These notes were first published in the Model Engineer, 3rd September 1976


by Robert Sier.

These notes are not intended as a complete guide to making hot air engines but hopefully written that they may stimulate an interest in the subject, if only scaled down to models.
One thing that seems to be little understood is how a hot air engine works. the principle on which these engines operate was first laid down by a Frenchman Sadi Carnot who published in 1824 a slim volume entitled Reflection on the motive power of fire and machines fitted to develop this power. He laid down the following cycle of operations:

1. A quantity of air of air at volume V and temperature T is compressed to Volume V2 with no change in temperature (i.e by applying a heat sink).
2. The air is then further compressed to Volume V3 during which the temperature rises to T2 (heat sink removed).
3. A heat source at temperature T2 is then applied to the air to expand which is allowed to expand from V3 to V2 (no change in temperature).
4. The heat source is then removed and the air allowed to expand back to its original volume V with the temperature falling from T2 back to T.

Carnot found by experiment that the amount of energy produced by expansion of the air from V2 back to V was greater than that required to compress the air from V to V2, giving an excess of power. "The air then", Carnot stated, "has served as a a heat engine: we have in fact, employed it in the most advantages manner possible, for no useless re-establishment of equilibrium has been effected by the caloric."
Carnot also realised that the power developed depended on the temperature drop and established the general proposition The motive power of heat is independent of the agents employed to realise it, its quantity fixed solely by the temperature of the bodies between which it is effected, finally, the transfer of caloric. This means that the theoretical efficiency depends only on the limits of temperature between which the engine works i.e ((Tmax - Tmin)/Tmax) although Carnot realised that could only take place if there was no direct heat transfer between bodies of different temperature.

The Practices

From the above brief summary we can see that the main points of design are:

1. A means of obtaining isothermal compression at a low temperature.
2. A means of obtaining isothermal expansion at a high temperature.
3. Highest possible difference in temperature.
4. No direct heat transfer between hot and cold ends.

A study of hot air engine design over the past 200 years will show that none of the above can be fully embodied in a practical design and a compromise has to be struck between the theory and what is easily achieved with materials at hand.

The layout that has proved the most successful and popular over the years is the design first invented in 1794 by, Englishman, Thomas Mead and then later taken up and developed, in Scotland, by the Stirling brothers and others. This design (Fig. 1) consists of an open ended tube fitted with a power piston P and a displacer piston D. The top end is kept cold and the bottom kept hot. D serves to shift the enclosed air from the hot to the cold end of the chamber. The mode of operations is as follows:

1. With D at the bottom of its stroke and P at the top of its stroke. The enclosed air is at the cold end.
2. P moves to the bottom of its stroke so compressing the enclosed air, any heat arising from compression of the air being removed by the cooler. (Isothermal compression at Tmin.)
3. D moves from the bottom of its stroke to the top so shifting the enclosed air from the cold to the hot end, the air will become heated and the pressure will rise. (Heat transfer at constant volume.)
4. P is then driven back to the top of its stroke. (Isothermal expansion at Tmax.)
5. D moves from the top to bottom of its stroke, the air is moved back from the hot to the cold end and the cooler removes remaining heat from the air. (Heat transfer at constant volume.)
6. The cycle is repeated.
For simplicity the heater and cooler are omitted from the diagram.

From Meads design of 1794 to the present time all hot air engine designers have faced the following problems and practically every patent taken out since then has been for improvements in one or other.

1. How to efficiently transfer heat from the heat source to the air.
2. How to efficiently abstract the wast heat at the cold end.
3. How to reduce the heat transfer along the heater chamber walls and through the displacer.
4. How to drive the displacer and shift the air between the hot and cold ends.


As can be seen in the pages of Model Engineer, the problem faced in making hot air engines is not so much on of evolving an efficient design but making one that actually works! The following designs have been evolved by experiment by the author and give a fairly compact engine layout, which though thermodynamically not very efficient is capable of giving a reasonable power output.

Fig. 2 shows a layout to Stirlings design of 1815 with the following design parameter:

i. length of displacer chamber L = 3 times its diameter.
ii. length of heater chamber = 2/3L
iii. length of cooler = 1/3L
iv. swept volume of displacer = 1.5 times swept volume of piston cylinder.
v. length of displacer = 2/3L and stroke = 1/3L.

The idea of having the hot chamber longer than the cooler is to get a temperature gradient from hot to cold end of the displacer cylinder. Even when using thin walled tubing for the heater there is bound to be some heat conduction along the tube and extending the length is one way of reducing it; This design feature is found in many old engine designs but in modern designs special metals are used to overcome this problem. The displacer cylinder is best made in two parts joined with a low heat conducting washer. I use brass tube since it is easy to work with, but stainless steel would enable higher temperatures to be used; this type of heater is not very efficient but is the simplest to make.
This ratio of swept volume of displacer and piston gives a reasonable compression ratio, ideally it should be nearer unity, but this gives rise to greater mechanical losses through friction which are difficult to overcome in a small engine. In general the greater the compression ratio the greater the power output, but it seems that you cant scale nature, for the smaller the engine the greater the frictional losses in proportion to the power developed.
(Note: in low temperature Stirling engines the swept volume ratio is large, i.e, with the swept volume of the displacer much greater than that of the piston. In general terms at high temperatures the swept volume ratio should be small but increased as the operating temperature differential is lowered.)

