The defining characteristic of the Kansas race was the surprising number of engine problems. Many of those problems can be attributed to the change in rear gear from a 3.89 to a 4.00. At 190 mph at a track like Kansas, your wheels make 2270 revolutions per minute (rpm). If you watch the telemetry on the television broadcast, you know that the engine is rotating around 9500-9900 rpm. Since the engine is attached to the wheels, there has to be something to change the rotation rate between the engine and the gears.

## Gearing Up

That something is the transmission and the rear gear. As shown at right (with the values given for a Corvette ZR-1), the engine rotation passes through the transmission and then through the rear-end gear before reaching the wheels. A 4.00 gear means that the ratio of rpm in to rpm out is 4.00:1. It takes four revolutions of the input to produce one revolution on the output. If you have something rotating at 8000 rpm and you add a 4.00 gear, then the rotation is reduced to 8,000 rpm/4.00 = 2,000 rpm.

Note that NASCAR does not allow 5th or 6th gears and does not allow overdrive (when the first number is smaller than the second). The lowest gear you can have is 1:1 in NASCAR.

Let’s compare running at 190 mph with the two different gears. Last year, a 3.89 gear was used. At 180 mph, you’d better be running in 4th gear (which means 1:1 and the speed coming into the rear end gear is the same as that coming from the engine. The engine speed required to go 190 mph is this 3.89*2270 rpm = 8830 rpm. This year, with a 4.00 gear, you’d need to be running at 9080. If you’re running 200 mph, last year you needed 9293 rpm and this year it would be up around 9556 rpm. You’re basically running 250 rpm (or so) higher this year than last year at the same speed.

Andy Randolph, Engine Technical Director at ECR Engines tells me that engines were running at 9800 rpm for sustained times. Although the engine rotates that fast at some places, doing it continuously places huge stress on the mechanical parts – that’s why most of the failures were due to mechanical breakage. (Because I know he’s too modest to mention it, I’ll point out that none of the engines that had problems at Kansas were from ECR.)

## The Math

For those of you wondering about where my numbers come from, here’s a calculation I did for Las Vegas. The only difference is the slight variation in tire circumference. If you plug in the numbers to the formulas and don’t get what I got above, I probably screwed up on the calculator.

Left-side and right-side tires have difference circumferences. The circumference of a left-side Vegas tire in 2008 was 87.4″, while the right-side tires had a circumference of 88.7″.

To calculate how many times the tires rotate each minute, I first convert the speed into inches per minutes. I know to use those units because I’m trying to get an answer in revolutions per minute, so I need to convert hours to minutes. I also know that every time a right-side tire makes one complete rotation, it has traveled 88.7 inches, so I’m going to convert miles to inches because I know I will need that later. Convert 45 mph to inches:

45 mph corresponds to 47,520 inches per minute. Looking at the right-side tires (for no particular reason), the car travels 88.7 inches every time it makes one full rotation. The number of times the tires rotate each minute is 536 rpm, as shown below.

## Please help me publish my next book!

The Physics of NASCAR is 15 years old. One component in getting a book deal is a healthy subscriber list. I promise not to send more than two emails per month and will never sell your information to anyone.

Diandra, I don’t understand how friction in gear trains would affect the ratio between engine rpm and tire rpm. Friction wouild make a difference in horsepower losses, but the gear ratios are fixed ratios and I don’t think friction would change that. Please correct me if I’m wrong. I wish I could attend some of your classes. I’ll bet they woul;d be a real hoot, and I’ll bet even I could learn something from them.

Jack: You are right that the gear ratios don’t vary; however, there is energy loss along the route. The rotational speed is proportional to the energy. If you lose energy, you can’t spin as fast — even though you are 100% right that the gear ratios do not change. Most of the energy is lost to friction – between the gear teeth, in bearings, etc. In order to run at, say 180 mph, the engine has to run even faster than the gear calculations would suggest because not all the energy produced at the engine makes it all the way back to the wheels.

Thank you for the compliment: I’m not sure my students find my classes ‘a hoot’ – especially during the final week of classes for the semester!

I will have to respectfully disagree with your statement about the engine having to run faster. Unless there is a fluid coupling in the drivetrain somewhere, the ratio between the engine and the wheels remains the same. Friction in the drivetrain, to me, means that the engine has to work harder to produce the same rotational speed at the wheels. It seems to me that if the engine was turning more rpms than were required to run(using your example) 180 mph, then the vehicle would be traveling more than 180. I guess I just don’t understand what you are trying to say. I will admit that I am old and don’t learn things as fast as I used to.

I have to agree with jack that each revolution of the engine will complete a given revolution of the tire. friction can’t change that, except for the friction created because there is a difference of tire size between the left and right side tires. It still doesn’t alter the number of times the tire is rotated per engine RPM.

The energy needed to rotate something with rotational speed omega is 1/2 * I (moment of inertia) times omega squared. If you think about the energy flow from the engine to the rear tires, losing energy means losing rotational speed because you can’t lose moment of inertia. You’re right that the gears tell you how they should rotate – but that’s not exact because the gear equations assume massless parts. DLP