Thermal Expansion Engines

Gallery opened: 17 May 2015

Updated: 27 Nov 2018

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A solid-expansion engine derives power from the thermal expansion and contraction of solid material as it is heated and cooled.

Almost all engines work by the expansion of gases, a notable exception being the Malone engine worked by the expansion of fluids. It seems logical to ask if anyone has attempted to make an engine powered by the thermal expansion of solids. The answer of course, humans being what they are, is yes.


There are immediate difficulties. The amount by which solid materials expand is very small, though the force behind it can be very large, certainly enough to buckle railway lines. This implies we need to do some serious gearing up before we consider anything like driving a dynamo. The other big issue is that thermal expansion depends on the bulk temperature of the material, and the properties thermal conductivity and specific heat set limits on how quickly a solid can change temperature.

This table gives the linear thermal expansion coefficents in parts-per-million per degree K:

Aluminium 23.1
Mercury 61
Brass 19
Molybdenum 4.8
Carbon steel 10.8
Nickel 13
Copper 17
Platinum 9
Diamond 1
Quartz 0.33
Glass 8.5
Silver 18
Invar 1.2
Tungsten 4.5
Iron 11.8
Water 69
Lead 29
Zerodur 0.02
Magnesium 25
Zinc 29.7
Invar is an alloy of 36% nickel and 64% iron, invented in 1896 by Charles Edouard Guillaume. At this composition the expansion coefficent hits a deep minimum. Guillaume won the Nobel Prize for physics in 1920 for this invention, as it enabled more accurate scientific instruments to be constructed.

Zerodur is a lithium aluminosilicate glass-ceramic produced by Schott AG for use in large telescope mirrors. It's about the lowest-expansion material that is anything like commonly available. As you can see from the table, it's considerably better than invar.

Firstly, we want our expanding material in the form of a long rod as that increases the movement, and will allow the material to be heated and cooled more quickly; from this point of view we want our rod to be as thin as possible while still bearing the forces involved. A rod under tension would be better than one under compression because it cannot buckle.

The speed of heating and cooling is actually a bit of a red herring. We could make a thermal expansion engine that alternately heated and cooled metal rods by steam and cold water, but the slow rate of heat transfer would make the power output tiny, and I don't like to think what the thermal efficiency would be. About the only remotely sensible approach is to accept that the power output is very small and rely on free heating in the shape of solar energy, even though this gives only one cycle of heating and cooling per day; it might be enough to wind a church clock.

Of the common metals that are solid at room temperature, zinc has the largest expansion coefficient at 29.7 x 10^-6. Lead is almost as good, but its low mechanical strength makes it unsuitable. If we take a zinc rod 1 metre long, and heat it from a room temperature of 20 degC to the boiling point of water at 100 degC, which should be quite practicable, then it will increase in length by 80 x 29.7 x 10^-6, or 2.38 mm. That, I imagine will take several hours to develop fully, and clearly gearing that movement up to run a dynamo is going to be quite a challenge. On the other hand there is considerable force behind it, which can be increased easily by increasing the cross-section of the rod, (though at the expense of increasing the thermal capacity and slowing things down even more) and I can easily imagine that with a realistic amount of gearing we could do something like wind up a clock spring.

Now, how to get the power out? If we have light loading most of the expansive force will do nothing. On the other hand, if we constrain the rod completely there is no expansion and no power output- instead the energy has set up a tensile or compressive stress in the rod. By analogy with matched electrical loads, I think we will get the maximum power out when we allow the rod to expand by half of what it would have done when unrestrained; an engineer friend of mine agrees with me. It should therefore be possible to calculate the power output per cycle from the force required to limit the expansion to one half. If the zinc rod is under compression it will almost certainly need intermediate supports to prevent buckling. It will be simpler to keep our rod in tension with a hefty spiral spring, and far fewer if any supports will be needed.

If our expanding zinc is in tension, then it could be in the form of a wire. (I have checked and you can buy zinc wire) While this might make construction simple, it misses the point- the expanding element has to withstand a lot of force, and I suggest the energy available per heating/cooling cycle is proportional to the mass involved; a wire is thin so this will be low. So we will stick with a rod. You can buy zinc rods, though the maximum length available is not yet established.

And so on to the next problem; if our zinc rod is fixed at one end, so we get the full 2.38 mm at the other, well, what is it fixed to? We need a metal chassis which can contain the force of the expansion without significant extension. If we made it out of, er, zinc, then it would thermally expand by the same amount as the rod and the net movement would be zero. Obviously a material which expands less- preferably much less- than zinc is going to be desirable. The table tells us that Zerodur is as good as it gets but it is unlikely to be a practical choice because of cost, if nothing else. Invar is made of nickel and iron, and so should be reasonably cheap. A metre of it under the same 80 degC rise will expand 80 x 1.2 x 10^-6, or 0.096 mm. We therefore have the difference of 2.28 mm to work with, which is 95.8% of the zinc expansion. If instead we used steel, which is presumably the cheapest material on the list, its expansion would be 80 x 10.8 x 10^-6, or 0.864 mm, and we have lost over a third (36%) of the expansive movement; perhaps we should stick with invar. To get the 80 degC differential, I envisage our zinc rod being mounted on the church roof in a linear parabolic reflector; you can buy these off the shelf for solar water heating. The rod will be painted dull black for maximum solar absorption, and perhaps some sort of textured finish will improve the absorption. This sort of thing is no doubt recorded in the annals of solar energy.

