41.2.3.3. Lateral force

The later force depends on the Vertical force (\({{F}_{z}}\)), Current coefficient of friction (\(\mu\)). And Fiala defines a critical lateral slip (\({{\alpha }^{*}}\))

(41.32)\[\alpha^*={\tan}^{-1} \left( \frac{3 \times \mu \times |F_z|}{\eta} \right)\]

\(\eta\): Partial derivative of lateral force (\({{F}_{y}}\)) with respect to slip angle (\(\alpha\)) at the zero slip angle.

The lateral force peaks at a value equal to \(\mu \times \left| {{F}_{z}} \right|\) when the slip angle (\(\alpha\)) equals the critical slip angle (\({{\alpha }^{*}}\)).

1. Elastic Deformation State: \(\left| \alpha \right|\le {{\alpha }^{*}}\)

   (41.33)\[{{F}_{y}}=-\mu \times \left| {{F}_{z}} \right|\times (1-{{H}^{3}})\times sign(\alpha )\]

   where,

   \(H=1-\cfrac{\eta \times |\tan \alpha|}{3\times \mu \times | {{F}_{z}} |}\)

2. Sliding State: \(\left| \alpha \right|>{{\alpha }^{*}}\)

   (41.34)\[{{F}_{y}}=-\mu \times \left| {{F}_{z}} \right|\times sign(\alpha )\]