Solar Heat Engines

Ideal Stirling Cycle Spreadsheet

June 24, 2008 – 6:55 pm

 

This Excel 2003 spreadsheet stirling-cycle-ideal-v-02 lets you input the basic values for a Stirling cycle engine and calculates various quantities such as pressures, work in, work out, heating, cooling, and ideal efficiency.

Don’t use this spreadsheet with the idea that your engine will get close to the values it shows unless you have an engine that truly approximates the ideal Stirling cycle. Most Stirling engines that use a crankshaft to drive the power piston and displacer including the engines I’ve built so far cannot possibly put out more than about 77% of the work per cycle of an ideal Stirling engine. This is assuming piston, displacer, crankshaft and all related mechanisms are frictionless.

A large source of uncertainty when using this spreadsheet is in the minimum and maximum temperatures. The spreadsheet assumes these are the cold and hot temperatures of the working gas in the engine. These temperatures are difficult to measure in an operating engine. I usually measure the hot and cold temperatures as close to the gas as I can. Typically I measure the temperature of a metal plate that directly interfaces with the working gas or the water temperature adjacent to the metal plate. The temperature spread between the hot and cold gas may be only 50% of what I measure or even less depending on the heat transfer. In the future I’ll be working more on the heat transfer efficiency of my engines.

If I use the numbers for my large engine (engine 3d) in the spreadsheet and use the temperatures I actually measure on the metal plates, then I am getting about 11% of the net work out predicted by the spreadsheet (so far). Even if I were to use more realistic hot and cold temperatures, I might still be seeing only 25% of the spreadsheet-predicted work output. Where is the missing work?

Part of the work is lost to friction, something not covered by this spreadsheet at all. In another post I’ve talked about measuring the friction losses on your engine with a flywheel spin-down test. Other friction losses are due to pushing the operating gas around in the engine, especially through the regenerator. Any gas leaks in the engine will also reduce engine power.

This spreadsheet also does not take into account dead space. Any space that is not swept by the displacer or piston is dead space. This includes the space where the regenerator material is placed and also includes internal clearance space above and below the displacer. As a rough approximation the ratio of live volume to total volume (live + dead) will be the ratio of work put out by the engine compared with the ideal output. If your live and dead volumes are equal, then you’ll at best see about 50% of the work out predicted by the spreadsheet. This is after you’ve lost 77% to your engine not following the ideal cycle. My engine 3d has approximately 80 in^3 minimum volume and 41 in^3 dead space including the regenerator. That gives me 77% x (80/121)= 51%.

The idea Stirling cycle also assumes that the compression and expansion of the gas is an isothermal (constant temperature) process. In practice it is normally not possible to closely approximate the isothermal process. A slow turning engine typically can come closer than a high-rpm engine. If no heat is transferred during the compression or expansion cycles, it is an isentropic process. Real engines operate somewhere between isothermal and isentropic and can be simulated by using a polytropic process. I plan to add this feature to a future simulator.

With all these inaccuracies you may be wondering whether this spreadsheet is useful at all. The real value of this spreadsheet is to put an absolute upper bound on a Stirling engine’s work per cycle and efficiency. This spreadsheet also shows the importance of a regenerator, especially in low temperature engines (although it doesn’t assume any volume is required for it).

Using the spreadsheet

I’ve included brief instructions with the spreadsheet. If you aren’t familiar with the Stirling cycle, I suggest this primer as a good starting point.

Notice that this is a cycle spreadsheet so the output is work not power. If instead you’d like to know power then you need to compute the power based on the number of cycles per second. For example, at 10 hz (600 RPM) a joule output per cycle is equivalent to 10 watts.

Posted in Analysis Tools, Simulation | No Comments »

Simple Stirling 1 performance with and without regenerator

June 9, 2008 – 12:02 pm

 

I’ve tried a variety of regenerators on the Simple Stirling 1 engine and the one shown in the photo is simple to make and performs as well as or better than all of the other ones I’ve tried. The test results on the engine with the original displacer and with the modified displacer containing the regenerator are shown in the plot. As you can see for the same delta T (temperature difference between the hot and cold plates), the displacer with a regenerator provides much higher RPM.

