In this paper, we will give some optimal estimates on the rotation number of the linear equation $\ifmmode\expandafter\ddot\else\expandafter\"\fi{x} + p(t)x = 0,$ and that of the asymmetric equation: $\ifmmode\expandafter\ddot\else\expandafter\"\fi{x} + p(t)x_{ + } + q(t)x_{ - } = 0,$ where / p( / t) and / q( / t) are almost periodic functions and $x_{ + } = \max \{ x,0\} ,\;x_{ - } = \min \{ x,0\} .$ These estimates are obtained by introducing some kind of new norms in the spaces of almost periodic functions.