How Does a Flywheel Prevent a Car from Rolling Over in High-Speed Turns?

[SadieLou]

help -- what's a flywheel?

This is a somewhat nasty homework problem from Kleppner and Kolenkow that I don't even know how to begin to set up (never spent much time with cars, I guess.)

"When an automobile rounds a curve at high speed, the loading (weight distribution) on the wheels is markedly changed. For sufficiently high speeds the loading on the inside wheels goes to zero, at which point the car starts to roll over. This tendency can be avoided by mounting a large spinning flywheel on the car.

"a. In what direction should the flywheel be mounted, and what should be the sense of rotation, to help equalize the loading?

"b. Show that for a disk-shaped flywheel of mass m and radius R, the requirement for equal loading is that the angular velocity of the flywheel, omega, is related to the velocity of the car v by

omega = 2v(ML)/(mR^2)"

What is a flywheel and where does it go -- inside the car, somewhere on the outside, or what? I imagine you'd want to create a downward torque near the inside wheels, but I can't see where the flywheel would attach.

On the lucky chance that somebody stops by and knows what to do about this, thank you.

 

[berkeman]

You want to use precession of the flywheel/gyroscope to generate a counter torque as you say, to push the inside wheels down. The source of the precession is the torque on the flywheel as the car turns.

So look up precession of a gyroscope (at wikipedia or in your text, for example), and look at which way the gyroscope precesses for an input torque on the axle. Then think about how you would mount the gyroscope (flywheel) on the car to make the turning motion put in the forces onto the flywheel axle to cause precession that keeps the inside of the car pushed down.