The most effective means of cooling is with a water jacket as shown, natural air cooling fins to give rise to overheating unless quite large, and forced air air cooling can absorb nearly all the power of the engine. Small models can be heated by a meths burner, and larger engines by a gas flame, the use of a flame guide (F) helps to keep the flow of gasses along the heater wall, the gap between it and the heater will depend on the size flame being used, to small a gap will reduce flow and choke the flame.
The piston can lapped in to give a good seal with a couple of oil groves. alternately a soft rubber O ring can be fitted. The piston can be fitted slightly looser than with a lapped piston and a grove machined to take the O ring, care must taken with the fit of the ring so as not to give to much drag; the depth of grove recommended for use in model steam engines will give to tight a fit. O rings can also be used to seal the displacer drive rod. Provided sufficient lubrication is given the rings work very well and appear to give less drag than a lapped type seal. Only thin oil should be used, and any oil that gets into the heater chamber will carbonise and impair heat transfer; however I have that a mixture of paraffin and Redex (an upper-cylinder lubricant for IC engines) as lubricant seems to over come this as it does not carbonise.

A flywheel, sufficiently heavy to carry the engine over the compression stroke at normal operating speeds will be needed to give even running and is best mounted on ball or needle bearings. This can make a high speed / high compression engine difficult to start for it will have to be spun up to speed before it starts running; but it is a mistake to fit too heavy a flywheel. To further reduce friction, ball races in the power piston connecting rod are well worth fitting as the frictional losses in compressing the air can with a poor design exceed the power output, and no amount of heat will ever make it work.

Many designs have been evolved for driving the displacer, in some old engines cams were used to give intermittent movement to the the displacer, the idea being to get the indicator diagram as near as possible to the ideal air cycle, but additional mechanical losses outweigh any advantage that might have been gained. The simplest method is to have the piston and displacer operating with a phase displacement of between 90° to 110°, this gives a continuous sinusoidal movement of the displacer, and it will found that a greater part of the compression takes place in the cold end and a greater part of the expansion in the hot end, so the conditions for a surplus of work to be produced are still fulfilled. The indicator diagram becomes oval in shape. Using an angle of 90° enables a simple linkage to be used.

In the cycle of events, the maximum pressure obtained will depend on the amount of air taking part in the process. This causes a factor called dead space to be considered, this is the mass of air that takes no part in the process and assumes an average temperature; too large a dead space will reduce the overall efficiency by reducing Pmax. Fig. 3 shows a layout following Meads design, as improved by Robert Stirling in 1816, which is much more compact. The overall length of the displacer needs to be extended to accommodate the power piston, but however need not be extended to cover the complete stroke of the piston since as shown by the graph the strokes of the displacer and piston can be made to overlap, so reducing the amount of dead space. The displacer drive rod is passed through the center of the piston. Since the power depends on the amount of air being moved by the displacer, the power can be varied by varying the stroke of the displacer. The power can also be increased by using denser air, i.e compressed air, but there is of little advantage unless a sealed crank-case is used, the crank-case being pressurised up to the minimum operating pressure of the engine. By arranging for the crank-case to communicate with the interior of the engine when the piston is at the end of the power stroke the power can be be simply varied by altering the crank-case pressure.

Most old air engines designs ran at atmospheric pressure, with an open cylinder, with inevitable losses of working fluid through leakage, eventually leading to the engine working with a pressure cycle that alternated above and below atmospheric. To overcome this many designs incorporated a non-return calve that allowed air into the engine when the pressure fell below atmospheric. In a model this valve needs to be lightly loaded so that it opens with the minimum of pressure difference across it.

In all the forgoing designs the piston is placed at the cold end; ideally to ensure that the air expands at a constant temperature the cylinder should be at the hot end. However, operating and lubricating the piston at very high temperatures is not easy. James Stirling experimented with the idea but reverted back to the cold piston, the only air engines that expanded hot air against a piston were Ericssons ship engines and the furnace gas engines based on the work of Sir George Cayley, both of which had heat shields fitted to the piston, and many furnace gas engines had water jackets to prevent the piston from overheating, however these machines worked on a different principle. One of the few displacer type engines to be built with a hot piston were those built by Henry Essex in America. The Essex model E , a kitchen exhaust fan, hat the hot cylinder acting as the power piston, the cylinder sliding up and down inside cooling fins forming the cold end.

The Economiser

As early as 1797 it was found that greater economy in running could be obtained in air engines by utilising some of the the wast heat, but the development of the regenerative principle was largely due to the work of Robert and James Stirling. In many old air engines the regenerator was completely omitted, since simple construction and was a greater selling point that economy in running. The engines themselves were usually so grossly inefficient, that there would have been little point in fitting a regenerator, but many of them worked steadily with little or no maintenance for upwards of 50 years which was all that was required.Those were days free from energy crises when an extra few buckets on the fire mattered little.
It might be argued that, because of possible extra losses, there is little point in fitting a regenerator to a model engine, but they do run better with one fitted. The type that was fitted to the Robinson engine is the easiest to fit (Fig. 4.). I fitted two perforated discs to the displacer rod with a diameter less than the internal diameter of the displacer cylinder, and the distance between them corresponding the required length of the displacer. Fine wire wool is then wrapped round between the discs, the wire wool is quite springy and when first fitted into the cylinder will be fairly stiff to move, but if the engine is turned over by hand with the heater on, the heat soon takes the spring out and the wool fits snugly against the wall of the cylinder.

Further increase in efficiency can be obtained by using the exhaust gasses from the burner to pre-heat the incoming air to the burner, but this is not easy to do with small spirit burner and is is not really worth bothering with unless a more efficient type of heater chamber is used.