# Plausibility of the distance estimation in a cycle ergometer gym exercise

A friend of mine pedaled for an hour on a cycle ergometer, a stationary bicycle in a gym.

At the end of the ride the cycle computer reported a distance of $40\:\mathrm{km}$ and an average power of $250\:\mathrm{W}$.

I would like to know whether the reported data are meaningful or comparable with a real ride on road.

The average power can be reasonable: see for example a ride of a professional cyclist with an average power of $\approx200\:\mathrm{W}$.

I have some doubts about the distance: I have no idea how the cycle ergometer computes it but I would like to do anyway a meaningfulness check.

The problem is that I can think only to a very simple model: the mean speed is $v=40\:\mathrm{\frac{km}{h}}$ and the energy she spent is $E=1\:\mathrm{h} \times 250\:\mathrm{W}=0.25\:\mathrm{kWh}$; if I assume that, in an hypothetical road ride equivalent to her gym exercise, all the energy she spent is converted into kinetic energy $E=\frac{1}{2}mv^2$ then I get for the total mass (her mass plus the bicycle mass) $m=\frac{2E}{v^2}=\frac{0.5\:\mathrm{kWh}}{1600\:\mathrm{\frac{km^2}{h^2}}}=14600\:\mathrm{kg}$ that is obviously wrong because it is too high.

If my model was good enough then I would state that the distance is not plausible and so perhaps the cycle ergometer need to be calibrated or its algorithm is not working well.

But I suspect that my model is not a good one and so what is a more adequate model to help to assess the plausibility of the reported distance?