Gear and Tire Applet

by Terry L. Howe


User Guide

The document is a user guide for the Gear and Tire Applet. The first section describes general use of the applet and the other sections contain more specific information about tires, transmissions, transfer cases, and ring and pinion, The general section covers what the Gear and Tire Applet is and what it can be used for. It also covers general information on ratios and the input and output of the Gear and Tire Applet.

What is the Gear and Tire Applet?

The gear and tire form is designed to assist you making gear and tire selections for your four wheel drive vehicle. Larger tires gain ground clearance, increase maximum fording depth, and increase the angles of departure and approach, but they often don't work well with OEM gearing. Auto manufactures build trucks for the street, which means they select high gearing for fast acceleration and better gas milage. When larger tires are put on these trucks, the driver may find themselves burning through clutches because first gear is so high. Engine performance and gas milage may suffer because the engine is forced to work outside of it's optimal RPM ranges. Top speed on the highway will increase, but so will low speed on the trail.

There are two main motivations to regear, the first is to return the truck to the manufactures operating ranges to improve engine performance and decrease wear and tear on the clutch and transmission. The second is to increase offroad performance with lower gearing. Lower gearing allows the offroader to go slower through obstacles giving the driver better control so there is less chance of vehicle damage and occupant injury. There is a penalty for low gears on top highway cruising speed. The gear and tire form is designed to allow the user to try different configurations and see what performance will be like for different configurations before going through an expensive gear swap.

General Information on Gear Ratios

One important aspect of gear ratios is numerically large gears are the low ones. Gear ratios are normally stated in the form x.xx:1, e.g. 6.32:1. This translates mathematically to 1/6.32, and since 1/2 is more than 1/6, 6:1 is lower than 2:1. The ratio means that for every 6.32 revolutions from the input the output will rotate once. This happens to be granny low first gear on a Ford T-18 transmission. When you are in first with the T-18, the engine does 6.32 revolutions for every 1 revolution the transmissions outputs. Fourth gear on the T-18 is 1.00:1, so for every revolution of the engine, it outputs one revolution.

Input for the Gear and Tire Applet

The Gear and Tire Applet takes as input your tire size, transmission ratios, transfer case low range, and ring and pinion.

The tire field will accept input in English or metric sizes. The entire metric size must be input to calculate diameter, but the prefix 'P' or 'LT' are optional. For example the tire size P225/75R15 could be entered without the 'P'. For English sizes, the gear and tire form is only interested in the diameter in inches. The rest is not needed, but if it is typed it will be ignored. For example '32x11.50R15LT M+S' can be just entered 32.

Input of Transmission ratios, transfer case low range, and ring and pinion all have the same basic form. The Gear and Tire Applet is looking for the ratios and ratios are commonly expressed in the form x.xx:1. To save some typing the ':1' part does not need to be entered. You can enter it if you like but, it will be ignored. If you have tooth counts, for ring and pinion for example, just divide the big number by the small. For example 41/10 ring and pinion translate to 4.10:1.

The user has the option to produce output in kilometers per hour or miles per hour. No output is produced until the 'calculate' button is pressed. This document is available by pressing the 'help' button.

Output for the Gear and Tire Applet

When the calculate button is pressed output is created in both graphical and tabular form. The graph is a line graph with RPM on the x-axis ranging from 0 to 4000 RPM. The y-axis is either MPH or KPH depending on user input. MPH range from 0 to 80 MPH. KPH range from 0 to 120 KPH. Each transmission gear is printed out as a seperate line in the graph first being red, second blue, third green, fourth black, and fifth yellow. A check box at the botton of the graph allows the user to "shift" the transfer case into low range. The title of the graph gives the users tire size and ring and pinion ratio.

The tabular output is also produced each time the calculate button is pressed. The title on the tabular output indicates the units of output either KPH or MPH. It also indicates the users selection of tire and ring and pinion and allows the user to enter different RPMs to see the table at various engine outputs. Each row of the table represents a gear of the transmission first, second, third and so forth. The columns represent high and low range of the transfer case.

The crawl ratio, which is often used to compare gearing set ups, is also included in the tabular output. The crawl ratio represents compound low, or first gear of the transmission and low range of the transfer case. For example, many Wranglers have a first gear around 3.83:1, the transfer case low range is 2.72:1, and the axle ring and pinion is 3.07:1. This means the crawl ratio is 3.83*2.72*3.07 or around 32:1. Put some big tires on that Wrangler and it will be difficult to control on a technical trail. A crawl ratio around 60:1 is often good target.

There is more detailed help on tires, transmissions, transfer cases, and ring and pinion, see the special sections for these topics.

Tires

As mentioned in the overview the tire input field will accept input in English or metric sizes. The entire metric size must be input to calculate diameter, but English sizes only require the diameter in inches to be entered. Sorry, the Gear and Tire Applet does not support old tire sizing conventions such has H78 etc. If you actually have tires this old, you'll have to break out the tape measure and input the diameter in inches.

This section covers the method metric tires are translated to inches and how tire size changes speed.

