calculating power

Recently I’ve been thinking about getting a power meter for training. If you know your optimum power output, you can use a power meter to control your efforts on a climb.

However, even without a power meter, you can calculate your average power output over a given time.

Notes:
1. These calculations ignore all external effects and inefficiencies such as the wind, road surface effects, friction in the bike drive chain, etc.
2. The gear used for the climb affects the efficiency of the rider’s own power output. It does not affect the power that must be transmitted through the wheels to make the climb.

The equation for power is:

power = work / time (equation 1)

So to calculate power we must first calculate the work done:

work = force x distance (equation 2)

The distance is the vertical height climbed (in metres).
The force is equal to the force of gravity, which the climber overcomes.

force = mass x gravity (equation 3)

Mass is the weight of the rider plus bike (in kg).
Gravity (or more accurately, the acceleration due to gravity) is 10 metres/second/second.

So putting these into equation 3, and then that into equation 2 we get:

work = weight x 10 x height (equation 4)

And putting this into equation 1 gives us:

power = (weight x 10 x height) / time (equation 5)

This equation gives the average power output (watts) required for a given weight (kg) to climb a given height (metres) in a given time (seconds).

Examples:

Yesterday’s climb on Komura Pass.

My weight: approx 77kg. My bike: approx 10kg. Komura Pass 225m. My time: 10 mins 41 secs (641 secs):

power = ((77+10) x 10 × 225) / 641

= 305.4 watts (the average power needed for the climb)

My best time on Yahiko.

My weight: approx 77kg. My bike: approx 10kg. Yahiko steep side 420m. My time: 19 mins 02 secs (1142 secs):

power = ((77+10) x 10 × 410) / 1142

= 312.3 watts (the average power needed for the climb)

Fight the power!!!