How does increasing the horsepower/torque to a piston engine in an airplane increase top speed if the propeller size and rpm stay the same?
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Increasing the prop pitch is one way for sure. Increased power can help the engine tackle more potent prop angles and throw more air back per revolution.
In an aircraft with a constant speed prop you increase thrust by taking bigger “bites” of air by changing the angle of the blades relative to the airflow. So when you increase the engine power the blades take bigger bites which keeps the RPM the same since the bigger bites increase drag on the prop.
By changing propeller pitch. On many aircraft blade angle can be manipulated similarly to the throttle in order to affect the thrust produced and the load on the engine.
Some prop planes have variable pitch propellers. That means the angle of each propeller blade can be adjusted to be able to move more or less air past them.
This works because the shape of a propeller is an airfoil, just like the wing of the plane. The more aggressive the pitch (angle of attack) the propeller has the more air it can move using the same amount of power. Eventually though, as the angle of attack reaches its limit, the airfoil will enter a stall and stop working.
Different conditions such as temperature, air density, wind speed, air speed, fuel efficiency, etc can influence why you might want to change the pitch of your prop.
All this is to say, combining variable pitch propellers with different output power options can enable more control over the aircraft for certain flying conditions.
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