Stunt Science: The Physics of Loop The Loop

When I was a kid one of my favorite toys was my HotWheels race track. I had the Criss-Cross-Crash which sent cars around a figure eight track and crashing into each other where the tracks crossed. Later they came out with the Double Dare Loop. It had the same basic concept, but instead of a figure-eight, cars would run separate tracks into a single loop where they might or might not crash. It was a great game of imagination in which we would pretend the tiny realistic cars were full size cars driven by us.

Fast Forward, someone actually did this with real CARS!

Image Via Hot Wheels

Centripetal Force

What’s really awesome about this is how slow the cars are going. The video is in full speed, not slow motion. The cars are going 52 MPH, but seem to be going very slowly. They almost lumber through the loop, casually driving upside down. How does that work? Centripetal Force is the answer. It is a force that keeps our moon in the sky and gets the water out of out pants in the washing machine. Here’s how it works.

Acceleration

As you move forward in a straight line at a constant speed you are not accelerating. Acceleration is a change in speed or direction of a moving object. If you are in a car and you turn to the left or right, you accelerate even if the speedometer does not register that the wheels are turning any faster. You might also slide across the back seat into your little brother, or be pinned to one side of your car seat. The force that pushes you is Centripetal Force. Your mass, and the mass of the car would go in a straight line at a constant speed unless acted upon by the steering wheel [Inertia]. When the car turns, your arms, legs and guts all get yanked in another direction.

Formula

The Formula for calculating centripetal force is a function of the mass of the object, the radius of the circular path it is traveling and the speed at which it is traveling around that path.

Fcentripetal = M v2/r

  • Centripetal Force
  • m: mass of object
  • V: velocity/speed
  • r: radius of the circular path.

 Estimated Centripetal Force or a Life Size HotWheels Car

Just for fun, let’s calculate the force on the tires of the cars in the video above.

  • The cars are replicas of the HotWheels toys, which weigh about 3000 pounds, or 1,400 Kilograms. [LA Times]
  • The loop is 66 feet (20m) in diameter so r=10m
  • The cars are traveling at 52 miles per hour [23 m/s]

You can use the handy force calculator above to execute the formula. The result, 74,060 N, is expressed in Newtons which is a standard unit for force. 1 Newton is the amount of force required to accelerate a mass of 1 kilogram at the rate of 1 meter per second squared [Wikipedia].

G-Force

The articles about the Hot Wheels Loop state that the drivers experienced 7 Gs during their trip through the loop. A G is the amount of pressure you feel due to the pull of gravity while standing on the surface of the Earth at sea level. As you go through a loop, you are pulled against your seat and feel simulated gravity against it. In order to not fall off the loop when you’re upside down, you ned to be generating enough centripetal force to experience at least 1 G between you and the track. So let’s calculate the G-Forces on these drivers and see if we can verify the claim.

ForceHotWheels=(23m/s)2/10m

FHotWheels=52.9 m/s2

1G=9.8 m/s2   To compare the two you divide one by the other: 52.9/9.8 = 5.39 G

So by my calculation they were about 2 Gs off from their claim. But do check my math it you can…

CORRECTION:

I originally had r = 20m above and have changed it to 10m

-Mike

Sources