Formulas
You ask what 3rd direct would be... I don't know. But the following formulas work once you're in overdrive.
Overall Ratio = (3. 54)(trans overdrive)
[transmission overdrives: Pre '94 auto 727 = 1. 0, auto 518 = . 69, 5 speed = . 77. Post '94 47RH = . 69, 5 speed = . 74]
Example: 3. 54 x . 69 = 2. 4426
MPH = (RPM)(Tire Diameter)/(Overall Ratio)(336)
Example: (1950 rpm)(31. 6" tire dia)/2. 4426 x 336 = 75. 08 mph @ 1950 rpm
RPM = (MPH x 336 x Overall Ratio)/ Tire Diameter
Effective Differential = (stock dia/new dia) X stock diff
Example: (30. 5" stock dia/31. 6" new dia) x 3. 54 = 3. 41 Effective Differential
another simple way is to go 31. 6/30. 5 = 3. 60% change
which is very close to 3. 54 - 3. 67% = 3. 41
Side Note If you change your speedometer transmission gear to adjust for different size tires, remember that if you go to a TALLER tire than stock, you need to go to a SMALLER tooth gear. There is an INVERSE relationship between the tire and the gear.
Example 31 tooth / 30 tooth = 3. 3% change in speedometer reading - which is closest to the above 3. 6% change in tire size.
Issue #17 page 34 and 35 has some examples but note that the editors not at the bottom of page 35 is NOT correct. He indicates that going to a larger tire means going to a larger gear. This is NOT true. Going to a larger tire, you need to go to a SMALLER tooth gear to properly adjust the speedometer.
If you have a porgrammable calculator, make a siimple program using the MPH formula. You'll have 3 unknown variables, the RPM, the Tire Dia. , and the MPH. Once you get your known tire diameter entered, you'll only need to input either the mph or the rpm value and have it solve for the other.
I went from a 30. 5 inch tire to a 31. 6 inch tire (3. 6% change) therefore I went to a one tooth smaller speedo gear 31 tooth / 30 tooth = 3. 33% (closest match, 29 tooth would be too much).
This dropped my effective differential from 3. 54 to 3. 41 = better mileage, lower rpm's - but not as strong getting from a dead stop to rolling. I haven't noticed any decrease in power since going to the taller tires, but I haven't worked it at GVW yet either. With the torque that my truck is putting out I'm not worried. It has power - period!
I'm using 235/85's vs my former 265/75's. I REALLY like the taller tires.
Note: I'm not a Dually. Just trying to help you with the formulas. I have a similar post from today to help out a friend with the tires on his Dually.
Issue #37 pg. 142 has a good article on Gearing and gear Ratios that discusses tires sizes and their affect on the differential ratio.
Good Luck
- Ben