Indicated thermal efficiency may be defined as the proportion of the total heat of combustion which appears as work done by the explosion and expansion upon the piston. Brake thermal efficiency may be defined as the proportion of the total heat of combustion which appears as work given out by the engine available for overcoming external resistances; that is, brake thermal efficiency is the effective efficiency of the engine for doing work. In the early gas engines the indicated thermal efficiency was only 16%, as shown by tests of Otto engines from about 1877 to 1882, but now indicated thermal efficiencies of from 35% to 37% are often obtained. Some experimenters claim even higher efficiencies, but even 37% is higher than ordinary best practice of 1909. Table I. has been prepared to show this advance. It shows, in addition to indicated thermal efficiency, the brake thermal efficiency and the mechanical efficiency, together with other particulars such as engine dimensions, types and names of experimenters. It will be seen that brake thermal efficiency has also increased from 14% to 32%; that is, practically one-third of the whole heat of combustion is obtained by these engines in effective work available for all motive power purposes.
Table I.—Indicated and Brake Thermal Efficiency of Four-Cycle Engines from 1882 to 1908.
| No. | Mechanical Efficiency. | Names of Experimenters. | Year. | Dimensions of Engine. | Indicated Thermal Efficiency. | Brake Thermal Efficiency. | Type of Engine. | |
| Per cent. | Diam. | Stroke. | Per cent. | Per cent. | ||||
| 1 | 87.6 | Slaby | 1882 | 6.75″ | × 13.7″ | 16 | 14 | Deutz |
| 2 | 84.2 | Thurston | 1884 | 8.5″ | × 14″ | 17 | 14.3 | Crossley |
| 3 | 86.1 | Society of Arts | 1888 | 9.5″ | × 18″ | 22 | 18.9 | Crossley |
| 4 | 80.9 | Society of Arts | 1888 | 9.02″ | × 14″ | 21 | 17 | Griffin (6-cycle) |
| 5 | 87.3 | Kennedy | 1888 | 7.5″ | × 15″ | 21 | 18.3 | Beck (6-cycle) |
| 6 | 82.0 | Capper | 1892 | 8.5″ | × 18″ | 22.8 | 17.4 | Crossley |
| 7 | 87.0 | Robinson | 1898 | 10″ | × 18″ | 28.7 | 25 | National |
| 8 | 83 | Humphrey | 1900 | 26″ | × 36″ | 31 | 25.7 | Crossley |
| 9 | 81.7 | Witz | 1900 | 51.2″ | × 55.13″ | 28 | 22.9 | Cockerill |
| 10 | 85.5 | Inst. Civil. Eng. | 1905 | 14″ | × 22″ | 35[1] | 29.9 | National |
| 11 | 77.1 | Burstall | 1907 | 16″ | × 24″ | 41.5[2] | 32 | Premier |
| 12 | 87.5 | Hopkinson | 1908 | 11.5″ | × 21″ | 36.8 | 32.2 | Crossley |
Thermal Efficiency of Two-Cycle Engines.—It has been found that two-cycle engines present greater practical difficulties in regard to obtaining high indicated and brake thermal efficiencies, but the thermodynamic considerations are not affected by the practical difficulties. As shown by Table II., these engines improved in indicated thermal efficiency from the value of 16.4% attained in 1884 to 38% in 1903, while the brake thermal efficiency rose in the same period from 14% to 29%. The numbers in Table II. are not so well established as those in Table I. The four-cycle engines have been so far subjected to much more rigid and authoritative tests than those of the two-cycle. It is interesting to see from the table 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 | 7½″ | .. | .. | 15 | Atkinson |
| 75 | Meyer | 1903 | 265⁄8″ | × (2″×37½″) | 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.