This paper reports new analytical formulas for the longitudinal slip lengths for simple
shear over a superhydrophobic surface, or bubble mattress, comprising a periodic array
of unidirectional circular menisci, or bubbles, protruding into, or out of, the fluid. The
accuracy of the formulas is tested against results from full numerical simulations; they
are found to give small relative errors even at large no-shear fractions. In the dilute limit
the formulas reduce to an earlier result by the author [Phys. Fluids, 22, 121703, (2011)].
They also extend analytical results of Sbragaglia & Prosperetti [Phys Fluids, 19, 043603,
(2007)] beyond a small protrusion angle limit.