 

Ideally, a regenerator makes a Stirling engine more efficient because it performs part of the heating and cooling of the working gas as the displacer cycles it back and forth between the hot and cold chambers. After the gas leaves the regenerator it enters the active heating or cooling regions. A regenerator is a passive component. It cools the hot gas as it flows in one direction through the regenerator and heats the gas when it returns back the other direction. The heat is transferred to the steel wool in the regenerator I’m using and is transferred back on the return trip.

The regenerator isn’t totally free. The steel wool material causes some friction with the air, causing a larger pressure differential on the two sides of the displacer that makes additional work for the engine. The volume taken up by the regenerator also adds dead space to the engine, making the engine slightly less efficient. Despite these disadvantages, the net gain is substantial.

 

Incidentally, making more clearance around the side of the displacer to make the air flow easier (with no regenerator) actually caused such a large drop in power the engine wouldn’t run at any reasonable temperature. I cut the displacer down from approximately 3.4″ diameter to 3.25″. The reason it causes such a drop in power I believe is because the tight clearance between the displacer and the cylinder wall accelerates the air as it flows past. The air speed is high enough to make the air swirl around in the hot or cold chamber and have good heat transfer with the hot or cold plate. The larger clearance reduces the air speed, possibly causing laminar flow instead of turbulent flow, and reducing the heat transfer.

Modifying the displacer to add the regenerator is probably self-explanatory if you look at the photos. I used a spade bit to drill the four 7/8″ diameter holes. You could probably use a 3/4″ hole instead of 7/8″. To keep the steel wool in place I used 5 minute epoxy to attach a disk of aluminum window screen on the bottom of the displacer and then divided up 0.6 grams of #0000 steel wool among the 4 holes. Try to fluff it up to fill the volume and make sure there are no straight through holes where the air can go without going through the steel wool. Test run the displacer to make sure you’re getting reasonable performance and then epoxy a screen on the top of the displacer to lock the steel wool in. In the photos you can see that I put masking tape on the screen to mark the circle and hold the screen in a circular shape.

If you test your engine without the regenerator and then add it, you’ll probably be as blown away as I was that 0.6 grams of steel wool (this is almost nothing) can make such a huge difference.

It’s quite possible you may be able to come up with a regenerator that works even better. I’m still planning to try some fine copper wool. 

Posted in Simple Stirling 1 | 3 Comments »

Simple Stirling 1 Engine Materials List

May 24, 2008 – 9:55 pm

The bill of material for the Simple Stirling 1 Engine is now available. Together with the 3D model, the part drawings, and assembly drawings, you now should have sufficient documentation for building the engine. I believe I’ve covered every single part including nuts, machine screws, and washers.

Posted in Simple Stirling 1 | 4 Comments »

Simple Stirling 1 Plans and Assembly drawings

May 20, 2008 – 6:13 pm

I have added color to the 3D CAD model. You can see it compared above with the physical prototype. There are a few difference between the two—the four support rods on the prototype are about 1.5 inches longer than on the plans. You might also notice I have the crankshaft set 180° from the CAD model.

The Adobe viewer for the 3D model gives you lots of flexibility to examine the design as a whole and the individual parts. You can even change the lighting and the rendering.

Parts drawings

The CAD parts drawings for all the parts are available. There are 16 unique parts that you have make. The only parts I didn’t put up are things like brass tubes and music wire that only have to be cut to a specified length. I’ll cover these in the bill of materials.

Assembly drawings

CAD assembly drawings plus the 3D model should make it pretty clear how everything goes together. I’ve put up 11 assembly drawings with section views.

I have to say the Alibre 3D design software has really saved me a lot of work. I’ll have to put up a post on that later.

What’s left?

