PROCEDURE		WHY?
1.   START BY PREPARING THE FRAME THAT WILL HOLD THE FLYWHEEL AND SHAFT.  YOU'LL NEED A BASE, TWO SIDES WITH HOLES FOR A BUSHING, AND TWO BUSHINGS TO HOLD THE SHAFT.		THIS WILL HOLD THE SHAFT OVER THE MOUSE SENSOR.  NOTE THAT I HAVE ALUMINUM BUSHINGS IN THE PICTURE.  THIS IS A BAD IDEA; USE BRASS BUSHINGS AND SHAFT, OR IF YOU HAVE THEM, BEARINGS.
2.  ASSEMBLE THE FRAME, MAKING SURE THAT YOUR MOUSE ELECTRONICS WILL FIT BETWEEN THE SIDES.  BE SURE THE FLYWHEEL IS ATTACHED SECURELY AND WELL BALANCED.
3.  ATTACK YOUR MOUSE AND REMOVE THE CASING.  DISCARD ALL THE EXTRA PLASTIC, LIKE THE LIGHT PIPE, BUTTONS, SCROLL WHEEL MOUNT, ETC.  I ALSO CUT THE OPTICAL SENSOR OUT OF MINE, BUT DO SO AT YOUR OWN RISK, IT MAY KILL CERTAIN MICE.		THE ONLY THING WE'RE INTERESTED IN IS THE SCROLL WHEEL ENCODER.  I REMOVED THE OPTICAL SENSOR SO THAT SHOULD I BUMP THIS DEVICE MY COMPUTER CURSOR DOESN'T MOVE. AS BEST I CAN TELL, THE SENSOR IN AN INTELLIMOUSE IS ONE OF THE BEST; GOOD TO 30,000 RPM.  OLDER MICE ARE MUCH LESS SENSTIVE.
4. THE SCROLL WHEEL SENSOR IS ATTACHED (ON THIS MOUSE ANYWAY) VIA A RIBBON CABLE.  IT NEEDS TO BE POSITIONED SOMEWHAT CENTRALLY SO THAT IT CAN BE PLACED UNDERNEATH THE SHAFT.  I USED SOME PIECES OF CARDBOARD GLUED TO THE MAIN BOARD AND THEN GLUED THE SENSOR BOARD ON TOP.		THIS HELPS RAISE THE SENSOR CLOSER TO THE SHAFT, AS WELL AS HOLDS IT IN PLACE.
5.  ATTACH THE MOUSE WITH DOUBLE SIDES TAPE SUCH THAT THE SCROLL WHEEL SENSOR IS DIRECTLY BELOW THE SHAFT.
6.  FINALLY, ATTACH A SEMI CIRCULAR PIECE OF PLASTIC OR OTHER OPAQUE MATERIAL TO THE SHAFT, SUCH THAT FOR HALF OF THE SHAFTS ROTATION THE PATH BETWEEN THE IR LED AND THE IR SENSOR IS BROKEN.		THIS PIECE REPLACES THE ENCODER WHEEL THAT LIVED IN THE MOUSE.  BY LOWERING THE NUMBER OF SLOTS FROM ABOUT 20 TO JUST ONE, THE SENSOR CAN NOW RESOLVE MUCH HIGHER SHAFT SPEEDS.  THIS SACRIFICES SOME RESOLUTION, HOWEVER.

SOFTWARE

I WROTE SOME SOFTWARE THAT CONTINUOUSLY PLOTS RPM, TORQUE, AND POWER, AS WELL AS CAN EXPORT TORQUE AND POWER VS RPM CURVES TO EXCEL IN .CSV FORMAT.  OBVIOUSLY YOU COULD WRITE YOUR OWN IF YOU DESIRE; ACCESS TO THE SCROLL WHEEL IS EASILY ACCOMPLISHED WITH WINDOWS APIs.  I'LL GO OVER HOW TO USE MY OWN SOFTWARE:

DOWNLOAD SCI-SPOT.COM DYNAMOMETER
DOWNLOAD SOURCE

LAUNCH THE DYNO SOFTWARE AND CLICK SETUP:

THEN CLICK SENSOR SETUP.  ENSURE THAT THE SENSOR IS SET TO ONE ("1") SLOT:

...

