How do you calculate G-forces?

On April 29, 2001, CART (Championship Auto Racing Teams) officials cancelled a race at the Texas Motor Speedway because the drivers experienced dizziness after as few as 10 laps. The combination of high speeds and tight turns at Texas Motor Speedway produces forces of almost 5 Gs in the turns. One G is the force of Earth's gravity -- it is this force that determines how much we weigh. At 5 Gs, a driver experiences a force equal to five times his weight. For instance, during a 5-G turn, there are 60 to 70 pounds of force pulling his head to the side. Let's see how to calculate how many Gs a car pulls in a turn and how these Champ cars can stay on the track under so much force.

Calculating the G-forces on the drivers is actually quite simple. We just need to know the radius of the turns and the speed of the cars. According to Texas Motor Speedway's Track Facts, the turns on the track have a radius of 750 feet (229 meters). During practice, the cars were turning laps at around 230 miles per hour (370 kph).

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When a car goes around a turn, it accelerates the whole time (this is why, when you make a turn in your own car, you feel a force pulling your body toward the outside of the car). The amount of acceleration is equal to the velocity of the car squared divided by the radius of the turn:

Let's run the numbers:

• 230 mph is 337 feet per second (f/s).
• (337 f/s)2 / 750 feet = approximately 151 f/s2.
• The acceleration due to gravity (1 G) is 32 f/s2.
• 151 / 32 = 4.74 Gs experienced by the drivers.

How can the car stay on the track under this kind of force? It's because of the banked turns.

The Texas Motor Speedway has 24-degree banking in the turns. The banking doesn't really affect how we calculate the G-forces on the driver, but without the banking the cars could never go around such a tight turn at 230 mph. Let's see how the banking helps.

If a Champ Car tried to make a flat turn at 230 mph, it would slide right off the track because it doesn't have enough traction. Traction is proportional to how much weight is on the tires (the more weight, the more traction). Banking a turn allows some of the G-forces created in the turn to increase the weight on the tires, increasing the traction. To figure out what portion of the Gs gets adds weight to the tires, you multiply the G-forces by the sine of the banking degree. In our example:

So with a 24-degree banking, 1.93 Gs adds weight to the wheels. In addition, a portion of the 1 G from Earth's gravity also puts some weight on the tires: 1 G x cos24° = 0.91 Gs. Together, 2.84 Gs (or 2.84 times the weight of the car) push down on the car during the turn, helping it stick to the track.

The car's aerodynamics also create significant downforce at 230 mph. On an airplane, the wings provide lift. A Champ Car has spoilers that are like upside-down wings, providing the opposite of lift: downforce. The downforce keeps the car glued to the track with a downward pressure provided by the front and rear wings, as well as by the body itself. The amount of downforce is amazing -- once the car is traveling at 200 mph (322 kph), there is enough downforce on the car that it could actually adhere itself to the ceiling of a tunnel and drive upside down! In a street-course race, the aerodynamics have enough suction to actually lift manhole covers -- before the race, all of the manhole covers are welded down to prevent this from happening!

Between the downforce and the G-forces, well over four times the weight of the car holds the tires to the track when it goes around one of those 24-degree banked turns at 230 mph.

Drivers take an enormous amount of punishment on a track like this. This level of acceleration is higher than most people ever experience. Even the space shuttle only develops 3 Gs when it takes off. What's even more amazing is how long these drivers tolerate this kind of force. The Texas Motor Speedway is 1.5 miles (2.4 km) long: The front stretch is 2,250 feet (686 m) long, and the back stretch is 1,330 feet (405 m) long. At 230 mph (337 f/s), the drivers take about 6.5 seconds to go down the front stretch, and then they are slammed by almost 5 Gs of force for the next 6.5 seconds as they go around the turn. It only takes about 4 seconds to make it down the back stretch before the next turn and another 6.5 seconds of almost 5 Gs. If the planned 600-mile (966 km) race had taken place, the drivers would have gone back and forth between 5 and nearly zero Gs a total of 800 times.