A few more things I have left to post on this design:

1. The BOM (bill of materials)
2. Building instructions—I’ll put up some general instructions and some specific ones where I think they would be helpful.
3. Running the engine—this part should be fairly simple.
4. Modifications—Making it even better. For those who would like to get more RPM and power I’ll try out a version that uses a metal can for the displacer cylinder instead of the ABS (plastic) one. You’ll be able to run at higher temperatures.

Posted in Simple Stirling 1 | 2 Comments »

The Simple Stirling 1 Plans are done !

May 19, 2008 – 12:45 am

The plans all drawn up. You can see a 3D pdf model that gives you the ability to look at every single part from any angle. If you haven’t used this Adobe 3D view make sure to try both mouse buttons and the mouse wheel for navigating the drawing. There is a directory tree that lets you highlight parts or hide them. I’ve put up a second page that has a sample drawing for one of the parts. I’ll be getting the remainder of the drawings up in the next few days plus some directions on building the engine.

Posted in Simple Stirling 1 | 2 Comments »

The Stirling Cycle—Ideal and Practical

May 7, 2008 – 2:54 pm

 

Click on photo to enlarge

 

The above diagram of the ideal Stirling cycle shows how a displacer-type engine (gamma configuration) would implement the cycle. Note that the displacer and power piston operate independently. During the expansion and compression phases the power piston moves and the displacer is stationary. During the heating and cooling phases the displacer moves and the power piston is stationary.

One could implement the ideal cycle action by using cams to drive the displacer and power piston independently. More commonly the Stirling cycle is implemented imperfectly with the following arrangement:

Click on photo to enlarge

 

In the above implementation of the Stirling cycle, the power piston and the displacer are essentially driven by two cranks on a single crankshaft. The displacer leads the power piston by 90°. This simplification results in the loss theoretically of about one-quarter of the work.

The engine shown in both of the above diagrams is a schematic diagram of my engine 3d. It has some simplifications. During a cycle the working gas moves between the hot and cold ends by passing through the narrow opening between the displacer and the cylinder wall. My original engine used this design. Later I added a regenerator by boring four holes vertically through the displacer, filling them with regenerator material, and creating a better seal between the displacer and the cylinder wall to force the gas through the regenerator. This modification doubled the engines power output by improving the rate of heat transfer.

Why use the Stirling Cycle?

The Stirling Cycle is an implementation of the Carnot Cycle, the most efficient thermodynamic cycle possible for a heat engine. The theoretical limit is:

Efficiency = 1-Tc/Th

where:

            Th = Absolute temperature of the heat source (K or °R)

            Tc = Absolute temperature of the cooling sink

The following diagram shows the theoretical maximum efficiency for the Carnot Cycle for some low temperatures.

These theoretical efficiency numbers cannot be achieved with real engines. There are several barriers to achieving ideal efficiency including:

1. The isothermal expansion and compression would need to happen very slowly to maintain near constant temperature to allow for heat transfer.
2. The regenerator would need to transfer heat efficiently without friction. At any reasonable gas flow rate through the regenerator the gas will experience friction losses.
3. Ideal efficiency assumes all heat transfer is between the working gas and the appropriate heat source, cool sink, or regenerator. Any paths that take heat from the heat source to the cool sink and bypass the working gas are wasted energy and contribute to engine inefficiency.
4. All the usual sources of energy loss including friction on bearings, moving seals, and airflow.

Some Stirling engine developers have measured efficiencies approaching approximately half of the theoretical efficiency. The most efficient engines have heat sources operating at much higher temperatures (over 1000 deg F) and very high pressures (over 1000 psi).

More information on the Stirling Cycle:

Wikipedia Stirling Engine

One should keep all this ideal thermodynamic cycle discussion in perspective. Other thermodynamic cycles such as the Brayton cycle can also approach Carnot efficiency and have their advantages. For example, no one has figured out how to implement the Stirling cycle as continuous flow process, allowing use of axial flow compressors and turbines. The Brayton cycle is commonly used with turbine engines. Stirling engines are probably confined to lower-power systems (tens of kw)  using pistons. Megawatt scale systems require an array of Stirling engines.

