The following numbers are based on what I have seen in the above video or statements the speaker has made and in a few cases, guesses based on what I can see. All my dimensional estimates are strictly eyeball and may easily be off by 20% or even more.

Sunpulse Stirling engine generating electric power

power piston diameter: est. 48 inches
power piston stroke: est. 2.5 inches
displacer diameter: est. 48 inches
displacer stroke: variable, est. 2.5 to 6 inches
flywheel diameter: est. 72 inches
flywheel rim: est. 0.5 inches thick by 4 inches wide
Operating RPM: est. 60 to 90
Heating and cooling pumps: est. 2 inch diameter by 3 inch stroke, double-acting
2×9.4 cubic inches per cycle = 312 grams (for water)
Operating temperatures: Hot oil or water at 5 bar pressure, 150 to 200 deg C. Water cooling, est 25 degC or higher

Estimate operating gas temperature Th=180 deg C, Tc=40 degC
Power output of generator: 1.5 kW
Engine pressure variation: +/- 0.1 bar (approximate in video of gauge)
Hot oil with possibly gravel stored in elevated barrel est. 55 gal barrel

Stirling engine driving water pump

flywheel diameter: est. 48 inches
flywheel rim: est. 2.0 inch diameter steel
displacer stroke: est. 5 inches
claimed pumping output:
400,000 liters/day, zero head
(110,000 gal/day or 9200 gph for 12 hr day)
80,000 liters/day, 10m head
(22,000 gal/day or 1800 gph for 12 hour day)
15,000 liters/day, 50m head
(4100 gal/day or 340 gph for 12 hour day)

total solar collection diameter est. 11 feet including mirrors

There are several interesting features of this engine that I’ve tried to capture in these stills taken from the video. First, the robust power piston with what I would describe as a conical truss. If you want to get significant power out of a low-temperature Stirling engine, you need a big power piston. I estimate the power piston at 48 inches in diameter. combine that with a pressure fluctuation of about 0.1 bar (1.5 psi) shown on the gauge in the video and you have a peak piston force of around 2700 lbs.

An atmospheric Stirling engine such as this will have an approximately sinusoidal pressure versus time with two power peaks per revolution. One half the cycle will be above atmospheric pressure and one half will be below atmospheric pressure . The average force =.64 x peak force or about 1730 lbs. I estimate the power piston stroke at 2.5 inches so for a complete cycle the travel is 5 inches for a total of 8650 in-lbs of work or 721 ft-lbs per cycle. At 60 RPM this would be about 980 watts. This gets you in the ballpark of 1500 watts. At rated power this engine might be turning 90 rpm, the pressure might be even higher, or my power piston diameter and stroke estimates could be way off.

To me the most interesting feature of this engine was the variable-stroke displacer. The following photo labels some of the components. A motor-driven jack screw (which you can see operating in the video) adjusts a connecting rod anchor point on the lower displacer lever. When the connecting rod is close to the pivot the piston travel is long and when it is farther away the travel is shorter.

The reason you want to do this is to be able to quickly regulate the power output of the engine to match the load. The time constant for heating or cooling the engine might be minutes, but you need to adapt to electrical load changes much faster. This mechanism lets you operate the engine at a fixed temperature and be able to vary the displacer stroke to control the RPM. Closed-loop RPM control using this method is much better and less wasteful than say adding or dropping a dummy load to flat-load the engine.

The above photo also shows what I refer to as a rolling fabric seal around the circumference of the power piston that provides an airtight seal to the cylinder. The seal is probably a coated fabric that is flexible but does not stretch under the 1.5 psi operating pressure.

This last photo shows the engine-driven piston pumps that pump both the hot oil or water through the hot end of the engine and the cooling pump. Both of these pumps appear to be double-acting so they pump liquid twice per complete cycle.

This is quite an impressive project. Also see some information at Sunvention.

What this engine lacks in power it makes up for in reliable operation. I have more than 200 hours of operation under solar power and at least 100 more hours running under incandescent light. It shows no sign of wearing out.

I’m now trying to decide if I want to work on the next step which would be a new design for an all-weather version that could be permanently mounted outside. Whether I build that next design or not, I thought I would make the details of this prototype engine available to other Stirling engine enthusiasts.

I’ve put together a very detailed discussion of the parts and what is important in the design and construction. There are so many photos I’ve split the information among 4 different pages. I tell you not only what I did but what I would recommend to make it better (that part is for my own benefit too). Here are the links:
Part 1
Part 2
Part 3
Part 4

I hope you find this useful.

The only thing I haven’t covered in detail is the engine controller electronics and software. I may put that up in the future if I get requests. I’m assuming most people will just be interested in the engine, not the starter and electronics.

I chose to use a variable reluctance motor as the starter for my Stirling engine design for the following reasons:

Because I designed the motor using ordinary mild steel without laminations, it quickly becomes inefficient due to eddy-current losses and hysteresis losses at higher RPM. This is not a general limitation of variable reluctance motors, just of this particular design.