How to Convert Metric Tire Sizes

Metric tire sizes are made up of four components: prefix, width, aspect ratio, and wheel size. It takes three of these components to calculate the diameter of the tire. It sure is not a very straight forward sizing convention.

The prefix is used to indicate general use of the tire. The tire input field trys to ignore the prefix and if your prefix causes an error, just don't input it. The Gear and Tire Applet currently will successfully ignore 'P' for passenger car and 'LT' for light truck. When in doubt, drop the prefix.

The width simply the width of the tire in mm. For example the tire size P215/75R15 has a width of 215mm.

The next component is the aspect ratio. The aspect ratio is the percentage of the width that makes up the sidewall of the tire. In the above example the aspect ratio is 75 or 75%, so the sidewall height is 75% of 215 or 161.25mm. If you want the diameter of the tire, you need to take into acount that the diameter of the tire passes two sections of the side wall. This means the sidewall takes up 161.25*2 or 322.5mm of the diameter.

The next component is the wheel size. In the above example the wheel size is 15". If you convert the total sidewall into inches you get 322.5mm*0.03937in/mm or about 12.7". Add that to wheel size and you get the diameter 15"+12.7" is 27.7". So a P215/75R15 tire has a diameter of about 27.7".

How Tire Sizes Effects Speed

The formula for circumfrence of a circle is used to calculate how tire sizes effect speed. To calculate the circumfrence of a circle the Gear and Tire Applet uses the classic formula 2(pi)r, or given the diameter it is simply the diameter times pi. This means in the above example a 27.7" tire has a circumfrence of 27.7(pi) or around 87". Every time the tire rotates once, the vehicle travels 87". This can be converted to miles or kilometers for calculations of speed given the number of engine revolutions per hour. Anyway looking at the simple formulat d(pi) it is clear that a larger tire travels further for each revolutions since it has a bigger circumfrence. That is why when larger tires are swapped in, you go faster.

Transmissions

The Gear and Tire Applet allows you to enter up to 5 speeds and a reverse gear ratio. If you have a 3 speed or don't have the reverse ratio, there is no need to input the extra information. If you aren't sure what transmission you have you can use the generalizations here to get numbers that probably will be very accurate give or take a few KPH/MPH.

Generalizations About Manual Transmissions

Ratios for manual transmissions don't vary all that much. Most of the time first gear is around 4:1 unless it granny low truck transmission such as the T-18, NP435, SM465, SM420 etc. These transmissions have a first anywhere between 6.32:1 to 7.20:1. Generally, the final drive gear is straight through or 1.00:1 coupling the input shaft directly to the main shaft. I've never seen a 3 or 4 speed that didn't have a 1.00:1 final drive gear. Five speed transmissions have a 1.00:1 fourth and an overdrive. The overdrive fifth gear is typically around 0.75:1. So, when in doubt, use 4.00:1, 3.00:1, 2.00:1, 1.00:1 for a 4 speed.

Generalizations About Automatic Transmissions

The author of this document is not particularly knowledgable about automatic transmissions, but he is still willing to make some generalizations. Most automatics seem to have a first gear around 3:1 and final drive gear of 1:1. Overdrive automatics tend to have 0.75:1 overdrive.

Tranfer Case

It wouldn't be four wheel drive without a transfer case. The transfer case transfers power from the transmission to the rear and front axles. Typically, the driver has 2 high, 4 high, neutral, and 4 low. The Gear and Tire Applet supports the standard two speed transfer cases. If you have a three speed transfer case, you'll have to enter the ratios separately.

High range is assumed to be 1:00:1 for 2 high and 4 high. Low range is input by the user. Low range is typically around 2.50:1.

Ring and Pinion

The ring and pinion are located in the differential housing of the axle. The pinion takes input from the driveshaft and turns the ring. The ring spins the differential which turns the axle shafts. There are a fairly wide variety of ring and pinions ratios available anywhere from 2.73:1 to 6.50:1 depending on the model of the axle. Since transmission and transfercase ratios are fairly set, a change of ring and pinion is the easiest and least expensive way to modify the gearing of your 4x4.

Figuring out what ratio ring and pinion you have is not always easy. Depending on engine, transmission, and option package the manufacturer may have used any one of several ratios. The easiest way is to locate and try to read the tag on on the differential housing. Sometimes this tag is located on the differential housing cover, sometimes it is not. It may be a a code stamped in the housing that needs to be looked up in your technical service manual.

One sure fire way of determining your ratio is openning up the axle and taking a look. Often the ring is stamped with tooth count, ratio, and build date. Sometimes it isn't stamped, but you can still count the teeth yourself and divide ring teeth by pinion teeth to get the ratio.

An easier, but not as accurate method of determining your ratio is to jack one wheel off the ground and count the number of drive shaft rotations it takes to turn the tire one full rotation. Multiply this number by two and that is your ratio. If you have a looking or limited slip differential, you may find it difficult to rotate the tire by hand. If this is the case lift both tires off the ground and support the vehicle with jack stands to count rotations for one rotation of both tires.

One final note on ring and pinion, if you know the ratio of one axle the other should be the same give or take a few hundredths. So if you find a tag on the front, but nothing on the rear, go with the tag you found.

May 2, 1997