Speedo Gear Formulas

The published charts for a speedo gear swap after tire size or gear ratio changes are handy - but they're not all that accurate. I just went from 31/4.56 to 33/4.56 so went to the chart here: http://www.quadratec.com/jeep_knowledgebase/article-46.htm, which is pretty much a standard chart and decided to order the 39 tooth gear for NP231. Then I remembered seeing a couple formulas in Eric Zappe's Cherokee XJ book so thought I'd double check just for giggles (I like details). Turns out the chart was off by quite a bit because of actual tire diameter. Depending on tire manufacturer the 'advertised' tire diameter isn't always the real diameter (they're not going to call a 33 x 12.50 tire a 32.8 x 12.50). In my case (as in Eric's description in the book) my BFG 33 x 10.50 tires are 32.8" diameter. Doesn't sound like much but the difference between the chart and the actual tooth count was off by 1.37 teeth. I ended up with a 38 tooth gear instead of 39 which would make a considerable difference in speedometer accuracy, odometer accuracy and would affect my fuel mileage calculations.
I looked at the FAQ forum and found the 'how to' on changing the gear. The author of the piece cited and linked to a reference article that used one of the common formulas to build a chart but the chart was still off and was the same as all the other charts I've found. Not a criticism, just an observation. The charts are great if you're Ok with 'ball-parking'.
So - I guess I'm nit-picking - if anyone else out there is a stickler for accuracy I'd recommend doing the math by using one or both of these formulas rather than depend on the charts available out there.

Easy way to get these formulas is to buy Eric's book (shameless plug) but here they are if anyone gives a hoot. Good practice on old algebra if nothing else:

MSOD = Manufacturer's Stated Overall Diameter. www.tirerack.com is a good source to find this.

63360/(MSOD x 3.14159) x Axle Ratio/74.5 = Teeth in Speedo Gear

In my case:

32.8 x 3.14159 = 103.044152
63360/103.044 = 614.8829
4.56/74.5 = 0.0612
614.8829 x 0.0612 = 37.63 New Speedo Gear Tooth Count

Most XJs came with 3.55 gears and 225/75-R15 (28.29") tires. Adjustments to these numbers can be substituted in the following formula if applicable to your rig. There will be a slight difference in the two calculations between formulas but it should be minimal.

Old Tire Diameter/New Tire Diameter x New Gear Ratio/Old Gear Ratio x Old Tooth Count = New Tooth Count.

Again, in my case:

28.29/32.8 = 0.8625
4.56/3.55 = 1.2845
0.8625 x 1.2845 = 1.10788
1.10788 x 34 = 37.668 New Speedo Gear Tooth Count

I haven't calculated the percentage the speedo/odometer would have been off using a 39 tooth gear but I would think it significant. Also, as Eric did in his book, I chose the 38 tooth instead of 37 - the speedo will actually become more accurate as the tires wear.

Forgive me if this is a redundant post/thread - trying to help those of you who might also be anal..

Rock On!

I need to add:

The article in FAQ is a good one. I used it for my first speedo gear swap and it helped a lot. Don't want to come off as some kind of know-it-all-better. So thanks for that!

Gary

Yes. Every chart I looked at when doing research on that topic was inaccurate. Not only can you calculate it to a fraction of a gear tooth, this allows you to know if your speedometer is getting more accurate as your tires wear or less accurate.

I ordered a 39 tooth speedo gear when I jumped to 33s with 4.56 gears and I was more than impressed with the accuracy I was getting when comparing to a GPS unit. Spot on at all speeds. They are 33x10.5s BFG A/Ts so we are in the same situation. 92 speedometer gauge also. Your math does support a speedo gear with one less tooth so cheers.

However at the pump I always ball park my tank range because I can't trust that I am getting the exact amount of gas that the pump displays. Could be less could be more? My gas gauge doesn't even work well so I always have 5 gallons in a jerry can if I know I am going to be going for range.

Strange isn't it..

At least around here NHP won't generally even give you a glance at 80mph in a 75 zone on the Interstate.

The other thing is speedos read low stock. I have 235s (about a 29" tire) on an otherwise stock drive train and while it came with 225s from the factory the speedo still reads slightly low.

And 38 vs 39 tooth is a whooping 3% difference, so it would be off by 2 mph at 70 and 3000 miles on the odometer after 100,000 miles.