Stock Car Science

I have a new car (see below and 10 bonus points to anyone who can identify the make and model). The passenger (the mammal in the backseat) is my visual aid for the Science of NASCAR talks when I explain what the ‘hound dog position’ is.

The new car comes with a Sirius/XM Radio, which is perfect timing since my long-standing insomnia finally seems to be succumbing to the wonders of modern medicine (which means I can’t drive in NASCAR). But I also haven’t been lying awake in bed listening to the replays of NASCAR shows on channel 128. Since I was tooling around the city today catching up on errands like getting plates for the new hot rod, I got to listen in real time.

That actually got me in a bit of trouble when I mentioned to my husband how odd it was to hear Dave’s voice and not be in bed. I think we have that cleared up now, but if you’re in Dallas in November, Dave, I’ve hidden all the ammo just in case. Speaking of Dave, he challenged me some time ago to write a science blog in verse. I haven’t quite gotten to the level of a whole post yet, but I did write a limerick about Brian Vickers at the Nationwide race at New Hampshire. (Yes, I know I’m behind.)

The story of Loudon is writ
Speed and Vickers collided a bit
Scott said Brian slowed down
As the corner he tried to round
And Brian said, ‘Yeah, no (expletive)‘

Brian was simply expressing his understanding of Newton’s First Law, albeit in words Isaac Newton probably wouldn’t have chosen. (This, after all, is a man reputed to have died a virgin.) But it is what my colleagues in education call a “teachable moment".

Newton’s first law says (among other things) that when a car is going straight, it’s going to keep going straight unless something makes it change its direction. Sort of like if you’re lying down watching TV, you’re going to keep lying down watching TV until your spouse tells you to get your butt off the couch and take out the trash. If Newton had married, he would have come up with that one as well.

The force needed to make something turn is the centripetal force, which is proportional to the mass of the car (m) times the speed of the car squared (v²) divided by the radius r of the turn.

It takes more force to turn faster. A lot more. If you double your speed, it takes four times as much force to make the same turn. Similarly, it takes more force to make a tight turn. That’s one reason cars slow down going into the corner.

Depending on the turn and the speed of the car, it can take as much as 6 or 7 tons of force to make a stockcar turn. All that force comes from the friction between the tires and the track. How much friction you get is a combination of the stickiness of the tire, the track surface and banking, the mechanical downforce (the weight of the car pushing on the tires) and the aerodynamic downforce (the force of the air pushing down on the car, which pushes down on the tires). All those forces added up have to provide a force equal to mv²/r. If they don’t provide enough force, you don’t turn. You crash.

Track banking helps the car turn because the banked track actually pushes the car in the direction it should be turning. The more banking, the more centripetal force the track provides and the less force has to be provided by mechanical and aerodynamic downforce. The angle of the banking actually changes as you take the turn, so you get different amounts of help turning in different parts of the corner.

The other two factors - aerodynamics and mechanical force - push the car’s wheels into the track, which creates more friction. The problem is that they don’t push each tire with the same force, and the force changes throughout the corner. I’ve talked in previous blogs about the fact that weight ’shifts’ when you change direction or speed. To review:

• When you brake, the rear wheels lose grip and the front wheels gain grip.
• When you accelerate, the rear wheels gain grip and the front wheels lose grip.
• When you turn left, the right side wheels gain grip and the left side wheels lose grip

The important thing to remember is that you can only turn as fast as your least grippy tire. So if you have a lot of force on your right rear and very little force on your left front, you are limited by the left front.

When a driver talks about ‘rolling through the corner’, he’s talking about the part of the turn in which he’s traveling at roughly constant speed. The car’s already shifted load to the front wheels and he’s off the brake. The load’s shifted from left to right and he’s just waiting for the right moment to get on the gas.

Two cars going into the corner one behind the other are experiencing the same force from the track. The cars have the same mass, so the things that distinguish how one car turns from how the other car turns are the aerodynamic downforce and the rate at which the load shifts. That’s why springs, shocks and swaybars are so important. These components can’t change how much load shifts in a turn, but they can change the rate at which it shifts.

The next couple posts will address the coyote hood ornament they were discussing on Tradin’ Paint and Suzy Q’s tummy gurgles. And why the switch to Fuel Injection is just for show…

The black helicopters were out over Indy on Sunday, or so suggest some Juan Pablo (a.k.a. Juablo)fans. This happens every time someone leading a race (or contending for the lead) gets a pit road penalty.

On This Week in NASCAR, Micheal Waltrip opined that if NASCAR caught you speeding, you were speeding. Juablo maintains that he wasn’t. It’s possible for both statements to be true.

