Dumb question 2 - transmission gear ratio math

Ok - trying to figure out some overdrive ratios for T5 for comparison purposes.

I know the advertised OD ratio for the two transmissions, but when I count the teeth, I can't get there from here.

1st T5 is Jeep with .86 OD ratio. Power transmission is into the input gear, down to the front cluster gear, out the rear cluster gear, up to 5th output gear.

Input teeth = 21
front cluster = 37
rear cluster = 53
Output = 23

Determining the ratio of the input to cluster is easy 21/37 = .5676
Determining the ratio of the cluster to output is easy 53/23 = 2.3043

I can't seem to figure out how to get .86 with these two ratios - what am I doing wrong? If I multiply these two like you would for any other compound ratio, I get 1.3299. If I divide them, I get either 4.060 or .2463

I'm obviously doing something wrong, but I'll be damned if I know what it is.

Can you solve for X?

 

Nobody? Somebody? Anybody?

 

If you multiply, it comes to 1.3079. If you invert that number it's .76 That's close to the s-10?

At GM we used to multiply by zero and add the right answer. If you use a slide rule you can get any answer you need.

Sorry, I can't figure this either.

Frank

 

Yeah, I tried the inverted thing - I also thought perhaps the gearing had been changed as .76 is close to some of the factory ratios.

But I got another gearset from an Astrovan with an OD ratio of .82 and can't make it work either:

Input teeth = 22
Front cluster = 35
Rear cluster = 55
Output teeth = 27

This one is supposed to add up to .78, but it doesn't either...so I figured I probably didn't miscount ALL of the teeth on both sets of gears and I also figured both sets of gears probably weren't wrong.

I'm looking at this to see if there's any benefit to swapping 5th gears around between trannys - so the other way I tackled this was to look at the 5th ratios themselves.

The Jeep T5 rear cluster & output shaft is 53/23 or 2.3043
The Astro T5 rear cluster & output shaft is 58/27 or 2.1481

2.3043 - 2.1481 = 0.1562 difference

0.1562 / 2.1481 = 0.0727 or 7%

0.78 - 7% = 0.73

So I gain a little bit using the Jeep 5th gears with the Astrovan gearset...

For my car, the change from .78 to .73 is only 150 RPM @ 70 MPH (2130 vs 2280)...

 

Once more for the smart guys up late at night...

 

I had to search for some basics of gear train calculations and found that the ratio equals the number of output gear teeth divided by the number of input gear teeth. Thus the example of 22 teeth of the input shaft and 35 teeth on the cluster and 55 teeth on the rear of the cluster driving 27 teeth on the out put becomes:
(35/22) x (27/55) = 1.591 x .491 = .781

And the 21 teeth on the input to the 37 on the cluster and the 53 teeth on the rear of the cluster driving the 23 teeth on the output is:
(37/21) x (23/53) = 1.762 x .434 = .765

These numbers look more reasonable but I don't know why they aren't closer to the .82 or .86 numbers you mentioned.

 

BillM,

Yes, I found that too & came up with the same numbers - closer, but still not quite right. I'm going to re-count the teeth - again - just to be sure.

Thanks

EDIT - Discovered I had the wrong OD ratio for the Astrovan - it's supposed to be .78, so this forumula is correct!!. Still need to recount the Jeep gear teeth...probably miscounted for the ratio to be off that much.

Also, my 7% guess wasn't accurate - plugging the numbers in, I get .69 with the Jeep 5th gears in the Astro gearset! With my tires & rear ratio, that's 2000rpm at 70mph - about perfect!