Home link Ragnarok Engineering
Stirling Engine cycle used backwards as Heat Pump


This wind powered heat pump can be either a cooler or heater by using a slip eccentric.

The operating principle is the 'Stirling Cycle', same as a 'Stirling Engine' but backwards – the crank is driven and the output is a temperature differential:   Compressing air causes it's temperature to rise – likewise when air is expanding, its temperature drops. – This is therefore a Heat Pump without any chemical refrigerant, only hot air as the working fluid.

The key feature of using the Stirling Cycle for this application is being a heat pump independent of electricity, therefore it is unaffected by severe solar flares or corona ejections.   It does have the downsides of large bulk in comparison to conventional heat pumps of the same output, and the need for wind, so intended for rural and upland use.

A storm force spring overload mechanism is also provided on the turbine head to prevent over-speeding.

The 'Hot Air' Engine was first patented in 1816 by Rev. Robert Stirling, a Scottish Minister of religion and Engineer, initially as a safer alternative to steam engines as it did not have the risk of boiler explosions (a serious problem back in those days) ...nor the need for a boiler.   Later in their development the higher thermal efficiency was to become the key feature. However early Stirling engines always suffered from the unavailability of modern stainless steel to resist high temperatures. For industrial use, they were replaced by the more compact power and speed control of internal combustion engines, though for specialised application they are still being made and developed today.

Kontax Stirling Engine
Contemporary model Stirling Engine by the Kontax company, so precisely built that it will work (slowly) on the heat of the palm of your hand!


Stirling Cycle Machines, both motors and heat-pumps always have two Pistons arranged to move so that one lags behind the other, typically by 90 degrees of crank angle. A multitude of variations are possible, but always these two pistons out of phase to each other.

Stirling Cycle machines operate on a temperature differential, that means one part of the engine is always at a different temperature to the rest of it.   The working gas, in our case simple air, is trapped within the machine and continually cycles round.

With this hardware, the Stirling Cycle has 4 legs...
* Two where the volume changes but temperature is constant
    (the curved lines on the graphs)
* Two where the working gas is moved between hot and cold chambers.
    (the vertical straight lines on the graphs)

This is often represented on a Pressure – Volume diagram, though the temperature changes are inconveniently not shown, as this would require a three dimensional image.   It all follows the thermodynamic general gas equation, which is the combination of Boyle's and Charle's gas laws.

    Pressure x Volume = Constant

Note: The temperature must be the absolute temperature in degrees Kelvin, where 0 degrees Centigrade = 273 degrees Kelvin.

To provide this constant temperature of compression and expansion, an internal temporary heat store is require which in Stirling engine terminology is called a 'Regenerator'. In the current machine, this is encompassed within the loose fitting piston called a 'Displacer'. This cyclically moves the working air between the hot and cold chambers.

So the Pressure-Volume ideal graphs are shown for the Stirling Cycle below, the only difference between Heat Pump and Motor is we go round the cycle the opposite way!

PV diagram PV diagram

The same Stirling Cycle can be used as either a Heat Pump or Motor.

These are idealised diagrams, on practical engines the P-V diagram looks more like a curved ellipse but the principle is exactly the same. The area enclosed by the loop is energy transferred per cycle, per cylinder.   Using SI units, pressure is measured in N/m2 and volume in m3. So multiplied together for the area, we get:

N.m3   =  N.m  =   Joules


Practical Stirling Cycle machines have the 4 legs of the cycle blended together due to the sinusoidal motion of the cranks, which effectively produces a curved elliptical shaped graph, but the principle is the same. Area enclosed is the energy per cycle.

Note: This describes the continuous heat and work flow, after the machine has warmed itself up to operating temperature.

   For Motors we talk about Efficiency = Power Out / Heat In

For Heat Pumps, the energy is delivered at the hot chamber and mechanical work has to be inputted to raise the temperature. The term Coefficient of Performance 'COP' is used which is the inverse of efficiency.

   COPheat pump = Heat Out / Power In

For reversible cycles, like the Stirling Cycle, the theoretically best possible efficiency is the Carnot efficiency, and only depends upon temperatures.

   Carnot Efficiency = 1 – (Tc / Th)

...where Tc and Th are the cold and hot chambers absolute temperatures in degrees Kelvin.

Therefore the COP for a perfect Stirling Cycle is the inverse of the Carnot efficiency, and only depends upon temperatures as there are no phase-change losses as with refrigerants.

COPheat pump  =  1

1 – (Tc / Th)

This means the lower the temperature difference (∆T) the greater the heat output! – This is the opposite way round to heat engines which improve with increased temperature differential.   It follows that Low Temperature Differential designs with large displacers, which generate nominal power as an engine, are theoretically very good as heat pumps!   So Stirling Cycle heat pumps despite their large bulk, are actually very efficient and make good use of a relatively modest wind power input.

In Stirling Cycle Heat Pumps, the compression ratio determines the operating temperature Th so avoiding dead volume becomes most important.

Current Machine

Basically it is of the Low Temperature Differential 'gamma' type Stirling machine with large displacers, but reversed as a Heat Pump rather than a motor. The Mk1 currently has two cylinders, though more are intended in a radial formation for the planned Mk2 machine.   The current crankshaft is open, but will be enclosed in a crank-case for the Mk2.

The heat pump can either be a cooler or heater through using a slip eccentric, this is tripped by one of two pawls whilst in motion. There are two eccentrics, one fixed to the vertical shaft driving the compression pistons, the other displacer eccentric free to turn, but driven by one of the pawls. Such that the displacers either lead the pistons by 90 degrees, or trail behind them at 90 degrees.

model stirling engine on the bench
The Mk1 Stirling machine on the bench.

Crankshaft with eccentric and pawls
The vertical 'crankshaft' with eccentrics and pawl leavers.
These switch between heater or cooler mode.

The loose fitting Displacer piston which is also the Regenerator...
Regenerative Displacer

Regenerative Displacer

Regenerative Displacer

Regenerative Displacer Displacer with acetal flanges mountings

The current machine an experimental model, a test rig for developing the idea before designing the full size machine, which is anticipated as being about four times larger.   The production machine needs to be both modular in its components, and moveable. It will also be fully enclosed and weather proofed.

This Stirling Cycle Heat Pump is intended for Ground Source heat input as it is stable, even on the coldest days.   Also, since the cost of foundations for the wind turbine tower has already been accepted, it makes sense to complete the installation of ground pipes.   Output could be either piped water or ducted air.


Index Page