So far we have considered a 1-metre rod of zinc (plus 1-meter invar chassis) but given the size of the average church roof I think a 10-metre rod is entirely practicable. (I'm starting to feel like xkcd here; what if we used more power?) That proportionally increases the movement to 22.8 mm, nearly an inch, and we have ten times the power available. I think gearing that up to wind a clock should be relatively straightforward.

At this point I began to wonder about the cost of a 10-meter invar chassis. But the point of our chassis is not that it must have a very low expansion coefficent, but that it should not expand or contract. They are not the same thing. I reckon the cheapest chassis would be a simple steel beam, suitably lagged so that its temperature does not vary significantly over the 24-hour cycle. That should save a bob or two.

But we are not finished yet. We can have multiple zinc rods arranged in parallel, with levers at each end to transmit the movement from one to the other so that they are effectively in series, equivalent to a 100-metre zinc rod, all mounted in the same linear parabolic reflector. That increases the power by ten times again and the movement to 228 mm, so we can really get some work done. We can't afford any backlash in the system so it would be kept under tension by a spring as noted above. Friction is to be minimised by teflon bearings or roller bearings.

With suitable design of the thermal collector the top temperature could no doubt be higher than 100 degC. Best not to carry this too far, for the melting point of zinc is fairly low at 419 degC. I imagine it loses mechanical strength long before it melts; perhaps someone who knows more about zinc than I do can help us here. Another issue may be thermal creep- the zinc rods elongating over time.

I think that's a sort-of-practical design, but I'm sure it could easily be improved. Do feel free to join in.

Looking at the table above, mercury has a linear expansion coefficient that at 61 x 10^-6 is more than twice that of zinc. Presumably this refers to mercury confined in an infinitely stiff pipe so only the ends move. Unfortunately mercury is heavy, expensive, and poisonous, so it is not exactly the ideal working material, but this did not deter some people from large-scale experiments with mercury as a working fluid in a boiler and turbine.

Water expands even more, its linear expansion coefficient being 69 x 10^-6. Being very cheap and wholly non-toxic it would be a much better choice than mercury, though it has the awkward property of freezing when exposed to the sort of temperature range found on our church roof. But water expands when it freezes, and perhaps this could also be exploited for harvesting some extra power...

Ethanol has an expansion coefficient of 250 x 10^-6, more than three times greater than water. Even better is gasoline at 317 x 10^-6 but it is a rather inflammable working fluid; ethanol will be safer.

However, we are getting away from the subject of this page which is solid expansion engines. The expansion of water for power generation has been tried, notably by Malone, but without great success. Malone claimed to have generated 50 HP in this way, which I'm sure is more than anyone ever got out of a solid thermal expansion engine.

We will stick with solids. We do not have to confine ourselves to metals, though their strength may be helpful in building the machine. A moment's thought shows that thermal expansion engines are all around us; you may even have one in your kitchen. Cars have thermostatic valves that control the flow of water through the radiator to control cooling. These valves are operated by the expansion of paraffin wax when it liquefies; OK, maybe we're not confining ourselves to solids completely. Using paraffin wax in tension is not going to work, so we will put it under compression in a pipe and make it push a piston as it expands. Hopefully the pipe will not have to be invar; if the wax expands enough we may be able ignore the expansion of a steel pipe. Other existing applications are the wax motors sometimes used to unlock washing-machine doors and operate ventilators.

Comparison with the linear expansion of solids is tricky, but here are some numbers. Paraffin wax is characterised by the number of carbon atoms. C36 has a free volume expansion of 22% when heated from 30 degC to 80 degC.


The earliest suggestion of thermal expansion for power generation that has been found so far is in a book by James White, called A New Century of Inventions, published in 1822. One of the inventions is titled "A mechanical essay in drawing power from expanding metals" and a proposed machine is illustrated in Plate 34. It is however purely a theoretical machine; White proposes using steel rods 20 feet long, heated and cooled by hot and cold air in a way that is not specified. He suggest the engine could be use to pump water, but admits he has no idea of the likely power output. I came across this book at a London book fair; the price was 750, and I am afraid Museum funds do not run to that.

Left: White's plan for a solid thermal expansion engine: 1822

More details have been obtained without paying out 750.

If I have understood this correctly, the main drawing is a plan view of the engine. The three members that make up the triangle are heated and cooled. The movement of the corners of the triangle is magnified by the three members connected to the central pump-rod, as shown in the side-view behind the main drawing. W is a heavy weight, and X is a very small pump considering the size of the engine.

It is not a practical engine.

James White (1762-1825) was a civil engineer and a prolific inventor; one hopes that his other inventions were more practical than this one. He died aged 63 in December 1825, in Manchester.


