Abnormal geodesics in 2D-Zermelo navigation problems in the case of revolution and the fan shape of the small time balls

In this article, based on two case studies, we discuss the role of abnormal geodesics in planar Zermelo navigation problems. Such curves are limit accessibility set, domain where current is strong. The problem set frame geometric time optimal control, control heading angle ship and context, shown to separate minimal from maximal both small-time minimizing maximizing. We describe balls. For bigger time, a cusp singularity can occur direction, which corresponds conjugate point along non-smooth image. It interpreted terms regularity property value function.