Monday, January 19, 2015

The Physics of the Racing Line: How to Have the Absolute Quickest Lap Times

The Physics of the Racing Line: How to Have the Absolute Quickest Lap Times

From the February 2015 issue of Car and Driver

Whether you’re aware of it or not, you learned the basic rules of track lapping in kindergarten: Get in line, stay in line, and follow the line. And no hitting others. Mastering the concept, however, requires a physicist’s understanding of how dramatically a slight misstep can adversely affect your lap times. Here’s a primer on how to find and keep the correct racing line, as demonstrated by the Chevrolet Camaro Z/28 on Virginia International Raceway.

1. Hit the marks
Rather than tracing the shortest path around a track, the optimal line is the largest-radius arc through a corner, raising the speed possible at the limit of cornering grip and reducing the power consumed by tire scrub. Failure to properly execute the three main elements of a corner—the turn-in, apex, and track-out points—results in a slower speed and a longer lap time. At Virginia International Raceway (VIR), the largest arc through Turn 3 has a radius of 270 feet. Knowing a car’s maximum skidpad grip, we can use the formula shown above to calculate its highest possible speed through the bend. In this case, a car with 1.10 g’s of stick can hold the line through Turn 3 up to 66.7 mph. If you don’t use the full track and miss the turn-in, apex, and track-out points by one foot each, the radius falls to 263 feet and the theoretical speed drops to 65.9 mph.

2. Fast corners make for fast straights
The constant-radius, steady-speed corner is a simplification of the ideal racing line. In most turns, it’s more important to maximize exit speed than the average speed through the corner. That’s because an extra mile per hour at the corner exit adds roughly 1 mph to the average speed over the duration of the subsequent straight. Exit VIR’s Turns 11 and 12 and you enter a 2387-foot straight and, in the Camaro Z/28, begin 15 or so seconds of full-throttle acceleration. The straight culminates in a top speed of 135.2 mph with an average velocity of 110.3 mph. Drop that average speed to 109.3 mph through here and your lap time becomes 0.13 second longer.

The Physics of the Racing Line: How to Have the Absolute Quickest Lap Times

3. Going slower to go faster
Optimizing corner-exit speeds means improving on the constant-radius arc. Moving the apex past the midpoint of the corner increases the radius in the second half of the turn, and unwinding the steering wheel reduces the cornering load on the tires. More traction is now available for full-throttle acceleration.

Our GPS data from the Z/28 running through VIR’s Turn 13 reveals that our modified line was faster than a constant-radius path, with trail braking and a late apex allowing for an earlier throttle application. Compared with a constant-radius arc, this line raises the average speed by 1.3 mph and increases the Camaro’s speed by 10 mph at the corner exit.

4. Braking points
Just as the fast line blends cornering and acceleration on corner exit, braking lightly in the Z/28 while turning in shortens the car’s lap time. Controlled deceleration increases front-tire loading while diminishing rear-tire loading, two effects that enable a higher rate of yaw, or rotation of the vehicle toward the apex. In VIR’s Turn 13, a 148-foot stretch of trail braking in the Z/28 trims 0.19 second versus a rigidly segmented brake-turn-go approach.

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