{"id":112,"date":"2011-12-24T13:15:09","date_gmt":"2011-12-24T12:15:09","guid":{"rendered":"http:\/\/www.edy.es\/dev\/?page_id=112"},"modified":"2024-02-12T16:15:38","modified_gmt":"2024-02-12T15:15:38","slug":"pacejka-94-parameters-explained-a-comprehensive-guide","status":"publish","type":"page","link":"https:\/\/www.edy.es\/dev\/docs\/pacejka-94-parameters-explained-a-comprehensive-guide\/","title":{"rendered":"Pacejka ’94 parameters explained – a comprehensive guide"},"content":{"rendered":"

This guide explains how each parameter of the Pacejka ’94 specification<\/strong> affects the resulting curve, as well as their typical range of values.<\/p>\n

The Pacejka \/ Magic Formula (MF) equations were conceived to fit the data gathered from experimental tests with real tires. Real Pacejka\/MF data sets are heavily protected intellectual property of the tire manufacturers. However, when used in video games where gameplay is important, the Pacejka curves can be fine tuned in a variety of ways to achieve the desired result.<\/p>\n

\"\"<\/a>Longitudinal Force<\/h2>\n

Pacejka ’94 Longitudinal Force parameters:<\/p>\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
Parameter<\/th>\nRole<\/th>\nUnits<\/th>\nTypical range<\/th>\nSample<\/th>\n<\/tr>\n
b0<\/td>\nShape factor<\/td>\n<\/td>\n1.4 .. 1.8<\/td>\n1.5<\/td>\n<\/tr>\n
b1<\/td>\nLoad influence on longitudinal friction coefficient (*1000)<\/td>\n1\/kN<\/td>\n-80 .. +80<\/td>\n0<\/td>\n<\/tr>\n
b2<\/td>\nLongitudinal friction coefficient (*1000)<\/td>\n<\/td>\n900 .. 1700<\/td>\n1100<\/td>\n<\/tr>\n
b3<\/td>\nCurvature factor of stiffness\/load<\/td>\nN\/%\/kN^2<\/td>\n-20 .. +20<\/td>\n0<\/td>\n<\/tr>\n
b4<\/td>\nChange of stiffness with slip<\/td>\nN\/%<\/td>\n100 .. 500<\/td>\n300<\/td>\n<\/tr>\n
b5<\/td>\nChange of progressivity of stiffness\/load<\/td>\n1\/kN<\/td>\n-1 .. +1<\/td>\n0<\/td>\n<\/tr>\n
b6<\/td>\nCurvature change with load^2<\/td>\n<\/td>\n-0.1 .. +0.1<\/td>\n0<\/td>\n<\/tr>\n
b7<\/td>\nCurvature change with load<\/td>\n<\/td>\n-1 .. +1<\/td>\n0<\/td>\n<\/tr>\n
b8<\/td>\nCurvature factor<\/td>\n<\/td>\n-20 .. +1<\/td>\n-2<\/td>\n<\/tr>\n
b9<\/td>\nLoad influence on horizontal shift<\/td>\n%\/kN<\/td>\n-1 .. +1<\/td>\n0<\/td>\n<\/tr>\n
b10<\/td>\nHorizontal shift<\/td>\n%<\/td>\n-5 .. +5<\/td>\n0<\/td>\n<\/tr>\n
b11<\/td>\nVertical shift<\/td>\nN<\/td>\n-100 .. +100<\/td>\n0<\/td>\n<\/tr>\n
b12<\/td>\nVertical shift at load = 0<\/td>\nN<\/td>\n-10 .. +10<\/td>\n0<\/td>\n<\/tr>\n
b13<\/td>\nCurvature shift<\/td>\n<\/td>\n-1 .. +1<\/td>\n0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Pacejka ’94 longitudinal formula<\/h4>\n\n\n\n\n\n\n\n\n\n\n\n\n
Coefficient<\/th>\nName<\/th>\nParameters<\/th>\nFormula<\/th>\n<\/tr>\n<\/tbody>\n
C<\/td>\nShape factor<\/td>\nb0<\/td>\nC = b0<\/td>\n<\/tr>\n
D<\/td>\nPeak factor<\/td>\nb1, b2<\/td>\nD = Fz \u00b7\u00a0(b1\u00b7Fz + b2)<\/td>\n<\/tr>\n
BCD<\/td>\nStiffness<\/td>\nb3, b4, b5<\/td>\nBCD = (b3\u00b7Fz2<\/sup> + b4\u00b7Fz) \u00b7 e<\/em>(-b5\u00b7Fz)<\/sup><\/td>\n<\/tr>\n
B<\/td>\nStiffness factor<\/td>\nBCD, C, D<\/td>\nB = BCD \/ (C\u00b7D)<\/td>\n<\/tr>\n
E<\/td>\nCurvature factor<\/td>\nb6, b7, b8, b13<\/td>\nE = (b6\u00b7Fz2<\/sup> + b7\u00b7Fz + B8) \u00b7 (1 – b13\u00b7sign(slip+H))<\/td>\n<\/tr>\n
H<\/td>\nHorizontal shift<\/td>\nb9, b10<\/td>\nH = b9\u00b7Fz + b10<\/td>\n<\/tr>\n
V<\/td>\nVertical shift<\/td>\nb11, b12<\/td>\nV = b11\u00b7Fz + b12<\/td>\n<\/tr>\n
Bx1<\/td>\n(composite)<\/em><\/td>\n<\/td>\nBx1 = B \u00b7 (slip + H)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

F = D \u00b7 sin(C \u00b7 arctan(Bx1 – E \u00b7 (Bx1 –\u00a0arctan(Bx1)))) + V<\/strong><\/p>\n

where:<\/p>\n