Originally Posted by signes
A buddy of mine shared this with me to see what would theoretically be possible.
Just worked the numbers out on this and surprisingly, this turns out to be quite possible for a stock E92 M3!
Assuming a frontal area of 22.5 sqft, and drag coefficient of .31; you would need about 414 HP to push 204 mph. FYI, I even used a slightly greater frontal area (actual 21.3) to make the numbers less optimistic, and it worked out to 414 HP – the exact power BMW specifies for the car !!
HP = 0.000007 x Cd x FA x (speed)^3
FA = frontal area in sq ft.
Cd = coefficient of drag = 0.31
Speed = drag limited top speed
Almost! You simply assumed (or missed) that the formula is power at the wheels, not power at the crank. All in metric we have:
Vmax = ( 2 x P / (rho x Cd x A) )^1/3
P is power in watts
rho is air density in kg/m^3
A is frontal area in m^2
Assuming at least a 15% power loss in the drive train and about 10% loss just due to losses in the rubber/steel belts in the tires. Tire losses are absolutely in this range, nearly negligible at speeds at or below 60 mph but then building steadily and becoming quite significant at high speeds. So with the values below:
A = 2.17 m^2
Cd = .31
rho = 1.2 kg/m^3
P(wheels) = .75 x 414 hp = 231539 W
Vmax = 83.1 m/s = 186 mph
Now adding about 4% for the speedo error you will find the car to top out at about 193 mph indicated (assuming the 186 actual calculation was accurate in the 1st place).