It is said that piston engines have constant power output, and thus their thrust is inverse to speed (e.g. here), while turbines have relatively constant thrust. I'm looking for an intuitive explanation why is this the case.
I understand that from the energy conservation point of view it makes sense: kinetic energy is proportional to velocity squared, so it is easier to accelerate air from 0 to 100 m/s than from 100 to 200 m/s.
I'd like to better understand what is the direct cause of that. Why can't we simply increase the propeller speed with increasing air speed using a higher gear ratio? It seems to me that if the air comes at us with twice the speed as it did, we should be able to increase the speed of the propeller to match the speed increase. Then, it seems that the propeller blades should interact with the air in the same manner as before, as relative speeds remain the same: the air is twice faster but so is the blade, and it pushes the air with twice the speed. Why is the (physical) work to be done greater?
I'm not sure whether this is the right place to ask this question. Perhaps physics.stackexchange.com would be better?