Force Based Roll Centers with Suspension Springs Inclined from the Vertical

In this work the location of the roll center (RC) is investigated for the cases where suspension springs are not vertical. For typical FSAE cars, the lower end of the suspension springs is attached to the wheel upright, while the upper end is anchored to the chassis, inclined away from the wheel. Such inclined springs will transmit a force composed of a vertical component, which will counter gravity, and a horizontal component which will be resisted by the suspension links. When cornering, the vertical component, the normal reaction upward from the road, and the frictional force combine to make a resultant that goes through the center of rotation of this suspension system. When the horizontal component is added, the resultant no longer goes through that center. Where the resultants from the outer and inner wheels intersect, there will be a temporary force based roll center (FBRC). Using the dimensions of a representative FSAE car, the RC is spaced about 100 mm laterally away from the static central RC. Consequently, as such a car turns from one direction to the other, the FBRC will move 200 mm from the left to the right.