I could go through calculations on that (working to figure out the drag on the blades at, say, 0.85 M, and seeing if 1500 HP can't still spin it). That seems like a lot of work, so I'll ponder if there is a simpler way to show it.
Put your pen down for a minute Brooke. I think you are confusing drag on the plane (=force pushing the
plane backwards) and drag on the blade. I am not an aero-engineer, but lets try to think this over together. Lets assume that your engine has enough HP to keep the constant RPM regardless.
The usual description of lift and drag is with respect to the bulk airflow, so forces directed along the flow are drag and those perpendicular to it are lift. Now look at the flow from the point of view of the blade. It has airflow coming at it due to rotation at speed w*r (w=rotation frequency, r=radius of prop element) and another component of speed due to the travel of the plane through the air: v.
This gives an angle "b" to the total flow:
tan(b)=v/(w*r)
In order to have a positive angle of attack, the blade has to be pitched at an angle greater than "b" (pitch=0 is idle, pitch=90 is feathered). As you can see, the angle depends on "r" and this is why props have a twist to them, to keep the angle of attack constant
at a certain optimized speed v! (w is constant).
Now lets look at the blade as a wing. It has lift Lb and drag Db. I use the "b" in Lb and Db to emphasize that we are looking through the point of view of the blade. Lb and Db are relative to the airflow on the blade. I'm sure you can convince yourself that this flow is tilted at an angle 90-b from the direction of travel of the plane. Therefore, only part of Lb contributes to pulling the plane forward and part makes it harder to rotate the blade. Same for Db, some of it slows the plane down and some resists the rotation of the blade.
The thrust for the
planeis:
T=Lb * cos(b)
and the "anti-thrust" or "prop drag" that tries to slow down the
plane is:
D = Db * sin(b)
You can already see that when the plane's speed "v" increase, "b" increase and therefore T goes down, while D goes up! The lift and drag on a wing have very similar expressions except for a different coefficient for lift and drag, which are a function of the angle of attack. If the lift coefficient is CL, the drag coefficient CD scales like CL^2. Therefore we get approximately:
D/T = CD/CL * v/(w*r) ~ CL * v/(w*r)
You can see that if "v" is getting larger than the blade rotation velocity w*r, you tend to produce more prop drag than thrust. At some point the net prop drag will be larger than the thrust. From here you can also see that increasing the the RPM (w) is generally more efficient than increasing the angle of attack (increasing CL), as long as you do not go sonic with the blade.
The complete picture is worse. We did not include form drag on the blade which will increase hugely when it goes supersonic. Since this operates in the same direction as Db (which we used as induced drag only) it will also have a component in the direction opposite of the plane travel. Also, the blade has a twist, i.e. a variable pitch angle as a function of length, which as we mention is optimized for a given RPM ("w") and plane velocity ("v"). If you increase "v" much beyond the optimized conditions, parts of the blade can get into a negative angle of attack and produce even more effective prop drag. Think of an infinite "v" (effectively v>>w*r) - the blade does not rotate and is pitched entirely into the airflow as if it was feathered. Part of the blade produce lift that tries to rotate it one way and the other part produce opposite lift, and both parts produce induced drag that slows the plane down.
