Principle of Operation

The operating principle of a reciprocating internal-combustion spark-ignition engine is based on the Otto cycle, as shown in Figure 5. Named after Nikolaus Otto, who built the first successful four-stroke piston engine in 1876, the cycle underpins modern gasoline-fueled engines. A cam synchronizes the piston’s up-and-down movement with the opening and closing of the two valves (intake and exhaust). This allows sequential entry of the fuel-air mixture, followed by compression and combustion, and then the exhausting of the combustion products.

In summary, the operation of the engine consists of four strokes, as shown in the animation in Figure 6, namely:

1. During the intake stroke, the piston moves downward in the cylinder, and the cam opens the intake valve. A carburetor or fuel injection system draws the air-fuel mixture into the cylinder.
2. The compression stroke is the period during which the intake and exhaust valves are closed. The upward-moving piston compresses the fuel-air mixture, raising its pressure and temperature before ignition.
3. The power stroke is the period during which a spark plug ignites the compressed mixture. The resulting flame front propagates through the mixture by deflagration, and the expanding gases force the piston downward in the cylinder, driving the crankshaft.
4. The exhaust stroke occurs when the exhaust valve opens, and the upward-moving piston forces the exhaust gases out of the cylinder before the next four-stroke cycle begins.

A piston engine may also operate on the principle of the Diesel cycle, where the much higher compression in the cylinder raises the temperature sufficiently to cause the fuel to burn without the use of a spark plug. Another advantage of a diesel engine is its better thermal efficiency and lower specific fuel consumption. In many countries, diesel fuel, which is chemically similar to jet fuel (Jet-A), is also less expensive than gasoline. However, diesel engines are not used much in aviation applications.

Thermodynamics

The Otto spark-ignition cycle consists of four internally reversible processes for a fixed mass of fuel-air mixture, typically modeled as air behaving as an ideal gas. As shown in Figure 7, the cycle begins at state 1, with the piston at bottom dead center (BDC) and the cylinder filled with the air-fuel mixture. From state 1 to 2, the piston moves upward with both valves closed, producing an isentropic compression that reduces the volume from to and raises the pressure and temperature without heat exchange. The compression ratio, , is typically about 8.5:1 in naturally aspirated engines. Supercharging increases the intake manifold pressure and the mass of air inducted into the cylinders, increasing power output without changing the geometric compression ratio.

From state 2 to 3, constant-volume heat addition occurs when the spark plug ignites the mixture. The temperature and pressure rise abruptly at fixed as heat is added per unit mass. From 3 to 4, an isentropic expansion takes place as the piston moves from top dead center (TDC) back to BDC. The gas does work on the piston, and the pressure and temperature decrease during this power stroke. From 4 to 1, a constant-volume heat-rejection process occurs when the exhaust valve opens, releasing heat per unit mass at fixed volume , thereby completing the cycle.

On the – diagram, the compression and expansion legs follow , joined by vertical constant-volume lines for heat addition and rejection. The infinitesimal work done by the gas is

(1)  

so that over one complete cycle, then

(2)  

This equals the signed area enclosed by the loop on the – diagram, which is positive for a power-producing engine cycle. With the usual convention that work done by the gas is positive, the ideal Otto cycle is traversed clockwise on the – diagram. For a fixed mass of working gas, the corresponding specific work is .

On the – diagram, the two isentropic legs are vertical. For the constant-volume heat-addition process from 2 to 3,

(3)  

and for the constant-volume heat-rejection process from 4 to 1,

(4)  

For internally reversible processes, the heat transfer per unit mass is

(5)  

so the area enclosed on the – diagram represents the net heat exchange per unit mass, which equals the net work per unit mass according to the First Law of Thermodynamics. The heat interactions are

(6)  

giving the net work

(7)  

From the isentropic relations,

(8)  

the thermal efficiency of the Otto cycle becomes

(9)  

The efficiency depends only on the compression ratio and the specific heat ratio . In practice, is limited primarily by knock, which depends strongly on the fuel’s octane rating. Pre-ignition is a distinct abnormal-combustion phenomenon caused by ignition of the mixture from a hot surface before the spark occurs.

Effects on Power Output

For a piston engine, the power from the engine to the crankshaft (the so-called shaft brake power) scales with the number of cylinders, the swept volume per cylinder, the mean effective pressure in the cylinders, and the crankshaft rotational speed, i.e.,

(10)  

where is the number of cylinders, is the displacement (swept volume) of one cylinder, is the average or mean effective pressure produced in the cylinders, and is the crankshaft rotational speed in revolutions per minute (rpm).

