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      09-01-2008, 09:08 PM   #1
rzm3
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Arrow M3 Theoretical Top Speed Calculated

Update 2:

Question: why does BMW limit its cars to 155 mph intead of unlimited?

--------------------------------
Update 1:

Recalculated using frictional losses derived from a 320i coupe. Total frictional loss, which includes transmission loss, tire resistance, etc., adds to about 30%.

The updated top speed is 183.62 mph.

--------------------------------
Assumptions:
front wheel rolling losses not included (since power at wheels are found from a dyno, where the front wheels are stationary
Air density at standard sea level used
factors from gear ratio neglected

Result:
with a transmission loss of 13.29%, the M3 is capable of reaching a top speed of 196.95 mph.

Method:
when power generated by the engine equals the power induced by drag force, the car cannot accelerate anymore and thus reaches top speed.

Let me know if there is anything I can modify to make the calculation more sound.
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Last edited by rzm3; 09-02-2008 at 11:00 PM.
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      09-01-2008, 11:26 PM   #2
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Is 359 hp considered peak hp? If so, for this speed to be reached, you would have to assume this peak hp would be reached at the same time the theoretical top speed would be reached. So ignoring gear ratios might be erronous. In other words, is there a gear where this speed would be reached at approximately the same time that this peak hp would be reached? The hp curve would have to top out at the same time the speed curve does. Probably nitpicking as I assume this is just a theoretical excercise anyway.
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      09-01-2008, 11:55 PM   #3
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cool. i think somebody did this based on gear ratios before, but not with all this air density and frontal area stuff.
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      09-02-2008, 01:00 AM   #4
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Not a bad first cut. That is indeed the essence of the physics. The main missing factor in your calculation is the losses due to the tires. This would be in the neighborhood of 35-40 hp near top speed. Through simulation software I calculate the 6MT will peak out around 188. Don't forget the small effects of exact tire size (see Michelin website) and tire expansion.
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      09-02-2008, 08:46 PM   #5
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updated frictional losses
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