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Old 02-12-2014, 12:22 PM   #1 (permalink)
hat_man
Master EcoModder
 
Join Date: May 2010
Location: Illinois
Posts: 477

Oh Deer - '03 Ford Ranger XL
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Another math question

I was looking back at the formula Old Tele man gave about the relationship between speed/RPM/gearing and wondered how tire size would factor in. We can change our RPM at a given speed by changing trans. gearing or rear end gearing or tire size. Here is the formula I started with.....

MPH = [60/(G x A)] x [RPM/rpm]

MPH = miles per hour
RPM = revolutions per minute
rpm = revolutions per mile of tire
60 = conversion constant
G = gear ratio of highest forward gear
A = axle drive ratio



I found this formula and wondered if it would be closer to the "real world".

It was given as this:

Vc = (Ct x Ve) / (GRt x GRd)

Vc = car speed
Ve = engine speed
Ct = tire circumference
GRt = transmission gear ratio
GRd = differential gear ratio


I morphed it using the same lettering OTM used (with one exception) to come up with this:

MPH = (Ct x RPM) / (G x A)

I was thinking that Ct might work better than revolutions per mile because the tire circumference is different when the tire is "loaded". Also it is different at 35 psi than it is at 50 psi. Probably not enough to make any real difference, but I thought I would just throw it out there.

The thing I am having trouble with is the 60. I think in the original formula it's a way to "equalize" the rev's per MINUTE and the miles per HOUR. If it is...then why is it not used in the second formula? I'm no math genius. I can take a formula and do the sum, but as to how a formula is derived I don't have a clue. Is the second one different than the first or am I just looking at two sides of the same coin?

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