How it works

Conceptually the way the motor works is easy to understand. The photo above shows the motor with the flywheel-rotor removed. You can see there are six stator poles arranged in three diametrically opposite pairs. I’ve only used one coil on each pair of stators for simplicity. The motor would be more efficient and powerful with six coils instead of three. When one of the three coils is energized, the magnetic flux generates a force that attempts to align the nearest rotor poles with the stator pole. This motor operates on the familiar principle of an electromagnet attracting iron.

By energizing the stators in the proper sequence the motor can be made to rotate in either direction. The smoothest motion is generated by a three phase action although the motor will work with simple on-off switching of the coils. The video shows the operation with simple on-off switching of the coils. The controller I used also supports pulse width modulation for smoother control. I chose the on-off switching because that is what I’ll be using for simplicity in my application.

As is the case for all brushless motors, this one would operate best with rotor position feedback so you can energize and de-energize coils at the just the right time. In my motor I’m not using rotor position feedback which limits it to low speed operation. I’ve only run it up to 100 rpm.

To drive the motor I used an Arduino microcontroller board driving a motor shield. A 5Vdc power supply (I’ve used up to 7V) provides drive power to the motor shield and the shield switches the power to each of the three coils according to the signals sent from the microcontroller. Although the motor can be entirely controlled by the software, I used an external potentiometer and switch to experiment manually with the motor speed and direction. The controls above are actually part of the stepper motor coil winder I made to wind the coils. I simply disconnected the stepper motor’s four leads, connected the variable reluctance motor’s 6 leads, and reprogrammed the controller via the USB cable for the variable reluctance motor.

The video demonstrates acceleration to 100 rpm and fixed operation at 14 rpm. There is also a torque demonstration as it winds up a 47g washer around a 1.25 inch diameter at 40 rpm. This computes to 75 g-cm (29.4 g-in) of torque. Input power was approximately 2.5W (.5A at 5V) and output power was 0.036 w output power for an efficiency of 1.4%. The dismal efficiency is not a serious problem for my application because the motor will only be used for short periods. It does provide ample torque for my application even without a second set of coils.

Motor design

The motor uses mild steel throughout in the magnetic path. The core for the coil is .375 inch diameter made from a 1/4-20 bolt inside a 3/8 diameter steel tube. The steel tube is turned to the precise length needed to set the .020 air gap between the rotor and stator. The pole pieces and rotor are made from 3/16 steel. The rotor maximum diameter is 4.460 inches and the diameter between rotor poles is 4.00 inches. Each of the three coils have 1000 turns of 28 AWG copper magnet wire. The coils were wound on forms made on a lathe from .75 inch diameter acetal. The coils could be wound directly on the 3/8 steel tubes but the coil forms are more convenient to use and let you slip the coils off to try different numbers of turns or wire diameter to meet your needs.

The hexagonal steel bearing block is .75 inches long and 1.5 inches across. The air gap between the bearing block and the rotor is 3/16 inch.

If you are interested in building a motor of this type a good place to start is with a small test section like this:

You can make some torque measurements vs offset that will give you an idea of what torque a complete motor will have. No controller is needed, just a dc voltage on the coils. Make sure the currents in the two coils create a magnetic flux in the same direction or they will just cancel each other. Reverse the current in one of the coils to check if you aren’t sure. Torque at low speed will be roughly proportional to the current squared and the number of turns squared.

If you are interested in a higher speed variable reluctance motor then a better design for the motor with laminations might be something like this test prototype:

This motor is a planar design that could be built up from many thin lamination layers. Besides laminations you’ll need some type of position feedback to drive the motor reliably at high rpm.

The electronic parts used for the motor and winder with part numbers for
Jamecoare:

Adafruit manufactures the motor shield kit and provides excellent tutorials both for assembling the motor shield and using it. All software for the Arduino and motor shield are free.

I can provide a schematic for the circuits, but I’m guessing that anyone who wants to build one probably won’t need it. Leave a comment if you need more information on some aspect of this project.

coil winder

As mentioned and shown in one of the photos above, I built a simple coil winder to wind the coils. I used the Arduino with motor shield to drive a stepper motor with adjustable direction and speed up to 100 rpm. The controller keeps track of the number of turns and displays it on my computer. It also stops when it reaches the set number of turns. This isn’t the fastest way to wind coils but it has the safety feature of stalling with a reasonable force. Winding coils on a lathe or other powerful motor that isn’t going to stall can cause gruesome accidents–like slicing off flesh to the bone if a wire gets wrapped around your finger or limb. You can always wind coils by hand.

I plan to cover details of the coil winder design in a future post.

You don’t have to actually measure these angles, you can determine the solar elevation for a specific time anywhere on earth if you have the latitude and longitude using the NOAA solar calculator. All I have to measure is the time when the engine starts and stops.

