I am designing a remote controlled airship. I will tune it so that the lift given by Archimedes' Principle will exactly balance the weight of all the structure. It will be propelled by brushless motors with propellers on them.
As far as I have understood, for some given velocity $v$ the drag force $D$ will be given by the air pressure, some shape dependent drag coefficient $C_D$, the surface $S$ that the airship offers to the wind, and finally the squared velocity $v^2$.
Now, to keep some speed, obviously the thrust $T$ must equal the drag $D$. Now, I need to get to some equation for the power that I need to offer such thrust at such speed, given that I am using non-ideal engines, with non-ideal propellers etc. From a barely theoretical point of view, I know that if I want to apply some force to an object that moves at some speed, I will be using some power $P \sim Fv$. Now, since the thrust is generated in some way that actually looks very dispersive, I would like to know if there exists some relationship between the power $P$, the velocity $v$ and the thrust $T$, given some specific motor and some specific propeller. In particular, what are the parameters that one needs to know to get to this relation?
On example, I can imagine that some efficiency parameter for the engine, its RPM rate, its voltage, the diameter of the propeller, the pitch of the propeller, these are all going to be relevant to the equation I am looking for, but I wouldn't know how to explicitly figure out that.
It such a relation doesn't exist in an obvious or general way, could you just give me an idea of the efficiency of the propulsion? I mean, I know that $P \geq Tv$, but how much bigger is it in general? Do these quantities share the same order of magnitude, or the dispersion is very big compared to the actual propulsion?
As you can understand, I am not an expert at all on the subject, so I would appreciate anything that could get me started.
Thank you again!