202 



NA TURE 



[August 12, 1909 



whether the cycle followed is (i) the constant-volume cycle, 

 (2) the constant-pressure cycle, or (j) the constant-tempera- 

 ture cycle, an important discovery attributed to Profs. 

 Unwin and Callendar. The problem now arises to re- 

 calculate the thermal efficiency (yt) for a working medium 

 of which the specific heat is not constant. Most of the 

 important internal-combustion engines operate on the 

 constant-volume cycle, and if we re-calculate the equation 

 to suit this case, making the necessary approximations to 

 secure a workable result of sufficient accuracy, and using 

 the above linear law based on the British Association Com- 

 mittee's figures for specific heats, we find that the new 

 efficiency equals 



where T, is the maximum absolute temperature (centi- 

 grade) in the cycle, T„ the suction temperature, whilst ij 

 is the value obtained from the equation 



r) = l 





using here the value of y corresponding to the absolute 

 zero of temperature. The value of T„ is practically in- 

 dependent of the compression, and in round figures suitable 

 to this calculation may be written down as 400. The value 

 of T„ for a given richness of mixture will depend upon 

 the degree of compression before ignition, and can be 

 calculated therefrom. In this way a new expression for 

 the real thermal efficiency can be obtained in terms, not 

 of T;, but of r, and the following table shows a few com- 

 parative figures worked out in this way. The figures for 

 the " air-standard " efficiency are also given by way of 



comparison. 



Ratio of compression 



Thermal Efficiency. 

 " .\\v standard " 



Pe»l thermal 

 efficiency 

 (approximate figures) 

 0'30 

 0-45 



4 0-43 



10 060 



Ratio, air/gas = 9/1 



It will be seen that in each case the real efficiency is about 

 a quarter less than the " air-standard " efficiency. 



This discrepancy sufficiently explains why those associated 

 with the design and building of gas engines have expressed 

 their dissatisfaction with the " air standard " of efficiencv. 

 The adoption of the " air standard " has led to the setting 

 up as an ideal, to be aimed at and striven after, of a 

 series of figures which it now appears are about one-third 

 above the thermal efficiencies theoretically possible, and it 

 is not surprising that engine builders, who from their 

 practical work realised that there must be something 

 wrong with the theory as then put forward, should have 

 objected. It is not too much to say that had the engine 

 builders to depend in the past solely on scientific guidance 

 as the mainspring of their investigations, there would 

 have been far less progress made than has been effected 

 by the system of trial and error. Even now the state of 

 knowledge as to gaseous specific heats is so uncertain 

 that noaccurate quantitative theory of the thermodynamics 

 of the internal-combustion engine can be laid down. The 

 writer has. however, endeavoured to show here and else- 

 where how the problem may be investigated symbolically, 

 and so prepared for expression in numerical form as soon 

 as the thermal oroperties of the gases are actually known. 



_ Mr. Dugald Clerk, in his 1907 paper ' before the Institu- 

 tion_ of^ Civil Engineers, made some estimates of real 

 efficiencies based on theoretical maximum temperatures of 



1600° C. and 1000° C, and his results are given below. 



Ideal efficiencies 



If maximnm tem- If maximum tem- 

 ?- perature of cycle perature of cycle On air standard 



1600" C. 1000^ C. 



2 ... Oiqi; ... 0'200 ... 0'242 



3 ... 0-2S6 ... 0-291 ... 0-^56 



4 ■■• o';!;4 ... 0-356 ... 0-426 



5 ■•■ 0-384 ... 0-394 ... 0-475 

 7 ... 0-439 ... 0-443 ••• 0-541 



It was_ apparently contemplated that these figures might 

 be used in comparison with engine performances in which 

 1 Proc. I.C.E , vol. clxix., p. 145. 



Ko. 2076, VOL. Si] 



