Ronin of the Spirit

Because reality is beautiful.

Sterling Engine Analysis

In 1816, the Reverend Robert Stirling invented a engine. From time to time an astute reader will hear about this engine as the solution to the world’s problems in general, and as the perfect candidate for automotive hybrids specifically. Pure bunk and here’s why.

First, you have to know a little about hot gas. (Gas like air or CO2, not like gasoline.) When gas is heated, it wants to get bigger (ie. increase in volume). When it has its heat removed (cooled), it wants to decrease in volume. If it is in a sealed container, it can’t increase its volume, so it presses against the walls of the container all the harder when heated (pressure). That’s why aerosol cans say to not expose to temperatures of more than 120 degrees. They are full of gas at a certain pressure and if they get too hot, the pressure gets too high and they pop. (Also, if you have a weak container, like an empty closed pop bottle and stick it in the freezer, it will collapse. The removal of the gas’s heat causes a reduction in volume, which reduces the pressure, meaning the air pressure on the outside is higher, and it squishes in.) There are mathematical formulas that describe these relationships of pressure, volume and temperature called gas laws.

Nice suit!

A man named Carnot (above) put all of the gas laws together and drew some rational conclusions. He performed a thought experiment about the perfect heat engine. (An engine being a device for turning heat energy into mechanical energy.) The perfect heat engine would be made out of a magic material which would let heat in but not out at one point, and out but not in at another. It would have no friction, and would never leak. That way, any energy flow could be controlled and monitored.

(1.) Heat would be added perfectly instep with the expansion of the gas, so that no energy was wasted. (Heat is added but the temperature doesn’t increase, because it’s expanding instep.) It expands while taking heat, pushing the piston down.

(2.)The heat in the gas is then “used up” as the gas continues to expand without new heat. It expands while cooling, still pushing the piston down.

(3.)The heat is then removed from the gas, causing the gas to shrink (reduce in volume), pulling the piston in.

(4.) Now the piston is pushed in (further reduced in volume), raising the temperature of the gas back to the temperature it was before the heat was added in step 1.

For various reasons deduced from the gas laws, Carnot’s engine is the most efficient on earth. Since we know what perfect is, we know the best way to design any engine on earth.

Though every part of Carnot’s cycle is right, none of them are true, and therein lies the problem. There is no material which can conduct heat only in one direction, give us choice of direction, and switch direction at whim. There is no gas which behaves exactly as the gas laws say they should, though hydrogen approaches it. There is no material that is totally frictionless and perfectly sealing at the same time. Carnot’s engines says the key to efficiency is the difference between the temperature of the heat input in step (1) and the heat removed in step (2).

Material science is the kicker. The engine’s material must be a good conductor of heat or the heat in it will build up until it melts. But it must not be too good a conductor of heat or it will take heat out of the engine which the engine is supposed to be making power out of. It must allow a tight seal for the piston but without to much friction.

Long story short, the engine must be all at once: a good conductor, insulator, bearing surface, and pressure vessel. Due to the properties of combustion, it must do all of this while white hot and resistant to corrosion.

In the case of the Otto engine (the kind most likely in your car), you can add to all of those challenges this: the heat is not made outside the engine, but in it, and the gas not heated by an outside source, but within the cylinder itself by flame. Furthermore, there are the complexities of piping the gas in and out.

At this point one might cry, “Wait a moment! Do you mean to tell me that the efficiency of an engine is based of the difference between the temperatures at the beginning and end of the cycle? My exhaust manifold GLOWS red! I must be throwing away a huge amount of energy!” Yup.

And that’s a very good thing. The reason you can afford a car is because the Otto cycle, with all its oddities of valves and spark plugs and not reusing the working gas, dumps excess heat out the exhaust stream. If it didn’t, the engine block would need to be made of the same alloys that jet engines are made of, instead of cast aluminum or cast iron.

So, here’s the danger of a little information. (And full circle back to the Stirling engine.) The Stirling engine does not burn inside the engine, it burns outside of it. Its gas is sealed away inside. Of all the engines in the world, Sterling comes the closest to Carnot’s imaginary engine in its cycle. Only in its cycle. Remember that Carnot’s engine is imaginary and made of unobtanium? Carnot’s cycle only has meaning as a thought experiment because you can’t make an engine out of magic alloys which do not exist.

People read that the Stirling engine is theoretically the most efficient heat engine and assume they don’t have one under their hood because it was simply never maximized. Actually it is not that it has not been maximized but that it CANNOT be maximized. Though combustion creates temperatures of thousands of degrees, the Otto engine need not operate at that temperature. If a Stirling was going to operate at that temperature the heat would have to move through the engine and then into the gas. So the engine block, under full power generating stress, must be hotter than the low stress exhaust pipes of an Otto cycle.

Though invented in 1816 to save people from the danger of boiler explosions, the Stirling was never widely used. Steam engines are also external combustion engines, but they have the boiling of water to serve as a temperature regulator. Stirlings do not have this, and a frequent and persistent complaint is burnt out parts.

Another HUGE misunderstanding about Stirling engines is their ability to use very low temperature differentials; that is to say, freakishly small differences between input temperature and output temperature. It’s true. In a 72 degree room, a small Stirling can run off the heat of your palm. These tiny engines create just enough power to overcome their own friction. What would happen if you scaled it up? You would have an enormous engine with equally enormous bearings. Again, the engine would create just enough power to overcome its own friction.

