Nomenclature a = constant; Fig. 1 C, C 0 = constants k = roughness element height, ft N k = average roughness element height, ft L = vehicle length, ft M = Mach number n = exponent; Fig. 1 N R = Poll's transition parameter 29;30 ; Eq. (1) Re ke = roughness Reynolds number based on height k and edge conditions Re kk = roughness Reynolds number based on height k and conditions at k Re µ = Reynolds number based on height µ and edge conditions U = velocity component parallel to test surface or velocity component perpendicularto attachment line, ft /s V = velocity component parallel to attachment line, ft/s X = generalized disturbance parameter or axial coordinate along windward centerline x = coordinate perpendicular to attachment line, ft Y = generalized transition parameter ® = angle of attack, deg ± = smooth-wall laminar boundary-layer thickness, ft = Poll's length scale 29;30 [Eq. (2)], ft µ = smooth-wall laminar boundary-layer momentum thickness, ft ¹ = viscosity, lbm/ft ¢ s º = kinematic viscosity, ft 2 /s ½ = density, lbm/ft 3 Subscripts al = attachment line e = edge of smooth-wall laminar boundary layer k = based on conditions in smooth-wall laminar boundary layer at top of roughness elements tr = transition w = wall or based on wall temperature Superscript ¤ = properties evaluated at Poll's reference temperature 29;30 Daniel C. Reda recently joined the Space Technology Division at NASA Ames Research Center as a Senior Scientist, responsible for aerothermodynamics research to support access-to-space and planetary-entry missions. Previously, he was a Senior Research Scientist in the Ames Research Center Fluid Mechanics Laboratory, where he developed a global surface shear stress vector measurement method using liquid crystal coatings.