[ACE-OF-ACES]

Please note that an increase in HP would not necessarily increase the turn rate. The rate of turn depends on the radius which in turn influences the circumference. The radius of the turn depends largely on the wing loading and to a much lesser extent the lift coeff of the wing. Even though you might be getting more thrust the radius would be affected little and therefore the RATE of turn would still be the same as any tighter would result in a stall of the wing......what would happen is that you might have a little more excess power which would mean that you could climb a little better in the turn but the angular rate would still depend on the stall speed at any particular speed and g, which in turn would still govern the radius and the minimum (stall) speed v radius and be governed by the wing loading overall. In short it is multifactoral with each factor affecting every other factor.
regards,
Pike.

Interesting..

Looking at the forces, i.e.



To provide a vertical component of lift sufficient to hold altitude in a level turn, an increase in the angle of attack is required. Since the drag of the airfoil is directly proportional to its angle of attack, induced drag will increase as the lift is increased. This, in turn, causes a loss of airspeed in proportion to the angle of bank; a small angle of bank results in a small reduction in airspeed and a large angle of bank results in a large reduction in airspeed. Additional thrust (power) must be applied to pre-vent a reduction in airspeed in level turns; the required amount of additional thrust is proportional to the angle of bank. Therefore take two planes with all things being equal except for one having more power/thurst, the plane with more excess power/thrust would be able to offset more of the drag.. Right?