Sigma Sport BC-500 computer as an inexpensive tachometer.
In order to successfully spin cast paraffin grains for the hybrid rocket motor we need to be able to reproduce the same manufacturing conditions each time we make a new grain. One important consideration in doing this is making sure that we have an precise method of measuring and setting the RPM of the apparatus. It was recently brought to our attention that an inexpensive bicycle computer could be used as tachometer. The tachometer recommended is the Sigma Sport BC-500. It can be purchased for between $15 - $20 dollars and works quite well for our purposes. No major modification to the bicycle computer or to the spin caster needed to be made. The sensor works on the hall effect. The sensor was held with a small 'kwik clamp' fixed to the spin caster base and placed about 5mm away from the fixed magnet element that is held on the motor shaft with an elastic band.
The problem with this bicycle computer is that it doesn't actually give you a RPM output, but instead it gives and mph or km/hr output. Though it is possible to map this velocity output to a RPM output. This is done by making the bicycle computer prompt you for a wheel circumference or "Wheel size" and then giving it the value of 1667. This number is a conversion factor that will cause the computers km/hr output to be the same as Revolutions per Minute. only scaled down by a factor of 10. Explanation: We are trying to map revolutions minute km hr
the problem is that the units don't match

1 time

length time
we must convert our revolutions to a physical distance by revolutions circumferencwheel So then what is the required circumference to enter into the computer that will equate 1 RPM to 1 km/hr?? 1 revolution circumferencewheel 60 minutes 1 minute 1 hr 1 km mm

(EQ 1)

Solving for wheel circumference we get a value of 16667 mm. This is outside of the input range of the BC-500 computer so we scale it down by a factor of 10 and let: circumferencewheel := 1667mm Substituting this value back into EQ 1 we find that 1 RPM is equal to 0.1 km/hr or to put it another way 10 RPM is equal to 1 km/hr. Therefore what ever the display on the BC-500 says, we multiply this number by 10 and that is our RPM value.

Verification

To verify that what we are reading on the new BC-500 tachometer is in fact an accurate representation of the RPM of the motor we did a slow speed, manual count of the revolutions over a one minute interval (measured with a stop watch). A voltage was selected on the lab supply that was near the value that caused a single digit variation in the output of the BC-500. For example, the voltage that caused the display of the BC-500 to go from a 4 to a 5 should equate to the voltage between 49 to 50 RPM. Once the voltage was set and measured with a DMM we counted the revolutions of the motor in a 60 second period and recorded the data. We decided not to try a visual count of anything more than 60 cycles/min because it was a hassle and the few data points we can get at the lower RPM should give us an idea if the output is truly correct. Results of first test
Voltage 1.331 1.192 1.052 0.912 physical count scaled for later graphing 6.Sigma BC-3
For a second test we ran the lab supply to full scale and viewed the output on the BC-500 to see what kind of RPM range we could get. We then plotted the data to see how linear the behavior of the motor was. Results of second test
Voltage 15.96 15.00 14.00 13.00 12.00 11.00 10.00 9.00 8.00 7.00 6.00 5.00 4.00 3.00 2.00 1.00

Sigma BC-500 output 11 3

The two tests were graphed and a curve fit to the data with fairly good accuracy. We are confident that we can read the output of the BC-500 tachometer as a representation of the actual RPM of the spin caster to the nearest 10's, which should be good enough for our casting process. If it was necessary we could determine the actual RPM with higher resolution by using the formula ( RPM = 10*(8.09*voltage- 5.42) ) but in practice we will probably settle on the best RPM to spin the paraffin at from the display on the BC-500 and then in future runs just adjust the lab supply to the correct voltage that gave us that RPM.

RPM vs Voltage

RPM = 10*(8.088*voltage - 5.4151) R2 = 0.9999

RPM (x10)

BC500 reading vs. Voltage physical count vs. voltage

Linear (BC500 reading vs. Voltage)

0 0.00

Voltage
The procedure for altering the BC-500 is as follows:

STEP 1

STEP 2

STEP 3

You can now read the output of the computer directly as RPM..remember to multiply the number you read by 10!

4 digit Wheel Size Chart for models without Auto-Conversion
Baseline Models: BC400, BC500, BC700, BC800, BC1200, BC1200+ Topline Models: BC500, BC600, BC800, Targa, BC1200, BC1400, BC1600

2 1/2 x 1.1

Tire Size
16 x1.75x2 20x1.75x2 24x1 3/8A 24x1.75x2 26x1 26x1.5 26x1.6 26x1.75x2 26x1.9 26x1.95 26x2 26x2.1 26x2.125 26x1 3/8 26x1 3/8x1 1/2 26x3/4 47-305 47-406 37-540 47-507 23-571 40-559 44-559 47-559 50-559 52-559 54-559 56-559 57-559 37-590 37-584 20-571

WS mph 1296 1214

WS kmh 2086 1954
27x1 1/4 27x1 1/4 Fifty 28x1.5 28x1.75 28x1 1/2 28x1 3/8x1 5/x 2.0 700x18C 700x20C 700x23C 700x25C 700x28C 700x32C 700x35C 700x38C 700x40C 32-630 28-630 40-622 47-622 40-635 37-622 54-622 18-622 20-622 23-622 25-622 28-622 32-622 37-622 38-622 40-622

WS mph 1377 1381

WS kmh 2117 2224
Wheel size not shown above? Do the following: The correct wheel size measurement is the outer circumference of your tire in millimeters. (for MPH, divide total millimeters by 1.61!)

mm x 3.14

1. Measure overall height of the tire in inches; 2. Multiply by 25.4 to convert to mm. 3. Multiply by 3.14 to get the circumference of the wheel. km/h: 4. Divide by 1.61 for MPH WS = mm x 3.14 mph: WS = mm x 3.14 divided by 1.61 Questions? Call toll-free at: 888-744-6277