A dirty airplane will require more power to fly at the same speed as a clean one. In airplanes flight speed (or Mach number) is pre set (depending on a lot of variables like weight, altitude etc). The pilot or autopilot will apply the required power to maintain it. A dirty airplane is less efficient that a dirty one and will use more fuel. I agree that the effect may be negligible for a car, since the car is aerodynamically a lot less efficient and the speed is much lower, drag increase may be unnoticeable.

On the power, John is right. As the velocity doubles, the force quadruples as brewtoo says, but the power required is eight times larger (X8)

Jl