**Pedal Force**
Posted on

July 31, 2012by

sensiblecycling
Today’s post is going to form the basis for several future articles. We are going to take a look at what kind of forces a rider is likely to exert on the cranks. This has implications across a wide range of topics – from weight training to frame flexion.

We can calculate the force exerted based on a given Power, Cadence and Crank Length. So bring on the physics lesson:

“Work” is measured in Watts, and “Power” (which we often refer to by number of “Watts”) is technically Watts per second. Since Work = Force * Distance, we can substitute Power for Work where we are talking about a one-second duration

(Power = Force * Distance) -> (Force = Power / Distance)

Now distance is equal to Speed * Time. And since Time = 1, then in this case, Distance = Speed (of the pedal). Jumping ahead a bit… Speed = 2 * Pi * Crank Length * Cadence / 60. So if we substitute that back into our original formula:

Force = Power / (2 * Pi * Crank Length * Cadence / 60)

Or… Force = Power * 30 / (Pi * Crank Length * Cadence)

This gives us the average force acting on the pedal for a given power output, cadence and crank length. But note the fact that this is not the

*peak *force. The general consensus within the community (Footnote 1) is that for most riders, peak force (i.e. when the cranks are horizontal) is roughly double the average force. So in the examples below I’ll be calculating average force and doubling it to give peak force. Also, I’ll be converting Force in Newtons to an equivalent Force in kg (using G = 9.8)

To give you an idea of some various situations, I’m going to assume 172.5mm Cranks, a cadence of 85 and a 70kg rider. Why am I mentioning the weight? Well, based on average power/weight ratios, we’re going to convert the rider’s weight into a power figure depending on his level (Footnote 2)

A Grade Rider

Time Trial – 348 Watts:

**46kg**
Pushing Hard (5min) – 416 Watts:

**55kg**
Full Bore Sprint – 1378 Watts:

**183kg**
E Grade Rider

Time Trial – 193 Watts:

**26kg**
Pushing Hard (5min) – 235 Watts:

**31kg**
Full Bore Sprint – 902 Watts:

**120kg**
**Things to Note:**
Even when you’re riding hard over a short-ish distance, the force required per pedal stroke is quite low. In comparison to the maximum force your muscles are

*capable *of producing, you’re not asking very much. This has a bearing on the efficacy of weight training for cyclists.

The difference between a full bore sprint and “pushing hard” is massive. When talking about how “stiff” a bicycle is, it’s worth taking this into consideration

The above figures are not affected by gear ratio or whether it’s uphill or downhill. The only important factors are Power and Cadence.