32 Piston Engines & Propellers


A reciprocating piston internal combustion engine driving a propeller is often used to power relatively low to moderate-performance general aviation aircraft. An example of a Piper Cherokee airplane is shown in the photograph below, which has a 4-cylinder, 160 hp (119.3 kW) piston engine driving a fixed-pitch propeller.

Piper Pa-28 Cherokee flown by Dr. J. Gordon Leishman, as photographed over the western Maryland countryside. (Photo taken by Ashish Bagai.)

The advantages are that this propulsion system is reliable, affordable, and provides a reasonable propulsive efficiency. However, it is not easily scalable to larger aircraft because the power-to-weight ratio of a piston engine decreases rapidly with increased power output, making it unattractive for designers of larger aircraft. In such cases, a turboprop engine is often preferred if a propeller is desired.

Piston engines, including the higher efficiency afforded by types of diesels, may also be suitable for certain classes of drones and UAVs where the flight range and/or endurance cannot be achieved with the use of batteries alone, e.g., by using hybrid propulsion systems. To this end, engineers must understand the principles of aircraft piston engine operation, including the effects of density altitude on their power output, as well as the associated propeller performance in the conditions of flight.

Learning Objectives

  • Understand the basic principles of operation of a reciprocating piston engine, especially as it is used for aviation applications.
  • Appreciate the factors that affect the shaft power that can be developed from such an engine and know how to read an aircraft piston engine performance chart.
  • Understand the basic operational principles of a propeller, including the methods used to calculate thrust, the power required, and efficiency.
  • Know how to read and interpret a propeller performance chart.

Reciprocating Piston Engines

The first type of piston engine used for aircraft was a rotary engine, which saw extensive use up through the 1920s. In this type of arrangement, the cylinders are arranged in a radial configuration, and the entire crankcase and its attached cylinders rotate around it as a unit along with the propeller. The pistons are connected to the crankshaft using a master rod assembly, the remaining pistons and their connecting rods being attached to rings around the master rod. One advantage of this rotary design is good cooling because the cylinders rotate. However, a significant disadvantage is the large gyroscopic moments on the aircraft from the rotating engine mass, which led to several issues with flight handling qualities on early aircraft.

The radial engine is another early reciprocating piston engine used to power many pre-1950 airplanes, as shown in the photograph below. The radial engine has fixed cylinders that “radiate” outward from a central crankshaft like the spokes of a wheel; it somewhat resembles a star when viewed from the front, and indeed the type is sometimes called a star engine. In the radial engine, the propeller is attached to the crankshaft, and the gyroscopic effects on the airplane are much lower than for the rotary style of the engine. As a result, radial engines were much preferred over rotary ones, which became obsolete for aircraft use after WW1.

A radial engine design has fixed cylinders that radiate outward from a central rotating crankshaft to which a propeller is attached.

Fairly powerful radial engines with 12 or more cylinders have been built for aviation use, mainly for airplanes constructed through the 1950s, raising power output levels from 2,000 hp (1,491 kW) to 4,000 hp (2,983 kW) range. In addition, extra rows of radial cylinders can be added to increase the engine’s power. However, this approach rapidly drives up the engine’s weight and also results in cooling challenges for the downstream rows of cylinders. The most powerful piston aircraft engine ever built was the Lycoming XR-7755, which had 36 cylinders and a shaft power output of 5,000 hp (3,700 kW), but this engine never saw flight use.

Modern piston engines for aircraft are usually flat, horizontally opposed, as shown in the photograph below. They are manufactured with 4, 6, or 8 cylinders in power ratings from about 125 hp (147 kW) to 600 hp (441 kW), and in normally aspirated and supercharged (i.e., forced induction) forms. Supercharging or turbocharging may be used to increase the power of a piston engine and maintain its power output to higher flight altitudes; this is a good solution for higher-performance aircraft despite the penalty of extra weight and costs.

A reciprocating (piston) engine for aircraft use, in this case, a Continental IO-520, which has a 520 cubic-inch displacement and power output in the 300 hp (220 kW) class. The engine drives a propeller mounted directly to the crankshaft.