Figure 1: The heat collector section of my Stirling engine schematically looks like this:

The Stirling engine displacer operates vertically just below the heat collector.

The ideal solution to improve solar power at high incidence angles would be to just aim the heat collector at the sun. This is not an attractive solution on my engine for two reasons:

First, this requires the complexity of either the engine on gimbals with solar tracking or at least a mirror that tracks the sun. This engine is meant to stay in a fixed position.

Secondly, especially in the case of a low-power engine, the friction is considerably higher with side-loads on piston and displacer which result when the engine is not oriented vertically. This friction would further reduce the operating envelope and decrease the life of an engine that is meant to run every day for years.

To come up with a satisfactory solution to this problem I wanted to first analyze the input solar power I was getting at 59 degrees incidence because that is the minimum the engine requires to run. With that information I want to come up with a design that will provide at least the same input solar power at 66 degrees incidence.

I should point out that a transparent cover of some type over the heat collector is absolutely necessary on this type of engine to minimize convection losses.

Analysis of the problem

There are three basic ways I’m losing solar energy before it arrives at the heat collector:

1. Transmission losses through the acrylic cover:

Energy is lost by both reflection and absorption of the acrylic. Using a light sensor, light, and both glass and acrylic cover plates I measured the transmission levels in both the visible and IR portions of the spectrum. I didn’t cover the full sunlight energy spectrum so these measurements should not be relied upon too heavily. Here’s what it looks like:

The glass and acrylic responded very similarly within the limits of my measurement accuracy. You can see the cover plate only transmits about 90% of the light even at zero incidence and is flat out to about 45 degrees incidence. By 59 degrees the transmission is down to about 80% and by 66 degrees it is down to about 74%. It’s obvious that you’d like to keep the incidence angle of light on the transparent cover at or below 45 degrees.

2. Reduced energy on the heat collector as a function of the sun’s incidence angle.

This coefficient is simply cosine of the incidence angle on the heat collector plate. The more nearly the collector is perpendicular to the sun the more energy you get.

3. Transmission losses as a function of the solar path through the atmosphere.

Wikipedia has an article that discusses and gives formulas for energy losses through the atmosphere.

I learned that it is not accurate to think the attenuation is proportional to the distance through the atmosphere, it’s actually better. See the article for more details including attenuation due to air pollution. I’m assuming here a basically clear sky and minimal air pollution.

The pertinent equations for my application are:
The air mass length (AM) is approximately
AM = 1/ cos z where z is the incidence angle.
This is essentially how much atmosphere the light goes through.

I = 1.1 * I₀ * 0.7^(AM.678)
I₀ = 1353 w/m² solar intensity just above the atmosphere
I = solar intensity in w/m² on the ground at sea level.
When z = 0 degrees I = 1041 w/m². I’ll use this value as 100% of maximum solar intensity.

Here’s a plot of the solar intensity vs incidence angle on a clear day at sea level:

Combining all of the above information the percentage of maximum solar intensity on the heat collector should be:

I% = 100 * acrylic cover transmission coefficient *
cos(incidence angle) * 1.1 * I₀ * 0.7^(AM.678)

According to the above analysis I need at least 34% of the maximum solar intensity for the engine to run.

I can’t change the solar intensity losses caused by the atmosphere but I can work on the other two sources of loss.

Just sloping the acrylic cover so the incidence angle is 45 degrees or less will increase the maximum solar intensity at the collector (27%), but not enough for the engine to run. Figure 2 shows the design.

Figure 2: Sloping the acrylic cover and adding a reflective interior

One easy way to improve the energy density at the heat collector is to add the reflective vertical surface as shown in figure 2. This will cause up to double the energy falling on the heat collector when the sun is at low angles.

It’s easy to visualize this solar concentration. If you view the collector from the same angle as the sun at low elevation, you will see both the heat collector disk and also a reflected version of it on the reflective surface. When the sun elevation is higher, only a portion of the heat collector will be visible in the reflection. This vertical mirror acts to amplify the sunlight at low elevation angles (high incidence angles)
— just what is needed. It’s also underneath the acrylic cover so it won’t collect dirt.

I’ve tested the design shown in figure 3 with good results up to the target incidence angle of 66 degrees using just aluminum foil as the reflector. The face of the acrylic cover was at an angle of approximately 23 degrees.

Figure 3: Modified collector cover

Another way to increase the solar energy collected is shown in figure 4.

Figure 4: Collector with sloping face.

This design uses a collector plate with a sloped face. The collector could be made as a wedge-shaped section of an aluminum cylinder. This change requires a good heat insulating barrier around the wedge-shaped section to avoid high thermal losses. The larger heat collector could function as a heat reservoir too, although it would take longer to heat up before the engine could start in the morning.

