### Our Power Equation

The power produced while riding is made up of several components:

- Power produced to overcome the rolling resistance of forward motion.
- Power produced to overcome wind resistance.
- Power produced to overcome the pull of gravity (in the case of climbing hills).
- Power produced to accelerate from one speed to another.

The total power produced, P(total), is the sum of all four power components.

P(total) = P(rolling resistance) + P(wind) + P(gravity) + P(acceleration)

### P(rolling resistance)

The power required to overcome rolling resistance can be described by the formula **P = C _{rr} x N x v**, where

- P is the power required.
- C
_{rr}is the rolling resistance coefficient. We define this based on the type of bike (road, mtb, cross) you used. - N is the normal force of the bike and the athlete against gravity.
- v is the rider velocity.

### P(wind)

The power required to overcome wind resistance (drag) can be described by the formula **P = 0.5 x ****ρ x v ^{3} x C_{d} x A**, where

- P is the power required.
- ρ is the density of air.
- v is the rider velocity, relative to the wind.
- C
_{d }is the drag coefficient. - A is the the surface area of the rider facing the wind.

### P(gravity)

The power required to overcome the pull of gravity while riding up an incline can be described by the formula **P = m x g x sin(arctan(grade)) x v**, where

- P is the power required.
- m is the mass of the rider and the bicycle.
- g is the gravitational constant, 9.8.
- grade is the slope of the hill.

### P(acceleration)

**P = m x a x v**, where

- P is the power required.
- m is the mass of the rider and the bicycle.
- a is the acceleration between your starting speed and your ending speed within the sampling window.

### Strava Calculated Power vs. Power Meter

We have seen that in most cases our watts number are very close to the numbers provided by a Powertap or SRM. Note that Strava calculated watts are not the watts produced at the crank but the watts produced by the rider-bike system, this will create a slight difference between the powermeter data and the Strava watts. Lack of good chain lubrication and low tire pressure can rob you of the watts you see on your Powertap or SRM. Other reasons watts can be inconsistent include strong winds and bad elevation data reported by the Garmin. Our calculations are most accurate when climbing given accurate rider and bike weight.

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