While modern piston engines are mechanically reliable and robust, one concern is that they are relatively heavy compared to their power output. For this class of engines, their power-to-weight ratio is relatively low, which on average is only about 0.2 hp/lb (0.33 kW/kg) to 0.4 hp/lb (0.66 kW/kg). Therefore, when such engines are required to produce higher power levels, they can become prohibitively heavy for use on an aircraft. This reason is why a turboshaft engine is usually necessary to drive a propeller (i.e., a turboprop) after a certain power requirement for flight is reached. A turboprop has a much better power-to-weight ratio of about 0.8 hp/lb (1.32 kW/kg) to 1.2 hp/lb (1.97 kW/kg). While turboshaft engines have a higher capital and maintenance cost per unit of power, their better specific fuel consumption and overall better reliability make them very attractive for larger propeller-driven aircraft.

Worked Example #1 – Quantifying a Unit of Horsepower

The output at the shaft of an engine is often measured in “horsepower,” which is given the unit symbol “hp.” This unit is attributed to the Scottish engineer James Watt, who wanted to compare his steam engines’ power output to horses to help market the engines. Watt did various experiments and determined that a typical farm horse could, on average, steadily lift a 600 lb weight over a pulley system for an average distance of 63.9 feet in about 69 seconds. Using this information, explain how James Watt came up with the result that one hp = 550 ft-lb s^{-1}.

The work done by the horse will force \times distance, so with a weight W of 600 lb hanging over a simple pulley, that is also the force applied. Therefore, F = W and

    \[ \mbox{Work} = F \times d = W \times d=  600 \times 63.9 = 38,340~\mbox{ft-lb}\]

Power is the rate of doing work, so work per unit time, i.e.,

    \[ \mbox{Power} = \frac{\mbox{Work}}{\mbox{time}} = \frac{38,340}{69} = 555.65~\mbox{ft-lb s$^{-1}$} \]

This latter value is roughly the power produced by a horse, and James Watt settled on one hp = 550 ft-lb s^{-1}. Watt was not worried about accuracy. All he wanted was a simple but representative quantitative measure of the power delivered by a horse relative to what his steam engines could produce and so market his engines more effectively. In addition, the term made sense to farmers and others using horses to move equipment, etc., and so for a steam engine of 10 hp, the purchaser knew they were buying a machine equivalent to what could be done by ten horses. The unit of “horsepower” has since stuck and today is still used almost universally as a measurement unit of power output.

Principle of Operation

The principle of operation of a reciprocating piston internal combustion engine is based on the Otto cycle, as shown in the figure below. The up and down movement of the piston is synchronized with the opening and closing of the two valves (intake and exhaust) by using a cam, which allows the entry of the fuel/air mixture, followed by the compression and combustion process, and then the exit of the exhaust gases.

The principle of a reciprocating piston internal combustion engine is based on the Otto cycle. Left-to-right:  Intake stroke, Compression stroke, Power stroke, Exhaust stroke. The valves are opened and closed by cams geared to the crankshaft.

In summary, the operation of the engine consists of four cycles (or strokes), namely:

  1. The intake stroke is where the intake valve is open, and the air and fuel mixture is drawn into the cylinder, either from a carburetor or a fuel injection system.
  2. The compression stroke is where the valves are shut, and the upward-moving piston compresses the fuel/air mixture to the point that it will support combustion.
  3. The power stroke, where the mixture is ignited by a spark plug and the resulting flame front and expanding gases (called conflagration) progressively force the piston downward to drive the crankshaft.
  4. The exhaust stroke is where the exhaust valve opens, and the combustion products are removed from the cylinder before the entire four-stroke process starts again.

A piston engine may also work on the principle of the Diesel cycle, where the much higher compression in the cylinder is used to raise the temperatures sufficiently to cause combustion of the fuel without using a spark plug. Another advantage of a diesel engine is its better thermal efficiency and lower specific fuel consumption. In many countries, diesel fuel is also less expensive than gasoline.

Effects on Power

For a piston engine, the power from the engine P to the crankshaft (the so-called shaft brake power) is given by

(1)   \begin{equation*} P \propto \left( d \, \times p_e \times {\rm rpm} \right) \end{equation*}

where d is the total displacement, p_e is the mean effective pressure (pressure in the cylinder), and rpm is the revolutions of the crankshaft per minute. The name “brake” power comes from the fact that the power is measured using a brake type of dynamometer, which provides a resistance or braking torque at the engine shaft. Remember that a torque, Q, is the product of a force times a distance, so it has units of work. Power is the rate of doing work, so the power, P, at the shaft is the product of the torque and angular velocity of the shaft, i.e., P = Q \, \Omega.