NOW CLICK TEST MASS SETUP.  IN THIS WINDOW, DEFINE THE PARAMETERS OF YOUR FLYWHEEL AND SHAFT.  IF YOU'RE NOT USING A CIRCULAR FLYWHEEL YOU MAY CALCULATE THE MOMENT OF INERTIA BY HAND AND ENTER IT AT THE BOTTOM OF THE FORM.  ALSO, YOU NEED TO ENTER EITHER THE MASS OR THE DENSITY OF EACH PIECE.  YOU DON'T NEED TO KNOW THE MASS AND THE DENSITY.  (FOR PERSONS USING A CD, A STANDARD CD WEIGHS 15.6 GRAMS.  A MINI CD WEIGHS 6.7 GRAMS).

CLICK OK TO CLOSE THE SETUP BOXES.  AT THE MAIN FORM, CLICK START, AND THEN APPLY POWER TO YOUR MOTOR.  LOGGING AND PLOTTING WILL START AUTOMATICALLY:

NOTE:  THESE GRAPHS ARE SIMULATED BECAUSE I DID NOT HAVE THE DEVICE ON HAND WHEN MAKING THIS PAGE.

CLICK STOP WHEN YOUR MOTOR HAS REACHED IT'S MAXIMUM SPEED.  A BOX WILL APPEAR SO YOU MAY EXPORT THE OUTPUT VS RPM CURVES TO EXCEL.  HERE IS A SAMPLE GRAPH FROM THE EXCEL OUTPUT.  THIS IS FOR A SMALL PAGER MOTOR:

NOTE, THE PROGRAM PLOTS AN AVERAGE OF THE ACTUAL DATA COLLECTED; THIS PRODUCES SMOOTHER, MORE EASILY READ GRAPHS.  THIS DOES, HOWEVER, PRODUCE AN INACCURACY IN THE FIRST DATA POINTS IN THE TORQUE CURVE.  SIMPLY KEEP IN MIND THAT TORQUE DOES NOT EQUAL ZERO AT 0 RPM.

CALCULATIONS

THE MOTORS EFFICIENCY AT IT'S PEAK RPM CAN BE CALCULATED BY:

EFFICIENCY = MAX POWER FROM GRAPH / (VOLTS * AMPS)

FOR THE PAGER MOTOR SHOWN, THE EFFICIENCY IS ABOUT 2%.

READER QUESTIONS

JEREMY - Hello I had a quick question about your motor dyno: First, can I use a prop in place of the flywheel or would that make a difference as far as where the motor creates its most torque? Second, can I use a mouse with a USB port so I still have use of my other mouse? Thanks for the help.

ANSWER - No, do not use a propeller. You'll notice the program is set up to calculate the moment of inertia automatically for a disk only; you'd have to calculate your propeller's moment of inertia by hand. This is ignoring the major reason why you shouldn't use a propeller: the program cannot account for air drag. Obviously the drag on a simple spinning disk is low, but its HUGE for a propeller. This drag will not only produce a graph that shows lower than actual torque, but it will also shift the peak.

You may use any mouse that works in windows. Windows is very tolerant of multiple mice, just make sure the scroll wheel works (like you can scroll windows and stuff) before continuing.  The mouse I used was a USB mouse, in fact.

TIM - What actual math is done with the raw data (pulses that are directly proportional to the RPMs I assume) to get the torque and other information. I am asking because I am doing a science fair project a that involves the same stuff. Also, what "recommended reading" would you suggest for me? I am a junior in high school and am taking honors physics and calculus. Thank you in advance for any help you can provide.

Basically what I am doing is building a dynamometer for small glow engines which are used in RC cars and trucks. These can reach in speeds in excess of 40k rpm and the manufactures have unbelievably inflated horsepower and torque numbers (or so I have heard).  I'd like to find out if the numbers advertised for these engines are for real.