But just for the sake of argument, let’s say you had a truly enormous engine, one the size of a house. The hot part is in the sunshine, and the cool part is in the shade. The low temperature difference would be overcome by the truly enormous amount of energy available, right?

A qualified no. The smaller the temperature difference, the greater amount of gas the engine has to pump around to get the same amount of power. There’s no free lunch. For the same amount of power, high temp = small working mass, low temp = large working gas. The losses to pumping all that gas through the small passages necessary for heat reclaiming mount up very quickly. For this reason, efficiencies are very low. While low efficiencies with free power (like solar) are OK, it’s a niche application.

Another route to efficiency is high pressure. Reverend Robert made his Stirlings low pressure and large (For instance, about a cubic foot of displacement per horsepower, or 172,800% larger than an Otto cycle of the same HP.). The modern trend is to make them high pressure and small. But then they must be filled with inert gas and sealed just so, because if air and lube oil are pressurized and heated the Stirling engine becomes a bomb. This is also why Rev. Stirling could make his engines with a foundryman and bricklayer and modern engines are “lab queens” in college physics departments.

Finally, another story that pops up now and then is Ford’s Stirling research in the 1970’s. Yes, they made a Stirling engine. No, they didn’t produce it. They didn’t produce it for the exact same reason Chrysler didn’t produce its turbines nor GM its Wankle. Material science could not mass produce certain key components at low enough cost to get enough people buying. This, in turn, means mass production could not be used, further raising the price and decreasing the market in a vicious catch-22.

Don’t get me wrong. I think Stirlings are cool. I think they have applications to green science. But we will never see one in a car produced by market forces. Further, if you want to invest in expensive technologies, fuel cells have higher real world efficiencies than Stirling’s theoretical ones.

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April 9, 2008 - Posted by | Ecology, Engines, skepticism, Small Car, Uncategorized | , , , , , , , , , , , , , , , , , , , , , , , , ,

4 Comments »

  1. I stumbled on to this this post and found it quite interesting. I didn’t review the detail of your thermodynamic analysis, but your conclusions are accurate. I have a little experience with Stirlings, having worked on the referenced Ford program. A Stirling will not make it in automotive applications for the reasons you state.

    The only nit I would pick is the reference to “bomb.” High pressure Stirlings without inert gas can be engineered to be quite safe (at a price of course). The Ford program used hydrogen; the total energy in the working gas is quite small relative to the 20 gallons of gasoline in the trunk.

    Comment by godjeeringatheist | April 11, 2008 | Reply

  2. My, mistake, GJA. I was trying to keep it simple and misstated that a bit. You’re totally correct that Sterlings pressurized with non-inert gas can be made and will continue to be made. Sealing is a problem, but an expensive rather than impossible one. My reference to being a bomb was not aimed at sealed engines but engines that are sealed in the manner of automotive pistons and are running pressurized air. HIgh pressure/high temperature air (with all its oxygen) and the lube oil that slips past the seals creates a bomb if the vaporized oil ignites. Reverend Stirling’s engine’s always leaked when they were hot, and soon ran a partial vacuum, This made the BMEP less than 14.7 psi, and thats why it took 1728 cubic inches to make one horsepower.

    To be fair to the Reverend, his engines were obscenely efficient. Phillip’s small engine (of more than a century later) never achieved the specific fuel consumption of the Robert Stirling’s engines. My theory is that the combination of low pressure/high surface area to volume and slow speed reduces eddy formation in the working fluid. Since energy used to generate a vortex is un-reclaimable, it contributes to parasitic losses. (I also suspect this is why, despite the finite analysis software available, there isn’t a software that can accurately predict Stirling engine performance if the engine is fitted with a regenerator.

    I would truly love to see a company like Edlebrock be contracted to design a Stirling. They have the some of the most advanced flow-benches in the world, and I would love to see what a group of people with automotive/empirical training would do in comparison to the engineering/theoretically trained groups that generally work on them.

    Comment by truthwalker | April 11, 2008 | Reply

  3. I want a 15-50 horsepower stirling, weighing less than 500lbs which runs on a temperature differential of 20-50*F.

    Crazy?

    Comment by Pressureangle | April 24, 2008 | Reply

  4. I’m not an engineer, so I couldn’t run the numbers to tell you, but within reason you can do anything with enough money. Here’s the problem
    Due to the complexities of vortex formation in turbulent flow, and the fact that Stirling engine operation depends on flow, no computer models exist which can accurately predict sterling behavior.

    30 deg F is a narrow temperature range, so you need either very high pressures or very high volumes of gas. If you use very high pressure, the seals drag and the engine is very heavy. If you use very high volume the engine is huge.

    Lyle Cummins found that unpressurized air operating Stirling’s engines needed about 28 Liters per horsepower. You want say 30 horsepower, thats 840 L, or around 200 gallons engine capacity. If you made the cylinder of 2 feet in diameter and 12 feet long, you MIGHT be able to get the whole thing under 500 lbs, because the pressures as so small and rotation is so slow.

    Comment by truthwalker | April 28, 2008 | Reply


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