Posted in Thermodynamics | 2 Comments »

Maker Faire 2008

May 6, 2008 – 7:57 pm

From 2008_05_05 Ma…

 

 

I want to thank all the people who stopped by to see the solar power Stirling engine in operation. I appreciate the questions, comments and interest in the engine. I regret that I was unable to offer a better response to those that asked about the efficiency. I simply cannot make a meaningful measurement of efficiency on this engine because it has several thermal shorts that are part of the engine. I’ll post more details on efficiency and the low-temperature engine in a future post.

One of my goals in attending the Maker Faire was to get a feel for potential interest in the engine and see if there might be applications that could make use of the engine. My impression is that there is a lot of interest—I just need to deliver the power. I was showing a development engine with an output of about 1/10 watt. I think interest would be better for at least 100 watts, approximately the power a person puts out exercising, or preferably 1kwatt.

One application that sounded particularly promising is the possibility of using the engine to make use of the excess solar-heated water available in buildings that use solar hot water for space heating. Space heating requires considerable power, the cause of you high energy bills in the winter. In the summer these systems are essentially unused. I’ve heard from users that they’ve seen steam coming out of these systems as the temperatures soar in the summer. A hot water engine need not be highly efficient as long as it can generate power to pay for itself plus some extra.

I’m always interested in hearing about potential application where a low-temperature low-power engine might be useful. There are potential applications such a powering fountains or operating kinetic sculpture that might be able to use power in the 10 watt range. One benefit of the type of Stirling engines that I am designing is that they produce torque at low RPM so that they tend to be more useful for mechanical operations. High RPM power often requires a gear train to reduce RPM and increase torque.

As I mentioned at the Maker Faire, I’ll be putting out some free plans on this website for making a simple, small, Stirling engine. I’m still getting a few bugs out (mostly reducing friction) so that it can operate from sunlight. My goal is to have it done by May 18.

After that I’ll put out a simple simulator for Excel that will help you estimate the power output of a Stirling engine design. Essentially it will give you a maximum possible work per revolution and information on pressures during the cycle. It won’t tell you things like what RPM the engine will turn—that depends on the design of your engine and how efficiently you transfer heat and how low the friction is in your engine.

You can see a video of the Maker Faire 2008 Configuration

Posted in Uncategorized | 5 Comments »

Torque and Power measurement of low-speed, low-power engine

April 3, 2008 – 10:01 pm

I needed to measure the torque and power output of my Stirling engine so that I could compare it with the simulation. The engine currently spins up to 70 RPM and has torque levels up to around 2 in-lbs. My first attempt at a design to measure torque was easy to make and gave satisfactory results. I believe it would also be suitable for higher RPM and torque levels.

The first photo shows the torque arm assembly mounted on my engine and in use. The torque arm assembly mounts on the engine shaft. Because I don’t want to damage my engine shaft the torque arm slides on its own sleeve that is rigidly attached to the engine shaft with a collar.  As the engine turns the torque arm is held stationary by the vertical column resting on the electronic scale. The torque level is adjusted by increasing the spring force that squeezes the torque arm against the sleeve, increasing friction. By measuring the force on the scale multiplied by the radial distance out on the torque arm I have the torque produced by the shaft. Measuring the RPM using the low-cost tachometer I can compute the power output of the engine. The equations are:

Torque = force x torque arm

Power = Torque x 2π x RPM/60

In my case I want the torque in inch-lbs and I measure the force using a gram scale so:

Torque  (in-lbs) = force (grams) x torque arm (inches) x (1 lb/454grams)

Using this torque value in the power equations yields power in in-lbs/sec.

