(THIS IS "THEORY". FIND "APPLICATION" IN THE POST OF MAY 2, 2012)
So, here it goes:
Introduction
Sometimes, one has to know how fast a wheel or shaft or motor is turning. The measuring device for rotational speed is the tachometer. Tachometers are quite expensive and not easy to find. However, for our purposes it is cheap and easy to make a tachometer using a bicycle speedometer (the so-called cycle computer). The suitable cycle computer should let you enter the wheel circumference in millimeters; almost all of the commercially available do. After obtaining the suitable cycle computer these are the steps to follow:
(1) Mount the cycle computer magnet to your spinning wheel, engine shaft or whatever.
(2) Mount the cycle computer speed sensor near the path of the spinning magnet
(not more than 1/2 inch away)
(not more than 1/2 inch away)
(3) Your set-up should look like:
Theory and numbers
A cycle computer calculates the speed your bicycle is traveling by sensing how fast the wheels of the bike are spinning. It senses wheel speed through a magnetic switch that is mounted on the bicycle frame or fork, near the path of the spinning wheel. The cycle computer magnet is attached to a spoke of the wheel and when it goes by the magnetic switch, the switch closes for a moment, and this is recorded by the cycle computer. By timing how much time goes by between switch closings, it can compute how fast the wheel is spinning. When you first install the cycle computer for a bicycle, you have to enter the circumference of the wheel in millimeters. With this information, it can compute how fast the bicycle runs in <mph> or in <km per hour>. One can trick the cycle computer to report speed in rpm. For this purpose,
(i) if the cycle computer is reporting speed in <km per hour> enter 167 mm for the wheel circumference.
(ii) if the cycle computer is reporting speed in <mph> enter 268 mm for the wheel circumference.
Here is the math behind this trick:
For <km per hour>
The bike display is showing us:
<km per hour> = rpm * 60min/hr * circumference(m) * 0.001m/km
i.e.: if we had a 1m circumference wheel turning 1 rpm, it would turn 60 rotations per hour. 60 rotations is a distance of 60 * circumference or 60m. 60 meters is 0.06km, which means the readout would show 0.06 <km per hour>.
To get a <km per hour> readout of 1 for 100 rpm:
1 = 100 * 60min/hr * circumference * 0.001m/km
circumference should be 1 / (100 * 60 * 0.001) or 0.1667m or 166.7mm
For <mph>
Remember that 1<mph> = 1.61 * <km per hour>
In the <mph> case therefore, the bike display is showing us:
<mph> = [rpm * 60min/hr * circumference(m) * 0.001m/km]/1.61
i.e.: if we had a 1m circumference wheel turning 1 rpm, it would turn 60 rotations per hour. 60 rotations is a distance of 60 * circumference or 60m. 60 meters is 0.06km, which means the readout would show 0.06/1.61 <mph>.
To get a <mph> readout of 1 for 100 rpm:
1 = [100 * 60min/hr * circumference * 0.001m/km]/1.61
circumference should be 1.61/ (100 * 60 * 0.001) or 0.2683m or 268.3mm
Notes
== Some cycle computers might not be able to accept a number below 200mm for the circumference. In this case and if available, choose the <mph> reporting and enter 268mm for the circumference.
== Some cycle computers also record cadence, which is how fast one is pedaling; this number is rpm and in this case the cycle computer is also a tachometer. However, usually this reading has a maximum of 199 rpm, which is way faster than a person can pedal anyway. This mode could work for tachometer applications to measure really slow speeds.
== A cycle computer automatically records how much time the device has been spinning. This could be useful if one wants (for example) change the oil on an engine every -say- 100 hours of operation.
== A cycle computer also records maximum and average speeds, which could be useful in some situations.
Set up and Fire
Josie used his own cycle computer (a CATEYE ASTRALE CC-CD 100) to display in photos his set up. In his case, the cycle computer is set up to read speed in mph and therefore it is programmed for a wheel circumference of 268mm as per the photo.
After that, as soon as his device started spinning, his cycle computer red the speed. The big numbers are the speed in hundred of rpm. In the following picture, reading is 2810 rpm. His device has been running for 0 hours, 13 minutes, 21 seconds.
Market smart
Cycle computers can be acceptably cheap or extremely expensive. However, one can find a cycle computer meeting his/her needs at Wallmart, at Praktiker etc. depending on which part of the globe he/she resides (or even at e-bay). I got mine from the Lidl Discount Super Market in Athens, GREECE, for just about 6 EUROs (!). It is a CRIVIT -SPORTS- Z31093 UNIVERSAL CYCLE COMPUTER marketed exclusively (as it seems) at Lidl. I am attaching its manual in English, in a two pages pdf file here (it is ~3MB of size). Most probably it would be useful to get a better idea of what has been posted and some hints on how to reprogram your own cycle computer in case you are not able to discover the operation notes.
Further reading (other links for similar applications)
Several have published similar applications. Check, for example, with the following:
(a)
(b)
(c)
(d)
(e)
(f)
Petropoulos, N.P., "Raglan Little John Mk.2 Bench Lathe - Post 2 - Tachometer (theory)", 2012; add URL; add access date.
Any citation will be much appreciated.
