Potential flow over an n -family of undulated airfoils

This paper presents a general potential-flow solution for an n-family of undulated lifting cylinders and their corresponding conformally mapped undulated airfoils. The analysis first derives a unified closed-form solution for potential flow around undulated lifting cylinders using a perturbation technique that enforces the no-penetration boundary condition on geometries with arbitrary undulation amplitudes and wavenumbers. The resulting formulation yields explicit analytical expressions for the stream function, enabling direct evaluation of geometric effects on streamline curvature, the velocity field, and surface pressure distributions. Building on this undulated-cylinder framework, the solution is subsequently mapped into the airfoil plane via the Joukowski transformation, yielding a solution for an n-family of undulated lifting airfoils. Unlike classical general airfoil theories that rely on inverse formulations, the present approach proceeds directly from undulated cylinders to undulated airfoils while preserving analytical tractability throughout. The unified framework provides a versatile analytical foundation for investigating the aerodynamics of undulated lifting bodies and creates new opportunities for flow-control strategies, aerodynamic performance optimization, and bio-inspired design. Overall, the formulation constitutes a canonical analytical generalization of classical potential flow to geometrically modulated lifting bodies.