The term “brake power” refers to power measured with a brake-type dynamometer, which applies braking torque to the engine shaft. Remember that a torque, , is the product of a force times a distance, so it has units of force times distance and can do work when acting through an angular displacement. Power is the rate of doing work, so the power, , at the shaft is the product of the torque and angular velocity of the shaft, i.e., .

For any reciprocating engine, the cylinder volume varies between the clearance volume at top dead center (TDC), , and the maximum volume at bottom dead center (BDC), . The swept volume of one cylinder is

(11)  

so the total engine displacement is

(12)  

It is convenient to define the mean effective pressure, , as the equivalent constant pressure that would produce the same net work per cycle for one cylinder when acting over the swept volume , i.e.,

(13)  

where, for the thermodynamic (Otto) cycle,

(14)  

so that

(15)  

For power, is the work obtained from the cylinder pressure-volume loop, thereby giving the indicated mean effective pressure (IMEP). For brake power at the shaft, the corresponding quantity is the brake mean effective pressure (BMEP), which is lower than the IMEP because of mechanical friction, accessory loads, and other losses between the cylinder gases and the output shaft.

For two-stroke engines, the thermodynamic cycle differs somewhat from the ideal Otto cycle because of the overlap of intake and exhaust processes, so the corresponding – loop includes additional losses associated with scavenging and gas exchange. If the crankshaft rotates at revolutions per minute, then the power cycle frequency per cylinder is for a four-stroke and for a two-stroke, expressed in cycles per second. In a four-stroke engine, one complete thermodynamic cycle (intake, compression, power, exhaust) requires two revolutions of the crankshaft, so a power-producing cycle occurs every two revolutions. In a two-stroke engine, the cycle is completed in one revolution, albeit with lower thermal efficiency, so a power-producing cycle occurs every revolution. The power production is then

(16)  

or, equivalently,

(17)  

Therefore, the power output from a piston engine is directly proportional to the mean effective pressure in the cylinders (the loop area on the – diagram), the swept volume per cylinder, the number of cylinders, and the number of cycles per second.

Detailed dynamometer testing is typically conducted to accurately assess an engine’s performance across various parameters and operating conditions, including intake design, carburation (or fuel injection), overall mechanical design, and exhaust system type. Additionally, forced-induction systems (e.g., superchargers or turbochargers) increase the mean effective pressure in the cylinders, thereby increasing overall power output, and are especially useful for maintaining power at higher flight altitudes.

Power Limitations

It will be apparent from Eq. 10 that the power output from the engine can be increased by:

1. Increasing the swept volume, i.e., by increasing the cylinder bore, stroke, number of cylinders, or all of these things.
2. Increasing the pressure in the cylinder by the appropriate design of the combustion chamber and/or the piston shape, or by turbocharging the air entering the cylinders.
3. Running the engine at higher values of rpm.

There is a practical limit to all of these factors, partly due to the mechanical stresses and temperatures within the engine that prevent failure. To a large extent, the design of a piston engine depends on selecting high-strength, high-temperature materials and appropriate metallurgical treatments to ensure reliable operation and durability, particularly for the exhaust valves. In aviation engines, which operate at high power settings and average temperatures, the exhaust valves are often filled with sodium, which enhances thermal conduction away from the valve stems and seats, thereby keeping the engine cooler. The maximum attainable engine rpm is also limited by the propeller tip speed, which should be kept below the speed of sound (Mach 1) to maintain propulsive efficiency and reduce noise levels. Propellers with tip speeds approaching the speed of sound are usually inefficient and very noisy.

Altitude Effects

As the aircraft’s altitude changes, available engine power decreases, as shown in Figure 8. Lower air density reduces the mass of air, and therefore the oxygen mass, inducted into the engine cylinders during each intake stroke. Because engine power output is directly related to the amount of fuel-air mixture that can be burned, a decrease in air density reduces engine performance. Cooler air can partially offset this effect by increasing the intake charge density, but density altitude remains the most useful single measure of the combined effects of pressure altitude and temperature. The power output decreases as density altitude increases.

An approximation for the effects of density altitude on the power output of a normally aspirated (non-supercharged) piston engine is to assume that

(18)  

where is the power available at altitude and is the power available at mean sea level conditions. Remember that the density ratio, , of the air, which is a surrogate measure of the oxygen content, can be calculated using the ISA model from measurements of pressure altitude and outside air temperature at that altitude. An empirical correction for a normally aspirated engine that is often used in practice is

(19)  

Supercharging

It can also be seen that supercharging can maintain a piston engine’s rated power at much higher altitudes. This outcome occurs because a supercharger increases the mean effective pressure (MEP) and air density at the engine intake, thereby raising the manifold pressure and the oxygen content of the inducted air. The result is that more fuel can be burned, thereby increasing the engine’s power at lower altitudes and maintaining it at higher altitudes.

