When you increase Nr speed, you gain more lift from the rotor system at any given collective pitch setting.
I get this part anyway - the rest??
How about as RPM goes up, torque goes down if power remains constant, or put another way, if RPM goes up and torque remains constant, power goes up?
So RPM goes up, you get more lift for the same drag and more power for the same torque. Now about that "using up the engine horsepower available in excess of what can be applied to the xmsn/drive train"...