  We derive expressions for shock formation based on the local curvature of the
flow characteristics during dynamic compression. Given a specific ramp adiabat,
calculated for instance from the equation of state for a substance, the ideal
nonlinear shape for an applied ramp loading history can be determined. We
discuss the region affected by lateral release, which can be presented in
compact form for the ideal loading history. Example calculations are given for
representative metals and plastic ablators. Continuum dynamics (hydrocode)
simulations were in good agreement with the algebraic forms. Example
applications are presented for several classes of laser-loading experiment,
identifying conditions where shocks are desired but not formed, and where long
duration ramps are desired.