The swept volume by the piston as it moves up and down in the cylinder equals the displacement of one cylinder, so the total engine displacement is that value times the number of cylinders. It will be apparent from Eq. 1 that the power from the engine can be increased by:

  1. Increasing the swept volume, i.e., by increasing the cylinder bore or stroke, or both.
  2. Increasing the pressure in the cylinder by the design of the combustion chamber and/or the piston shape and/or by turbocharging the air entering the cylinder.
  3. Running the engine at a higher rpm.

There is a practical limit to all of these things, partly by the allowable mechanical stresses and temperatures in the engine to prevent failure. To a large extent, the design of a piston engine comes down to the selection of high-strength and/or high-temperature metals and appropriate metallurgy to give the engine good operational reliability and durability, especially for the exhaust valves. On aviation engines, the exhaust valves are often sodium-filled, which improves thermal conduction from the valve stems and seats.

The maximum attainable rpm of the engine will also be limited by the propeller tip speed, which should be kept below the speed of sound (Mach 1) to maintain its propulsive efficiency and keep noise levels down. Propellers with high tip speeds that approach the speed of sound are always very noisy.

As the flight altitude of the airplane changes, so does the engine power available, as shown in the figure below. This effect occurs because the mass flow and air intake manifold pressure at the engine decreases with the lower density of the air found at altitude, i.e., power output decreases or lapses with increasing density altitude because of the lower oxygen content in the air. A reasonable approximation for the power available at altitude for a normally aspirated engine is

(2)   \begin{equation*} P_{\rm alt} = P_{\rm MSL} \left( 1.133 \sigma - 0.133 \right) \end{equation*}

where P_{\rm alt} is the power available at altitude and P_{\rm MSL} is the power available at mean sea level conditions. Remember that the density ratio, \sigma, 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.

The effects of altitude on both normally aspirated and supercharged engines. While supercharging can maintain power to higher altitudes, it comes at the price of weight, cost, and perhaps some loss of overall engine reliability.

It can also be seen from the above figure that the use of supercharging can maintain the rated power of a piston engine at much higher altitudes. This result is obtained because a supercharger increases the pressure and density of the air being supplied to the engine intake, i.e., boosting the manifold pressure and the oxygen content of the inducted air. The consequence is that more fuel can be burned, thereby increasing the power available from the engine at lower altitudes as well as maintaining that power at higher altitudes. Notice that when the exhaust gases power the supercharger, it is known as a turbosupercharger or, more commonly, a turbocharger.

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

(3)   \begin{equation*} \frac{P_{\rm alt}}{P_{\rm MSL}} = \frac{\varrho}{\varrho_0} = \sigma \end{equation*}

where the power at altitude P_{\rm alt} decreases linearly with density from the reduced mass flow and oxygen content into the engine. Such an equation, however, is obviously valid only for an engine without turbocharging. A better empirical correction for a normally aspirated engine that is often used in practice is

(4)   \begin{equation*} \frac{P_{\rm alt}}{P_{\rm MSL}} = 1.132 \left( \frac{\varrho}{\varrho_0} \right) - 0.132 \end{equation*}

There may be a further boost in engine power as the flight speed V_{\infty} increases. The pressure of the air p_e entering the engine will generally increase by an amount proportional to the dynamic pressure, i.e., \frac{1}{2} \varrho V_{\infty}^2. Therefore, the power from the engine increases somewhat from a ram air effect. Ram air can be significant for some aircraft, especially those flying at airspeeds above 250 kts. 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 for lower-speed general aviation aircraft, so the ram air effect can usually be ignored as far as it might affect the engine performance. From a design perspective, it would be inadvisable to rely on ram air effects at any airspeed when sizing an engine to an airframe.

Engine Performance Charts

Detailed charts are provided by the engine manufacturers to allow engineers to calculate shaft power available at any combination of altitude and temperature, an example being shown in the figure below. Notice that there are two sides to this chart, the left-side being the mean sea-level (MSL) power output performance and the right-side being the performance at altitude.

A piston engine performance chart, in this case for a normally aspirated Lycoming IO-360. The chart’s left-side can be used to determine MSL power output performance, the right side of the chart being used to determine the power output at altitude.

