Making a Prony Brake to Measure the Power of My Hot Air Engines

[vtsteam]

It was a lot of fun when rehabilitating No. 83, my hot air engine to see how fast it would go after each change. But top RPM is not a very good measure of a hot air engine. Since I want to go further with modifications, I really need a way to look at power output. And I'd like to build other hot air engines as well (in fact I've already started on No. 84, a Rider type engine) so a tool for the job is needed.

Enter Professor Dennis Chaddock and his Prony brake dynamometer for hot air engines, featured in September 1976 Model Engineer. This simple device was used to compare model hot air engines submitted for a new competition slated for the upcoming 1977 Model Engineer Exhibition.

This device used a steel brake drum and brake shoes of hardwood, with a notched and graduated aluminum balance arm with moveable weights. The moment was used to figure momentary torque, and in conjunction with a clockworks tachometer the power output could be arrived at arithmetically.

I'm going to use some of Professor Chaddock's design, but use a digital tach, and scale, since I already have both. Somewhat less visually elegant, but a lot easier to work out the power curve -- particularly since I can do it in Watts with minimal units conversion, by comparison with his original inch and ounce torsionometer.

Another slight variation, his was designed for a standardized motor shaft of 5/32" diameter and mine will be for 8mm, since that's what No. 83 has, and is a standard I intend to continue. Also he modestly referred to his cool little dynamometer as "a bit of oak" because of the brake shoes. Mine will be "a bit of cherry," in that case since I have a lot of that hardwood, which I cut and milled on my own property.

Here's a start, parting off the brake drum on my homemade lathe:

 

And here's the cherry wood I'll be using, milled out. It's kind of surprising how small this all is, after having looked at the plans many times over the years in the magazine.    It really is just a little bit of... whatever!


 

[vtsteam]

First step in making the torsion arm is gluing the two blocks together temporarily with tacks of super glue. I put two dots at either end on both sides and just let them wick a small way into the joint from the side. I used a toothpick to pick up a small amount of glue from a drop that was placed on the waxed paper. I really didn't want the blocks to be glued together permanently, and they would have been impossible to separate if I'd applied it directly from the tube.

 

I don't have accelerator, and wood sometimes slows down superglue's cure. So I used a couple small pinches of bicarbonate of soda, which effects an almost instant cure.

 

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[vtsteam]

I marked out and drilled all of the hole locations in the torque arm, and drilled the smaller ones full size.

The large hole for the drum was drilled undersize with a Forstner bit.

 

Professor Chaddock recommends boring on the lathe, but I find centering an odd shape like this one difficult without some kind of initial pilot hole, particularly on wood. Much easier to pre-drill on the drill press. A large hole in the piece was actually easier to center on the lathe than a small pilot would have been. I just clocked in the ID with a gauge. Then I did the final boring to size.

 

[vtsteam]

The Chaddock design calls for two 1-1/2" long 8 BA adjustment screws nuts and washers. These are approximately equivalent to US 2-56. To me that's pretty thin -- I have stock small screws of all common US sizes down to 4-40, but nothing in 2-56, and certainly not anything near that size 1-1/2" long. So time to make some. Luckily I do have 2-56 taps and a die.

The other problem however was what to use for wire stock? I eventually found some odd size brazing rod, slightly oversize for the job, but it did accept the die without complaining So I started the slightly laborious job of hand turning 3" of 2-56 screw thread. That's 336 half turns of the die handle, not including backing off twists! Actually, of course, all part of the fun: making something from nothing.

 

[vtsteam]

Then it was on to the adjustment nuts. Finally something straightforward in the lathe, out of metal! These were drilled tapped, knurled, and finally parted off in my homemade lathe, the most enjoyable part of today's work:

 

[vtsteam]

After making the hardware, it was time to split the blocks apart again. My good old Swiss Army knife seemed a better (and longer) wedge shape than an Xacto, so that's what I used.

