Turning at Bristol: A Weighty Matter

Even though Bristol Motor Speedway is a smaller track than Daytona, turning at Bristol is harder than it is at Daytona. Because Centripetal Force.

A lot of drivers cite Bristol as one of their favorite tracks. It’s a great exhibit for the argument that racing is more than just pure speed. High banks (which we know mean speed!) and a short track, which means tight racing.

But a lot of drivers will also tell you that Bristol is one of the most exhausting, physically demanding tracks on the circuit because turning at Bristol is hard. Add to that the inherent stress of short-track racing, where 43 cars are operating in a limited (half-mile) track.

Turning (i.e. Centripetal) Force

Regular readers know that the force it takes to turn a race car is given by:

\text{Turning Force}= \frac {\text{mass} \times \text{speed} \times \text{speed}} {\text{turn radius}}

So it is harder to turn (i.e. you need more force)

• if your car is heavier
• when you’re going fast
• when making tight turn

So when you compare a thousand foot turn radius like at a superspeedway with the 250-foot turn radius of Bristol, it’s four times easier to turn at Daytona  — if you’re turning at the same speed.

Turning Force

Using a typical weight for a Gen-6 car (3300 lbs of car and 180 lbs of driver), we can figure out how much force it takes to make a car turn.

Newton’s First Law says that a car going straight down the frontstretch at Bristol will keep going straight (and into the wall) unless a force acts on it and causes it to turn.

Consider a soccer ball rolling past you. You want to change its direction, so you kick it at a right angle to the direction it’s headed. The faster it’s moving, the harder you have to kick it to change its direction. The direction it goes is a combination (a physicist would say “a vector sum”) of the direction it had been heading and the direction of the force (the kick) you applied to it.

Turning Force at Bristol vs. Elephants

An adult male African Elephant weighs, on average, 15,400 pounds. Turning a NASCAR race car at Bristol at 130 mph requires a force slightly greater than the weight of an African Elephant.

Let’s look at the force needed to turn a racecar as a function of speed. Note that the turn radii at Bristol are different for turns 1/2 and 3/4. Turns 1/2 have a turn radius of 242 ft, while 3/4 have a turn radius of 256 ft.

Compare this to Daytona, which has higher speeds, but also larger turns.

Conclusion: It’s easier to turn at Daytona. Even though speeds are a higher, you’ve got four times more turn radius.

Acceleration

We can also look at the Bristol turning force in terms of acceleration. One g is 32 feet per second per second. Here’s how many g’s drivers pull at Bristol.

Just for reference, most amusement park rides top out at about 3G; however, some roller coasters go up to 4G (SheiKra Rollercoaster at Tampa) or 4.5G (e.g. the Titan Rollercoaster in Texas).

Although the “G” is the acceleration due to the Earth’s gravity (which always points to the center of the Earth), we use G to measure acceleration in any direction: up or down, back or forth, or sideways.  Drag racers experience accelerations of about 5G backward at take off.  When you’re turning at constant speed, the acceleration is sideways (which engineers call ‘lateral’).

The green line is on there because around 5-6 G’s, drivers start to be impaired because the forces actually change the ability of the blood to circulate through the body. Drivers may experience greyout, which is a loss of color vision, tunnel vision (loss of peripheral vision), blackout (complete loss of vision, but still conscious) and finally G-LOC (which is loss of consciousness because of gravitational forces) .

Now, if you’re paying close attention, you will notice that the graph of ‘G’s and the graph of forces look very similar. In fact, they are the same trend because you get the g’s by dividing the turning force by the mass of the car and the acceleration due to gravity (32.2 ft/sec/sec).

The Effect of Banking: Inside Line or Outside Line

One of the most interesting things about Bristol is that it has graduated banking – from 24 degrees to 28 degrees. As we’ve discussed before, the higher the banking, the more the track helps the car turn. But here’s the twist: If you go up high to take advantage of the higher banking, you actually have to travel a longer distance.  The racing surface width is 40 feet. Now, one of the problems with the way track measurements are specified is that you don’t actually know where they measured the track length.

Let’s assume for the purposes of argument that the 0.533 width was measured at the apron – which means that the end of the track at the outside wall is 40 feet further out. The distance down the front and back stretches are the same, so all we’re worried about is the difference in the turns.

If you take the outside line rather than the inside line, you’re going about 125 feet more distance than your competitor who takes the inside line. So you have to find out, given your car’s setup, whether the additional banking helps you turn faster.

If you take the outer line then at 130 mph, you need 13,910 lbs of force, compared to the 16, 235 lbs you need at the inside. You pull 4.00 gs instead of 4.67 gs on the inside. At 130 mph, you’re covering 190 feet per second, so the time it takes you to traverse the extra 125 feet is a little more than half a second. Not much, right?

Except lap times run around 15 seconds.

At the April race, final practice times ranged from 15.043 seconds (Kurt Busch, in first place) to 15.818 seconds (Alex Kennedy in 43rd place).  Half a second takes you from first to 40th place. So you darned well better be faster if you’re traversing the outside.

I don’t know where the 242.45 feet for the turn 1/2 radius was measured. If it was measured at the midpoint of the track, then the differential is smaller, but I figure I’d take the most extreme case to make the point.

NOTE: This post was updated on Saturday, September 19, 2020. It was edited for length and the illustrations were cleaned up.

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