This engine is based on the simple Stirling with some significant improvements although still quite simple. The changes are:

1. A ball bearing supported crankshaft.
2. Machined aluminum power piston for close fit in power cylinder to provide better compression.
3. A 5 inch diameter aluminum disk on top for collecting solar heat with an acrylic cover to reduce convection losses.
4. Polycarbonate displacer cylinder (transparent) to make the displacer visible and for higher temperature operation.
5. A data acquisition and controller unit that measures hot and cold plate temperatures and crankshaft speed.

The controller unit sequences the engine start operation when the temperature ratio is high enough for operation. The unit also displays the following information:
1. Th
2. Tc
3. Temperature ratio Th/Tc
4. Hz and RPM
5. Number of engine starts
6. Number of failed engine starts
7. Engine starting temperature ratio
8. A log of engine speed versus temperature ratio.
9. Engine running time

The ball bearing supported crankshaft and machined piston were the major changes that allows this engine to operate at low temperature ratios (below Th/Tc of 1.050). That is equivalent to 27 deg F for Th-Tc measured at the hot and cold plates for typical operating temperatures. Although I have experimented with other designs this engine has proven to be quite reliable. Running usually between 5 and 7 hours per day, this engine is accumulating quite a bit of operating time. An additional improvement may include ball bearings for the crank pin – connecting rod interface. The goal for this engine is to operate when heat is sufficient for 10 years. That probably represents 2000 hours per year or 20,000 hours total and 100 million revolutions. The only reason I think this is possible is that the engine only needs to turn, it doesn’t need to produce much power.

The starter is very simple with the stepper motor being the only actuator. Counterclockwise rotation engages the starter and then clockwise rotation turns the engine through two revolutions, accelerating the engine to 60 rpm and disengages the starter. Currently I consider a start a failure if the engine runs for less than 2 minutes. About half the time the start fails and the controller waits one minute, increases the starting temperature ratio, and then attempts another start. The second start has never failed although the controller will still try a few more times at increasing temperatures before assuming a mechanical fault. Unless the engine is shaded by something (a tree, a cloud, etc) it normally runs the full day on its one or two starts.

The controller was actually fun to development because the electronics was so quick and painless.

The heart of the controller is an Arduino Uno with an Atmega 328. This is a micro-controller board you can connect to your computer with a USB cable and develop your computer program on the provided integrated development environment. The micro-controller accepts digital and analog inputs and drives digital outputs. This board reads and processes the outputs of the two analog temperature sensors and the digital speed sensor. It also drives the LCD display.

The Arduino board cannot drive the stepper motor directly, that requires another motor driver board that is stacked on top of the Arduino Uno. The motor shield, as it is officially referred to, will drive two stepper motors and other types of motors too. Most of these products were purchased from Adafruit. You don’t really need to know much about stepper motors or anything else because Adafruit provides online tutorials and libraries that allow you to just program at a simple level in the C language. Numerous examples make it easy and it’s all open source so you don’t end up having to buy any software. Adafruit, by the way, doesn’t pay me, I’m just a satisfied customer.

The engine controller logs the performance. Here is the data for September 19, 2011. I set the engine out at 10:00 AM PDT and it started at 10:06. The engine stopped running at 4:29 PM. At that time the sun was 30.1 degrees above the horizon.

For simplicity this engine is designed to use solar heat without concentration so that no solar tracking is required. The current solar collection method is a flat aluminum plate painted flat black and covered with a transparent acrylic cover. There is a 0.25 inch airspace between the plate and cover. The current configuration will operate the engine when the unobstructed sun is at or above approximately 30 to 31 degrees above the horizon. The ambient temperature is not critical because the engine operation depends on the temperature ratio of the hot source and the cold sink.

Minimizing the cold sink temperature requires not only shading the heat rejecting surfaces but also minimizing radiant heat and reflected light. On a typical summer afternoon the air temperature where I live might be around 80 to 90 degrees F while the ground temperature typically measures 130F to 140F for dirt or brick. Asphalt will be hotter, concrete a few degrees cooler. The radiant heat can raise the cold sink temperature considerably. Shading both the top of the cold sink from direct sunlight and providing a shaded surface that blocks the radiant heat from the ground or nearby walls helps reduce cold sink temperatures.

Surface wind is does not seem to have a large effect on power output. Improved cooling of the cold sink is balanced by more cooling of the heat source probably caused by increased cooling through the acrylic cover. The wind does help reduce peak temperature. Peak collector temperature for the operating engine so far has been about 160 deg F.

The least satisfactory part of the system currently is that the engine stops running when the sun reaches about 31 degrees above the horizon. While that provides about 6 hours of operation midway between winter and summer, on the shortest day, December 22, at the location these engines are to be used the sun elevation at noon is 31 degrees above the horizon. I’d like the engine to be able to run for about 4 hours on that date (assuming clear skies). That requires operation down to about 22 degree sun elevation. I’ll discuss this topic more fully and my solutions in a future post.

Basic engine specifications:
Displacer cylinder : 3.50inch OD x .125 inch wall x 2.75 inches long
Displacer: 3.1 inch diameter x 2.0 inches long
Displacer stroke: .63 inches
Power cylinder: .625 inch bore x .875 inch stroke

What about power?

