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# Vehicle in a turn

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Hello. This is not a homework question, but as i was doing my seminar work, i came to a question that it has been bugging me for a while now. I do not need this for my project, but it came to my interest as it isn’t specified anywhere, but there must be some complex physics behind it. question: i’m doing construction engineering and i have been researching into importance of good road and surface design for maximum amount of friction between a car and tyre. What doesn’t add up are coefficient of friction of tyre, and rules and regulations for building roads. In the latter, coefficient of 0.037 was used(which i calculated backwards from a formula), but the tyre manufacturers state their coefficient of friction to be between 1 and 0.5(depending of size, model, intended use,… of tyre). So if i use coefficients of tyre of manufacturers in the formula for banked turn with friction, i get unrealistic results. So i’m thinking, how would i, at least approximately calculate that to get realistic results? Do i have to include many various different factors, from height and length of the car, suspension, air drag, weight, centrifugal and centripetal force, angle, as well as a safety factor, for when snow falls on the surface. So how would a formula like that look like? It seems to me it could get very complicated, that’s why i am asking as i do not have a deep physics knowledge. Thank you for your time.

Kristjan

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