the real maximum temperatures were also it)00° C. and 

 1000° C. This, hoxvever, would be open to several objec- 

 tions. As an instance, tal<e the case of an engine which 

 by improved design was made capable of giving for the 

 same mixture and the same compression ratio a higher 

 maximum temperature and pressure. Such an effect might 

 be produced, let us say, by decreasing the ratio of cool- 

 ing surface 10 volume th'ough an alteration in the amount 

 of poclceting. This new engine, on the basis of compari- 

 son with an ideal cycle having an identical maximum 

 temperature, would probably show little, if any, improve- 

 ment in relative efficiency over the old engine. Such a 

 result would tend to defeat the purpose for which com- 

 parisons with ideal cycles are made. It would seem to 

 the author that the better way would be to compare both 

 old and new engines with an ideal cycle having a maxi- 

 mum temperature corresponding to the known richness of 

 the mixture, its calorific value, and the ratio of com- 

 pression. 



A factor that has affected most advantageously the 

 recent progress of the internal-combustion engine is the 

 great improvement that has taken place in engine 

 indicators. The old moving lever design, although 

 thoroughly serviceable for most steam engines and for 

 many slow-moving internal-combustion engines, has 

 been found entirely untrustworthy with modern high- 

 speed internal-combustion engines. A new form of 

 instrument has been devised in which the recording 

 lever is a beam of light, which, having no inertia, has 

 no time-lag. This vitally important improvement in the 

 indicators was due. in the first instance, to the prescience 

 of Prof. Perry,' and in its later stages to the experimental 

 skill of Profs. Callendar and Hopkinson. The writer has 

 recently calculated out the case of an indicator of which 

 the free periodic time of oscillation was 1/300 sec, and 

 has shown that explosion= occurring even in so short a 

 time as i'2oo sec. could be adequately followed and re- 

 corded. We believe that this oscillation period represents 

 about the sensitiveness of one of the reflecting indicators 

 used by Prof. Hopkinson at Cambridge, and the calcula- 

 tion serves to sho-.v how accurately the new instruments 

 can be made to follow extremely rapid explosions. 



It would be useless to base any deductions on the 

 records given by one of the old type of instruments 

 in such a sharp explosion as this. Errors of as much 

 as 5 per cent, are now known to have occurred 

 in the measurements of horse-power made by the old 

 instruments. On the other hand, it cannot be denied 

 that the older type was a great deal easier to handle, and 

 that it could be used by comparatively untrained persons. 

 The new reflecting kind, despite its accuracy of measure- 

 ment to within i per cent, of the power, is rarely seen 

 in workshops, and the measure of " indicated horse- 

 power " has been very commonly abandoned in favour of 

 the measurement of " brake horse-power " both in the 

 case of large and small engines. In the case of the 

 numerous small high-speed petrol engines, the practice of 

 actually measuring brake horse-power is often replaced by 

 the use of a rating formula giving a " nominal " horse- 

 power. It seems at first sight extraordinary that there 

 should be a reversion to the old unscientific " N.H.P.," 

 but, despite their apparent similarity, the " N.H.P." of 

 the old days of the steam engine and boiler, and the 

 " rating H.P." of the modern petrol engine, are really 

 based on very different considerations, and, as there 

 appears to be every likelihood that the latter will be 

 constantly revised with the aid of the best scientific advice 

 possible, there is little real foundation for any scientific 

 objection to it. The pioneer work done by Prof. Callendar 

 in promoting this advance cannot be too gratefully acknow- 

 ledged. Others have also worked at the problem since, and 

 a considerable " output " of rating formula; has resulted. 



D-.N 

 That in most common use is H.P. = — '■ — , where D is 



2'S 



cylinder diameter in inches and N is the number of 

 cylinders. This formula was put forward with the 

 authority of the Royal .Automobile Club, and experi- 

 ence has shown that in the great majority of cases 

 it gives wonderfully good results. It may even bp 

 doubted whether any of the far more complicated 



' " The Steain Engine," by Prof. Perry, p. 117. 



