# Power to Weight Numbers

### Why Power to Weight Numbers?

Why did Andrew Coggin choose Power to Weight numbers? W/P numbers are an accepted metric for characterizing a cyclist’s training level,  and actually tell us something about their ability to ride flats and hills. It also provides an excellent training target and  particularly for climbing.

### Getting the Units Straight

Before proceeding, we should clarify exactly what we mean by Weight in this computation. Weight in metric units is a force  computed in Newtons, while body mass is computed in kgs. They are not the same. So am I dividing Watts by kgs or nwts.

This is another example of where Physics never got its act together in units. Kilograms are sometimes used to refer to force and sometimes to mass. Here, weight is actually referring to mass in kilograms and not in Newtons. The following is the conversion formula and this is what goes in the denominator:

m(kg) = m(lb) × 0.45359237

### What do P/W tells us about riding ability?

Sprinters tend to be larger than climbers. Why? More massive riders are capable of generating more raw, absolute power. On the flats, gravity is a minimal factor and the ability to generate larger amounts of power more than compensates for the slight increase in rolling resistance and the need to be effective in body shaping to minimize drag. Absolute Power P wins on flats and P/W is less important.

On hills, gravity becomes the critical factor and P/W important. Consider two cyclists of equal absolute power abilities P,  but with one weighting more than the other. Who has the easier time getting up the hill? Clearly the lighter one. The P/W of the cyclists would also suggest this. The heavier cyclist would have a lower ratio. Even if one cyclist had a higher P but weighed more, the increase weight can result in a smaller P/W and negate their power advantage.

So comparing cyclist’s P/W numbers suggest the higher P value wins on Flats and the higher P/W numbers wins on climbs.