Superchargers and turbochargers have been used extensively to maintain the power output from aeroengines. Some of the earlier high-powered radial engines employed a combined system known as a “turbo-supercharger,” which combined a supercharger and a turbocharger to maximize performance across a broad range of altitudes. As shown in Figure 9, the engine mechanically drives the superchargers, typically via a crankshaft accessory belt. The engine’s exhaust gases drive the turbochargers, which consist of a turbine and a compressor connected by a shaft. The exhaust gas drives the turbine, which, in turn, rotates the compressor, thereby increasing air flow into the engine and, consequently, into the fuel management system. Turbochargers often provide better net efficiency than mechanically driven superchargers because they are powered by energy extracted from the exhaust stream rather than by shaft power taken directly from the crankshaft. However, this exhaust energy recovery is not entirely free because the turbine can increase exhaust backpressure and pumping losses.

The mass flow rate of air into the engine is proportional to the air density and the engine displacement volume, so increasing the intake density increases the available mass flow rate, i.e.,

(20)  

where is the mass flow rate of air into the cylinders, is the volumetric efficiency, is the intake manifold air density, is the number of cylinders, and is the displacement, or swept volume, per cylinder. Notice that

(21)  

where is the engine speed in revolutions per minute. Assuming a roughly constant air-fuel ratio, increasing permits a proportional increase in the fuel flow rate , and hence, a proportional increase in the work done per cycle. This effect may be expressed in terms of the indicated mean effective pressure, , where

(22)  

and so the indicated power from all cylinders is

(23)  

For a given engine displacement and speed, supercharging increases power output by increasing charge density and raising the effective pressure in the cycle. The ideal power increase from boosting can be estimated as

(24)  

where is the boosted power output, is the rated power at the reference condition, and are the absolute intake manifold pressure and temperature, and , , and are the corresponding unboosted reference values.

The efficiency of a mechanically driven supercharger must also account for the power required to drive the compressor. This mechanical load reduces the net power output, i.e.,

(25)  

where is the net shaft power available from the engine after driving the supercharger, and is the shaft power required to drive the supercharger.

Compressing the intake air through supercharging not only increases its pressure but also raises its temperature. According to the ideal gas law, increasing the temperature at a given pressure reduces air density, partially offsetting the benefits of compression. The temperature rise through an ideal isentropic compression process is given by

(26)  

where and are the inlet and outlet temperatures across the supercharger, and are the inlet and outlet pressures, and is the ratio of specific heats, which is approximately 1.4 for air. For a real supercharger, the outlet temperature will exceed the ideal value because of compressor inefficiency. An intercooler may then be used downstream of the supercharger to reduce the charge temperature before the air enters the cylinders, increasing and improving the power increase.

Intercoolers are used to reduce temperature rise and maximize intake air density. An intercooler is a heat exchanger placed between stages of compression (in multi-stage supercharging) or between the compressor and the engine intake (in turbocharged systems). The intercooler cools the compressed air before it enters the engine cylinders, thereby increasing its density and improving the mass flow rate into the engine.

The benefit of intercooling can be quantified by considering the reduction in intake temperature, which results in a denser charge and a greater available oxygen mass per cycle. The net effect is improved engine power output, better fuel efficiency, and a reduced tendency for detonation (engine knock) at high manifold pressures. Aircraft engines that employed two-stage supercharging often incorporated intercoolers or aftercoolers between stages. In turbocharged systems, such as those used on high-altitude bombers during WWII, intercoolers were critical for maintaining engine performance and reliability at altitudes above 25,000 feet.

There may be a further boost in engine power as the flight speed increases. The stagnation pressure of the air entering the engine can increase with the dynamic pressure, although inlet losses typically reduce the realized pressure rise. Therefore, engine power increases slightly from the ram air effect. Ram air, a dynamic-pressure effect, can be significant for some aircraft, particularly those operating at airspeeds above 250 knots. However, pressure losses in the ducting between the air intake and the engine tend to reduce the significance of this potentially beneficial effect. Nowadays, reciprocating engines are used in lower-speed general aviation aircraft, so the ram-air effect can usually be ignored in terms of its impact on engine performance. From a design perspective, relying on ram-air effects at any airspeed is inadvisable when sizing an engine to an airframe.

