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

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Posted by marc b on December 24, 2000 at 18:43:27:

Ok, revised numbers based on 175mph top speed of Z06. Based on similar drag numbers of the M3 and Z06, the top speeds should be very similar. The M3 has roughly 10% less power, corresponding to roughly 8-9mph difference in top speed, but having narrower tires than the steamrollers on the Z06 reduces tire losses, gaining back a little. Also, you have to look at the gearing, since cars have an integral number of gears, you may not be at the max. power number at the max aero speed, regardless of what gear you are in.
So, lets look at what the torque numbers of both cars are at roughly 175mph. Fortunately, the overall rolling diameter of the Z06 and M3 rear tires are roughly the same (actually, to within 2mm they are the same).
Both cars will be in 5th gear, so the Z06 is at 6718rpm @ 175mph (based on an overall ratio of 2.87:1 (3.42 rear, 0.84 trans). The Z06 redline is 6500rpm, so it actually needs to be in 6th gear to hit 175...But, for the time being, lets assume it can hit 6700rpm, so 175 is its top speed. That means that the car is putting 281ft-lbs*2.87 (281 ft-lbs is 360hp at this speed, since the Z06 develops max power of 385 at 6000rpm, this kind of loss at the high end is conservative) or 808ft-lbs of torque to the road (not counting drive-line loss, but we will assume that the M3 and the Z06 have the same driveline loss).
The M3 at 175mph will be in 5th gear for a total ratio of 3.46 (the rear ratio, as 5th gear is 1:1). So the M3 is at 7775rpm, or below redline (so we don't need to cheat like in the Z06). The M3 develops its max power of 333hp @ 7800 so its at its max. power point at 175mph, for a total torque to the road of 333hp*(5250/7800)*3.46 = 816ft-lbs, or MORE than the Z06. The M3 is roughly 71" wide and 52" tall, compared to the Z06 which is 73x47. Since the vette is less squared up than the M3, the vette frontal area is 21.3ft^2 and the M3 is roughly 23sq-ft. The M3 thus has roughly 1% more power to the ground than the Z06, and assuming roughly the same Cd, the Z06 has about a 10% advantage in frontal area, so the M3 should lose about 3% top speed vs. the vette, for a top speed of 170mph. However, according to C&D, the drag limited top speed of the vette was 168mph (redline at 6500 in 5th gear) so the vehicles have very similar top speeds (+/-2-3mph or so). Ok, so I take back my 180mph for the M3, and say 170+/- is the top speed.

The M5 on the other hand, has roughly the same drag as the M3 (lower Cd, slightly higher frontal area) and with a 3.15 rear end is at 6700rpm, or roughly the power peak of the M5 at 175mph. 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.

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. BMW is known for matching trans and rear ratios well for the cars (except for the 2-3 shift where the ratios are a little far apart, but even that seems intentional as they wanted 2 to be as numerically high a ratio as possible to get good acceleration figures, and keep 3 a little lower to extend the mph range of that gear, as on a relatively faster race course where you would spend most of your time between 63 and 80mph in turns, you don't want to have to shift too early). So BMW chose a rear end ratio that was a compromise between low speed acceleration and top speed.

If the Z06 ran a fractionally taller (numerically lower) rear end, its top speed could be in the 180 range (by making 180mph near the power peak of the motor).

I hope this all helps, and please no flames. If you guys want me to get out the car silouettes, the actual precise Cd numbers and the actual precise dyno curves I will, but all these should be accurate to within 5mph or so, and atmospheric differences due to weather make more of a difference than that (example, on a 20C (78degF) day a car will run rougly 0.8% slower than on a 10C day. Before you jump on this number, here is the backing facts. the Air is 3.5% denser on the 10C day, increase intake charge density (and thus hp) by roughly the same amount (please don't split hairs here), while the drag increases by the same amount. But, as the drag increases by the speed squared, the drag only increases by 1.7% on the colder day, so the car actually has a 1.7% surplus in power vs. the hot day, which corresponds to a 0.8% top speed increase (or roughly 1.5mph) Throw in barometric pressure changes and even minor winds (a "calm" day may have almost undetectable 2-3mph breezes) and +/-5mph is totally reasonable.

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

CONTINUED IN PART 2 With some fun calculations
-m





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