Q:

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.
$\qquad\qquad\qquad$
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.

A:

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