Making the Measurements

To make the torque measurement I locate the vertical column at the torque arm distance I want. For my measurements I use 3 inches and have a pin installed on the torque arm at this distance. Because the vertical column contacts the pin I don’t need precise lateral alignment on the torque arm. Make sure the torque arm is horizontal when making the measurements. The digital scale is convenient for making these measurements because it has very small displacement unlike a beam balance or spring scale. Raise the torque arm off the vertical column and tare the scale. Lower the torque arm onto the vertical column and read the force on the scale.

To make accurate measurements the torque arm should be balanced on the shaft axis. You can also test this by making torque measurement then letting the torque arm rotate 180 degrees and making another torque measurement. They should be identical. On my torque arm I’ve balanced the asymmetrical weight of the spring with additional washers and have a matching pin on the opposite side of the torque arm.

I experience very little drift in the measurements unless the RPM varies considerably. This only happens at low RPM (under 30 RPM on my engine) when torque levels are high and the flywheel inertia slows down between power pulses.

Torque arm assembly details

 


 

The torque arm assembly only requires a few parts. The sleeve is the most complex part and was made using a lathe. It could also be made from metal tubing and two collars. The sleeve is made to have a slip fit on the engine shaft (.25 inch on my engine). The outside diameter of the sleeve has two 5/8 inch diameter shoulders to keep the wood torque arm from sliding in or out on the sleeve as it turns. The diameter where the torque arm rides is ½ inch. The sleeve needs to lock firmly on the engine shaft to transmit the torque. I split the sleeve and used a collar to squeeze the split region against the engine shaft.

The wood torque arm started as one piece of .75×1.5×8 inch wood. I drilled a ½ inch central hole to match the sleeve OD between the shoulders and two holes for the bolts that squeeze the torque arm halves together. I also marked the radial distances out on the torque arm for locating the vertical column when making torque measurements. After that I used a table saw to rip the torque arm in half right through the center of the sleeve hole. If you don’t have a table saw for the ripping operation you could just make the torque arm from two pieces to start with.

I originally had the wood torque arm rub directly on the collar and this worked reasonably well but set up an annoying squeak at low RPM. I’ve since inserted felt which avoids the squeak but requires more squeeze force to get the same friction.

The bolts used to apply clamping force to the torque arm are just threaded rod with nuts and washers sandwiching the lower part of the torque arm. I use barrel nuts on the top for easy finger adjustment. On one side I fix the clamping bolt for an even gap in the torque arm and then make all the torque adjustments on the other side by compressing the spring with the clamping bolt to build force gradually for fine adjustment.

The vertical column used to transmit the force on the torque arm to the scale was made from two pieces of U-channel connected by a threaded rod. The rod is cut to length to make the torque arm horizontal.

Torque and Power Measurement Results

The following two plots show the results of some torque and power measurements on my engine. The data isn’t dead smooth and this could be from several causes. Changing power levels on the engine cause some drift. It’s difficult to keep the temperatures constant on this engine while changing the load. The torque measurements seem reasonably stable except at very low RPM. The RPM measurement gets more difficult at low RPM because it varies throughout a cycle and I have to try to average several RPM readings. One difficulty I’ve experienced is a zero drift on the digital scale. It’s usually quite stable but will sometimes drift a few grams. It’s best to check the zero reading before and after a measurement.  



Higher torque and power measurements

The power levels for my measurements have been less than one watt (8.85 in-lbs/sec = 1 watt) so I don’t have a big power dissipation problem. There is no reason you can’t scale up the design I have used here to measure higher torque and power levels (at higher RPMs too) as long as you pay attention to the power dissipation. I have used an aluminum sleeve for easy machining and good heat conductivity. Although I haven’t tested it, I expect this design should be able to handle at least 2 watts at 100 RPM or higher. Scaling up the design for more contact area between the wood and the sleeve and more exposed surface area on the sleeve to get the heat into the air would be desirable for higher powers. The wood will not conduct heat away very efficiently and will be the weak link. You should be able to smell trouble if you get it too hot. Too much power coming out of my engine for the torque system to handle is a problem I’d love to have. When it happens I’ll let you know how I solve it.

