Bike Speed and Foot Speed
As cyclists, we always know our current road speed. But have you ever wondered at how fast your feet are pedaling to move you at that speed? It is a simple calculation when you know two things: crankarm length and cadence.
Pedaling Motion and Geometry
Pedaling motion is straightforward. You may be riding for several hours, but in that time, your feet have gone around in circles, pretty much ending where you started. In that time, your feet move around a pedal circle that is determined by your crankarm length.
Cadence is a measurement you can get from your speedometer. It tells you how many complete revolutions you complete in a minute.
Crankarms are manufactured in standard, long, and short lengths. Why the different lengths is another blog. But for a standard roadbike, a crankarm of 172.5 mm or 6.79 inches is in the middle of the ranges. As far as cadences, recreational riders are urged to pedal in the 60 to 80 rpm range, while Elite cyclists will reach 100 rpm and above.
Computing pedal speed
You already have a measure of pedal speed from your current cadence, but let’s use that to get the pedal speed as it moves around the pedal circle.
From simple geometry, a circle of radius r has a circumference of (2π r). For a crankarm of 6.79 inches, that means your feet travel 42.68 inches or 3.557 ft per pedal revolution. Therefore, the distance covered in a minute is that number multiplied by your cadence. The only thing left is to convert the feet to miles and the time interval to hours to get our foot speed in mph.
Foot Pedal Speed as a Function of Cadence
We can combine all of these numbers into a formula expressing foot speed as a function of cadence, which produces the graph below where we have plotted if for cadences between 0 and 100 rpm.
FootSpeed(cadence) = (60 * 3.557/5280) * Cadence =
FootSpeed(cadence) = 0.0404 * Cadence
Recreational and Elite Cyclists Foot Speeds
Recreational cyclists have cadences nominally in the 60 – 80 rpm range, while Elite Cyclists are in the range of 80 to 120 rpm. From our chart, that translates into foot speeds of 2.43 – 3.23 mph for recreational rides, and 3.23 – 4.85 mph. for Elite.
Pedal Speed vs. Road Speed
Think about it. Pedaling with a foot speed greater than 4 mph is hard even for elite cyclists. Yet, your cycle is easily moving five times that fast. How a cycle works its magic to accomplish this is something we will cover in another blog.