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4412 airfoil section absolute coefficient additional distribution additional lift adjusted velocity distribution Ames Aeronautical Laboratory angle of attack axis base-profile velocity distribution basic lift coefficient basic lift distribution calculate the velocity Calculated by method change in shape chord chordwise lift distribution desired velocity distribution determined double-roof base profile drag elliptic base profile equation 28 example function of x/c given airfoil given velocity distribution Hence ideal angle induced velocity inverse problem Joukowski base profile Julian Allen leading and trailing leading edge leading-edge radius low-drag airfoil lower surface velocity mean camber line mean camber-line shape method of reference NACA 4412 airfoil NACA Rep numerical integration obtained ordinates and slopes plotted potential theory PRESSURE DISTRIBUTION profile is found quarter-chord moment coefficient reference 9 reference base profile reference profile Reynolds number semi-low-drag airfoil shape corresponding strut section superposition surface velocity distributions thickness ratio tion trailing edge trie United States Navy upper and lower viscosity