The instructions on the chart explain how it is used to determine the brake power of the engine. This chart is not what pilots would use in flight, but engineers use it to estimate the available engine power under different flight conditions. All of the needed measurements to determine power using the chart, i.e., pressure altitude, engine rpm, manifold pressure, and outside air temperature) can be made using normal cockpit instruments, which is very useful from a flight test perspective.

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

  1. Pressure altitude, which can be measured directly on the altimeter by setting the reference pressure in the Kollsman window to MSL standard conditions of 29.92 inches of Hg.
  2. Air temperature, which would be measured in flight by using an appropriately calibrated outside air temperature (OAT) gauge.
  3. 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, which can be measured on the manifold pressure gauge, which is also part of the standard cockpit instruments.

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

The next part of the process is establishing the engine performance at altitude, which is done using the right-side chart. After carrying point C onto the left chart, a straight line is connected between points C and A, point A being at the appropriate point on the rpm and manifold pressure map. To find the power available for a given pressure altitude, it is necessary to move along the line AC. Reading to the left axis will give the brake power output at altitude under standard temperature conditions. Finally, there is a minor correction for non-standard temperatures (the formula is given on the chart) to give the final brake power output at point F. Notice again that interpolation will be required throughout this process.

Engine Designators

Aircraft piston engines usually have a designator, e.g., IO-360-A. The question is what does this mean? However, decoding the designator is easy! The prefix “O” means horizontally opposed. The prefix “I” stands for fuel injection. The “360” is the swept volume of the pistons in cubic inches. The “A” is just a model of the engine, typically configured for a specific aircraft. An “AIO” prefix means that the engine is also qualified for aerobatics in that it has an oil system capable of inverted flight.

Brake Specific Fuel Consumption (BSFC)

The efficiency of a piston engine is measured in terms of power-specific or brake-specific fuel consumption (BSFC), which is often given the symbol c_b. The BSFC is a measure of the fuel used (in units of mass or weight) per unit of power supplied (in hp or kW) per unit time of engine operation (usually one hour). BSFC is used as a measure of the fuel efficiency of any engine that burns fuel and produces rotational or shaft power.

The BSFC is defined as

(5)   \begin{equation*} {\rm BSFC} = c_b = \frac{\mbox{Weight of fuel consumed}}{\mbox{(Unit power output)} \mbox{(Unit time)}} \end{equation*}

The units of BSFC are typically in lb hp^{-1} hr^{-1} in the U.S. customary system or kg kW^{-1} hr^{-1} in the SI system. Notice that the unit of mass (kg) is used in the SI units of BSFC, an anomaly of the SI system. However, the time units are in 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 0.5 lb hp^{-1} hr^{-1}, as shown in the figure below. There is usually some dependence of BSFC on flight altitude, with the values increasing somewhat. Notice that the best (lowest) BSFC is obtained with the engine operating at or near its rated rpm and power output. Today, the best performing and highest efficiency piston engines are supercharged types of diesel, which have better thermal efficiencies and BSFC values in the 0.35 to 0.4 lb hp^{-1} hr^{-1} range.

BSFC for a normally aspirated aircraft piston engine. The best BSFC occurs at sea-level and at the rated operating rpm of the engine (2,650 rpm). The various colored lines correspond to different operating altitudes.

Propeller Performance

A modern propeller is a remarkable accomplishment of aeronautical engineering, as shown in the photograph below. While the basic engineering principles used for aircraft propeller design have not changed in over a century, numerous detailed improvements have led to substantial gains in propulsive efficiency and operational reliability.

A modern constant speed (variable pitch) propeller designed for a high-performance turboprop airplane.

Design Features

Many types of propellers are in current use, from those that use just two blades to those with four or more blades, some fixed pitch, and others variable pitch. In addition, some propellers may have swept blades, which is a design feature used to reduce compressibility drag loss at the tips of the propellers when the aircraft operates at higher flight speeds. As engine power increases, more blades (or more blade area in general) are needed to deliver the power to the air. In some cases, to prevent the propeller diameter from becoming too large, counter-rotating propellers may be used to absorb high amounts of available power from the engine shaft.

There are many types of propellers, including those with different numbers of blades. For high power applications, counter-rotating coaxial propellers may be used.

Propellers with a larger number of blades also tend to be relatively more efficient (when compared based on the same thrust and total blade area). However, the propeller’s net efficiency depends on other factors, including its operating rpm, tip Mach number, diameter, and blade pitch. Today, there is an increasing emphasis on obtaining lower noise from propellers, which has driven modern propeller designs (even on general aviation airplanes) to have more blades and reduced diameters with lower tip Mach numbers.

