A circularly curved piece of LX-17 of square cross section was detonated at one end with a plane-wave lens. Detonation velocities along the inner and outer edge were measured with pins and a streak camera measured the detonation front curvature on the end face. A steady state "shadow" or inner curve velocity of 7.13 mm/mu s was measured for rib radii of 89 mm and 114 mm. Time constants for the change to steady state on the curve were derived. The outer time constant is set by the time for the energy to flow across the explosive, not by the reaction zone length, and this results in a considerable tilt of the front. The tilt causes the leading point of the front to move far inward, close to the inner edge. A simple theory for reaction zone lengths is used first on slabs and then on the rib. Because the tilt directs the front away from the inner edge, the inner edge of the rib can sustain a shadow velocity lower than the failure velocity of the cylinder or slab. The rib has been modeled with Ignition and Growth th in DYNA2D, producing a smooth set of detonation velocities that are slightly low. The production beta/program burn package in VHEMP produces a less smooth set of velocities that are too high.