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Steer the tire a little, and you get a slip angle, and this is input into the Pacejka Fy formula, giving a sideways force. Press the throttle, and the wheel starts spinning a bit; this gives a different ratio of wheel spin speed vs. ground speed, and this gives a forward (longitudinal) force.
Tire makers calculate the aspect ratio by dividing a tire's sidewall height by its width. If a tire has an aspect ratio of 70, it means the tire's height is 70% of its width.
For metric sizing, take the section width and convert it to inches (divide by 25.4), then multiply that by the aspect ratio (shown as a percentage) to get the sidewall height. Next, take the sidewall height, double it, add the wheel diameter, and you'll have the diameter of a metric tire.
The Magic Formula (Pacejka) tire model for the longitudinal force is described by the following mathematical expression:Fy=D·sinCA·arctan{BA·03ba2212EA·(BA·03ba2212arctan(B03ba)}for pure longitudinal (brake/drive) slip 03ba.
We know the diameter of the wheel is 15 inches, so the diameter of the tire is given by: tire diameter = wheel diameter + (2 Ă— sidewall height)