Propeller blades are significantly twisted along their span, i.e., they have a form of washout. As shown in the figure below, the local pitch angle changes from a relatively high value at the root (next to the hub) and progressively decreases in value from section to section when moving out to the blade tip. The net twist varies for different propellers, but washout angles may be as large as 40 degrees over the blade span; of course, these angles are much larger than those used on a wing. The primary purpose of using blade twist is to get the local angles of attack at each section along the span of the blade to be low enough such that it operates close to the aerodynamic conditions where the section is most aerodynamically efficient.

A propeller blade is inevitably twisted along its length, the twist being used to optimize the angles of attack for best efficiency and low aerodynamic losses.

Early propellers were made of laminated wood but did not have the strength or durability needed for the much higher-powered engines produced during and after WW2. Aluminum alloy blades solved this problem and performed much better because they could be made thinner and rotate at higher speeds before suffering losses from compressibility effects.

Metal blades also allowed for variable pitch or constant speed propeller designs, which are needed for high-performance aircraft. A speed governor is used to automatically adjust the blade pitch to maintain the propeller at a constant rotational speed. For takeoff and landing, a fine (low) blade pitch is used, and a coarse (high) blade pitch is used for cruise flight. Therefore, an aircraft with a variable pitch or constant speed propeller can maintain good levels of propulsive efficiency over a broader range of airspeeds. However, such a capability requires a mechanism to adjust the blade pitch during flight, which incurs weight and cost.

The most recent advances in propeller technology have used composite propeller blades made from Kevlar or carbon fiber, allowing thinner, swept blades to be made. As well as being lighter, modern propeller designs have shown substantial gains in propulsive efficiency and reductions in noise. Wooden propellers are still made today, however, and are often used on lower-performance aircraft because they are lightweight and relatively inexpensive.

Operational Principles

The basic operational principle of a propeller has been previously introduced, along with some results for its propulsive efficiency based on the application of the conservation laws in integral form. As shown in the figure below, each of the rotating blades is designed to produce a lift force, and so the propeller as a whole produces a net thrust. It takes torque to spin the blades, and hence power needs to be delivered at the shaft.

The propeller’s rotating blades are each designed to produce a lift force, and so the propeller as a whole produces a net thrust. A torque (and so power) is needed to do this, delivered through the propeller shaft.

Another way to explain the propeller’s performance is using the blade element theory. Developing a computer program to calculate the performance of a propeller using the blade element method is a relatively straightforward task. The principle here is to calculate the angle of attack and the lift and drag at each section of the propeller, as shown in the figure below. All propeller blades are twisted along their span from root to tip (which is done to give good aerodynamic efficiency), so the local value of blade pitch differs from point to point along the span.

The velocity vectors at any blade element are combined vectorially to give the resulting angle of attack and flow velocity. The resulting angles are generally different at all blade elements along the span.

Notice that the relative flow angles and hence the angle of attack of the blade element is obtained by using the vector addition of the relative velocity components, i.e., the vector sum of the rotational velocity \Omega y of the blade element as it spins about the shaft and the free-stream velocity V_{\infty}, where the span position from the rotational axis is denoted by y,

The local pitch of the blade is \beta = \beta (y), so the angle of attack \alpha of any blade section is then

(6)   \begin{equation*} \alpha(y) = \beta(y) - \tan^{-1} \left( \frac{\Omega y}{V_{\infty}} \right) = \beta(y) - \phi(y) \end{equation*}

The lift coefficient on the blade element then follows as the product of the angle of attack of the blade and the local lift-curve-slope of the airfoil section, i.e.,

(7)   \begin{equation*} C_l(y) = C_{l_{\alpha}} \alpha(y) \end{equation*}

where \alpha is measured from the zero-lift angle and recognizing that the lift-curve-slope C_{l_{\alpha}} will depend somewhat on the shape of the blade section used, as well as the local incident Mach number at the section and to some extent Reynolds number too. The lift on a blade element will be

(8)   \begin{equation*} dL (y) = \frac{1}{2} \varrho V^2 c C_l dy \end{equation*}

where c is the local chord of the blade (c dy is the area of the blade element) and the local resultant velocity V is

(9)   \begin{equation*} V = \sqrt{ (\Omega y)^2 + V_{\infty}^2 } \end{equation*}

When the lift on all the sections of the propeller blade are obtained, then the net thrust of the propeller can be obtained by resolution of the local lift vectors in the direction of the thrust component followed by spanwise integration, i.e.,

(10)   \begin{equation*} T = N_b \int_0^{R} dL \cos \phi \end{equation*}

where N_b is the number of propeller blades, and R is the propeller’s radius. The component of the drag as it affects the thrust can be ignored. Also, it is reasonable to assume that there is axisymmetry in the problem, so the angles of attack at any given blade station are the same for any rotational position of the propeller blades. The integration process is performed numerically.

