The reasoning is fairly simple. Given that there is a limited motor run duration (5 or 10 seconds), the height achieved will be roughly linearly proportional to the power.

No.

Anything to add Danberry?

My reasoning is this: the potential energy gained (i.e. work done) in reaching a height h is m x g x h, where m is the mass and g the gravitational constant. The rate at which this work is done is the power, and as the work has to be done in a fixed time interval (5 or 10 seconds) ) the height achieved will be linearly dependent upon power (increases in drag etc aside). Stated another way, a higher power means a higher rate of doing work and so, over a fixed time interval, a higher amount of work done (potential energy) and hence greater height.

Of course, drag cannot be neglected and so the model cannot reach that theoretical height and, since the work done against drag increases as the square of the velocity, the higher climb rate will result in proportionally higher energy dissipation. Consequently, the height climbed will fall somewhat below the linear proportionality upon power, but will still be greater than the square root dependence of the sink rate. This is verified by the observed climb heights and total durations of current models: both increase with increased power (other things being equal, such as the same airframe).

Paul.