This engine doesn’t provide any useful output power. I could put a generator on it that might deliver about 10-20 mW, enough to drive a small LED. That seems pointless to me. In fact this engine with controller, display, and starter needs an external power source. Right now that comes from an AC converter or a battery pack. Eventually it will be powered by a small PV solar panel.

Personally my primary goal with heat engines is to develop engines that generate some useful amount of power. Although this engine does not accomplish that, it has helped me with pieces of the puzzle that I need to work out for solar-powered heat engines. Solar tracking and concentration are probably necessary for an engine that does produce useful power. Having designed and built the controller and starter, tracking and concentration don’t seem like a big hurtle. A reliable, low-cost Stirling engine that does produce useful power is still a big hurtle.

This engine development is almost complete. I still need to extend the winter operating range. A secondary goal is to provide heat storage for engine operation into the evening. That goal is probably best achieved using solar heated water as the heat transfer and storage medium.

Although this engine may look a little crude, I designed it to minimize friction sources as much as possible within reasonable limits. The levers are used to perform mass balancing of the displacer and power piston. The long rod lengths keep side loads to a minimum.

Operating between 99 deg F and 74 degF my simulation shows .004 watts at 60 rpm. That is equivalent to lifting 16 grams one inch every second, not much power to divide among all the friction sources, but apparently enough to run. The engine will run down to a differential of about 21 degF.

Major friction sources

The major sources of friction are the displacer rod shaft running through the seal and the power piston. The power piston caused me less difficulty. Turning an aluminum piston until it just slips in the brass cylinder is not difficult and the leakage is reasonably low. With the cylinder port closed the 12-gram piston settles under its own weight at a rate of about .75 inches in 16 seconds. This type of arrangement works well but I have yet to try it over an extended temperature range. A thermal expansion coefficient mismatch can cause lockup or allow too much leakage if the temperature varies over a wide range.

The displacer rod seal caused me more trouble. The displacer is an ABS tube sealed on both ends and is quite heavy, around 60 grams. The .047” rod slips through a brass guide hole that is about .048”. This small clearance adds very little leakage. When I test the displacer pressure variation with a manometer, the leakage rate is quite low. The downside is that the rod must be carefully aligned. Oil or any lubricant is a disaster for friction. I found that polishing the displacer rod and running it completely dry gave the best performance. I did try drilling the guide out to .052 (the next drill size I had on hand). That extra clearance made the friction very low but the leakage made the engine inoperable. I need to try a drill around .049.

Designing for higher temperature vs operating at higher temperature

One of the design considerations that is very apparent on low temperature engines but applies really to all Stirling engines is the operating temperature ratio used in the design. There is a big difference between operating a given engine design at a higher temperature and designing it to run at the higher temperature.

The engine I’m discussing here was designed for operation between 100F and 75F. Thermodynamically it should have a gross power of .004 watts at 60 rpm (1.0 hz) and my elevation (900 ft). If I increase the temperature ratio (1.047) to 1.094, the power should double to .008 watts at 60 rpm. If instead I design a new engine for this temperature ratio, the gross power will be about .016 Watts. In the first case the power doubles, in the second case, the power goes up four times. The difference is that when designing for the higher temperature, I increase the pressure ratio (a larger piston or longer stroke) to match the higher temperature ratio.

When you design a Stirling engine the power increases roughly with the square of the temperature (assuming the same displacer volume and adjusting the power piston displacement to match the pressure ratio). This is why it is a mistake for people to think they can make a 200 degree delta T engine perform half as well as a 400 degree delta T engine of the same size.

The case actually seems to be worse than I’ve painted here. As the temperature increases you can usually budget more power to pumping and heat transfer losses and thereby operate at higher RPM.

The other side of this argument is that if you lower the operating temperature on an engine designed for a higher temperature it just quits running.

Let me point out that I have been discussing the gross engine power. For small engines a significant proportion of the gross power goes into overcoming friction. For the engine I just made, if I operate it at the elevated temperature ratio, I should measure about .004 Watts power output at 60 RPM. Of the .008W of gross power the engine should use .004W in overcoming friction. I know this because it runs with no load at this RPM when the gross power is .004W. The other .004W will be excess power that I should be able to measure at the shaft.

The above video shows a one-watt Stirling engine driving a one-watt LED. Conversion efficiency is not too high so I’m only driving the LED with about 0.38Watts (120mA at 3.2V). In the video the hot end of the displacer is covered up by a lot of insulation with a metal can over it and the cold end has some extra cooling fins. The photo below shows the bare engine. You’ll notice I recently added a diagonal brace to stiffen against the torque that was wracking the frame.

