Roll 2 Exercise
Konstruktion 7BS
Revised 06.12.05

What is unrealistic about the problem below is that the center of mass is unrealistically low.  The car would certainly slide before it turns over.  However, to avoid confusion by changing the problem, I would prefer to keep these numbers as they are, since some people have already completed the assignment and others are in the middle of doing so.  The numerical procedure is the same, regardless of the unrealistic results for the sideways acceleration needed for overturning.

1.    An automobile of mass 2000 kg deflects its springs 50 cm with its static load.  Its wheels are 150 cm apart, side-to-side.  Assume the unsprung mass is 10% of the vehicle's mass.  The car's CG is 10 cm high.  Its roll center is 5 cm high.  For the following problems, ignore the two additional effects discussed on pages 8/12-13 of Professor Iannce's book for this first analysis.

a)    What is the car's roll stiffness?

b)    Calculate the centripetal acceleration that will cause this car to overturn in a flat turn.

c)    What will be the roll angle of the car in a turn with this acceleration?

d)    We want to reduce this roll angle.  What would be the roll angle in such a turn if we increased the vehicle track to 160 cm?

e)    In addition to the change given in d), what would be the roll angle if the car's sprung mass were reduced by 10%?

e)    Design a sway bar that will reduce the roll angle to half that found in c).  Give the required roll stiffness, the roll stiffness supplied by the sway bar, and the dimensions of a round, carbon steel sway bar with the proper stiffness.  Let the sway bar lever arms be 15 cm. 

f)    What would be the angular twist of the sway bar in this turn?

g)    What would be the centripetal acceleration required to overturn this wider, lightened car with its new sway bar?