unique in having raised an interesting discussion amongst some members in anticipation of the actual meeting. The formula expressing the h.p. as a function of length and two other physical quantities was certainly quite startling, and there had been quite an. animated discussion as to how the h.p. could be stated without reference to time. The speaker went on to refer to the effect on different types of engines of bringing the moving masses to rest, pointing out that the flywheel effect varied very con• .siderably in different types of engines.
A Baffled Critic.
Colonel Crompton regretted that his position as chairman 'precluded his criticising the author's mathematics, but he -would take the opportunity to correct Mr. Lanchester's reference to the steam car in connection with the rating rule. Mr. Lanchester said that he did not think it was expedient to attempt to -run steam cars and those propelled by the internal-combustion engine in one class, because of the accumulative effect in the steam car. He certainly thought that Mr. Lanchester ought to know that steam cars had only come into competition with petrol engines since they lost their accumulative effect and developed
their power stroke by stroke in the same manner as the internalcombustion engine.
Author Replies on Discussion% Mr. Lanchester, replying on the discussion, referred first to the question of Professor Sharp on the subject of the flywheel effect, pointing out that in the generalised formula the stress applied to the stress in every part of the engine, and was the stress distributed over the whole problem. In one case he had divided that factor into two parts separating out that relating to pressure from that embodied in the specific strength of the material. The references to the problem of getting rid of the inertia of the moving masses related rather to the balancing of engines, and its bearing on the problems presented in the paper was comparatively remote. The conditions of the problem were
not altered by the phase in which the different cranks found themselves. The change of flywheel velocity due to giving and taking up kinetic energy was really small compared to the effect due to the taking up of the explosion energy. Referring to Mr. Russell Clarke's criticism it would be impossible in the time at his disposal to go fully into his method of dealing with the problem. The method adopted was not his, but that in use by leading physicists; it was a recognised method of research and it was not for him to raise questions as to its accuracy. It was true that the assumption of a definite pistpn velocity might make for clearness, but the limitation was not by piston speed being constant, but by stress being constant. Referring to the flattering observations of Professor Callendar and other speakers, for whose appreciation he was exceedingly grateful, there was little or no criticism to answer. He would, however, like to emphasise the fact that he had not overlooked the intimate relation of the weight problem to flying machine research. Many were aware that the subject of aerial navigation had engaged his attention before he entered upon automobile work, and it was largely the fact that he realised the petrol engine was the solution of the flight problem which induced him to take up motorcar work. At the present moment he had a work in the Press on the aerial dynamics of flight, in which he dealt with the problem from the mathematical standpoint. When flying machines became a matter of course, every designer would have to know how to design for the least weight, and he had no doubt it would be tabulated in all text books for easy reference. Professor Hele-Shaw had referred to the slight modification he proposed in the rating rule, and DO doubt the little index " n" in the corner appeared of very little importance, and might easily be overlooked. The alteration proposed would as a matter of fact have very far-reaching reresults. It was manifestly absurd for the Automobile Club to maintain their rule when a circular had been going round the trade suggesting that that rating should be dropped. It was admitted that the formula was not intended to be a scientific rating of horse-power, and having gone wide of the mark it was a very ingenious way out now to say the shot was not aimed at anything in particular. No organised attempt had been previously made to get a value for the index "n." At the present moment the automobile industry was much in the same position as in the early days of yacht racing, when the framing of a rating rule presented no particular difficulty, and it would be wise to nut the rating rule on a proper basis in order that it should lead to sound improvements and developments.