What is the relationship between the design lift coefficient and the section lift coefficient of a NACA5 airfoil?
The design lift coefficient determines the camber line of the airfoil. It is chosen such that the flow hits the airfoil exactly parallel to the start of the camber line when at the design lift coefficient. For a NACA 23015 this would be a lift coefficient of 0.15 x 2 = 0.3. The index i only denotes that this was held to be the ideal lift coefficient.
At this ideal lift coefficient the highest local curvature of the airfoil contour is right at the stagnation point and the pressure distribution downstream from there is smooth without the suction peaks which occur when the high curvature of the leading edge has to be negotiated by the upper (higher lift coefficient) or lower (smaller lift coefficient) side flow.