Engine Performance Charts

Engine manufacturers provide detailed charts that enable engineers to calculate shaft power for any combination of altitude and temperature, as shown in Figure 10. Notice that there are two sides to this chart: the left side represents the mean sea-level (MSL) power output performance, and the right side represents the performance at altitude.

The chart’s instructions explain how to use it to determine the engine’s brake power. This chart differs from the one pilots use in flight, but engineers use it to estimate available engine power under different flight conditions. The chart can be used to obtain all necessary measurements to determine power output. Standard cockpit instruments can be used to measure pressure altitude, engine rpm, manifold pressure, and outside air temperature, which is very useful for flight testing.

The power available at the engine shaft (the brake horsepower or bhp) can be determined given measurements of the following:

1. Pressure altitude can be measured directly on the altimeter by setting the Kollsman window reference to standard sea-level pressure (MSL) of 29.92 inches of mercury.
2. Air temperature would be measured in flight using an appropriately calibrated outside air temperature (OAT) gauge.
3. The engine rpm, which would be measured using a tachometer. While a tachometer is part of the standard cockpit instruments, an optical tachometer that counts the passage of the propeller blades is more accurate.
4. Manifold pressure can be measured on the manifold pressure gauge, which is also part of the standard cockpit instruments.

The process begins by entering the left chart (MSL performance) at the bottom using the manifold pressure measurement, then reading up to point B along the lines of constant engine rpm. Notice that interpolation will generally be required. Reading across the axis to the right at point C provides the engine brake power at MSL standard conditions.

The next step is to establish engine performance at altitude, which is done using the right-side chart. After carrying point C onto the right chart, a straight line is drawn between points C and A, with point A positioned at the corresponding point on the rpm and manifold pressure map. To determine the available power at a given pressure altitude, follow the AC line. Reading to the left axis will give the brake power output at altitude under standard temperature conditions. Finally, a minor correction is made for non-standard temperatures (the formula is shown on the chart) to determine the final brake power output at point F. Again, interpolation will be required throughout this process.

Brake Specific Fuel Consumption (BSFC)

The efficiency of a piston engine is measured by its power-specific or brake-specific fuel consumption (BSFC), often denoted by the symbol . The BSFC measures the fuel used (in units of mass or weight) per unit of power supplied (in horsepower or kilowatts) per unit of time of engine operation (usually one hour). BSFC is used to quantify the fuel efficiency of any engine that burns fuel and produces rotational or shaft power.

The BSFC is defined as

(27)  

The units of BSFC are typically in lb hp hr in the U.S. customary system, or kg kW hr or grams per kilowatt-hour (g/kWh) in the SI system. Notice that the unit of mass (kilogram or gram) is used in the SI units of BSFC, an anomaly of the SI system. However, the time unit is hours in both cases.

For a piston engine used on an aircraft, the values of BSFC are typically in the range of 0.4 to 0.6 lb hp hr (0.24 to 0.37 kg/kWh), as shown in Figure 11. These values are approximate and may vary based on factors such as engine design, operating conditions (e.g., cruising, takeoff, climb), and the specific engine model. Additionally, advancements in engine technology may improve fuel efficiency compared to older engines.

BSFC typically shows some dependence on flight altitude and mixture setting. Notice that the best (lowest) BSFC is usually obtained when the engine operates near an efficient combination of rpm, manifold pressure, and mixture setting. Diesel-cycle aircraft piston engines can have higher thermal efficiency than spark-ignition gasoline engines and therefore can achieve lower BSFC values, although the exact value depends on engine design, boost level, operating condition, and fuel type.

Turbocharging improves altitude performance by increasing intake manifold pressure and density, allowing the engine to maintain a higher air mass flow rate as ambient density decreases. This permits more fuel to be burned while maintaining an appropriate fuel-air ratio, thereby preserving power at altitudes where a normally aspirated engine would lose power. Because the turbocharger is driven by exhaust-gas energy rather than directly by the crankshaft, it can provide this boost with less direct mechanical power extraction than a gear-driven supercharger. However, the improvement is not free: the turbine increases exhaust backpressure and pumping losses, and compression raises the intake-air temperature unless intercooling is used.

Turbocharging may improve BSFC under some operating conditions, especially when it allows the engine to operate closer to an efficient power setting at altitude, but BSFC also depends on mixture setting, boost pressure, intercooling effectiveness, detonation margin, exhaust backpressure, and engine design. At high boost settings, mixture enrichment may be required for cooling and knock avoidance, thereby increasing BSFC.