By analogous arguments, the power required to spin the propeller will be

(11)   \begin{equation*} P = \Omega N_b \int_0^{R} (dL \sin \phi + dD \, y) \end{equation*}

where dD is the local profile drag that again depends on the shape of the airfoil used on the blade section and the incident Mach number. Notice the inclusion of the moment arm y to get to the torque (a torque is a moment, so the product of a force times a distance or “arm”) and power is just the product of torque and angular velocity. In this case, however, the component of the lift dL \sin \phi (which is the induced drag) will contribute to the net drag of the section and hence the torque and power required to spin the blades.

If the section drag coefficient is known, then

(12)   \begin{equation*} dD = \frac{1}{2} \varrho V^2 c C_d \, dr \end{equation*}

However, the challenge with a propeller is to properly represent the section C_d because it depends on Mach number, in this case the helical Mach number, i.e.,

(13)   \begin{equation*} M_{\rm hel}(y) = \frac{V}{a} = \frac{ \sqrt{ (\Omega y)^2 + V_{\infty}^2 }}{a_{\infty}} \end{equation*}

where a_{\infty} is the local speed of sound, i.e., C_d = C_d(M_{\rm hel}). Of course, if the helical Mach number becomes too large and exceeds the drag divergence Mach number of the airfoil sections, then the propulsive efficiency from the propeller will decrease rapidly.

Variable Pitch Operation

Obviously, the local angles of attack of the blade sections are critical as to how they affect propeller operation. Regulating the pitch angles of the blades allows the efficient operation of the propeller to be optimized as a function of the flight condition, especially for takeoff and cruise, as shown in the figure below.

The effects of blade pitch allow for much control over the thrust and overall performance of the propeller.

The highest section angles of attack attainable on the blades will be limited by the onset of stall, just as a regular wing is limited in its angle of attack capability by the onset of stall. However, because the local incident Mach number varies from the root to the tip of the propeller and the stall angle of attack of an airfoil decreases with increasing Mach number, the allowable angle of attack before stall will decrease from root to tip. Therefore, for takeoff conditions, the blades need to be placed in a fine pitch, but as airspeed builds, the pitch can be increased to maintain thrust and efficiency.

If the engine stops in flight, the propeller blades need to be “feathered” into the flow to reduce the otherwise high drag of the stationary blades. In this regard, strong springs are used on a constant-speed propeller so that if the propeller stops, then it is automatically forced into the fully feathered position. The drag of an un-feathered stationary propeller is considerable, so an airplane with a fixed-pitch propeller may have a poor glide ratio. In some cases, the propeller blades may be set to a negative pitch to produce negative thrust and act as an aerodynamic brake during landing. However, this latter feature is usually only included on high-performance turboprop airplanes.

Propeller Performance Charts

Propeller performance curves are presented in the form of thrust coefficient, power coefficient, and propulsive efficiency, respectively, analogous to how airfoil and wing aerodynamic coefficients are used. All propellers have their characteristics quantified in this manner, and there is a separate set of curves for each reference blade pitch angle. By convention, the reference pitch angle \beta_{75} is not the angle of attack of the blade sections of the propeller but the reference pitch at the 75% blade span (i.e., at y = 0.75 R), which is a geometric quantity and can be measured. Sometimes, the pitch of a propeller is measured in units of length, which refers to the helical pitch that the reference blade section traces out during one revolution, i.e., like a screw thread. Hence, the old name of a propeller is known as an airscrew.

