The effects of injection rate and strength of curvature on film cooling performance of gas injected through a row of holes on a convex surface are studied. Comparisons are made to film cooling of concave and flat surfaces. Three different relative strengths of curvature (ratio of radius of curvature to radius of injection hole), two density ratios (0.95 and 2.0), and a wide range of blowing rates (0.3 to 2.7) are considered. A foreign gas injection technique (mass transfer analogy) is used. The strength of curvature was controlled by varying the injection hole diameter. At low blowing rates, film cooling is more effective on the convex surface than on a flat or a concave surface. The cross-stream pressure gradient present in curved flows tends to push the jet into the convex wall. As the injection rate is increased, normal and tangential jet momentum promote liftoff from the convex surface, thereby lowering performance. In contrast, previous studies show that on a concave surface, tangential jet momentum, flow instabilities, and blockage improve performance on a concave surface as blowing rate is increased.