Aircraft Reciprocating Engine Efficiencies

Thermal Efficiency

Any study of engines and power involves consideration of heat as the source of power. The heat produced by the burning of gasoline in the cylinders causes a rapid expansion of the gases in the cylinder, and this, in turn, moves the pistons and creates mechanical energy. It has long been known that mechanical work can be converted into heat and that a given amount of heat contains the energy equivalent of a certain amount of mechanical work. Heat and work are theoretically interchangeable and bear a fixed relation to each other. Heat can therefore be measured in work units (for example, ft-lb) as well as in heat units. The British thermal unit (BTU) of heat is the quantity of heat required to raise the temperature of 1 pound of water by 1 °F. It is equivalent to 778 ft-lb of mechanical work. A pound of petroleum fuel, when burned with enough air to consume it completely, gives up about 20,000 BTU, the equivalent of 15,560,000 ft-lb of mechanical work. These quantities express the heat energy of the fuel in heat and work units, respectively.

The ratio of useful work done by an engine to the heat energy of the fuel it uses, expressed in work or heat units, is called the thermal efficiency of the engine. If two similar engines use equal amounts of fuel, the engine that converts into work the greater part of the energy in the fuel (higher thermal efficiency) delivers the greater amount of power. Furthermore, the engine that has the higher thermal efficiency has less waste heat to dispose of to the valves, cylinders, pistons, and cooling system of the engine. A high thermal efficiency also means low specific fuel consumption and, therefore, less fuel for a flight of a given distance at a given power. Thus, the practical importance of a high thermal efficiency is threefold, and it constitutes one of the most desirable features in the performance of an aircraft engine. 

Of the total heat produced, 25 to 30 percent is utilized for power output, 15 to 20 percent is lost in cooling (heat radiated from cylinder head fins), 5 to 10 percent is lost in overcoming friction of moving parts; and 40 to 45 percent is lost through the exhaust. Anything that increases the heat content going into mechanical work on the piston, which reduces the friction and pumping losses, or which reduces the quantity of unburned fuel or the heat lost to the engine parts, increases the thermal efficiency. 

The portion of the total heat of combustion that is turned into mechanical work depends to a great extent upon the compression ratio. The compression ratio is the ratio of the piston displacement plus combustion chamber space to the combustion chamber space, as mentioned earlier. Other things being equal, the higher the compression ratio is, the larger is the proportion of the heat energy of combustion turned into useful work at the crankshaft. On the other hand, increasing the compression ratio increases the cylinder head temperature. This is a limiting factor because the extremely high temperature created by high compression ratios causes the material in the cylinder to deteriorate rapidly and the fuel to detonate instead of burning at a controlled rate. 

The thermal efficiency of an engine may be based on either bhp or indicated horsepower (ihp) and is represented by the formula: 

Indicated thermal efficiency =                      ihp x 33,000                               
                                                 weight of fuel burned/min x heat value x 778

The formula for brake thermal efficiency is the same as shown above, except the value for bhp is inserted instead of the value for ihp. 

Example 

An engine delivers 85 bhp for a period of 1 hour and during that time consumes 50 pounds of fuel. Assuming the fuel has a heat content of 18,800 BTU per pound, find the thermal efficiency of the engine:

        85 ihp x 33,000         =     2,805,000  
.833 x 18,800 BTU x 778       12,184,569

Reciprocating engines are only about 34 percent thermally efficient; that is, they transform only about 34 percent of the total heat potential of the burning fuel into mechanical energy. The remainder of the heat is lost through the exhaust gases, the cooling system, and the friction within the engine. Thermal distribution in a reciprocating engine is illustrated in Figure.

Reciprocating Engine Efficiencies
Thermal distribution in an engine

Mechanical Efficiency 

Mechanical efficiency is the ratio that shows how much of the power developed by the expanding gases in the cylinder is actually delivered to the output shaft. It is a comparison between the bhp and the ihp. It can be expressed by the formula:

Mechanical efficiency =   bhp 
                                         ihp

Brake horsepower is the useful power delivered to the propeller shaft. Indicated horsepower is the total hp developed in the cylinders. The difference between the two is friction horsepower (fhp), the power lost in overcoming friction. The factor that has the greatest effect on mechanical efficiency is the friction within the engine itself. The friction between moving parts in an engine remains practically constant throughout an engine’s speed range. Therefore, the mechanical efficiency of an engine is highest when the engine is running at the rpm at which maximum bhp is developed. Mechanical efficiency of the average aircraft reciprocating engine approaches 90 percent. 

Volumetric Efficiency

Volumetric efficiency is a ratio expressed in terms of percentages. It is a comparison of the volume of fuel/air charge (corrected for temperature and pressure) inducted into the cylinders to the total piston displacement of the engine. Various factors cause departure from a 100 percent volumetric efficiency. The pistons of an naturally aspirated engine displace the same volume each time they travel from top center to bottom center of the cylinders. The amount of charge that fills this volume on the intake stroke depends on the existing pressure and temperature of the surrounding atmosphere. Therefore, to find the volumetric efficiency of an engine, standards for atmospheric pressure and temperature had to be established. The U.S. standard atmosphere was established in 1958 and provides the necessary pressure and temperature values to calculate volumetric efficiency.

The standard sea level temperature is 59 °F, or 15 °C. At this temperature, the pressure of one atmosphere is 14.69 lb/ in2, and this pressure supports a column of mercury (Hg) 29.92 inches high, or 29.92 "Hg. These standard sea level conditions determine a standard density, and if the engine draws in a volume of charge of this density exactly equal to its piston displacement, it is said to be operating at 100 percent volumetric efficiency. An engine drawing in less volume than this has a volumetric efficiency lower than 100 percent. An engine equipped with true supercharging (boost above 30.00 "Hg) may have a volumetric efficiency greater than 100 percent. The equation for volumetric efficiency is:

Volumetric Efficiency =   Volume of charge (corrected for temperature and pressure)  
                                                               Piston displacement

Many factors decrease volumetric efficiency, including: 
  • Part-throttle operation 
  • Long intake pipes of small diameter 
  • Sharp bends in the induction system 
  • Carburetor air temperature too high 
  • Cylinder-head temperature too high 
  • Incomplete scavenging 
  • Improper valve timing 

Propulsive Efficiency 

A propeller is used with an engine to provide thrust. The engine supplies bhp through a rotating shaft, and the propeller absorbs the bhp and converts it into thrust hp. In this conversion, some power is wasted. Since the efficiency of any machine is the ratio of useful power output to the power input, propulsive efficiency (in this case, propeller efficiency) is the ratio of thrust hp to bhp. On the average, thrust hp constitutes approximately 80 percent of the bhp. The other 20 percent is lost in friction and slippage. Controlling the blade angle of the propeller is the best method of obtaining maximum propulsive efficiency for all conditions encountered in flight. 

During takeoff, when the aircraft is moving at low speeds and when maximum power and thrust are required, a low propeller blade angle gives maximum thrust. For high-speed flying or diving, the blade angle is increased to obtain maximum thrust and efficiency. The constant-speed propeller is used to give required thrust at maximum efficiency for all flight conditions.