 

The original brake had bolts with heads, unlike my all-thread studs and it was suggested that a tight fit in the lower arm was needed to keep them from turning. Seemed to me that  a dab of epoxy on the threads would serve both purposes for my version, so that's what I did.

Then I sorted through my box of springs to find something of the specified size for the adjusment pressure (24 SWG, 3/16" dia) found one and cut off two sections 1/4" long with an abrasive disk in a Dremel tool. These were installed under the adjustment nuts, and the brake arm was reassembled to take a look.

 

 

[vtsteam]

Today I started on the stylus that will transmit the force of the brake arm to the digital scale I'll be using. I started with a piece of brass 3/16" and immediately ran into the problem that my 4 jaw chuck won't hold anything that small. That's a feature among others that bothers me about that chuck. Nevertheless I worked around it by taking my square ER collet holder, and clamping that in the 4 jaw. Kind of overkill for a piece this small, but it beats having to change chucks. Funny to see an ER chuck, in a 4 jaw chuck, mounted on a faceplate, but that's what got the job done today. I thinned the brass down to .134" for threading 6-32.

 

[vtsteam]

And thinking I'd break out my never before used tailstock die holder, ran into problem number two. Despite the fact that it had many different die holder recesses and attachments, it wouldn't accept a plain 1" hex sided die -- which was what I had for cutting a 6-32 thread. Rats! I should have made one myself instead of buying one to... ahem, save time.

Well, the ER collet holder to the rescue again, I started the threads in the lathe by holding a die handle and then transferred the collet holder block to the bench vise and turned the threads the rest of the way.

 

 

[vtsteam]

I cut the stylus to length, and rounded the end. Here it is finished:

 

[vtsteam]

I drilled and tapped the brake arm to accept the stylus at a distance of 10 centimeters from the center of the brake drum, then secured it in place with two nuts. The height of the brake arm is therefore adjustable, and should be set level. A 10 cm moment arm means that every gram registered on the digital scale will be approximately ten times the newton-meters of torque absorbed by the brake. So grams divided by 10 is ~ Newton-meters. From that, and RPM, Watts can be easily calculated.

With this work done, the Prony brake was operable, though I'm not finished. But I couldn't resist setting it up temporarily and trying it out! 

I was disappointyed when at first the engine wouldn't start at all with the brake just sitting, applying no pressure to the drum. And for the first 15 minutes the engine ran I could hardly even touch the drum without nearly stopping the motor. But eventually the engine seemed to loosen up and gradually increase speed to the point where I could attach the brake arm...but without the adjustment springs... just letting the parts run together.

This brake definitely needs to be run in -- it needs more of that. But eventually this evening I was able to adjust the thumbscrews (without springs) for very slight pressure, and get the engine to run at reduced speed, registering a torque reading on the digital scale. I was gratified to see it was a reasonable stable digital reading, probably helped by the inertia of the brass stylus, which, unlike the other parts does not weigh on the drum.

Here's a picture of the first run. I do need to do a little more work to get easier and more consistent readings, to work out a measurement procedure, and to finish it off, but I'm very happy that it works quite well already!

 

[Country Bubba]

Nice job, and am looking forward to seeing just how much power one of these engines puts out.  Have always wondered, but have never seen any results.
 

[vtsteam]

Hi CB thanks! I suspect fractional watt in its present form, without pressurization, snifter, etc. But we'll see once I have it working properly and a good procedure.

Problems off the bat:

The moment arm is wrong. It's not 10 cm. I thought of this this morning. It's really the length of the diagonal from the center of the drum to the point of contact on the scale. My bad! 

Too much friction to start the engine. This can be reduced, and will also reduce naturally by breaking in. Also need lighter springs.

The scale shuts itself off after a period automatically save batteries. Then if you hit ON again while the engine is running it tares itself at whatever the pressure plus stylus weight is. If you turn on while stylus is lifted, you can't tare the stylus weight.

