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TECHNOLOGY – SIMULATION


Equations 1


F


L = ! kb p


2


ka = initial coefficient of friction


kb = drop off of coefficient with load


Fz = load on the tyre 2


A l c p. = c p. =


P F


T Z


A .c p wt


Ac.p = contact patch area (m2) Fz = vertical load on the tyre (N)


wt = width of the tread (m) lcp = length of the contact patch (m)


3 µ= fn(P V T, L , s IN )T


u = coefficient of friction of the tyre


PL = local tyre pressure applied at the tyre


Vs = sliding velocity of the tyre


TINT = core temperature of the tyre


4 5


TC = fn F fn P RAD Z ΔFFFACT ΔFFFACT = _ ⋅ y ref _ ( ) ( )t


a _y cur − ay ref w adf


= change in force factor


ay_cur = measured lateral acceleration for the


change


ay_ref = measured lateral acceleration for the


base set up


wdf = weight distribution at the front


"a 2D model gives you a


good broad brush stroke, but lacks fidelity"


60 www.racecar-engineering.com • January 2012 Figure 2: an illustration of what you obtain from a 2D tyre model


Table 1: typical V8 Supercar set up Parameter


Value


Front roll centre Rear roll centre Front wheel rate Rear wheel rate


Front bar wheel rate Rear bar wheel rate Front track / rear track Front tyre spring rate Rear tyre spring rate c of g height


100mm 240mm 60N/mm 60N/mm 40N/mm 10N/mm


1.6m/1.6m 305N/mm 305N/mm 0.45m


y = k (1" kb ! F ! 1


a z ) Fz


Figure 1: typical 2D tyre modelling correlation using ChassisSim


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