Engine 3F showing displacer cylinder uncovered

The stepper motor used as a generator can get up to nearly 50% efficiency although at my power and RPM level it was operating at 38-40% efficiency. This conversion efficiency includes the diode bridges that rectify the AC voltage to DC. I was going to publish my test results for this stepper motor as I have in an earlier post on another stepper motor, but the company I bought it from, Jameco, no longer sells it. The motor was a surplus overrun item and they ran out. When I find a good replacement I’ll post the data on it. I believe the motor is still available (KP35FM2-044) from the manufacturer (Japan Servo) but probably costs over $20, not the $6 I paid for it.

I could also use an ordinary DC electric motor for power generation. DC motors with brushes can be reasonably efficient and don’t require rectification from AC. The main drawback for me is that my engine develops maximum power around 200 to 250 rpm and the DC motors I’ve tested don’t generate useful voltage and current until about 2500 rpm or higher. The stepper motor, a type of brushless motor develops good power around 600 rpm. This is much closer to my engine RPM and is connected by a 1:2.8 belt drive to match my engines power and rpm. The belt, incidentally, is a large o-ring with a 1/8 inch cross section and seems to work quite well. I need to measure the transmission efficiency on it but haven’t yet. My indirect measurements seem to indicate an efficiency of between 80-100%.

Ordinary brushless DC motors may be more efficient than stepper motors but I haven’t found a good source for them yet that is reasonably inexpensive and matches my power needs.

Electric heat source

For a heat source I use .035 inch stainless steel wire driven by a current usually in the 4-6 amp range. Stainless steel has poor electrical conductivity (for a metal) and about 50 inches uses 4.5 amps at 13.2 VDC in the video, delivering 59W to the engine. The wire is wrapped around the displacer with a layer of fiberglass cloth used as electrical insulation underneath to prevent electrical shorting to the displacer and another layer outside the stainless steel wires, then 3 stainless steel hose clamps to lock it all in place. Finally the hot end of the displacer is wrapped with fiberglass insulation to minimize heat loss to the surrounding air.

I use the above electrical heating method for two reasons: First, I can operate the engine without an open flame which is convenient for running the engine all day long at the Maker Faire. Second, it’s much easier to measure input power using electrical heat than it is to measure power when burning alcohol or propane, especially at the low power levels my engine requires. The only way to measure power levels in those cases that I have used is to measure the fuel consumed per hour and compute the heat content of the fuel. It’s time consuming to measure a few grams an hour to make accurate readings.

If you are interested in using the electrical heating method I use, be certain to work with safe voltages, probably 24V or less. While it’s okay to transform down AC to 24V or less, you are flirting with electrocution if you use the method I did using 120VAC. If the wire gets too hot, it will soften or melt the glass cloth and the wires can short to the engine. 12V auto battery chargers used within their normal current ranges work quite well. The biggest disadvantage to this method of heating is that my engine takes about 15 minutes to come up to full operating temperature. A propane torch can easily provide more than 20 times the 59 watts and heat the engine up in less than one minute.

Power computations

For those interested in making their own power measurements that might not be comfortable with the math involved, here’s what you need to do:
(1) To compute a rotary engine’s power output at any rotational speed you only need to know the torque and the rotational speed.

(2) In the video you can see the wood torque arm clamped to the main shaft and prevented from rotating by a beam that pushes against a scale. The clamping force is adjusted until the engine is stable at the rpm I want to measure the power at. The scale measures in grams and the torque arm transmits the force at exactly 3 inches so I measure the torque in gram-inches by multiplying the two numbers together:

63 grams x 3 inches = 189 gram-inches torque

There are 454 grams in one pound so:
189 gram-inches torque x 1 lb/454grams = 0.42 pound-inches of torque

(3) To convert from pound-inches of torque to inch-pounds of work, you need to multiple by 2pi:

0.42 pound-inches torque x 6.28 inches/revolution = 2.62 inch-pounds /revolution.

(4) Power is the work done per unit of time so we need to convert the inch-pounds/revolution to inch-pounds/sec. Multiplying the above result by the revolutions/sec give the power output in in-lbs/sec. If you’ve measured revolutions per minute (rpm) you’ll need to divide that by 60:

rpm x 1 minute/(60 seconds) = revolutions per second.
In the video I measured 3.4 hz (revolutions/sec)

2.62 in-lbs/rev x 3.4 rev/sec = 8.9 in-lbs/ sec

The engine is doing the work equivalent to lifting a one pound weight up (against gravity) 8.9 inches every second. Converting to other power units:
Watts are probably the most universal measure of power although most people in the US are familiar with horsepower (1 hp = 746 watts). Another convenient measure is foot-pounds/second (1 hp = 550 ft-lbs/sec).

