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Old 01-24-2012   #20
Paul Workman
 
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Join Date: Nov 2007
Location: Squires (near Ava MO in the Mark Twain N'tl Forest) - Missouri
Posts: 6,466
Default Re: Differential calc

Oh, hell...Going all the way around the barn here; rpm, inches per second...

Cutting to the chase:

Let the (effective reference) radius from the center of the wheel (A) to the contact patch = 1
Let the (effective) radius from the center of then new wheel (B) to the contact patch = 1.2
Let the current differential drive shaft to axel ratio (C) =1:1
Let "X" = the new differential ratio.

X = Bx2xPi/Ax2xPi x C
simplifying...
X = B/A(reference) x C
substituting values...
X = 1.2/1 x 1 = 1.2

Checking:

The reference case: The (effective) circumferance of (A) = DxPi, or radius x 2 x Pi = 1 x 2 x 3.14 = 6.28
The (effective) circumferance of (B) = 1.2(radius) x 2 x 3.14 = 7.536

The new driveshaft axel ratio: X = B/A x C = 7.536/6.28 x 1:1
The new ratio = 1.2:1 (check)

B (7.536) / 1.2:1 = 6.28 = A...Check!!

Proof #2:

Using a proportional computation: A is to B as 3.45 is to X expressed as-

1:1.2 :: 3.45:X

solving the proportion-

X = 1.2x3.45/1 = 4.14 (in this hypothetical case)

4.14/1.2 = 3.45 Check (again)

Cliff (Dynomite) is right, far as using the speedo reading and GPS doesn't address the gear ratio directly, leaving a lot to chance, unless you assume 100% accuracy of the speedo and GPS values. Direct measuring is always less likely to introduce hidden factors.

Dom, you measure the effective radius of your wheel (center to patch), and I'll measure mine (currently a F1 GS D3 315x35x17) and then we'll have a pretty good basis for predicting final ratio to equate to the 3.45:1 on stock wheels. K?

My radius = 12.25"

X = (your radius)/12.25 x 3.45 = your new ratio to exactly equate to the 3.45

I'm outta here. Oh, wait!...I'm outta here except to trade friendly jousts with your sister: Being a math teacher in public school is no glowing recommendation . I've had to teach logarithms to high school grads that couldn't balance their checkbook. I made a good living for several years teaching math to HS grads that didn't have a grasp of the 4 basic principles of arithmetic. (Did your sister teach you math too??)

P.

Last edited by Paul Workman; 01-24-2012 at 09:28 AM.
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