The rectilinear local crossing number of Kn

We determine lcr‾(Kn). More precisely, for every n∉{8,14},lcr‾(Kn)=⌈12(n−3−⌈n−33⌉)⌈n−33⌉⌉, lcr‾(K8)=4, and lcr‾(K14)=15.