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[DPRG] Speedometer

Subject: [DPRG] Speedometer
From: Sluggy! sluggy9912 at swbell.net
Date: Mon Jul 10 01:40:07 CDT 2006

--- Balter Wiggin <manny132 at hotmail.com> wrote:
> What i am planning is a 
> combination RPM counter by means of a magnetic
> encoder, and a speedometer, 
> probably fashioned through some modification of a
> tachometer. The purpose of 
> this is to successfully measure the distance and
> average speed of a bicycle 
> piloted around White Rock Lake.

With the one sensor, you can measure distance
travelled, as you established later in your message.
You get one "encoder tick" for every wheel rotation.
If your wheels is 26", then each encoder tick will
represent 81.6816 (2pi x radius (2x3.1416) x 13)
However, by precisely timing the interval between
ticks, you can also determine the speed.

Let's work the math out in reverse. If you have a 26in
wheel and you're going 1 mph, that would work out to
be 63,360 inches per hour (5280 feet times 12 inches
per foot times 1). One wheel rotation means you have
travelled a distance equal to the circumference of the
wheel. Divide that by the wheel circumference 81.6816
and that would be 775.695 ticks per hour. Counting
ticks per hour is not a very practical speedometer, so
divide that number by 3600 (the number of seconds in
an hour) and you get a much more manageable .215 ticks
per second. Take the reciprocal of that (1 second
divided by .215 ticks per second) and we're getting a
really usable number, 4.651 seconds, or 4651
milliseconds per tick for 1 mph.

Armed with this number, we can now measure the number
of milliseconds per wheel rotation tick, get the
reciprocal and multiply by 4651 and you get miles per
hour directly. For example, if it's 1500 milliseconds
between ticks (1/1500) x 4651 = 3.1 mph. If it's 561
milliseconds between ticks (1/561) x 4651 = 8.29 mph.
For the entertainment value, if it's 4 minutes between
ticks 1/(4x60,000) x 4651 = 0.0193 mph :)

In practice, a 26in wheel is almost never exactly
81.6816 inches in circumference. Even as the tire
wears, the circumference will shrink. In the
speedometer application, small errors in the
circumference measurement won't make much difference,
however, if the diameter is off by 1/10 inch, the
circumference calculation is off by nearly 1/2 inch.
Two rotations is off by about an inch. 30,000
rotations is off by about 1/4 mile. 

To correct for that, the most practical approach is
probably to directly measure the circumference of the
wheel rather than calculating it. Use a sewing tape to
measure the circumference of the wheel. This will be
much closer to the real number needed for an accurate
calculation of speed.

Another approach is to passively roll the wheel a
practical number of rotations, 10 for example, on a
smooth surface and measure the distance travelled with
a 100' tape, then divide by the number of rotations.

My little Taiwanese bicycle speedometer is calibrated
by entering the centimeters circumference of the
wheel. It included a chart showing the figure to use
for various brands of tire :)



tibi habere mamma. Ego malle mamma ab femina.

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