Catalytic assessment at the shock tube end-wall demands a better understanding of the velocity gradient. Unlike the authors' previous work, the present work investigates the velocity gradient based on the copper-coated material at the shock tube end wall. Both Goulard and Fay-Riddell heat transfer theories are applied to measure the velocity gradient. Uncertainty in the reference catalytic recombination value for the copper material is taken into account for the Goulard catalytic heat transfer under the partial catalytic wall assumption. In addition, the velocity gradient is computed based on a modified local heat transfer simulation method. By extrapolating the flow condition at the shock tube end-wall to flight condition, a corresponding blunt-body velocity gradient is computed. In that process, both equivalent incoming flow and blunt body geometry for flight condition that give similar heat transfer to those under the shock tube end-wall are investigated for the first time.