This paper conducts numerical simulations to delve into the phenomenon of tire-road separation using a half-car model. It scrutinizes scenarios where the tires lose contact with the surface, delving into the time response and phase portrait domains. This analysis captures vertical displacements and pitch dynamics in both in-contact and no-contact states. The research examines tire-road detachment for individual wheels and both wheels concurrently while also considering variations in road conditions and suspension structures. By comparing outcomes between scenarios where tires maintain contact and where they separate, the study offers valuable insights for vehicle designers, aiding them in selecting optimal suspension parameters to mitigate tire-road separation.