Is propeller pitch more related to RPM than aircraft speed?

[Jarfi]

I'm reading about propellers and trying to get some of the basics, and some things are confusing to me.

Namely, a quadcopter has a 12x6 prop, with a 6-pitch. That means in every rotation it should move 6 inches forward(up), but it doesn't do that at all since it's in hover mode. Wouldn't that mean that pitch is more related to RPM and Torque with forward acceleration simply being a by-product? And wouldn't that mean that it should have a pitch of 0 if it would theoretically never accelerate up?

Also I've been reading that Constant-speed propellers are the most efficient, which means the RPM stays exactly the same over all aircraft speeds. What is the reason for this?

Is it A: petrol engines run most efficiently at certain RPM(so CS-props wouldn't be most efficient for electric motors)

or B: the power input turned to torque/speed reaches a maximum at some sort of peak-RPM, given that the pitch can be adjusted.Also if anybody has any general tutorials on this sort of stuff it'd be nice. And is there a calculator out there where you can put in the needed speed, torque, and get the required power usage and propeller pitch and diameter from that number?

Thanks for reading,

-Jarfi.

 

[FactChecker]

Calculate pitch as though the propeller is cutting through a stationary solid, like a screw. Velocity and RPM do not enter into that calculation. The most efficient situation is to run the engine at it's most efficient RPM. Then the propeller blades can be changed to the pitch that will work best at that speed and RPM. I think that is the pitch that gives the highest lift/drag ratio for the blade. That depends on velocity and the constant RPM.