Mathematically Determine Your Gear Ratio For Any TrackPeople who have built and tuned race cars for years seem to develop a sixth sense when it comes to choosing rearend gears. Gearing is one arena where experience pays big. Matching a race car's engine power to its rearend gear ratio for optimum performance can make a big difference in lap times.
What is the best ratio for a certain track? Is the engine power maximized by gear choice? These questions always come into play-especially when the car seems to be 100 percent and the lap times are disappointing for no apparent reason.
Resorting to the "guessing method" may work some of the time, but there is a better way; it involves a calculator and a mathematical formula. Basically, the lowest gear ratio possible (a higher number like 4.10) provides the most significant amplification of an engine's power. Determining the upper limit of gear ratio (based on the maximum engine rpm before redline) and then working down from there is one strategy that can get results. Toss in tire performance, track conditions, and other performance issues, and the topic becomes a veritable rat's nest of confusion-but it's not an impossible knot to untangle.
Generally SpeakingOften, racers resort to the monkey-see, monkey-do method of gear selection (particularly when confronted with a new track). Asking the guy next door what they run seems good enough for some, but here's what's wrong with that approach: That person may not be telling the truth, his engine is probably producing different peak power at a different rpm, his transmission might have different gear ratios than yours, and finally, that person may not know what they're doing, so who cares what he has to say?
Ultimately, those who win races are not following someone else's advice; they calculate their way to the front based on their race car's performance and experience of tuning for a particular track. A $2 pocket calculator is the best "go-fast" tool in any toolbox. It's actually quite easy to calculate a rearend gear ratio based on an engine's physical limits-and it's really not a scary trip into "Mathland" as some may think. Determining which gear ratio is truly best requires a solid understanding of an engine's power and where it's located.
The formula for calculating rearend gear ratio consists of four components, all of which warrant discussion: tire diameter, maximum engine rpm, a constant number (conversion factor), and the expected top speed for the track. For the sake of discussion in this story, the output from the transmission to the rear differential is 1:1 (which is high gear with most manual racing transmissions, but not all). Consequently, references to final drive ratio and rearend gearing are interchangeable.
Maximum Gear RatioHow low should you go? The expert we consulted, Tom Reider, said to go as low as possible. Additionally, maximum gear ratio is a good thing to know if you don't want to blow an engine. The neck-snapping performance people enjoy in high-performance street cars is due largely to the vehicle's gearing. Without proper gearing, a powerful engine can't deliver its goods.
The gearing formula depicts a maximum gearing situation because it uses maximum engine rpm and maximum vehicle speed. (Take out the "maximum" elements, and the formula becomes a general gearing formula.) "Maximum gearing" specifically refers to the lowest gear you could use before sending the engine into the redline (or the rev limiter). Additionally, this formula can be tweaked to pinpoint specific engine rpm at a specific vehicle speed. Just solve for rpm. This formula can help target your gearing to best utilize an engine's strengths. You might wear out your calculator, too.
336The number 336, referred to as the constant, is a conversion factor that allows all the components in this formula to interchange between measurement units. Note that rotations per minute and miles per hour must be in the same measurement units. Basically, it brings the time measurements and the distance measurements together in a mathematically interchangeable fashion. The conversion factor starts with 1 mph equals 5,280 feet/mile and ends at 336 revolutions/minute. Revolutions/minute always cancel out with other units inside the equation. Don't worry, this number wasn't pulled out of thin air.
Tire DiameterCalculating the tire diameter (Remember Daniel can run twice as far as Randall? Daniel = diameter, Randall = radius) may sound as simple as measuring from the top of the tire to the bottom. Measuring across the face of the wheel is not the most accurate way to go about determining diameter, because it's impossible to verify that the measurement went through the wheel's true center. The best way to calculate a tire's exact diameter is to measure the circumference around the outside of the tire (in the very center of the contact patch), then solve for the diameter using:
|DIAMETER = ||Circumference |
| pi (3.14159265) |
More accuracy can be achieved by measuring the tires when they are at operating temperature. As a general rule, accuracy within 11/44 inch is acceptable on tires with a 27-inch diameter or so. Only 11/44 inch isn't going to have a substantial effect on the final rpm. Go-kart tires would be a different story, though.
Example:Max. Gear Ratio = 27 inches diameter X 6,100 max. rpm / 336 X 105 mphMax. Gear Ratio = 4.67:1
RPMAs many people may have already noticed, this gearing equation is really just a formula for calculating a gear ratio under any circumstance. How-ever, by using the maximum rpm and the maximum vehicle speed numbers, it actually determines what the lowest gear ratio should be. As previously mentioned, an engine's ability to transfer power to the ground is directly related to the vehicle's gearing. Since the rear axle is really a torque multiplier, the greater the gear ratio is, the greater the torque applied to the rear wheels. If, for instance, the rearend ratio is 4.0:1, then the torque to the axles and wheels is four times the engine torque. That's why you want the maximum final drive gear ratio.
The fastest lap times occur when an engine's peak horsepower band is utilized as much as possible during the course of a lap with as much gear ratio as possible. The torque band is also a factor, depending on the size of the track and how much acceleration is required when exiting the corners. Knowing where an engine's horsepower and torque bands peak (and the duration of those peaks) becomes an extremely useful tool in determining the proper gear setup. Obviously, a dyno sheet will provide the most compelling information about which gear to choose.
Other Useful CalculationsBy the magic of basic algebra, the gear ratio formula can be manipulated to determine any one of the other factors in the gear equation, as long as all the other variables are known. We rearranged the formula so you wouldn't have to. By using these variations of the gearing formula, it is possible to examine theoretical situations before wasting any track time by guessing and wrenching. Of course, the results are dependent upon a myriad of other factors such as driver input, suspension setup, tires, and anything else you can imagine. The bottom line-use common sense. A calculated guess is better than a wild guess.
|MPH = ||Tire Diameter (inches) X rpm |
|336 X Gear Ratio (must be Final Drive Gear Ratio) |
|RPM = ||336 X mph X Gear Ratio (must be Final Drive Gear Ratio) |
|Tire Diameter (inches) |
| TIRE |
|336 X mph X Gear Ratio (must be Final Drive Gear Ratio) |
|FINAL DRIVE |
GEAR RATIO =
|Transmission Input to Output Ratio |
| X Rearend Gear Ratio |
| ||example: Transmission Output = 1.2:1 |
| ||Rearend Gear = 3.89:1 |
| ||Final Drive Ratio = 1.3 X 3.89 = 5.057:1 |
Maximum Speed (mph)Maximum vehicle speed is the factor that compensates for track size and banking. Obviously, a large track with high banking will produce greater speeds than a shorter track with no banking. Maximum speed can summarize a typical oval for the purposes of gear selection. If the track requires shifting, then the gear ratio calculating process becomes a multi-part process.
Automatic TransmissionsAutomatic transmissions have slippage (meaning that input rpm is greater than output rpm) because of the use of a torque converter. Some stock converters allow for slippage of 10 percent or more. Meanwhile, automatic transmissions outfitted for racing (with high-performance torque converters) allow for 2 percent or less slippage. If you're using an automatic transmission, factor the appropriate loss into the rpm variable.