Calculating Your Wheel Circumference
In last weekend’s trial ride around the Steelman’s bike course, my cyclecomputer was acting up a little. It’s been doing this intermittently since I went for that ride in France and almost drowned in the rain - although it’s waterproof, I don’t think they reckoned on it ever getting that wet! Basically what seems to be happening is that I’m getting crosstalk between the wheel sensor and the cadence sensor, leading to some pretty strange numbers.
So earlier in the week, I picked up a replacement - exactly the same model as before, a Topeak Comp 140. It’s a great little computer, and simplicity in itself to operate - there’s only one button. Press & hold to reset the trip, and press momentarily to scroll through the display options - current speed & cadence, maximums, averages, trip time, etc. The one I tend to keep it set on is current speed, current RPM and trip time - that last one’s the critical feature for me, as it tells me when to drink (every 10 minutes) and when to eat (300 cals / hr - the interval depends on what I’m eating).
So anyway, I’m setting up the new computer this morning. The way these things all seem to work is you set the wheel + tyre circumference, and from that it works out the speed and distance information every time a magnet on one of the spokes passes a sensor on the forks.
The problem was though, the “common wheel & tyre sizes” table didn’t include my 700 x 23c set up. There was 700 x 20c (2092mm), and 700 x 25c (2125mm), but nothing in between. Now I could just have measured the circumference, by marking the tyre and a point on the ground, and rolling the bike forward one revolution of the wheel before measuring how far that is along the ground.
But I’m an Engineer, so that’s just far too simple. And would involve finding some chalk or whatever to mark the tyre and the road. And an accurate tape measure - with no-one around to hold the other end that’s a tall order.
So I figured out how to calculate the circumference of the tyre. You do it like this:
C = 2 x PI x R
Where C is the circumference, and R the radius.
For a 700 x 25c tyre, we can calculate the circumference (let’s call it C23c) from the unknown radius of a 23c tyre (let’s call it R23c) like this:
C = 2124= 2 x PI x (R23c + 2)
2124 = (2 x PI x R23c) + (2 x 2 x PI) = (2 x PI x R23c) +4 x PI
2124 - (4 x PI) = 2 x PI x R23c = The Unknown Circumference, C23c
C23c = 2 x PI x R23c = 2111.4
So the basic formula for calculating an unknown tyre circumference is:
Desired But Unknown C = Known C - (2 x PI x Difference in radii)
And who said that maths wasn’t fun!