How to Calculate Engine Efficiency
"Efficiency" is defined as the ratio of the work done by a system to the amount of energy the system absorbs in doing that work. For an engine system, the thermal efficiency tends to be of the greatest interest, although the mechanical efficiency also can be of interest to engine enthusiasts such as professional automobile racers. Many types of engines are designed for different purposes, each type with its own formula for thermal efficiency. A most practical example of the thermal efficiency calculation is one for a combustion engine that follows the Otto cycle.
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Instructions
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Draw a pressure-volume (PV) diagram of the engine process for one cycle from the information given about the system. This information can be found in a manufacturer's description of the engine or in a textbook (of the physical science variety) containing the problem. The shape of your graph should look like a closed quadrilateral. Each segment represents a step in the cycle. For the Otto cycle, the PV diagram looks like a skewed rectangle with two steps showing a change in pressure occurring at constant volume and the other two steps being adiabatic processes, or processes in which the net work done by the system is equal to zero.
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Write the equation for the efficiency of the system. This relationship is easily referenced if the name of the cycle is known. If unknown, the PV diagram can be used to determine (by inspection) which cycle it is. If still unknown, use the ideal gas equation, PV = nRT, along with the PV diagram to derive the necessary relationship from the previously mentioned definition of "efficiency." For the Otto cycle, the efficiency e = 1 - (1/(V1/V2)^(h-1)), where "V1/V2" is the compression ratio (or the ratio of the volumes in the two steps of the cycle where the pressure changes are the greatest), and "h" is the ratio of specific heats for the fuel air mixture.
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Identify the value(s) of the variables upon which the efficiency of the system depends. These values can be found in a problem statement, the engine manufacturer's specifications or by empirical measurement. If a specific heat is needed, reference it by the compound. The efficiency of the Otto cycle depends on the value of the compression ratio V1/V2 and the value of the specific heats ratio h. The idealized case for the Otto cycle with an air/gasoline mixture is a compression ratio of 8 and a specific heat ratio of 1.4.
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Plug the determined values into the efficiency equation using a calculator. The idealized case stated previously results in an efficiency of 56 percent.
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