Thrust Coefficient

The thrust coefficient for a propeller is a non-dimensional thrust (which can be determined from dimensional analysis) and is defined as

(14)   \begin{equation*} C_T = \frac{T}{\varrho n^2 d^4} \end{equation*}

where d is the diameter of the propeller and n is the number of revolutions of the propeller per second. If the rotational angular velocity of the propeller is \Omega, then n = \Omega/2\pi. Rotational speed is often measured in terms of revolutions per minute or rpm, so rpm is equal to 60 n. Normally, the results for the propeller characteristics are plotted  as a function of the non-dimensional tip speed ratio or advance ratio J, which is given by

(15)   \begin{equation*} J = \frac{V_{\infty}}{n d} \end{equation*}

Representative C_T versus J results for a propeller are shown in the figure below, with a separate curve for each reference blade pitch. Notice that results from the blade element method discussed previously (i.e., the “theory”) agree well with the measurements,

Representative propeller performance curves in the form of thrust coefficient C_T as a function of advance ratio J.

Power Coefficient

The power coefficient for the propeller is

(16)   \begin{equation*} C_P = \frac{P}{\varrho n^3 d^5} \end{equation*}

and the corresponding C_P versus J results for a propeller are shown in the figure below. Again, notice that the theory is in good agreement with the measurements.

Representative propeller performance curves in the form of power coefficient C_P,as a function of advance ratio J.

Propulsive Efficiency

Finally, the propulsive efficiency of the propeller is defined as

(17)   \begin{equation*} \eta \equiv \eta_p = \frac{T V_{\infty}}{P} = \frac{C_T \, J}{C_P} \end{equation*}

which is just a non-dimensional statement that the efficiency of the propeller is the ratio of the useful power to the input power. Corresponding representative \eta versus J results for a propeller are shown in the figure below, again with one curve for each reference pitch angle.

Representative propeller performance curve of propulsive efficiency \eta as a function of advance ratio J.

Notice that for a given propeller operated with any given blade pitch \beta_{75} and rotational speed n, its propulsive efficiency increases with increasing forward airspeed to reach a maximum and then diminishes rapidly after that. The consequence is that a propeller of a given (fixed) blade pitch cannot operate with high propulsive efficiency over a wide range of values of J (or airspeed for a given rotational speed).

This latter outcome occurs because propeller blades are wings (rotating wings). All wings can only aerodynamically operate efficiently over relatively small ranges of the angle of attack, i.e., local blade section angles of attack between 2 to 14 degrees, depending on the local Mach number and Reynolds number. The local sectional angles of attack on the propeller depend not only on the rotational speed of the propeller and airspeed or advance ratio but also on how the propeller is twisted along its span. So, as airspeed changes, pitch and n being constant, then the angles of attack on the propeller are progressively reduced. However, by progressively increasing the blade pitch, the best efficiency can be obtained over a much wider range of airspeeds, which is precisely the purpose of a continuously variable pitch or “constant speed” propeller.

Explanation of Propeller Performance

Therefore, with this understanding of the flow at the blade section and the creation of thrust from the propeller, the various curves of C_T, C_P, and \eta, as shown previously, can now be explained. At low values of J, the corresponding angles of attack of the blade sections are relatively high. So the blade sections produce relatively high lift but are close to the point of stall, and so the propeller produces thrust but requires high power and is not particularly efficient. As airspeed and J increase, the blade sections operate at lower angles of attack and closer to their best section lift-to-drag ratios. As a result, the thrust is maintained, but the drag on the blades decreases and so propulsive efficiency increases markedly.

The lowest angles of attack will not produce much lift on the blades or thrust on the propeller. However, there is a range of airspeeds then (assuming blade pitch does not change) for which good propulsive efficiency is obtained. Therefore, the best aerodynamic efficiencies will only be obtained when all blade sections (or most of them) operate at or near the angles of attack for their best lift-to-drag ratio, which is usually between 2 to 8 degrees, depending on the incident Mach number.

There is eventually a point at higher airspeeds (or high J) where the blade sections encounter diminished angles of attack and higher helical Mach numbers, simultaneously decreasing thrust and efficiency unless the blade pitch can be further increased. Eventually, the blade pitch cannot be increased to improve efficiency, so the efficiency drops off.

