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The Stirling Engine


The Stirling engine was invented in 1816 by the Rev. Robert Stirling who sought to create a safer alternative to the steam engines, whose boilers often exploded due to the high steam pressures used and limitations of the primitive materials available at the time. Like other heat engines the Stirling engine converts heat energy into mechanical energy. The essential features of the Stirling engine however are that it is a closed cycle, external combustion engine. This means that it uses a fixed amount of working fluid, usually air, but other gases may be used, enclosed in a sealed container and the heat consumed by the engine is applied externally. This allows the engine to run on just about any heat source including fossil fuels, hot air, solar, chemical and nuclear energy. It can also work with very low temperature differentials, as low as 7°C, between the heat source and the heat sink so that it can be powered by body heat and even the steam from a cup of coffee.

Since it can use heat from a constant flame and does not depend on explosions as in an internal combustion engine, the engine runs silently.


Diagram of an Internal Combustion Engine used for Electricity Generation


The diagram above shows three alternative heat sources which are typically used in electrical generating applications.


Working Principle

The Stirling Engine relies on the property of gases that they expand when heated and contract when cooled. (Charles' Law). If the gas is contained within a fixed volume, its pressure will increase on heating and decrease on cooling.

If the gas is held in a variable volume container, constructed from a movable piston in a cylinder closed at one end, the pressure increases and decreases will cause the piston to move out and in. Repeated heating and cooling will cause a reciprocating movement of the piston which can be converted to rotary motion using a conventional connecting rod and a crankshaft with a flywheel.

Unfortunately the rate at which the temperature of the gas can be varied by heating and cooling the cylinder is limited by the large thermal capacity of practical pistons and cylinders. This problem however can be overcome by maintaining one end of the cylinder at a constant high temperature and the other end at a constant cold temperature and moving the gas from one end of the cylinder to the other. This is accomplished by means of a loose fitting piston, known as the displacer, which moves back and forth inside the cylinder, thus shuttling the gas from one end to the other. As the displacer moves, the gas leaks around the gap between the displacer and the cylinder wall. The displacer produces no power itself and only uses enough energy to circulate the gas within the cylinder. Power is extracted from the thermal system by using the volume/pressure variations of the gas at the cold end of the cylinder to push a separate "power piston" back and forth. Many different piston and displacer configurations are possible and examples illustrating the most common types are given below.


Conversion Efficiency

The theoretical efficiency η of the Stirling engine is given by Carnot's Law thus:

η = (Th - Tc)/Th      or      η = 1 - Tc/Th

Where Tc is the temperature of the gas when it is cold and Th is the temperature of the gas when it is hot.

Practical engines with efficiencies of 50% have been produced. This is double the typical efficiency of an internal combustion engine which has greater pumping and air flow losses in the engine and heat losses through the exhaust gases and cooling system.


See also Heat Engines


Available Power

Although the engine has a high energy conversion efficiency, it unfortunately has low specific power in that it is quite large for the power produced and this limits its range of uses to low power applications. Specific power can be improved by the use of higher gas pressures and alternative working gases to increase the thermal capacity of the gas. See Applications below.


Stirling Engine Types

Stirling Engines come in many shapes and forms. Most are variants of four basic configurations, the alpha, beta, gamma and double-acting designs shown diagrammatically below.


The Stirling Engine (Alpha Configuration)

A fixed amount of air, or other working fluid, is enclosed within two cylinders, one hot and one cold, and shuttles forwards and back wards between the two. The air is heated and expands in the hot cylinder and is cooled in the cold cylinder where it contracts, giving up its energy to perform mechanical work in the process.

Note: The two pistons are connected to a crankshaft but their motions are 90 degrees out of phase with each other. This means that when one piston is at the top or the bottom of its stroke, the other will be half way between the top and the bottom. Many ingenious mechanisms have been developed to provide the delayed motion between the pistons. For the sake of simplicity only simple crankshafts are shown here.


Stirling Engine 1
Stirling Engine 2
Stiling Engine 3
Stering Engine 4

1. The working fluid (gas) is heated and expands pushing the hot piston to the bottom of the cylinder, turning the crank shaft, thus extracting work from the hot gas. Expansion continues causing the gas to flow towards the cold cylinder. The piston in the cold cylinder which is 90 degrees (a quarter revolution) behind the hot piston in its cycle is also pushed downwards extracting more work from the hot gas.

2. The gas is now at its maximum volume. The momentum of a flywheel on the crankshaft now pushes the piston in the hot cylinder towards the top of its stroke forcing most of the gas into the cold cylinder pushing the cold piston downwards. In the cold cylinder the gas cools and its pressure drops.

3. As the hot piston reaches the top of its stroke almost all the gas has now transferred to the cold cylinder where cooling continues and the gas contracts reducing the pressure even more. The reduced pressure allows the cold piston to rise. The power of the flywheel momentum, compresses the gas and forces it back towards the hot cylinder.

4. The gas reaches its minimum volume and forced into the hot cylinder where it starts to push the hot piston downwards. The gas is heated once more in the hot cylinder where its pressure increases and it expands pushing the hot piston downwards in its power stroke and the cycle starts again.


