I thought about the comments about the dreaded thirst of gas turbines. I looked at the power increase required to increase the speed of a Mooney 201. Let's look at increasing the speed by 50%, to 300mph. Drag increases by the square of the velocity, horsepower is proportional to the product of the speed and the force. Hence to power a 50% increase in speed I must increase the power of the engine by 1.5 raised to the power of 3, around 3.3 times. The Mooney would need to increase its power from 200hp to 660hp. Plus whatever drag would increase by owing to increasing main spar strength and up isconsequent weight. So apart from finding a 660hp piston engine we would probably need to go to a gas turbine. If it has the same thermal efficiency as the piston engine we are going to burn 3.3 times as much fuel. For the same range we are going to require increased weight for the extra fuel which will incur more drag etc etc. The exercise looks something like a TBM 800, a Mooney designed aircraft.
Speed alone I creases required horse power by dramatic amounts, probably why turbines seem to be very thirsty.