that the mechanical efficiency of the early Clerk engines was 84%,
while in the later large engines of the same type it has fallen to 75%.
Standards of Thermal Efficiency.—To set up an absolute standard of thermal efficiency it is necessary to know in a complete manner the physical and chemical properties and occurrences in a gaseous explosion. A great deal of attention has been devoted to gaseous explosions by experimenters in England and on the continent of Europe, and much knowledge has been obtained from the work of Mallard and Le Chatelier, Clerk, Langen, Petavel, Hopkinson and Bairstow and Alexander. From these and other experiments it is possible to measure approximately the internal energy or the specific heats of the gases of combustion at very high temperatures, such as 2000° C.; and to advance the knowledge on the subject a committee of the British Association was formed at Leicester in 1907. Recognizing, in 1882, that it was impossible to base any standard cycle of efficiency upon the then existing knowledge of gaseous explosions Dugald Clerk proposed what is called the air standard. This standard has been used for many years, and it was officially adopted by a committee of the Institution of Civil Engineers appointed in 1903, this committee’s two reports, dated March 1905 and December 1905, definitely adopting the air-standard cycle as the standard of efficiency for internal combustion engines. This standard assumes that the working fluid is air, that its specific heat is constant throughout the range of temperature, and that the value of the ratio between the specific heat at constant volume and constant pressure is 1.4. The air-standard efficiency for different cycles will be found fully discussed in the report of that committee, but space here only allows of a short discussion of the various cycles using compression previous to ignition.
Table II.—Indicated and Brake Thermal Efficiency of Two-cycle Engines from 1884 to 1908.
| Mechanical Efficiency. | Name of Experimenter. | Year. | Dimensions of Motor Cylinders. | Indicated Thermal Efficiency. | Brake Thermal Efficiency. | Type of Engine. | |
| Per cent. | Diam. | Stroke. | Per cent. | Per cent. | |||
| 84 | Garrett | 1884 | 9″ | × 20″ | 16.4 | 14 | Clerk-Sterne |
| .. | Stockport Co. | 1884 | .. | .. | .. | 11.2 | Andrews & Co. |
| 83 | Clerk | 1887 | 9″ | × 15″ | 20.2 | 16.9 | Clerk-Tangye |
| .. | Atkinson | 1885 | 712″ | .. | .. | 15 | Atkinson |
| 75 | Meyer | 1903 | 2658″ | × (2″×3712″) | 38 | 29 | Oechelhäuser |
| 75 | Mather & Platt | 1907 | .. | .. | 30.6 | 23 | Koerting |
For such engines there are three symmetrical thermodynamic cycles, and each cycle has the maximum thermal efficiency possible for the conditions assumed. The three types may be defined as cycles of (1) constant temperature, (2) constant pressure, and (3) constant volume.
The term constant temperature indicates that the supply of heat is added at constant temperature. In this cycle adiabatic compression is assumed to raise the temperature of the working fluid from the lowest to the highest point. The fluid then expands at constant temperature, so that the whole of the heat is added at a constant temperature, which is the highest temperature of the cycle. The heat supply is stopped at a certain period, and then the fluid adiabatically expands until the temperature falls to the lowest temperature. A compression operation then takes place at the lowest temperature, so that the necessary heat is discharged by isothermal compression at the lower temperature. It will be recognized that this is the Carnot cycle, and the efficiency E is the maximum possible between the temperature limits in accordance with the well-known second law of thermo-dynamics. This efficiency is E = (T − T1)/T = 1 − T1/T, where T is the absolute temperature at which heat is supplied and T1 the absolute temperature at which heat is discharged.
It is obvious that the temperatures before and after compression are here the same as the lower and the higher temperatures, so that if t be the temperature before compression and tc the temperature after compression, then E = 1 − t/tc. This equation in effect says that thermal efficiency operating on the Carnot cycle depends upon the temperatures before and after compression.
The constant pressure cycle is so called because heat is added to the working fluid at constant pressure. In this cycle adiabatic compression raises the pressure—not the temperature—from the lower to the higher limit. At the higher limit of pressure, heat is added while the working fluid expands at a constant pressure. The temperature thus increases in proportion to increase of volume. When the heat supply ceases, adiabatic expansion proceeds and reduces the pressure of the working fluid from the higher to the lower point. Again here we are dealing with pressure and not temperature. The heat in this case is discharged from the cycle at the lower pressure but at diminishing temperature. It can be shown in this case also that E = 1 − t/tc, that is, that although the maximum temperature of the working fluid is higher than the temperature of compression and the temperature at the end of adiabatic expansion is higher than the lower temperature, yet the proportion of heat convertible into work is determined here also by the ratio of the temperatures before and after compression.
