Description Variables associated with the tire kinematics as well as the contact patch forces/moments are shown in the figure below. Tire kinematics and force/moment calculations are performed with respect to ISO coordinates. The origin of the ISO coordinate system is the tire-surface contact point, C. The unit vector for the z-axis, ${\stackrel{^}{e}}_{z}^{\mathrm{ISO}}$, aligns with the surface normal vector which in turn is a result of defined surface geometry as explained in Surface. The unit vectors for the x and y axes, ${\stackrel{^}{e}}_{x}^{\mathrm{ISO}}$ and ${\stackrel{^}{e}}_{y}^{\mathrm{ISO}}$, are calculated using the following vector algebra equations: ${\stackrel{^}{e}}_{x}^{\mathrm{ISO}}={\stackrel{^}{e}}_{\mathrm{spin}}×{\stackrel{^}{e}}_{z}^{\mathrm{ISO}}$ ${\stackrel{^}{e}}_{y}^{\mathrm{ISO}}={\stackrel{^}{e}}_{z}^{\mathrm{ISO}}×{\stackrel{^}{e}}_{x}^{\mathrm{ISO}}$ where ${\stackrel{^}{e}}_{\mathrm{spin}}$ is the unit vector for the tire spin axis. The inclination angle or camber, $\mathrm{\gamma }$ is $\mathrm{\gamma }={\mathrm{sin}}^{-1}\left(\left({\stackrel{^}{e}}_{y}^{\mathrm{ISO}}×{\stackrel{^}{e}}_{\mathrm{spin}}\right)·{\stackrel{^}{e}}_{x}^{\mathrm{ISO}}\right)$ Tire revolution speed or spin rate $\mathrm{\Omega }$, which is needed for slip calculations, is derived using the following equation $\mathrm{\Omega }=\stackrel{&conjugate0;}{\mathrm{\omega }}·{\stackrel{^}{e}}_{\mathrm{spin}}-\stackrel{&conjugate0;}{\mathrm{\omega }}·{\stackrel{^}{e}}_{z}^{\mathrm{ISO}}\mathrm{sin}\left(\mathrm{\gamma }\right)$ where $\stackrel{&conjugate0;}{\mathrm{\omega }}$ is the angular velocity vector of the tire.