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Maximum Speed
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Power = Force * Velocity
Drag ~ constant * Velocity^2
Force = mass * acceleration
At maximum speed there is acceleration so sum of forces = 0
Total Force = 0
(Power / Velocity) - (Constant * Velocity^2) = 0
Power / Velocity = Constant * Velocity^2
Power = Constant * Velocity^3
The constant value, k varies from aircraft to aircraft and is a measure of how aerodynamic the airframe is.
Lets take an example.
Supermarine Spitfire Mk IA
Power = 1030hp
Maximum Speed = 571 kph
1030 ^1/3 (cube root) / 571 = 0.01768
Now to find out how fast it goes if we have 1185hp(Mk VC)
(1185 ^ 1/3) / 0.01768 = 598kph
The actual figure for Spitfire Mk VC is 602kph, only slightly different from predicted result.
Spitfire Mk XIV
Power = 2050hp
maximum theoretical speed = 718kph
Actual maximum speed = 721kph.
Its a quick and easy way of calculating maximum speed for different powerplants.