Hi Keith,
Thanks for your lucid explanations. Would you please point out where my logic is failing here.
Ignoring form drag for simplicity:
Consider an aircraft performing continuous rate 1 turns holding over a beacon flying at a speed of V. The wing develops lift and consequently induced drag ID.
Therefore, induced drag power = ID*V.
For sustained flight the thrust power from the propeller must match the induced drag power, therefore THP = ID*V
Consider the model aircraft in a vertical hover. The propeller is now a rotary wing. It is producing lift in a similar way to the aircraft wing, by moving through the air with some velocity Vp and consequently generating induced drag IDp.
The power required to spin the rotary wing (the propeller in this case) = IDp*Vp.
They look very similar to me.