Re: Part I (repost from below, but broad topic and (archive)

........The M5 is putting down 394hp*(5250/6700)*3.15 = 972ft-lbs of torque to the road at 175mph, or almost 19% more than the M3! (so with the same drag it should be able to go faster).

If we assume that the M5 hits is aerodynamic top speed in 5th gear @ 7000rpm (redline), the car is travelling 182mph, and would thus require roughly 15% more torque to overcome the aerodynamic drag (drag goes with the square of the speed), so, assuming the engine loses <4% of its torque from 6700 to 7000rpm (an ok guess), the M5 top speed is roughly 182mph.

The answer is close, but the calculation and the reasoning are wrong. The rear-tire size of an E39 M5 is 275/35ZR18. The redline speed in 5th gear is only ~169 MPH. The top speed is achieved in 6th gear instead at ~6300 RPM.

If you notice, its probably not coincidence that these educated guesses for top speed on the BMW's work out to redline in 5th gear for both cars........

Incorrect, as mentioned above.

So, in summary
Z06 170-175mph top speed
E46M3 168-173mph top speed
E39M5 178-182mph top speed

Your answer is close this time, although there were errors in the process. At least, you NO longer insist on 750 lb of aerodynamic drag at ~100 MPH........ :-) As far as the top speed is concerned, it is simpler to use the peak HP and assume that the gear ratios are by-and-large optimized. Because the top speed is mainly limited by aerodynamic drag, the total drag, fd, canbe approximated by the expression,

fd= b* v**2

where b is a vehicle-dependent drag coefficient and v**2 is the square of the velocity.

At top speed, vt, the accelerating force, f, of the vehicle is the same as the total drag and hence,

RWHP= f* v= fd* vt= b* vt**3

or,

vt= cube-root of (RWHP/ b)

where [RWHP= (1- Drivetrain loss)* HP]. While b, drivetrain loss, gear ratios, and torque-band shapes vary among different vehicles and test conditions, the cube-root dependence allows the approximation of [(1- Drivetrain loss)/ b] as a constant for practical purposes, since the variation is compressed by the cube-root operation. Putting it all together,

vt~ cube-root of (15000* HP)= 10* cube-root of (15* HP)

The above expression would give, for example,

~150 MPH for 225 HP
~160 MPH for 273 HP
~170 MPH for 328 HP
~180 MPH for 389 HP
~190 MPH for 457 HP
~200 MPH for 533 HP

or,

~153 MPH for an E36 M3
~155 MPH for an S4
~165 MPH for a 996 C2
~169 MPH for a Mustang Cobra
~171 MPH for an E46 M3
~174 MPH for a Corvette C5
~180 MPH for a Corvette Z06 or a Mustang Cobra R
~182 MPH for a E39 M5
~184 MPH for a 996 TT
~192 MPH for a Viper GTS

These numbers are consistent with the published test results, within the variations of total drag among the different vehicles and test conditions. (Part of the results here has been posted elsewhere by the author under a different screenname.)

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