The Numbers Game

Gear Ratio Calculating

February, 2009

By Bob Mehlhoff

148 0208 Gear Lead Z

Hot rodding is largely about relationships. No, we're not talking about the kind that your girlfriend or wife loves to discuss, but the optimal mechanical relationships for your car's performance. A few simple math formulas can help you select the right gear ratio and tire diameter to optimize your vehicle's performance. Because performance cars are often used for both street and track use, gearing a car to do both usually demands a compromise. Vehicle speed, engine rpm, overall gear ratio, and tire diameter are all related to a acceleration. For track use, an engine needs to operate within the rpm range where it makes the most power. For street use, optimal fuel economy and engine life warrant lower engine rpm. The good news is that, armed with some basic information, you can have a car that clocks impressive e.t.'s at the dragstrip and achieves plenty of low-rpm driveability on the freeway. Who said math was no fun?

What's in a Ratio?

An automobile uses gear ratios in both the transmission and the drive axle to multiply power. The two ratios multiplied together equal the final drive ratio. Spend a few minutes in any bench-racing session and soon you'll hear rear axle gear ratios discussed. For many performance cars, 3.73s and 4.10s are common gear choices. The rearend gear ratio refers to the relationship between the ring gear and the pinion gear. By simply dividing the ring gear tooth count by the pinion gear tooth count, the ratio is determined. For example, if we divide a ring gear with 41 teeth by a pinion gear with 10 teeth we find that the gear ratio is 4.10:1 (41/10 = 4.10).

Tire diameter will also have an effect on a vehicle's final drive ratio. As tire diameter changes, so will engine rpm at a given speed. We can demonstrate this with the simplified formula: rpm = (mph x final gear ratio x 336*) / tire diameter (*see "Formulas for Success" sidebar). For example, given 65 mph, a tire diameter of 30 inches, and a final gear ratio of 4.10, the engine speed will be approximately 2,984 rpm--(65 mph x 4.10 final gear ratio x 336) / 30-inch diameter tire. If we reduce the tire diameter to 25 inches, the engine speed increases to 3,581 rpm. By installing shorter tires, the vehicle will accelerate as though it has a 4.73 (higher numerically) gear without the expense of gear swapping.

Because transmissions are comprised of several gear choices, the transmission allows the vehicle to accelerate quickly with lower gears and to maintain a cruising rpm using higher gears. In the '60s and '70s, most transmissions offered three or four gears with a 1:1 high gear. Using a TH400 as an example, First gear is 2.48:1, Second gear is 1.48:1, and Third gear is 1:1. Multiplying the 2.48 First gear by the 4.10 rear axle results in a final drive ratio of 10.16:1 (2.48 x 4.10 = 10.16). For most street performance applications, a 10:1 final First gear ratio is usually considered optimal. The disadvantage of operating a 4.10:1 axle ratio on the street with a 1:1 high gear is excessive freeway engine speed.

Fortunately, today's transmissions frequently utilize Overdrive high gears in the neighborhood of 0.70:1, which allow reduced engine speeds. Combine these overdrive transmissions with a 4.10 axle ratio and you have a fuel-friendly final drive ratio of 2.87:1 (4.10 x 0.70 = 2.87) in high gear. A TH200-4R overdrive automatic utilizes a First gear of 2.74, a Second of 1.57, a Third of 1.00, and a 0.67 Overdrive. With this transmission's First gear ratio of 2.74 combined with a 3.73 axle ratio, the final drive ratio >> yields a 10.22 (2.74 x 3.73 = 10.22). In overdrive, the final drive ratio equates to a Bonneville-ready 2.49:1.

Making Torque Multiply

Acceleration is all about torque. One way to accelerate more quickly is to multiply the torque at low speeds to help move the vehicle forward. That's what a torque converter does. The torque converter features a component called a stator. The stator changes the direction of oil flow to the pump impeller's rotating direction and also incorporates a one-way clutch assembly. This redirection of fluid increases torque by applying the energy remaining in the oil.

By applying the basics of gear ratios and power leverage, you can easily improve acceleration without paying too steep a price in highway rpm. It's all in the ratios.