I’ve already covered in detail how teams determine the tachometer reading that puts them at pit road speed plus five mph minus just a little. In brief, the engine rotates around 9500 times each minute and the wheels somewhere around 2000 times per minute. Between the engine and the wheels are two sets of gears: the one closest to the engine is the transmission and the one closest to the rear wheels is called the rear end gear. The diagram shows the gear ratios for a Borg Warner MM6 manual transmission and a GU6 3.42 rear-end gear, as might be found in a Corvette. When you turn a larger gear with a smaller one, you decrease the rotation rate. If the gear ratio is 2:1, the smaller gear turns twice every time the larger gear turns once. Get a set of K’Nex and you can prove this to yourself. The gear ratio is the ratio of the number of teeth on one gear to the number of teeth on the other. (I have a two-speed K’Nex transmission on my desk. I have had to literally take the transmission out of the hands of more than one Ph.D. who was just amazed that simple machines actually work.)

Anyway, the teams know the gear ratios in the transmission and the rear end gear - you can see the calculations in the previous blog. Even before getting to the track, they know what the tachometer should read when the car is at pit road speed during the warm-up laps. NASCAR allows the cars 5 mph over the pit road speed, so 60 mph was the maximum speed you could go on Pit Road at Indy without getting a penalty. The engineer and driver will agree on a speed during the parade laps. If you’re listening in, you can hear the process.

This is what a tachometer looks like. The new ones are a little fancier - they have lights that can be set by the driver so that a yellow light comes on when they are getting close to the target rpm and a red light comes on when they darn well better get off the gas if they don’t want a penalty. Everyone always asks why they don’t just put a speedometer in the car. You can actually control your speed very precisely with a tach.

The divisions on the gauge are 100 rpm. If the driver can read the gauge to 100 rpm, for a typical gear ratio (i.e. let’s say a 1.45:1 second gear and a 4.22 rear end gear), each 100 rpm step on the tach corresponds (for 82.1 inch circumference tires) to 1.37 mph. If you assume that the driver can read the tach to 50 rpm, that’s 0.64 mph. So for a driver, there’s really no point in having a speedometer and a tachometer. They need the tach to help with shifting, and knowing how hard they are pushing the engine. If driver’s had speedometers, I assure you there would still be speeding penalties.

Ever looked at the speedometer from the passenger seat? What you see is different from what the driver sees due to something called parallax error. Look at something with just your left eye (closing your right eye), then with just your right eye. The object looks like it’s in different places because your two eyes are not located in the same place - they see things from different angles. When both eyes are open, your brain automatically interpolates between the two. (This is one reason that people who have lost the sight in one eye have problems with depth perception.)

The tach in a racecar is usually about 5 inches in diameter. Put yourself in Juablo’s place, coming out of your pit box, trying not to hit any other cars, trying to maintain your lead, and watching the tach. All you have to do is be off by 50 rpm.

I was looking back on a previous blog I started and didn’t ever publish and found something from Red Bull Racing engineer (and former crew chief) Josh Browne. Teams sometimes see discrepancies between their calculations and what they read on the track during the parade laps. If the pace car speedometer is off, that raises a bit of confusion, as you have to decide if the discrepancy is due to a problem on your end or on NASCAR’s. The other problem, he mentioned, is that tachometers are analog devices (in contrast to digital). And they aren’t always exactly accurate. Each team’s engineer gets a report each week that tells them what the offset is on the particular tach in the car. If the team is part of a multi-car company, they know the parameters for the other cars and can get the rpm reports from the other drivers and compare. Pit road is divided into segments and the car has to have an average speed less than pit road speed (+ the 5 mph buffer) in each segment. After the first pit stop, teams can ask NASCAR for their speeds on pit road and double check their calculations. They can get their numbers for each segment from NASCAR.

I know of at least one case in which people incorrectly set up the spreadsheet most teams use to find the pit road tach reading.

NASCAR measures the speed of each car in a series of segments, which are defined by wires embedded in the track. The car has to be below pit road speed + 5 mph in each segment. If you’re over in anysegment, you get penalized. Juablo was going 60.06 mph in Zone 2 and 60.11 mph in Zone 4. Do the math: 0.11 mph corresponds to 8 rpm and 0.06 mph corresponds to 4.4 rpm. Look at the tach and tell me you can tell the difference between 3850 and 3858 rpm.

Races shouldn’t be won or lost on being 0.11 mph over. After all, the whole point of the Pit Road speed limit is for safety and you aren’t going to hurt someone any less if you hit them going 60 mph or 60.11 mph; however, you have to draw a line. If you give them 6 mph, everyone will be going 61 mph and then people will complain about 61.06 mph being penalized. As Juablo said, “It is what it is". Them’s the rules and each team chooses how close they want to get to the line. If you’re leading the race or have a chance to win, you have to balance loosing positions on Pit Road because you’re slower than other cars with being sent to the tail end of the longest line for speeding.

It’s not stock car science per se, but it is about cars. Check out a blog I wrote over at cocktail party physics about how a Styrofoam cup can crack a windshield.

With Daytona coming up, I’ll put in a plug for the “Drag and Drafting” episode of the Science of Speed video series, which talks about why drafting – and bump drafting – are so important at a place like Daytona.