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Simple Mathematics to Find the Correct Gears

Posted in How To on December 1, 1999 Comment (0)
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Simple Mathematics to Find the Correct Gears

Long after you lifted your truck and realized the domino effect of truck building, but shortly after the last payment for the tires and wheels was sent out, you probably felt it was time to get back the acceleration that the big tires robbed you of. You could put the old dinky doughnuts back on, but then you'd lose the extra ground clearance and traction the big tires offer. Not to mention that the old tires don't look even close to as cool as the new meats. What to do?

Some people think they can throw money at the engine to fix the problem. But in reality the most effective method to regain acceleration and even increase power is to change the axle ratios.

Changing the gears in the axles isn't exactly cheap. Most trucks can be re-geared for $900 to $1,200, including new bearings, gears, and the installation. We recommend changing the bearings when you're doing a gear swap since they're relatively cheap when you look at the big picture. If the truck is somewhat new, you can retain the original bearings so long as you take care removing them from the original pinion and case if required.

Percentages

Several formulas can be used to find the proper ratio for your new tires. The easiest method is to use percentages. The new tires are some-percentage larger than the original tires that the truck came with. To compensate for the tires, the gears need to be that same percentage lower than the original gears. Simple. For example, if your truck came from the factory with 30-inch tires and 4.10 gears and you installed 33s, then you increased the tire size by ten percent. By increasing the original ratio by ten percent you find that 4.51 gears are needed. It can be figured out like this.

30-inch tire/100 percent = 33-inch tire/X percent

The 30-inch tires are the originals, so they are 100 percent. To find out what percent of the 30s the 33s are, we need to solve for the unknown, or X. To do this we need to multiply 100 by 33.

The result is 3,300. Then divide by 30.

3,300/30 = 110

So X equals 110. The 33s are 110 percent of the 30s, or 10 percent larger. To find the needed ratio, we can multiply 4.10 by 110 percent. Which equals 4.51. In most cases the exact ratio needed isn't available. However, something close will work fine. For this truck, 4.56 gears would be sufficient. Different axles have different ratios available for them. If the required gears come up in the middle of two available ones, then pick the lower gears (numerically higher) for more low-end. This can help compensate for wind and road resistance of the bigger tires.

Weak Pinions

As the ratio becomes lower, the size of the pinion gear and the number of teeth on it decrease. This creates more load on a smaller area, often causing teeth to break under abusive conditions. For this reason, 4.56 gears are the lowest available for some of the smaller axles (Dana 35s, AMC 20s, and some Dana 30s). Dana 60s and Ford 9-inch axles are strong and popular, so lots of ratios are available, some as low as 7.17. However, a 7.17 gear set is not as strong as a 4.56 set, or any higher ratio for that matter. If high horsepower and high rpm are used in the kind of four-wheeling that you do (sand, mud, wet rocks) you may be better off not getting the lowest gears possible. For other types of ’wheeling and daily driving, lower gears are a good idea.

Case Changes

Most axles require a case change to accommodate lower gears. The case is the heart of the axle. It is what houses the differential gears and holds the ring gear. In order to accommodate the larger pinion (more teeth) of higher (stock) gears the ring-gear mounting surface needs to be farther from the pinion than it would be with lower ratios. This is because the ring gear would become weak if it were to be machined too thin for clearance. Here are the ratios that require case changes for some of the more popular axles.

Some gear manufactures machine what are called thick gears. These low-ratio gears can be used on the high-ratio carriers. They save you money if you've already purchased some type of traction-adding differential for your stock gears. Spacers are also available, but we don't recommend using them. Changing a stock carrier is usually inexpensive, and the internals from the high-ratio case can be installed into the new low-ratio one.

When deciding what gear ratio to get, it is important to know your tire size. True tire size is usually not what you find on the sidewall. The true size is changed by air pressure and load on the tire.

To find the true height of the tire, you need to measure the static-loaded radius and then double it. This measurement is taken from the road surface to the center of the axle or hub while the vehicle is on the ground. When this measurement is doubled, you get the diameter of the tire as the engine and driveline see it. If we use the same numbers as before, we might find that the 30-inch tires have a static-loaded radius of 14-1/2 inches. Doubling it gives us a 29-inch true height. The 33s may have a static-loaded radius of 15-3/4 inches or a true height of 31-1/2 inches.

When we plug these true numbers into the equation, we find that the 33s are actually only 8.6 percent larger than the 30s. This would call for 4.45 gears or the closest available ratio for the axle. Most 4x4s came from the factory with metric-sized tires, 265/75R16s for example. Using the true static-loaded radius measuring method will provide useable numbers.

Ever wonder what size a metric tire really is? Here's how you can convert the metric numbers on the sidewall to inches. But first, we'll break down the tire's code. On a 265/75R16 tire, 265 is the width of the tire in millimeters. The 75 is the percentage of the width that the sidewall is high (remember, there are two sidewalls, top and bottom). In other words, this tire's sidewall measures 75 percent of what the width measures. The 16 is the diameter of the wheel in inches. The R indicates a radial tire.

Millimeters can be converted to inches by dividing by 25.4. This tire is 265 mm wide, so it's 10.4 inches wide. Since we know the sidewall height is 75 percent of 10.4, it's 7.8 inches (10.4 x 0.75 = 7.8). To get the total sidewall height, double the 7.8. This gives you 15.6 inches, to which you then add the diameter of the wheel (16 inches).

The claimed height of the tire is 31.6 inches. Generally, metric sidewall numbers are more accurate than their floatation size counterparts. It is, however, still a good idea to use the static-loaded radius measuring method when choosing gears. Here are the standard sizes for some of the more common 4x4 metric tires.

These pinions are from an AMC 20. The stock 2.73 is on the right, and a 4.10 gear is on the left. As the gears get lower, the number of teeth on the pinion and the angle in which the teeth ride on the ring gear decrease. This causes more pressure to be placed on each individual tooth, since they are effectively shortened. Less surface contact and higher pressures mean more heat. Lower gears run hotter than high (stock) gears do. These are some of the reasons you don't want to get carried away when gearing down.

It is a good idea to replace the bearings when changing gear ratios. The pinion bearings are more prone to wear because they spin faster than the carrier bearings. If you decide to use the old ones, be sure that there is no blueing from heat or pitting from contaminants.

The thickness of the ring gear is changed to compensate for a larger pinion. The 2.73 ring gear on the right is much thinner than the 4.10 on the left. Also notice the angle at which the teeth are cut. A steeper angle means a larger contact patch and less heat.

These are the two cases for an AMC 20. The 2.73 case (left) has a lower ring gear-mounting surface than the 3.07-and-up case (right). If it were not lowered, the ring gear would have to be very thin and weak. Lower gears will not work on high-gear carriers. However, not all axles require a case change. Check out the chart.

The ratio of a gearset is determined by the number of teeth the pinion has in relation to the ring gear. The 4.10 set (left) has 10 teeth on the pinion and 41 on the ring gear. If you divide the number of ring teeth by the number of pinion teeth, you get the ratio: 4.10. The 2.73 gearset on the right has 18 teeth on the pinion and 49 on the ring. If you don't know the stock ratio of your vehicle, you can figure it out by removing the diff cover and counting the teeth on the gears.

To measure the static-loaded radius, the vehicle should be on a level surface and the tires should be at normal street pressure. Measure the distance from the ground to the center of the hub or axle.

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