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

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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.
 :proj:

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!  :palm:

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!  :smart:

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!  :med:

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

Thanks!

vtsteam:
Wait, no....

I'm wrong about the diagonal bit.  :bang:

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.....  :doh:

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 }

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