Posted in Performance testing | 1 Comment »

Tachometer Part 2

March 19, 2008 – 12:48 pm

After using my bicycle speedometer-tachometer for a while, I decide to test the Schwinn speedometer that I saw on Amazon for $10. Although it uses the same programming values that I show in the table from my earlier Low-cost Tachometer article, it has some differences that I thought I should point out.

1. The maximum “speed” on the readout is limited to 99.9 (mph or kph). You can accommodate 100 RPM or 1000 RPM or whatever you want to program, but the resolution will remain 1 part in 1000. The earlier Bell Speedometer specifies a limit of 200.0 mph or kph and I assumed a max reading of 199.9.  It turns out to my surprise that the display has another digit and goes well past that. I’ve had mine up to 458.0. Even at the documented 200.0 mph or kph limit you have 1 part in 2000 resolution. So the Bell Speedometer gives a little better resolution if that is an issue.
2. The update time on the Bell Speedometer is one second and the update time on the Schwinn speedometer is two seconds. This has plusses and minuses. If you’re trying to grab an RPM reading quickly as in the Flywheel Spin-down work measurement application, you might want the one second update. For most of my work I prefer the 2 second update because the longer period lets it read lower RPM and have less variation. Using 4 magnets and programming the units so I read 1 kph as 1 RPM the minimum speed on the Bell Speedometer is 15 RPM and on the Schwinn it is 8 RPM. The Schwinn speedometer also has a larger display that is easier to read at a distance although the Bell Speedometer display is quite usable.
3. For either unit don’t plan on using the included magnet for mounting on a bicycle spoke (unless you’re using it for that application). Us a strong magnet and use larger magnet if possible so you can have more clearance between the magnet and the pickup. I use these units to measure RPM in a variety of temporary applications and the larger magnets let me locate the pickup about half an inch from the magnets. Smaller magnets typically require smaller clearances.

Posted in Performance testing | 2 Comments »

Flywheel Spin-down work measurements

February 24, 2008 – 3:01 pm

One way to measure the friction on a rotating machine such as an engine or motor is to spin it up and record the appropriate data while it slows down without power. By measuring the time elapsed between two RPM measurements and knowing the moment of inertia, you can compute the lost energy from the flywheel and the frictional work. I am applying this method to a Stirling engine I’m developing.

Currently the Stirling-cycle engine is producing about one inch-pound of net work per revolution. My Excel-based simulation showed a gross output of 4 to 12 inch-lbs of work per revolution depending on the temperature differential and RPM. The rest of the work is either being lost to friction or my simulation is overly optimistic. I’m using the flywheel spin-down method to measure the engine’s frictional losses and track down the distribution among the various parts of the engine.

An outline of the technique:

1. If possible use a flywheel with plenty of inertia so it will spin down slowly.
2. Compute the total flywheel moment of inertia
3. Set up the configuration to test. I’ll start with only the flywheel and crankshaft, then add various components—piston without compression, displacer, etc.
4. With a tachometer (such as the low-cost tachometer) and stopwatch ready, spin up the flywheel to a suitable RPM, note RPM1, start the stopwatch, let the flywheel spin down to a lower RPM, stop the stopwatch and record RPM2.
5. Make a series of runs over RPM values appropriate for your setup.
6. Use a spreadsheet to compute the energy lost based on the change from RPM1 to RPM2 and the flywheel inertia. Compute the energy lost per unit time (work) versus average RPM.

Flywheel Moment of Inertia

My flywheel is built from 3 components as you can see in the photo. The basic flywheel is an 11.9 inch diameter by 3/16 inch thick aluminum disk. Because I needed more inertia, I added a plywood club to the flywheel. The club supports two ¾ inch bolts with 8 washers each to add mass on an 18 inch diameter.

You can compute the total moment of inertia of your flywheel by adding up the component parts. Here are the equations that are appropriate for a typical flywheel:

Solid disk with constant thickness

I_disk=mR²/2  moment of inertia. For a conventional flywheel the center hub might be modeled as disk.

m= mass, Weight-lb/g

g = acceleration of gravity, 32.2 ft/sec². Note that the pounds you measure on a scale are weight; you need to divide by g to get mass (in the unattractive unit of “slugs”.)

