Will this simple equation (pic attached) produce a rough estimate of the top speed of a prop driven aircraft? Calculating the approximate top speed of a vehicle is straightforward.

$v = \sqrt[3]{\frac{2P}{c \cdot D \cdot A}}$

where


v = velocity of the vehicle
P = power of the engine
c = coefficient of friction
D = density of the air
A = the area of the front of the vehicle


Using this equation you can get a rough idea of the top speed of a car if you know its engine power, the body’s coefficient of friction and the area of its front profile.

Is it possible to use this same equation to determine an approximate top speed for subsonic aircraft?  No doubt engineers at Boeing have to account for 100 additional variables, but is it good enough to produce a decent approximation for props that fly less than 500mph?

Also does the picture I attached below show the correct way to account for variables $A$ and $c$?



If $c$ represents the friction along the entire surface of the aircraft does this suggest that all things being equal an aircraft with twice the surface area would have twice the coefficient of friction?  Or am I looking at $c$ incorrectly?
The short answer is no, that will not give you a very accurate estimate. As other mentioned, your equation does not include lift. Given some basic engine specs and aerodynamic properties, the top speed for aircraft can be estimated by determining the intersection of required power and available power. Available power is based on selected engines and propellers, and required power is based on the wing loading, lift coefficient, and other parameters that describe the amount of power required to sustain minimum lift.