The results also explain the differences in propulsive efficiency of fixed-pitch versus constant-speed propellers. Notice that if the propeller pitch is fixed, its propulsive efficiency increases slowly with airspeed, reaching a maximum and decreasing rapidly. The relatively low efficiency of a fixed-pitch propeller at low airspeeds means that the aircraft’s takeoff and climb performance will be relatively poor. Further increases in airspeed beyond the airspeed for peak efficiency will cause propeller efficiency to decrease precipitously. This behavior means that the useful power delivered to the airstream decreases, effectively setting an upper barrier to the airspeed achievable by the airplane

The preceding situation is very different for a variable pitch or constant speed propeller, which can be set into a fine pitch for takeoff, giving good propulsive efficiency and low airspeed and so giving the airplane markedly better takeoff and climb performance. As airspeed builds, the blade pitch can be increased (to maintain a constant rpm schedule), so the propeller efficiency can now closely follow the envelope of peak efficiency. This outcome is also why airplanes with constant-speed propellers have much better overall flight performance and will be able to cruise at much higher airspeeds.

Worked Example #2 – Estimating the Power Required for Flight

A general aviation propeller-driven aircraft has an in-flight weight of 2,105 lb and is cruising at a true airspeed of 120 kts. The lift-to-drag ratio of the aircraft is 8.59. If the propeller efficiency, \eta_p,  is 0.78, then how much brake horsepower is required for flight?

In level flight then L = W and T = D, so the thrust required for flight, T, will be

    \[ T = \frac{W}{L/D} = \frac{2,105}{8.59} = 245.0~\mbox{lb} \]

where L/D is the lift-to-drag ratio of the aircraft. We are given the true airspeed, V_{\infty}, in kts (knots), which needs to be converted to ft/s, i.e., 120 kts = 202.54 ft/s. The power required, P_{\rm req}, will be

    \[ P_{\rm req} = \frac{ T \, V_{\infty}}{\eta_p} = \frac{245.0 \times 202.54}{0.78} = 63618.3~\mbox{ft-lb/s} \]

Converting to horsepower (hp) by dividing by 550 gives P_{\rm req} = 115.7 hp.

The problem can also be worked in SI units. A true airspeed of 120 kts = 61.73/s and a thrust of 245.0 lb is equal to 1,090 N. Therefore, the brake power required is

    \[ P_{\rm req} = \frac{ T \, V_{\infty}}{\eta_p} = \frac{1,090 \times 61.73}{0.78} = 86.25~\mbox{kW} \]

Summary & Closure

A reciprocating piston engine driving a propeller is commonly used for low to moderate-performance aircraft and is favored for its robustness, affordability, good propulsive efficiency, and low fuel consumption. These characteristics make it ideal for general aviation airplanes and certain classes of UAVs. However, for larger aircraft, the lower power-to-weight ratio becomes a drawback and alternative systems, such as turboprops, are often preferred for their higher power output and improved scalability.

Propellers are a simple and robust system for producing thrust and are widely used in aviation. A fixed-pitch propeller has limited operational characteristics and efficiency, but the use of a variable-pitch (constant-speed) propeller increases its operational envelope, albeit with some added weight and cost. Propellers are not just used with piston engines, they are also used with turboshaft engines, such as in the case of turboprops. Proper matching of the propeller with the engine is essential for optimal performance.

The current trend is toward using smaller diameter propellers with more blades helps to reduce blade tip speeds and noise, which is an important consideration in modern aircraft design. The challenge is to match the engine and propeller to achieve a good overall propulsive efficiency and low specific fuel consumption over a wide range of flight conditions. This goal requires careful consideration of the engine and propeller characteristics, as well as the design of the entire propulsion system, to ensure that the optimal combination of efficiency, performance, and noise is achieved.

5-Question Self-Assessment Quickquiz

For  Further Thought/Discussion

  • In a trade study of choosing a reciprocating engine versus a gas turbine engine to power a new airplane, consider the power-to-weight ratio of each engine and try to establish a crossover point where the piston engine may prove too heavy.
  • What might be the trades in using a smaller propeller with a larger number of blades versus a larger propeller with a fewer number of blades? Discuss.
  • Would it be desirable to use a fixed-pitch propeller or a constant speed propeller for a UAV? Discuss.
  • Why does the use of a swept blade on a propeller generally help give the propeller better efficiency?

Other Useful Online Resources

  • Learn in this ERAU video about the components that make up a piston engine powerplant used on a Cessna.
  • A good video on the 4-strokes of the piston engine.
  • For a video explanation of the piston engine check out this WWII training video of Piston Aircraft Engine Types. 
  • Watch an animation of how a rotary engine works.
  • An older but excellent film on how airplane propellers work.
  • A video explaining the differences between superchargers and turbochargers.
  • Propellers in action –  great video of the coaxial propellers of the Antonov An-70.