The constant volume cycle is so called because the heat required is added to the working fluid at constant volume. In this cycle adiabatic compression raises the pressure and temperature of the working fluid through a certain range; the heat supply is added while the volume remains constant, that is, the volume to which the fluid is diminished by compression. Adiabatic expansion reduces the pressure and temperature of the working fluid until the volume is the same as the original volume before compression, and the necessary heat is discharged from the cycle at constant volume during falling temperature. Here also it can be shown that the thermal efficiency depends on the ratio between the temperature before compression and the temperature after compression. It is as before E = 1 − t/tc. Where t is the temperature and v the volume before compression, and tc the temperature and vc the volume after adiabatic compression, it can be shown that (vc/v)γ−1 = t/tc, so that E may be written
| E = 1 − ( | vc | ) | γ−1 | , |
| v |
and if vc/v = 1/r, the compression ratio, then
| E = 1 − ( | 1 | ) | γ−1 | . |
| r |
Table III.—Theoretical Thermal Efficiency for the Three Symmetrical
Cycles of Constant Temperature, Pressure and Volume.
| 1/r | E | ||
| 12 | 0.026 | 17 | 0.55 |
| 13 | 0.36 | 110 | 0.61 |
| 14 | 0.43 | 120 | 0.70 |
| 15 | 0.48 | 1100 | 0.85 |
Thus in all three symmetrical cycles of constant temperature, constant pressure and constant volume the thermal efficiency depends only on the ratio of the maximum volume before compression to the volume after compression; and, given this ratio, called 1/r, which does not depend in any way upon temperature determinations but only upon the construction and valve-setting of the engine, we have a means of settling the ideal efficiency proper for the particular engine. Any desired ideal efficiency may be obtained from any of the cycles by selecting a suitable compression ratio. Table III., giving the theoretical thermal efficiency for these three symmetrical cycles of constant temperature, pressure and volume, extends from a compression ratio of 12 to 1100th. Such compression ratios as 100 are, of course, not used in practice. The ordinary value in constant volume engines ranges from 15th to 17th. In the Diesel engine, which is a constant pressure engine, the ratio is usually 112th. As the value of 1/r increases beyond certain limits, the effective power for given cylinder dimensions diminishes, because the temperature of compression is rapidly approaching the maximum temperature possible by explosion; thus a compression of 1100th raises the temperature of air from 17° C. to about 1600° C, and as 2000º C. is the highest available explosion temperature for ordinary purposes, it follows that a very small amount of work would be possible from an engine using such compressions, apart from other mechanical considerations. It has long been recognized that constant pressure and constant volume engines have the same thermal efficiency for similar range of compression temperature, but Prof. H. L. Callendar first pointed out the interesting fact that a Carnot cycle engine is equally dependent upon the ratio of the temperature before and after compression, and that its efficiency for a given compression ratio is the same as the efficiencies proper for constant pressure and constant volume engines. Prof. Callendar demonstrated this at a meeting of the Institution of Civil Engineers Committee on thermal standards in 1904. The work of this committee, together with Clerk’s investigations, prove that in modern gas-engines up to to 50 h.p. it may be taken that the best result possible in practice is given by multiplying the air-standard value by .7. For instance, an engine with a compression ratio of one-third has an air-standard efficiency of 0.36, and the actual indicated efficiency of a well-designed engine should be .36 multiplied by .7 = 0.25. If, however, the compression ratio be raised to one-fifth, then the air-standard value .48 multiplied by .7 gives .336. The ideal efficiency of the real working fluid can be proved to be about 20% short of the air-standard values given. (D. C.)
GASKELL, ELIZABETH CLEGHORN (1810–1865), English novelist and biographer, was born on the 29th of September 1810 in Lindsay Row, Chelsea, London, since destroyed to make way for Cheyne Walk. Her father, William Stevenson (1772–1829), came from Berwick-on-Tweed, and had been successively Unitarian minister, farmer, boarding-house keeper for students at Edinburgh, editor of the Scots Magazine, and contributor to the