I think the solution here is to weigh while the engine is stationary, and make up an indexing weight to equal that amount. Then if the scale turns off during a run, lift the stylus, add the indexing weight, and turn on the scale. Once it tares, remove the weight and lower the stylus.

Finally the math: I thought that by going w/ metric grams, 10 cm, watts etc. it would be simple multiplication and possibly moving decimal points, but it's not. Newtons isn't grams by a conversion factor and RPM needs to be converted to radians per second to get watts, so math is just about as complicated as good old imperial to figure.

No problem however for a spreadsheet formula, which I've made up this morning, so on with the show! 

[vtsteam]

Further thoughts today:

I was thinking about drilling a new hole in the arm for the stylus to correct for the fact that 10 cm along the wooden arm is not the same thing as 10 cm along the moment arm to the point of contact on the scale.

But then I started thinking, as long as I'm drilling a new hole, can I also put it somewhere to eliominate some of the other math requirements, and simplify things that way?

Well, yes probably. So In the case of say 1000 RPM, 10 centimeters arm, and a reading of 3 grams, if I multiply speed times weight I get 3000 "pretend watts". But in reality if I do the proper math (RPM * Pi /30 * grams * arm length * .00009807 ) I get .3081 real watts.

Ignoring the decimal points for a moment that's 3081 real watts vs 3000 pretend watts, or a correction value of 3081/3000 = 1.027.

Or inverted, .974. So if I move the stylus location inboard to (10cm * .974) 9.74 cm that should apply just enough additional pressure on the scale to do the math for me.

Except I gotta remember to move the decimal point over to the left four places.

Oh yeah, I forgot also..... that 9.74 cm has to be the length of the diagonal from the center of rotation to the contact point on the scale.

Well we can figure that out also. The height of the stylus to the horizontal centerline of the brake drum is 4.1 cm.

The diagonal will be 9.74 cm. That's the hypotenuse of a right triangle. Therefore, its length squared equals the sum of the lengths of the other two sides squared. So 9.74 squared is 94.9, and 4.1 squared is 16.8. Subtracting: 94.9 - 16.8 is 78.1. Taking the square root of 78.1 we arrive at 8.84 cm. Or 88.4 mm. That should be the length along the brake arm to drill our new hole.

If we do that, and I have my figures right above, I can take a reading of RPM, and reading of the scale, multiply them together, and move the decimal point 4 places to the left, to yield an answer in proper watts.

Nice thing about that also... the closer distance now than my original 10 cm will put less braking force on the engine, and make it easier to start. All good: less math, bigger number, less stress! 

Check me if I'm wrong guys, etc.......

Thanks!

[vtsteam]

Wait, no....

I'm wrong about the diagonal bit. 

It shouldn't matter how long the stylus is, right? The force is applied at the joint, and is a pure vertical vector.

If there were a real diagonal arm, the vector components wouldn't all be vertical.

This is tough to visualize correctly..... 

So just drill the new hole at 9.74 cm, not 8.84 cm.........I think.

[BillTodd]

I think you were right first time.

The force is measured perpendicular to length of the torque arm (a radius).  Your scale will, to some extent correct for forces that are not perpendicular to its face (making the length of the arm; the distance from the centre of the axle , to a point vertically above the scale level with the axle centre) , but you would be better off eliminating as many small geometric errors as possible, just to give yourself a fighting chance.

How about a raising the scale, or adding a small vertical stand off, to keep the point of contact with the control arm level with the centre of axis, and adding a knife edge to ensure  its location.

  (ATM your brass screw seems to do this BUT because it is held perpendicular to the arm , not the scale, it changes the geometry }

[Country Bubba]

I agree and was thinking that when  you first proposed the diagonal idea.  It made me think back to my ME lab many years ago and it was the horizontal distance that was measured.  Sometimes we think to deeply.  KISS! (Keep It Simple S)

[vtsteam]

Thanks Art, Bill!    I'm chucking the diagonal notion out the window! 

