Stirling Cycle

A Scottish minister named Robert Stirling invented the Stirling engine around 1816. Various manufacturers built Stirling engines over many years, but those engines usually had low power compared to their weight (low specific power). Although pressurizing the cycle can achieve a higher specific power, sealing of the gas often proved problematic. To overcome this difficulty, William Beale, a professor at Ohio University, invented the free-piston Stirling engine in the early 1960’s. He realized that with a proper design, the engine did not require any mechanism and could be easily hermetically sealed. In the early 1970’s, Beale founded Sunpower, Inc. to continue the work he started at Ohio University.

The theoretical Stirling cycle has the following four stages in its cycle as shown in the graph below:

  • (1-2) Isothermal Expansion
  • (2-3) Constant Volume Cooling
  • (3-4) Isothermal Compression
  • (4-1) Constant Volume Heating

Practical engines however have smooth continuous motions represented by the ellipse within these bounds.

One could build an engine which operates as shown in the diagram with alternate heating and cooling within a single space, but losses would exist caused by the alternate heating and cooling of the metal walls. There would also be significant stress and material issues with such an engine.

In actual engines, the hot and cold spaces are separated and the gas is shuttled between them. This configuration requires an added mechanical component to displace the gas between the hot and cold spaces.


The animation above illustrates a “Beta” type Stirling engine in which the gas is displaced between the hot and cold spaces by the upper moving component (the “displacer”). In simple engines (as shown) a clearance gap around the displacer allows for the movement of gas. In more complicated engines, external heat exchangers are included and a seal is fitted to the outside of the displacer to force gas through the heat exchangers.

The lower moving component (the “piston”), causes compression and expansion of the gas, represented by the horizontal motion of the dot on the Pressure-Volume (PV) diagram below. Heating and cooling is accomplished by the displacer motion, represented primarily by the vertical motion of the dot on the PV diagram.

Clicking on the “Kinematic Stirling Engine” button displays a configuration in which the piston and displacer motion are caused by the mechanism at the bottom.

Clicking on the “Free-Piston Stirling Engine” button displays an engine without a mechanism at the bottom. This configuration is accomplished primarily by giving the displacer a higher natural frequency than the piston so that it will lead the motion of the piston. By correctly sizing the area of the displacer rod that passes through the piston, the resulting motions will produce the gas space variations required for the engine to operate. Clicking on the “Free-Piston Stirling Generator” button displays an engine with a linear alternator connected to the piston to generate power on the wires penetrating the (usually) sealed outer vessel of the engine. In the simplest implementation of such a generator, magnets (shown in red) connected to piston pass by a coil of wire thereby generating AC current.

  • ContactUs