Converting to other power units:
8.9 in-lbs/sec x 1 ft/12inches = .74 ft-lbs/sec x 1 hp/(550 ft-lbs/sec)= .0013 hp x 746w/1 hp = 1.01w

First a few key features:
1. Inexpensive: New this stepper motor costs $2.95 in single quantity. At this price it probably isn’t worth scrounging for one out of an old printer, especially since I’m going give you the performance specifications for this motor when used as a generator.
2. Stepper motors generate power at low RPM. You can get usable power at just a few hundred RPM. For Stirling engines, wind turbines and other low RPM power sources this means you can drive the stepper motor directly from the source without having to use gearing.
3. Efficiency above 40% is possible depending on how you load the motor. While not great (I’d consider above 75% great) it’s pretty decent for these low power levels and considering the low price. Keep in mind that not having to using gearing or belts means you won’t lose more power to friction.
4. Stepper motors are brushless motors so the only wearing parts should be the shaft against the bearings.
5. A stepper motor used as a generator puts out alternating current and must be rectified to produce dc. For some applications, such as driving LEDs, you can use two LEDs so that one conducts in each direction without the need to rectify the output.

This article is written for people with some electronics background. If that doesn’t include you, don’t despair, I’ll provide a future article with more of a cookbook approach for a few circuits that you might want to use with the stepper motor generator.

The following chart shows the voltage output versus RPM for the stepper motor with various load resistors.

You’ll notice the above chart show Vdc. The measurements were made with the circuit shown below. The key components are the diode bridges and the filter capacitor. Although I used Schottky diodes, the stepper motor as generator has sufficient compliance that ordinary silicon diodes will work. You can also use an ordinary bridge rectifier IC instead of individual diodes. For the highest power output the Schottky diodes will provide a slight advantage.

This stepper motor has a 7.5 degree step size so you get 48 steps per revolution. The frequency of full wave rectified pulses should be 48 * RPM/60 for computing your filter capacitor. At 300 RPM you are already at 240 Hz so flicker on LEDs even without filtering is not visible. If you need low ripple for the DC voltage then filter capacitor value required is even less than for working from a standard rectified 50 or 60 Hz AC power.

This next chart provides the same data as the first but in a current vs RPM format.

One property of stepper motors that can be useful in their primary application is detent torque. This torque holds the motor in discrete rotational steps, even when no power is applied. To overcome this torque resisting rotation requires a relatively high drive torque and causes inefficient operation at low power levels.

Even with zero electrical power output, the minimum torque starts at just above 40 g-cm. To achieve reasonably high efficiency you need to operate the stepper motor with a reasonable load.

Also worth noting is the torque dropping rapidly at higher RPM for the 47 ohm load case. I don’t have sufficient expertise in motor/generator design to be sure, but I’m guessing this is a magnetic saturation effect. Note that even though the torque is decreasing, the overall input and output power are still increasing, although they are doing so more slowly.

The following chart shows the efficiency (% efficiency = 100*electrical power out/mechanical power in).

Notice that the maximum efficiency occurs with a 100 ohm load over the full RPM range. The 47 ohm load will result in higher current but lower efficiency. You can see from the chart that higher RPM might continue improving the efficiency (slightly) at loads for 100 ohms and above.

I obtained this stepper motor from Jameco. The part number is 171601. Jameco provides a link to the data sheet for the part; a few of the specifications are:
MABUCHI MOTOR COMPANY
PF35T-48L4
Mounting hole spacing: 1.65 in (42mm)
Shaft diameter: .078 in (2mm)
Motor dia: 1.38 in
Motor depth: .58 in

The motor has a dual shaft and a 10 tooth brass gear on one shaft. The other shaft (actually the other end of the same shaft) is just visible in the photo.

Peter Gross in Tasmania built this engine with a few modification. Most notable are the use of a PVC displacer cylinder (ABS is apparently not readily available where he is) and the use of a CD to attach flywheel weights.

And some detail photos of his engine:

Peter Gross also offers this advice for cutting the brass tube for the piston, cylinder, and other small brass tubes:

1. Using a drill press, drill a hole exactly the same size as the tube OD in a small piece of wood (eg. 8x2x0.75″ dressed pine) then clamp the wood in a vice.
2. Push the tube through the timber to the required length then cut against the wood using a “junior” hacksaw with a sharp fine blade while holding the tube from the other side of the wood.
3. After cutting the end of the tube can be smoothed accurately using a fine file against the wood. This gives a nice square end on the tube without crushing it or cutting your fingers.
4. The wooden jig can be used many times by simply drilling extra holes of the required size. For the larger tubing sizes I used a hole saw.

Powered by dry ice

Ryan Proctor built this simple Stirling engine. The video shows it running backwards using dry ice. Ambient air becomes the heat source. Ryan later went on to design and build a larger Stirling engine as a college project.

A common problem Stirling engine designers face is how much volume should the power piston sweep in comparison with the displacer? This of course only applies to a Beta or Gamma engine; an alpha engine designer faces a related problem of what phase angle to use between the hot and cold pistons. The answer for an ideal Stirling engine is that a larger piston will always give you more power. This isn’t true for a real Stirling engine.