ANSWER - First off, a gas engine will be a good challenge, but I believe you can accomplish it. Some things to consider:

-You’ll need a large test mass. If I recall my RC car days correctly a good .21 was claimed to be ~2.2 horsepower, which is about 1500 watts. You’ll need to use that figure to ensure that your motor accelerates the cylinder nice and slowly. I’d expect your flywheel to be on the order of several pounds.

-Clutches will be your largest challenge. You’ll need a clutch because it’s unlikely that you’ll get the engine started with such a large mass (flywheel) attached. At the same time, measuring power and torque after a clutch could give you distorted numbers because of slippage. Of course, taking some slippage into account gives you a better view of what you’ll see in your RC car, since the clutch will be a factor there as well.

-You’ll need a good test stand. And by good I mean VERY good. High quality bearings, and ¼” or larger (3/8 or ½ wouldn’t be overkill) shafts. That motor will never reach 40k RPM loaded with a flywheel this larger, but a mass the size that you’ll need is NOT something you want breaking loose, even at 10k RPM. It would easily devour your leg, the wall behind it, and any passing cars in the street.

-A reduction belt is trivial with respect to the other engineering and fabrication you’ll be doing. Moreover its an excellent idea. Obviously the belt will keep the speed of the flywheel in the range of the mouse’s optical sensor, but moreover using a belt will lower the tip speed of the flywheel, which lowers your losses due to air drag. Keeping things moving slow is always an excellent idea. Go belt.

Now for the math:

Some constants:

w = d(phi) / dt = angular velocity = RPM * 2 *pi ©¬ (note the 2 * pi, not phi.)

dw / dt = angular acceleration in radians

T = torque

W = work = change in energy

t = time

n = number of samples recorded

dn / dt = samples recorded per second = n / sample rate

Some fundamental physical truths:

dw / dt = T / I

I = ½ m * (Ro^2 + Ri^2) where m is the mass of the flywheel and Ro and Ri are its inner and outer radii.

P = T w

Practical equations:

As you know, the program samples the mouse sensor every few milliseconds. The mouse reports back with the number of samples its recorded since last time it was asked. This number is n. The program asks the mouse for this data every “i” seconds (i is chosen as a random variable, you get my point). Thus:

dn / dt = n / i

Now, a parameter of your device will be the number of ‘slits’ you put in on the shaft. Each slit will count as a sample (n) as it passes the sensor. If your disk has one slit, then the mouse will report one sample for each rotation. If you have two slits, then you see two samples per rotation etc. The advantage of using a single slit is that the mouse can read ~10k samples per second, which is 10k RPM. If you use two slits, then this 10k samples corresponds to only 5k RPM. The advantage to using more slits is you get higher resolution data, and lower error. One slit is fine for the speeds involved here. Consider S as the number of slits on the shaft, thus:

w = 2* pi * n / (i * S)

Now we can find w many times a second by querying the mouse sensor and applying that equation. For human minds, RPM is easier to understand and can be found with:

RPM = 60 * n / (i * S)

As stated above, dw / dt = T / I which means T = I * (dw/dt). dw/dt can be found by querying the mouse for w, and then comparing the calculated value of w with the value calculated the previous time you asked for it (w0).

dw / dt = (w – w0) / i

Recall “i” is the number of seconds between queries of the mouse sensor, and “w0” is the w calculated from the previous sample. Now simply:

T = torque
   = I * dw /dt
   = ½ * m * (Ro^2 +Ri^2) * (w – w0) / i

Voila, half the battle is done. Power is simply P = T w so:

P = T w
   = I w dw /dt
   = ½ * m * (Ro^2+ Ri^2) * w * (w - w0) / i


And there you have it. Regarding actually getting this data from the mouse into vb, simply download the source code for my program. It‘s available below the program itself on the Dyno page.

As far as required reading is concerned, I’ve never been one for reading my text books, so I’m not very knowledgeable.  One online resource of impeccable quality is HyperPhysics (http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html) which has answered more questions for me over the course of my education than I could count.

RICH - I have been fiddling with your little Dyno and have a few suggestions.

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