Stock Car Science

Listen for me on Dave Moody’s show, Sirius Speedway, this Thursday (May 22nd) at 3:40 p.m. Eastern time. We’ll be talking about how the cars looked at the All-Star race and I’ve learned a couple new things about yaw that I haven’t had time to put in a post yet, but hope to talk about. I’ll also be out at Speed Street in Charlotte on May 24th from 4 to 5 p.m. at the NASCAR Library tent signing books. If you’re in the area, stop by and say hello.

A special congrats this week to Chad Johnston and Kiwi Duncan, the race engineer and shock specialist respectively for the No. 9 car. They were both with the No. 19 last year when I was following it for my book and I am really happy that they were part of Kasey’s winning the All-Star race. The folks at GEM have had a rough couple of years and it’s really nice to see people like Chad and Kiwi getting ahead.

Drivers talking about the new car overwhelmingly ask for two changes: lower the center of gravity and increase the car’s travel. This entry will cover the first one and I’ll talk about travel in a second posting.

The center of gravity (which we abbreviate CG) is the point in an object at which it perfectly balances. The center of gravity of an object with a uniform distribution of mass is at the object’s geometric center. For example, a meterstick balances at the 50 cm point, which is exactly halfway along its length.

A race car (especially a race car with a driver sitting in it) does not have a uniform distribution of mass, so finding its center of gravity is a little trickier. NASCAR mandates a minimum weight of 1700 lbs (out of the 3450 lbs total minimum car weight) on the right-hand side. Teams like to keep as much weight as possible on the left-hand side, so we’ll assume that they put 1750 lbs of the car’s weight plus a 150-lb driver on the left-hand side. The center of gravity is a little to the left of the car’s centerline and close to the midpoint of the car front/back.

Josh Browne (and big congrats to Josh on the No. 84 winning the Sprint Showdown!) tells me that the height of the CG in the new car is about “at the driver’s tush”. That’s a couple of inches higher than it used to be in the old car. Why does that matter? Load transfer.

Braking creates a torque that transfers some of the car’s weight from the rear to the front, which means that there is more weight on the front tires than on the rear tires when the car is breaking. Acceleration causes weight transfer from front to back and cornering causes weight to shift from the inside wheels to the outside wheels.

A car’s grip is proportional to how hard the wheels are being pushed into the track. When you brake, you’re transferring weight from the back wheels to the front, which means you’re losing grip in the rear wheels and gaining grip in the front wheels. When you accelerate, you’re losing grip in the front wheels and gaining grip in the rear wheels.

The CG is important because the amount of weight that shifts is proportional to how high off the ground the center of gravity is. For a car on a flat surface, the amount of weight that is transferred is given by:

Note that when you plug in the acceleration, you only insert the number of gs. That’s because of the British units and the differences between mass and weight. The acceleration due to gravity is there in the weight of the car. The fraction of the weight transferred is the weight transferred divided by the weight of the car, which we then multiply by 100 to get a percent.

For simplicity, I’m going to appeal to symmetry. Assume a 3600 lb race car with the weight equally distributed: 1800 lbs on each side. The track (or tread width) is the distance between the two wheels, as shown in the drawing below. In a NASCAR car, the track has to be between 61-1/4” to 61-1/2”.

With a CG height of 15”, at a lateral acceleration of 1g, the weight transfer leaves you with about 920 lbs on the left-side tires and 2680 lbs on the right-side tires. (I’m assuming, of course, that we’re turning left.) Note that it’s the same amount of weight, but it’s distributed differently between the tires.

Now let’s raise the CG to 17.5”. Keeping everything the same acceleration and track, you are left with only 770 lbs on the left-side tires and 2830 lbs on the right-side tires. You’ve lost 150 lbs of grip on the left side just by raising the CG. You can only go as fast as the tire with the least amount of grip, so more weight transfer means less grip.

I’ve only considered left/right transfer in this example, but remember that there also is front/back load transfer. I also haven’t included in my calculation the fact that the turns are banked or that the CG isn’t actually along the centerline of the car.

A number of drivers have suggested that simply lowering the center of gravity would make a big difference in how the cars handle; however, the height of the center of gravity is determined by how the mass is distributed in the car. To lower the CG, they would either have to increase the total mass of the car (for example by adding mass to the framerails, but then the engine has to move a larger mass), or they would have to move mass from the top of the car to the bottom without compromising safety. Making the cars wider would also decrease the weight transfer, but I can only imagine what that would do to the car’s side force.

As soon as I can get just the right picture of my hound dog (nose down, tail up), I’ll be ready to tackle the second most frequently heard driver suggestion for improving the new car, which is to increase the travel.

UPDATE (in response to Jeff’s comments): Mark Aumann has a series of articles about the NASCAR R&amp Center on nascar.com. He notes that the official NASCAR press release cites 52 employees for the R&amp Center. They don’t break down the number, but it’s a fair guess that number includes administrative and other non-technical personnel. Thanks to Mark for the info!