The brake-specific fuel consumption remains defined as

(28)  

where is the fuel mass flow rate and is the brake power output. In U.S. customary practice, BSFC is often reported using fuel weight flow in lb hr, giving units of lb hp hr. In SI practice, it is normally reported using fuel mass flow, giving kg kW hr or g/kWh. Turbocharging increases the available brake power at altitude primarily by increasing the inducted air mass per cycle; whether the BSFC improves or worsens must be determined from engine performance data.

Fuel Types for Piston Aeroengines

Piston aeroengines rely on specialized fuels to ensure reliable combustion, efficient power output, and safe operation across a range of altitudes and atmospheric conditions. The most widely used fuel for piston-powered aircraft is aviation gasoline (AVGAS), which is formulated to meet the demanding requirements of flight. Aviation gasoline is characterized by high chemical stability, a high energy content, and a controlled vapor pressure to prevent vapor lock during altitude changes. Today’s most common grade is AVGAS 100LL, where “100” denotes the fuel’s octane rating under aviation testing conditions and “LL” indicates low lead content. Despite the “low lead” designation, AVGAS 100LL contains tetraethyl lead (TEL), a chemical additive that significantly improves knock resistance by inhibiting premature combustion (detonation) within the engine cylinders. AVGAS 100LL is dyed blue for easy identification. Historically, grades such as AVGAS 100/130 and 80/87 were also used, but these have largely been phased out.

The octane rating is a measure of a fuel’s resistance to detonation. Aircraft engines, particularly those operating at high compression ratios or under high manifold pressures, require fuels with high knock resistance to avoid engine damage. In aviation fuels, two octane ratings are often specified, such as 100/130, where the first number denotes the octane rating under lean-mixture conditions and the second under rich-mixture conditions. Detonation is particularly hazardous in aircraft engines because it can cause rapid mechanical failure; therefore, properly formulated and rated fuel is essential.

The industry continues to rely heavily on leaded fuels, but environmental and health concerns have accelerated the development of unleaded alternatives. One example is G100UL, a 100-octane unleaded aviation gasoline approved by the FAA through an Approved Model List Supplemental Type Certificate for broad use in the piston-aircraft fleet. However, distribution remains limited compared with AVGAS 100LL, which is still the dominant aviation gasoline in current operations. In some cases, aircraft engines are certified to use automotive gasoline, also known as mogas. While mogas is widely available and often less expensive, it is not a direct substitute for aviation gasoline. Its higher vapor pressure can cause vapor lock at altitude, and the absence of lead additives reduces its knock resistance, making it unsuitable for high-performance aviation engines unless properly certified. Additionally, mogas formulations can include ethanol blends, which present risks of water absorption and corrosion within the aircraft’s fuel system.

The energy content of aviation gasoline is approximately 43 MJ/kg, and its density at standard conditions ranges from about 0.68 to 0.74 kg/L. For proper combustion, piston aeroengines typically operate near a stoichiometric air-fuel ratio of about 14.7:1 by mass, corresponding to a fuel-air ratio of approximately 0.067. Deviations from this ratio are often used to control engine temperature and performance. Rich mixtures provide additional cooling by increasing latent heat absorption during fuel vaporization. In contrast, lean mixtures improve fuel economy but carry an increased risk of detonation if not carefully managed.

Summary & Closure

The reciprocating piston engine remains an important propulsion system for low- to moderate-performance aircraft. Its robustness and affordability ensure that it remains accessible and reliable, particularly for general aviation and certain classes of uncrewed aerial vehicles (UAVs). The engine’s good propulsive efficiency, relatively low fuel consumption, and overall mechanical reliability contribute to its continued use in various applications, providing an economical and effective solution for many aviation needs. However, as aircraft size and performance demands increase, the limitations of the reciprocating piston engine become more apparent. Its lower power-to-weight ratio constrains its applicability in larger, more demanding aircraft operations.

This limitation has driven the adoption of turboprop engines, which offer higher power output and greater scalability for larger aircraft. Turboprops also bridge the gap between piston and jet engines, providing an optimal balance of power, efficiency, and operational flexibility for larger airplanes. While reciprocating piston engines will continue to play a vital role in aviation, particularly in general aviation and specialized applications, the transition to more advanced propulsion systems, such as turboprops, will enable the aviation industry to meet the growing demands for higher performance and greater efficiency in larger airplanes. The correct selection and handling of fuel are critical to piston aeroengine operation, directly affecting performance, efficiency, and safety. Knowledge of the properties of different aviation fuels, as well as the operational consequences of fuel mixture control, is essential to basic aerospace engineering practice.