Toppling speed on level rails ($v_0=\sqrt{gRd/(2h)}$)

A vehicle with centre of mass midway between level rails separated by d, at height h, follows a turn of radius R. Vertical force balance and cross-sectional moment balance give inner rail reaction $mg/2-m{v}^{2}h/(Rd)$. Its first zero occurs at the displayed speed. This is a toppling criterion under maintained lateral contact, not a guarantee against sliding or suspension instability.