One other flaw in my messing around with what I already had was:

True, a hole at 9.74 cm would indeed give me an easy way of calculating watts in my setup, however, with a hole already at 10 cm, drilling results would be bad.

What I can salvage from all the unnecessary calculation of that post is the correction factor of 1.027.

I can just multiply the product of my readings by .0001027 to get true watts. I don't have to go through all the operations with radians, etc.

[vtsteam]

I made a 9.0 gram compensating weight to solve the auto-shutoff problem with my scale.

 

When the engine is stationary and the arm is loose on the drum, the brake arm puts 9.0 grams of weight on the scale. If at any point while the engine is running I need to tare the scale, I can now just lift the arm, and substitute the brass weight, and hit tare. Then remove the weight and lower the arm again.

On Professor Chaddock's Prony brake, he uses a permanently affixed lead counterweight behind the arm to balance it. I could have done that also, but to me this puts additional dead weight on the drum while running, applying additional unwanted braking pressure at all times. His system works on the principle of a balance scale, so this is necessary in his case.

[vtsteam]

Extremely preliminary test on No. 83 with the Prony brake not broken in yet and a nearly empty Sterno can and a handheld tach (somewhat flakey: to be replaced) = 4.0 grams at 982 RPM = 0.403 watts. That's about what I expected for a starting figure.

[vtsteam]

Scale 4.5 @ 1060 RPM = .490 watts. With a fuller can of Sterno, again really too preliminary to take as anything more than ballpark. Lots of consistency problems controlling brake pressure and reading RPM and scale simultaneously.

Issues:

1.) The brass thumbnuts loosen from vibration. They are very free running on the brass screws. No springs yet. Need to wear in the brake pads enough to allow them.
2.) The laser tachometer is difficult to get focused on the flywheel, the reading button often doesn't work (it's old), the flywheel black paint wears (not intended to be permanent) so creates false readings from scratches.
3.) The heat source is variable.
 

To do:

1.) Varnish arm (not pad wear surfaces) and then oil pads, and just wear-in so they seat better -- they are already greatly improved from running this small amount.  Get lighter springs onto the brake, add some sort of sticky compound to thumbnuts to inhibit loosening while running.

2.) Add a hall effect digital tach for continuous reading of RPM.

3.) For proper testing, use the electric heater at a consistent wattage.

4.) Disassemble and clean the engine.

I am presently using a 3/4" thick padding block of white pine on top of the scale (per Bill Todd's suggestion above) rather than the long brass stylus. The main advantage of that is lessening of the weight of the arm. The block is self-taring when turning on the scale, unlike the stylus attached to the arm.

I would normally need a new compensating tare weight as well for the now lessened weight of the arm. Also if I varnish the arm, that compensating amount will change. I think the easier course from here on out would be to eliminate a brass weight altogether, and just compensate by subtracting the most current compensating figure from the scale reading when tabulating the data. That would allow for quick adjustments whenever the arm weight changes, rather than making new weights each time.

[Country Bubba]

I think there is a good possibility the springs will stabilize and help maintain the brass nut position. Think the spring on a needle jet of a lawnmower engine?

[vtsteam]

Yes CB I was thinking that also, presently the pressure needed is so light that the springs have no locking effect.

I've put a tiny dab of silicone rubber sealant on the bottom of the thumb nuts and that seems to be working to increase friction without adding so much that they are hard to turn.

Other changes yesterday: I Tung oiled the brake arm instead of varnishing. Disassembled and cleaned engine (see the No 83 thread).

I tried to set up a digital Hall effect tachometer with a panel meter and transducer received from Ebay, but it seemed defective.  It just read 7777 or LLLL when powered up (depending on how you look at it). Today, I tested on a loose flywheel with magnet and figured out this was normal behavior, unlike my other Hall tach on my lathe, which shows 0000 when stationary. I had initiated a return, but cancelled it once I realized it worked. This could have been avoided by including a one line instruction sheet. Oh well, on with the show....