I grew up 30 minutes from Sonoma Raceway and every Wednesday night for $15 you could drag race down the quarter mile. E.T. bracket racing was a lot of fun and kept me off the streets foolishly goofing around with my car buddies. At only 16 years old, I didn’t know much about engineering or mechanical systems, but I did know this: if you wanted to go faster down the drag strip you needed a 4.11 gear ratio. I didn’t really know what 4.11 meant, but I knew I needed to score one and install it in the rear end of my El Camino. Yes, I drove an El Camino at 16. Don’t judge.
Obviously, for a rear-wheel drive Chevrolet, 4.11:1 gears were referring to the final drive ratio. 4.11:1 was a great gear for ripping off quick quarter mile times, but a horrible gear for fuel economy. I learned quickly as a teenager that gear ratios had a certain balance, good and bad. For road racing, gear ratios are just as important as they are in drag racing. The only difference is that the calculation for the correct gear is much more complex because the racetrack isn’t just a flat 1,320-foot straight line.
Back in high school, I was short on money, but had lots of time, so I spent my days in wrecking yards trying to find a replacement rear end for my El Camino with that elusive 4.11:1 posi-traction in it. What I found is it’s hard to really know what gear ratios are inside differentials unless you take off the cover, start counting teeth and do some arithmetic. Years later, while road racing with NASA, I ran into the same issues. I have front-wheel-drive transmissions in the shop that I don’t really know what exactly their final-drive ratios are. I got tired of guessing and decided to figure it out. How hard could it really be? Gear ratios are just that: ratios, something over something else. My cellphone has a calculator in it. I don’t even have to be a smart person.
There is nothing mathematically complex about calculating a gear ratio, the hard part is determining the different variables. What is the final drive? What is the gear ratio for first gear? How tall is diameter of the tire? Some of this information can be sourced through the Internet, car forums, manufacturer specifications etc., while other parts of the equation can be calculated, like tire diameter.
There are different tire calculators found on the Internet that will give you specifications. I decided to use the formula above and just create an Excel spreadsheet with the math inside. I could enter any tire size I wanted and determine what the diameter would be. Once I had that figured out, the next step was to see what resultant final gear ratio changes would come from changing tire size or tire aspect ratio. I created the spreadsheet below to help me see what changes would come from tire size adjustments.
Playing with the different formulas in the spreadsheet I started to really nerd out with the math and began creating a spreadsheet that would examine each gear, final drives, RPM, miles per hour, tire size changes, etc. Using the formula for gear calculation along with the formula for tire diameter, I created the spreadsheet below for our Honda Challenge 4 car.
The yellow fields are cells where I input data from the car (tire size, final drive ratio, gear ratios 1-5) and the rest is created mathematically in the spreadsheet. The gear ratios for gears 1 through 5 were determined based on Honda specifications for a stock 92-93 Acura Integra YS1 transmission. The final drive ratio was installed in the car by Synchrotech Transmissions.
This information was based on what “should” be in the car. But, I really didn’t know if that was true or not unless I verified it. Near the right side of the spreadsheet in green is the calculated resultant gear ratio based on gear ratio multiplied times the final drive. Essentially, what it equals in first gear is 15.21 revolutions of the engine for one revolution of the front tire. For fifth gear it equals 3.49 revolutions of the engine for one revolution of the front tire.
The next thing to do was to verify if the actual number of rotations on the engine matched the calculated number of rotations of the front tire for each of the five gears from the spreadsheet. I put a piece of tape on the tire and fender to mark wheel rotation and I put a piece of tape on a socket and began to rotate the engine.
After things were marked with tape it was time to start turning the crank and counting revolutions. This was a boring process that required concentration remembering how many times I had turned the engine over. Essentially, I needed everyone else in the shop to shut up for five minutes. This is a difficult request at the Double Nickel Nine Motorsports shop.
After lots of turning and counting, I found that the final drive I thought I had in the car, wasn’t the final drive that was actually in the car. I went back to the spreadsheet and tried a few different final drive options that were available on the market. I suspected there was a 4.92:1 final drive in the car as opposed to the 4.71:1 I thought I had. Using the new data from the spreadsheet I started the process over, lots of turning and counting, and I determined my suspicions were correct. The wrong final drive was installed.
With just a couple pieces of painters tape, a socket, and a spreadsheet, I was able to accurately determine exactly what final drive was in my car. The spreadsheet also offered me the opportunity to compare and contrast different final drive ratios, different tire sizes and the resultant miles per hour and RPM associated with each gear. If you think you know what is in your car, you may want to take a moment to turn the engine and count wheel rotations and be sure your gear ratios are optimal and legal for your class. Happy turning!
Rob Krider is a NASA National Champion and author of the novel “Cadet Blues.” To read more, or to contact him, go to www.robkrider.com.