page_title: Stirling cycle
section_title: Piston motion variations
hierarchical_section_title: Stirling cycle / Piston motion variations
caption_attribution_description: English: Model of an ideal Stirling cycle
context_page_description: The Stirling cycle is a thermodynamic cycle that describes the general class of Stirling devices. This includes the original Stirling engine that was invented, developed and patented in 1816 by Robert Stirling with help from his brother, an engineer.
  The ideal Otto and Diesel cycles are not totally reversible because they involve heat transfer through a finite temperature difference during the irreversible isochoric/isobaric heat-addition and heat-rejection processes. The irreversibility renders the thermal efficiency of these cycles less than that of a Carnot engine operating within the same limits of temperature. Another cycle that features isothermal heat-addition and heat-rejection processes is the Stirling cycle, which is an altered version of the Carnot cycle in which the two isentropic processes featured in the Carnot cycle are replaced by two constant-volume regeneration processes.
  The cycle is reversible, meaning that if supplied with mechanical power, it can function as a heat pump for heating or cooling, and even for cryogenic cooling. The cycle is defined as a closed regenerative cycle with a gaseous working fluid.
context_section_description: Most thermodynamics textbooks describe a highly simplified form of Stirling cycle consisting of four processes.  This is known as an "ideal Stirling cycle", because it is an "idealized" model, and not necessarily an optimized cycle.  Theoretically, the "ideal cycle" does have high net work output, but it is rarely used in practical applications, in part because other cycles are simpler or reduce peak stresses on bearings and other components.  For convenience, the designer may elect to use piston motions dictated by system dynamics, such as mechanical linkage mechanisms.  At any rate, the efficiency and cycle power are nearly as good as an actual implementation of the idealized case.  A typical piston crank or linkage in a so named "kinematic" design often results in a near-sinusoidal piston motion.  Some designs will cause the piston to "dwell" at either extreme of travel.
  Many kinematic linkages, such as the well known "Ross yoke", will exhibit near-sinusoidal motion.  However, other linkages, such as the "rhombic drive", will exhibit more non-sinusoidal motion.  To a lesser extent, the ideal cycle introduces complications, since it would require somewhat higher piston acceleration and higher viscous pumping losses of the working fluid.  The material stresses and pumping losses in an optimized engine, however, would only be intolerable when approaching the "ideal cycle" and/or at high cycle rates. Other issues include the time required for heat transfer, particularly for the isothermal processes.  In an engine with a cycle approaching the "ideal cycle", the cycle rate might have to be reduced to address these issues.
  In the most basic model of a free piston device, the kinematics will result in simple harmonic motion.
caption: A model of a four-phase Stirling cycle