Thermal Expansion Engines

Gallery opened: 17 May 2015

Updated: 21 May 2015
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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.

Of the common metals that are solid at room temperature, zinc has the largest expansion coefficient at 29.7 x 10^-6. 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 minutes 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. I don't like to think what the thermal efficiency would be.

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 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 may need intermediate supports to prevent buckling.

So far so good, even if we have ignored the minor problem of heating and cooling the rod. Maybe we don't bother, and just let ambient temperature variations provide the movement; this will reduce the power output to one cycle a day, but it might be enough to wind the church clock.

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? Assume we have a metal chassis which can contain the force of the expansion, and we made it out of, er, zinc, then it would 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. 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.


WASHBURN'S THERMAL MOTOR

George I Washburn of Massachusetts took out a US patent on July 4, 1865, (No 48607) 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.

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.


THE NOVEL MACHINE OF DOCTOR A S CARR

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.

THE RUBBER-BAND WHEELS

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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