Caloric engines use heat to produce mechanical motion. This page illustrates a gamma-type Stirling arrangement: a large displacer shifts enclosed gas between hot and cold spaces, while a separate power piston connects to a crankshaft. It is an explanatory example, not a replica of a particular historical engine.
Caloric Engine Interactive Calculator
Change the temperature reservoirs, regeneration effectiveness and crank phase. Compare a thermodynamic ceiling with an ideal-cycle regeneration model, and see the two connected piston drives move. The animation does not calculate actual engine power or starting behavior.
Equation Used
- Temperatures use kelvin in thermodynamic expressions. Reservoir temperatures are not a solved gas-temperature field.
- The four-process ideal cycle uses fixed volume ratio 2 and Cv/R=2.5. Regeneration effectiveness reduces external heat required; it is not multiplied directly by Carnot efficiency.
- The gamma cutaway shows constant-length rods, a loose displacer and a sealed power piston. Crank planes are separated schematically.
- Crank motion is prescribed. Shaft power, torque, starting, heat-transfer rates and actual engine efficiency are not calculated.
- Temperature ranges are theoretical inputs, not material or product temperature ratings.
Rebuilt as an explicitly generic gamma Stirling example, not a reconstruction of every caloric engine. Retained four input/output IDs. Replaced invented phase-loss/work-index formulas with an ideal-cycle regeneration calculation and phase fraction.
Displacer and power piston have different jobs
The gamma-type example keeps its working gas enclosed. A loose displacer moves that gas between hot and cold regions; clearance around its edge provides a passage. A smaller sealed power piston changes the enclosed volume. Two cranks set the relative timing.
The drawing shows both rods connected throughout their travel. Crank phase changes their relative motion. Slow prescribed rotation makes the parts visible; it does not establish whether the engine could sustain that motion under load.
A teaching example within a wider engine family
Caloric and hot-air engines include different constructions. This gamma Stirling illustration explains separate displacer and power-piston roles. It is not a dimensional reconstruction of a Rider or Ericsson engine, nor a model of their measured performance.
An ideal-cycle comparison
Convert both temperatures to kelvin. The Carnot ceiling is 1−Tc/Th. For a four-process Stirling cycle with volume ratio r, net work divided by nR is (Th−Tc) ln(r). External heat input divided by nR is Th ln(r) + (1−ε)(Cv/R)(Th−Tc).
The calculator divides those quantities, using r=2 and Cv/R=2.5. The second heat term accounts for imperfect recovery during constant-volume regeneration. At ε=1 the expression reaches the Carnot ceiling; at ε=0 it remains finite. This is not a fitted real-engine efficiency formula.
The smooth crank animation does not follow four perfectly separated thermodynamic processes. Its adjustable phase is reported as a fraction of one turn, not a calculated torque penalty.
Try temperature and regeneration changes
At 550°C hot and 40°C cold, the temperature difference is 510°C and the Carnot ceiling is about 62.0%. With 80% regeneration, the stated ideal-cycle comparison gives about 42.8%.
Changing crank phase moves the displacer relative to the power piston. It leaves these ideal-cycle efficiencies unchanged. Raising the cold temperature reduces both efficiency figures.
What remains outside the model
Real engines have finite heat transfer, gas-flow losses, leakage, friction and dead spaces. This calculator does not quantify those effects. The regeneration input belongs to the ideal-cycle comparison, rather than to a detailed model of the illustrated displacer or a particular heat-storage matrix.
Questions about the animation
Is the large displacer a sealed power piston?
No. Gas can pass around it. The smaller piston is sealed.
Does changing phase predict power?
No. It changes the relative crank positions. Actual performance needs a more complete model.
Are these actual engine efficiencies?
No. They are a Carnot ceiling and a stated ideal-cycle comparison.
References
Kontax Engineering: Stirling engine cutaways, for the distinct displacer, gas passage and power-piston roles.
University of British Columbia: Stirling engine and ideal cycle, for the four ideal processes and their distinction from practical piston motion.
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