The problem centers around the ideal isothermal compression and expansion cycles. In a real engine you can’t realize perfect isothermal compression. It’s probably safe to say that the higher the cycle rate and the more powerful the engine is, the more difficult it is to get close to isothermal compression.

A ready example of the difficulty in achieving isothermal compression is a typical shop air compressor. Compression cylinders normally have cooling fins that get very hot when the compressor is operating coninuously.The air inside the compression cylinder is even hotter than the cylinder fins. Those cooling fins are used to get as close to isothermal compression as practical because isothermal compression uses the least amount of power.

An ideal Stirling engine uses isothermal compression and expansion cycles. Concentrating for the moment on the compression cycle, the gas has moved through the regenerator and cooling tubes (if used) and into the cold end of the displacer cylinder before the compression cycle begins. The compression cycle (besides increasing pressure) adds heat uniformly to all of the working gas. Remember this is after the gas has gone through cooling in the regenerator and the cooling tubes. During the compression cycle the only components to help cool the gas are the cylinder walls and the piston. Isothermal compression is just not the reality for real engines.

On one hand we have isothermal compression as an ideal best case. On the other hand we have the corresponding ideal worst case of adiabatic compression. In the adiabatic or isentropic compression case, no heat leaves the gas during compression. This would be the case if you had all material contacting the gas be a perfect insulator. The isentropic compression case is computed using the equation:

T2/T1 = (V1/V)^(k-1)
where k = cp/cv (about 1.4 for air at typical temperatures)
T1, T2 are beginning and ending absolute temperatures
V1/V2 is volume ratio (maximum volume to minimum volume)

If you have a volume of air at 0 degrees C (273K) and compress it down to half the volume, the air would double in pressure for isothermal compression and of course stay at 0 degrees C. For isentropic compression the temperature would increase to about 87 degrees C. Because the temperature is higher in the isentropic case, the pressure would be more than double the initial pressure.

Real world compression gives you a result somewhere between the isothermal and isentropic cases. Machinery’s Handbook (27th edition) suggests air compressors typically operate about midway between isothermal and adiabatic compression. A Stirling engine may perform better or worse than that depending on its design and cycle rate.

Also note that everything I’ve covered here that applies to the compression cycle applies equally to the expansion cycle. The only difference is that during expansion while the gas is doing work pushing the power piston, you’d like the gas to remain isothermal for the most power, but the gas will be cooling due to the expansion.

In my simulator, I include an output labeled isentropic compression heating that is listed as a percentage. This value is calculated using the engine volume ratio and assumes completely isentropic compression and expansion. What this means is that if you have a delta T (=Th – Tc) of 100 degrees and you see 25% for the isentropic compression heating, then 25% of the temperature swing (25 degrees) would be caused by compression heating and expansion cooling. The power output value listed by the simulator is based on strictly isothermal compression and expansion. To correct for the isentropic compression heating and expansion cooling losses, I subtract the 25% value (or whatever the simulator shows) from the power output value to get a more accurate value of the power output. This result approximates adiabatic rather than isothermal compression and expansion. Using this corrected value gives a conservative estimate although you might want to use something midway between isothermal and adiabatic if you have a reason to be optimistic.

To show how the results are affected, the plot below shows the power output based on both isothermal and adiabatic compression and expansion as the power piston varies in size and alters the % compression heating on my engine 3F.

You might be tempted to design your engine for isentropic compression heating values of up to 40% or even higher because the plot even for the worst case adiabatic compression has not reached a peak value. In reality that may not give you the most power. Typically as you increase the piston diameter or stroke to increase the compression, two things happen.

First, you’ll pick up more friction with the larger piston or longer stroke. As you approach the nearly level part of the power curve, you may end up with less net power due to friction.

Second, the higher the compression, the more likely you’ll experience power loss due to gas leaks past the piston. Gas leaks past the piston (or leaks anywhere) reduce the pressure ratio and will reduce engine power even at low compression. The losses become greater as the compression increases.

Once you have an operating engine you can determine the lowest temperature ratio the engine will operate at. This will give you more insight into how close you are to the adiabatic curve vs the isothermal. Of course the engine must overcome all sources of friction to run, so you aren’t seeing the real zero-power level, but you’ll get an idea. Another problem is that the effect of any gas leaks is magnified when the engine is operated at a minimum rpm condition. Yet another problem is actually measuring the hot and cold gas temperatures in the displacer. I end up measuring the external temperature of the displacer cylinder which is not an accurate measure of the gas temperature. For the engines of mine that I’ve tested, the minimum operating condition seems to be in the 30% to 50% compression heating region (based on external temperatures).

You can’t just blindly assume some ratio of piston diameter to displacer diameter, even for engines operating at the same temperature ratio. The dead volume can have a huge effect on the volume ratio and thus the appropriate piston diameter. A high temperature engine can easily work with a power piston displacement as large or even larger than the displacer swept volume while a low temperature engine may need a power piston displacement that is a small fraction of the displacer swept volume.