The regenerator located in the air passage between the two pistons is not strictly necessary but serves to improve the efficiency of the engine. It is typically a metal or ceramic matrix with a large surface area capable of absorbing or giving up heat. As the gas cycles from the hot cylinder to the cold cylinder, some of its heat is transferred to the regenerator thus helping to cool the gas. As the cold gas returns to the hot cylinder it picks up heat from the regenerator on the way back. This reduces both the amount of heat which must be put into the gas by the heat source and also the amount of waste heat which must be removed from the gas by the cooling system. It thus reduces the fuel consumption and improves the overall working cycle efficiency.

The gas transfer passage between the two cylinders is essentially dead space and in most designs this kept as short as possible.


The working fluid may simply be air but other gases such as Hydrogen, Helium and Nitrogen may be used to increase the specific power.



The Stirling Engine (Beta Configuration)

The thermodynamics of the Stirling beta engine are similar to those of the alpha engine but the physical configuration is quite different.

The beta engine has only one cylinder which is heated at one end and cooled at the other. A single power piston is arranged coaxially with a displacer piston and both pistons move within this cylinder. The displacer piston does not extract any power from the expanding gas but only serves to shuttle the working gas back and forth between the hot and cold ends. As in the alpha engine, the cyclic motions of the pistons are 90 degrees apart with the motion of the displacer piston leading the power piston by a quarter revolution of the crankshaft.

The mechanism for linking the motions of the two pistons is quite complex. The connecting rod for the displacer is made up from two parts. The upper link is rigidly attached to the displacer and passes through the centre of the power piston and must maintain an airtight seal with the piston so that the working gas does not escape. The second part of the displacer linkage is a normal connecting rod connecting the upper link to the crankshaft. Since the displacer mechanism occupies the space normally occupied by the power piston connecting rod, the linkage for the power piston must also be split into two parts, one on either side of the displacer linkage to maintain balanced forces on the power piston.


Stirling Beta Cycle 1
Stirling Beta Cycle 2
Stirling Beta Cycle 3
Stirling Beta Cycle 4

As the gas heats up in the hot end of the cylinder it expands and is forced through the regenerator into the cold end of the cylinder.

As the displacer moves up, the gas moves into the cold end it and pushes the piston downwards

As the displacer reaches the top of its stroke, all the gas is transferred to the cold end where is cooled and contracts. At the same time the piston follows the displacer upwards.

As the displacer begins to move down the piston continues to move up and the cold gas is transferred to the hot end of the cylinder and the cycle starts again.

The engine may also incorporate a regenerator to improve efficiency. For clarity this has been shown as being separate from the cylinder. In practice it is more likely to be incorporated into the cylinder wall. In some designs, the displacer piston itself acts as the regenerator.



The Stirling Engine (Gamma Configuration)

The Stirling gamma configuration is simply a Stirling beta engine in which the power piston is not mounted coaxially with the displacer piston but in a separate cylinder. This avoids the complications of the of the displacer piston linkage passing through the power piston.


Stirling Engine Gamma Cycle

A fixed amount of working fluid (gas) is maintained within the cylinders by the pistons which form a gas tight seal with the cylinder walls. The displacer is a loose fit within the hot cylinder, allowing the gas to pass down the sides as it moves up and down. As with other Stirling engines, the gas is alternately heated and cooled causing it to expand and contract as it shuttles between the hot and cold cylinders transferring its energy to the power piston in the cold cylinder.



Double - Acting Stirling (Swash Plate) Engine

This configuration has fewer mechanical parts than the other designs and is more suitable for higher power applications.

Double-Acting Stirling Engine
Swash Plate Drive

The working gas is shuttled back and forth via regenerators between adjacent cylinders which are heated at the top and cooled at the bottom. This arrangement does not need displacers as the pistons in the adjacent cylinders perform this function. The cylinders must be closed at both ends and the connecting rods must pass through seals in the lower cylinder caps so that the gas in the cylinders does not escape. It has the advantage that the force exerted by the expanding gas on one side of the cylinder is augmented by the force due to the contracting gas on the other side, or to put it another way, the effective pressure differential across the pistons is increased.

In the case of a four cylinder machine, the movement of the pistons is 90 degrees out of phase with each of its neighbours. The reciprocating movement of the pistons is converted to rotary motion by a swash plate drive.

The cylinders are arranged in a fixed ring around a rotating shaft which incorporates an inclined swash plate which also acts as a flywheel. As the plate rotates its surface appears to rise and fall as it passes beneath the cylinders and this harmonic motion is linked via the connecting rods to the reciprocating pistons.



Stirling engines have been used in a variety of forms since the 1930s as motive power in a range of vehicles and engines of 75kW and more have been developed. Although early engine developments were for automotive use, because of its low specific power the Stirling engine is better suited for stationary applications and recent years have seen it used more for generating electrical energy.


  • Combined Heat and Power
  • The Stirling engine is ideal for use in small Combined Heat and Power installations for capturing waste heat. Stirling engine generators with electrical power outputs between 1 kW and 10 kW are available for domestic applications with the waste heat being used by the central heating boiler. Overall thermal efficiencies of these installations can be as high as 80%.

    See the Hybrid Power pages for more information.

  • Solar Power
  • In the USA, banks of 25 kW Stirling engine generators are being used to generate electricity from the thermal energy captured by large solar thermal arrays. See also small Solar Thermal installations for details.


See also Generators


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