Why Turning is Hard

Why Turning Fast is Hard

If Isaac Newton had been a racing fan (which I’m sure Sir Isaac would have been if had cars been invented in the 1600’s), he might have stated one of his laws this way:

A race car going straight down the backstretch at 180 mph will keep straight going down the backstretch at 180 mph — unless a net force makes it turn.

Race tracks are rarely circles, but as a first approximation, we can consider each turn to be part of a circle and model the turning of the racecar using uniform circular motion. Uniform circular motion basically means that the object is moving in a circle at constant speed.carturning

If I tie a string to a tennis ball and swing it at constant speed in a circle of radius r over my head, the only reason the ball goes in a circle is because the string is constantly pulling it toward the center of a the circle.  The string forces the ball to turn.

Just like the tennis ball, a turning car needs a force to make it turn. If you want the car to turn left, you have to exert a force to the left.  At each point in the turning circle, the force that makes the car turn is perpendicular to the direction the car is moving, which makes the force always toward the center of the circle.  This center-pointing force is called the centripetal force, and it depends on the mass of the car, the speed of the car and the turn radius of the track.

EQ_CentripetalForceWords

This equation tells you:

  • The heavier the car, the more turning force it takes
    • Because mass only appears one, if you double the mass of the car, you need twice as much turning force
  • The higher the speed, the more turning force it takes
    • The speed is squared — if you double your speed, you need four times as much turning force.
  • The larger the turn radius, the less turning force it take.
    • The turn radius is in the denominator, so it acts oppositely to the mass and the speed.

The Numbers

Let’s look at some numbers:  The minimum weight of a Gen-6 car is 3300 lbs for a driver of 180-lb, so I’m using a total weight of 3480 lbs (and dividing by 32.2 ft/s2 to get the mass).  Let’s look first at a wide sweeping track like Talladega, with a turn radius of 1100 ft and a speed of 180 mph throughout the turn.  According to the formula, that car needs 6848 lbs of turning force.
Let’s do the same calculation for Richmond, where the turn radius is only 365 ft.  Whoa — you’d need 20,636 lbs to turn at 180 mph.  Why?  The turn radius at Richmond is about 1/3 the turn radius at Talladega, so you need about three times more turning force.  This is why you slow down coming off the exit ramp on a cloverleaf.  70 mph is reasonable on the expressway, but when you’re turning and especially if the turn is tight, then you need to slow down. This is also why cars don’t take the corners at Richmond at 180 mph.
Let’s run the numbers at a more reasonable speed for Richmond, like 100 mph. Then you get about 6,370 mph.  But if you want to go 1oo mph around the corners at Bristol, you need 9,606 lbs of turning force because Bristol has even tighter turns than Richmond.  I put the numbers in a table for easy reference.

Track Turn radius
(ft)
Speed
(mph)
Turning Force
(lbs)
G’s
Talladega 1100 180 6,848 1.97
Richmond 365 180 20,636 5.93
100 6,370 1.83
Bristol 242 100 9,606 2.76

“G”

A “G” is a unit.  Just as we call twelve eggs a dozen, we likewise can measure acceleration in units of the earth’s gravitational pull.  A “G” is a unit of acceleration equal to the acceleration of the Earth’s gravity.  One “G” is 32.2 feet per second per second, or 22 mph per second.  An acceleration of  “2Gs” just means twice the acceleration due to gravity. 2G = 64.4 ft/s2 or 44.0 mph/s.

Acceleration is how fast you’re changing speed.  Anything falling with only the force of the Earth’s gravity acting on it will move 32.2 feet per second (or 22mph) faster for every second it is falling.  If you drop a penny, it will be going 22 mph after  one second, 44 mph after two seconds, etc.   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).  Accelerations over the 5-6G range cause problems because your heart can’t pump blood well enough to ensure that it makes it everywhere in your body and you’re subject to blacking out.
It seems like a G should always point downward, but just like a dozen eggs could be hen’s eggs or goose eggs, acceleration can be in any direction.  When you’re on a roller coaster coming down a hill, or if you’re falling, the acceleration is downward; however, when you’re taking a corner, the acceleration is sideways.  I talked to one driver who said he can’t handle roller coasters.  He doesn’t mind sideways Gs, but he really hates the up and down Gs.

G-Force

Please don’t ever use the term “G-force”.  A G is a unit of acceleration, not force.  Force is obtained by multiplying a mass times times an acceleration.

At this moment, you are being pulled toward the center of the Earth.  If the surface of the Earth weren’t there holding you up, you’d be falling and gaining 32.2 feet per second in speed every second you fell.

If you step on a scale, the scale measures the force with which the Earth is pulling down on you.  That force is your mass times one G – which we call your weight.  A drag racer experiencing 5G of acceleration feels a force five times his or her weight.  The number before the “G” is the multiplier for how much force you feel in terms of your weight.

The reasons people use Gs is because you can talk about acceleration independent of mass.  If Danica Patrick and Tony Stewart experience 2 Gs around the corner at Kansas, Patrick (who weighs about 100 lbs) feels a force of 200 lbs.  Stewart (who weighs 180 lbs)  feels a force of 360 lbs.  They both feel the same acceleration, but because they have different masses, they feel different forces.  Everyone throws around numbers like ’50 Gs’, but without understanding that G is really the acceleration due to Earth’s gravity, those numbers have very little meaning.

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