George I Washburn of Massachusetts took out a US patent on 4 July, 1865, (No 48,607) for a motor powered by thermal expansion. The expansion of metal rods drove a ratchet which could be used to wind the mainspring of a clockwork motor. The patent gives no details of how the rods might be rapidly heated and cooled to increase the output power.

Left: Washburn's attempt at a solid thermal expansion engine: 1865

The two rods M were supposed to be heated and cooled to move the ratchet arm L up and down. This really doesn't look practical; from the drawing the rods M would have to expand by about 5% before the ratchet wheel would move on by one tooth. Assume the rods are zinc, which as we saw above has a expansion coefficent of 29.7 x 10^-6; to get 5% expansion its temperature would have to be raised by 1683 degC. Since the melting point of zinc is fairly low at 419 degC, I think you can see the problem here.

This is a good example of how you can get a patent for a machine that is not so much impracticable as impossible.

Later in the patent there are more complicated arrangements of pulleys for increasing the range of the motion, and references to using a bag of air or liquid instead of solid expansive elements. These refer to a Figure 7, which does not appear in the patent supplied by Google Patents.

This is presumably the same George I Washburn who took out a US patent for a motor powered by a mixture of air and steam. One is left with the feeling that Mr Washburn did not have much of a grip on the realities of power generation.


Left: Solar thermal expansion engine: 1932

This contraption positively reeks of impracticability. No wonder the man on the right is turning up his nose and washing his hands of the whole affair.

The text gives the general idea; tungsten wires expand and contract and (in theory) turn the drum around; I doubt if it could even move itself. Why tungsten wires? Something to do with not melting? Iron wire would have been much cheaper and as the table above shows, expands more than twice as much as tungsten.

No US patent for this idea has so far been found, but there was a Jesse J Walker taking out phonograph patents around this time.

From Modern Mechanix December 1932


Left: Exhibit at the Chicago Century of Progress exhibition engine: 1938

A conventional pendulum would move too quickly for a thermal drive system to work, so whoever conceived this demonstration used a compound pendulum which can be made to oscillater very slowly by suitable choice of weights and lengths.

Why someone saw fit to raise the question of perpetual motion I do not know. The machine will obviously only work when power is being supplied to the electric heaters. The power conversion efficiency must have been microscopic.

From Popular Mechanics December 1933


Left: Alleged solid thermal expansion engine: 1938

This article allegedly shows a solid thermal expansion engine, and it clearly states that power is "generated by the expansion and contraction of metal". Absolutely nothing about its operation is revealed beyond the heating and cooling arrangements.

I've tried hard to give this article the benefit of the doubt, but I can't believe the claims. If the engine is capable of driving a lathe, then it clearly produces power at several hundred rpm, which doesn't stack up well with the slowness of normal thermal expansion and contraction. The output of 2 - 3 horsepower is also very hard to credit. However, the whispers of doubt become deafening when the inventor claims at the end: "It would be very cheap to run, as fuel is not needed.". Yes, that would make it cheap to run, but it would also make it a perpetual motion machine. So what's the blowlamp for, Doctor?

From the look of it, and the heating/cooling arrangements, I think that's a hot-air engine, the heat coming from the blowlamp. Perhaps Doctor A S Carr was having a laugh. He is unknown to Google.

From Newnes Popular Mechanics December 1938.


Left: Adams' thermal expansion engine: 1967

John L Adams of Santa Maria, California, patented this thermal expansion engine based on multiple bimetal strips. A disc is mounted eccentrically on the output shaft 64, and around this is a sort of collar attached to the housing 54, which rotates so that the bimetal strips are in heating or cooling zones as appropriate. This pushes round the output shaft, though not, I think, very quickly. The patent makes no attempt to estimate the power output.

Apart from the patent, Mr Adams' engine is unknown to Google, so it clearly went nowhere.

From US patent 3,430,441 of March 1969

Left: Adams' thermal expansion engine: 1967

The arrangements for heating and cooling the wheel. Box 20 is a heat-exchanger intended to increase efficiency by heating the incoming fluid with the outgoing fluid.

From US patent 3,430,441 of March 1969


Left: Bicycle wheel thermal expansion engine: 2013

The simplest way to make a solid thermal expansion engine, is to get a bicycle rim and use rubber bands for spokes. Here two spot-lamps are fixed either side of the spokes, to heat them.

This example was uploaded to YouTube by Jonathan Pegues in 2013. He says "It rotates counter-clockwise because the heated rubber bands expand causing the center of mass to move towards the higher tension which is to the left (not the right), hence counter clockwise rotation." I struggled to make sense of this- on that basis should not the wheel should go round the other way? The answer is that when rubber bands are heated, they don't expand- they contract. Therefore the greater tension is on the right, so there is more weight on the left , so the rim at left goes downward. Your comments are invited.

Here's another rubber-band wheel on YouTube; once again the side of the wheel away from the heat source moves downward. A simple cardboard version was described in C L Stong's book "The Amateur Scientist", published by Heinemann in 1962; see p557. Yes, once more the cool side of the wheel goes downwards.

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