# Power curve calculation

I have a power curve relating to a turbo trainer I use on my bike.

I save my sessions on a website called strava using speed, cadence, heart rate and time.

Using the power curve I've been given I wish to calculate the gradient of the curve, providing me with a power calculation for a given speed.

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I've got a rough table of figures that can be used to plot a graph, but I can't remember the maths I need to work out the formula.

$$\begin{array}{c|r} \text{speed} & \text{power} \\ \hline 5 & 25 \\ 9 & 50 \\ 12.5 & 100 \\ 17 & 200 \\ 20.5 & 300 \\ 23 & 400 \\ 25 & 500 \\ 27 & 600 \\ \end{array}$$

Thanks for any advice you can give me.. even better if you can provide the completed formula.

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The power curve seems to be approximately of the form $P=cv^{2}$, where $P$ is the power, $v$ is the speed and $c$ is a constant that we need to find. To reduce the error I computed the following mean based on your figures $$\begin{equation*} c=\sqrt[8]{\frac{25}{5^{2}}\frac{50}{9^{2}}\frac{100}{12.5^{2}}\frac{200}{ 17^{2}}\frac{300}{20.5^{2}}\frac{400}{23^{2}}\frac{500}{25^{2}}\frac{600}{ 27^{2}}}\approx 0.75. \end{equation*}$$

So the approximate equation of the form $P=cv^{2}$ is $$\begin{equation*} P\approx 0.75v^{2}\qquad \text{(}P\text{ in Watt and }v\text{ in mph),} \end{equation*}$$

or $$\begin{equation*} v\approx 1.16\sqrt{P}. \end{equation*}$$

This approximation gives

$$\begin{eqnarray*} v(600) &\approx &28.4 \\ v(300) &\approx &20.1 \\ v(100) &\approx &11.6. \end{eqnarray*}$$

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excellent. I'd tried plotting against p=cv^2 and couldn't get beyond that in terms of a relationship. Thank you. –  Simon Forster Sep 3 '12 at 15:31
@SimonForster You are welcome. –  Américo Tavares Sep 3 '12 at 15:33