cerb wrote:..conversely, thanks for coming with some actual numbers/science!

I like the chart March83 posted from Alex's photobucket. Who went to the effort of working all of this out?

I did.

It only requires one to solve this equation:

it's not as bad as it looks, although it's much trickier when dealing with dynamic scenarios involving accelerations*. Calculating power from speed is relatively easy (provided you have all the relevant inputs).

Calculating speed from power is somewhat harder as it requires having all the relevant inputs as well as solving a cubic equation and there is no a closed form solution (e.g. Cardano's method) that works for all scenarios. So I use the closed form solution when it works and revert to Newton's method when it doesn't (typically when assessing steep negative gradients).

* I've solved those as well using a method known as

*forward integration*, e.g. when considering the impact of wheel rim mass on acceleration performance when the old weight v aero argument comes up.