R= radius of disk, ft

Flywheel rim or concentrated mass

I_rim=m(R_ave)²

R_ave= average Radius of a concentrated mass. The concentrated mass could be the two bolts shown in the photo of my flywheel, or it could be the rim on a conventional flywheel. R_ave is measured in ft.

m = mass, Weight-lb/g. This is the total mass of the rim, or in my case, the total mass of the two bolts and washers.

Spokes

I_spoke= m(r_o² – r_i²)/3

r_o = Outer radius of the spoke, ft

r_i = Inner radius of the spoke, ft

m = Total mass of all the spokes, Weight-lbs/g

In this case I can treat the club as a spoke with an inner radius of zero. The total weight of the club takes care of the two sides of the club. This equation assumes the spoke has a uniform mass distribution along its length.

I_total = I_disk + I_rim + I_spoke

Kinetic Energy

The total kinetic energy of a rotating mass is:

KE = I_totalω²/2

ω = rotational speed in radians/sec

Converting to RPM:

KE = I_total(.1047 * RPM)²/2

What we really want is the difference in kinetic energy between two different RPMs:

ΔKE = .0055 * I_total(RPM1² – RPM2²)

If you’ve used the units I’ve suggested the result of ΔKE will be in ft-lbs of work. I usually multiply this by 12 to work in in-lbs for my engine.

The remaining computations:

RPM_ave = (RPM1 + RPM2)/2

Energy lost from flywheel per unit time (ft-lbs/sec):

Work = ΔKE/ (spin-down time)

Set up the test configuration

For a first test configuration I used just the flywheel and crankshaft. This should give you the minimum amount of friction and the plenty of time to measure the RPM and spin-down.

For RPM measurements the bicycle speedometer  gives accurate measurements, especially if you can use four equally-spaced magnets to give you direct RPM readout. It’s important that the magnets be equally spaced or you’ll have varying RPM measurements. The bicycle speedometer I used updates at exactly one second intervals so I use the stopwatch to count out the seconds, starting and stopping the stopwatch when the speedometer reading changes. I don’t use the actual stopwatch reading but the closest second reading—because that’s when the speedometer made the measurement. So 18.13 seconds I record as 18 seconds.

Even with accurately spaced magnets the RPM measurements may vary if the rotating mass isn’t near perfectly balanced (does your flywheel always seek the same rest position)? This is one of the sources of variation in the measurements and why you’ll want to take a series of measurements.

The Results

When you get done you should end up with data you can plot that may look something like this:

This plot is for my flywheel and crankshaft with nothing else attached. So at 60 rpm the total friction from bearings and air friction is about .15 in-lbs/sec.

A series of configurations combined on one chart tells the whole story:

The data is relatively clean for the flywheel configuration but gets fairly noise for the more complete configurations. Running the data through a least-squares curve fit provides equations that are useful for analytical work. The generated curves are shown with the data.

The engine open configuration with no compression includes all the frictional sources except compression and a small amount of air friction on the displacer moving back and forth. At 60 rpm the work lost is about 2.6 in-lbs/sec. The engine has to generate approximately that much power just to turn unloaded at 60 rpm.  

These plots give me a very good idea of the frictional losses in the engine. I still need to account for some missing work. One possibility is compression leakage around the piston and around the displacer shaft seal. I’ll look into those in the future.

I have provided a spreadsheet you can use that will perform the moment of inertia computations from your flywheel measurements. It also provides a table for entering your RPM and timing measurements to generate the energy lost table and plot the results.  

If you don’t have Excel here is a version for Google’s free spreadsheet that you can use for your computations and plotting. You’ll need to save this spreadsheet as your own before you can use it.

Copyright 2008 Doug Conner

Posted in Performance testing | 7 Comments »