Mathematical Model for Takeoff Simulation of a Wing in Proximity to the Ground

Aircraft flying close to the ground benefit from enhanced efficiency owing to decreased induced drag and increased lift. In this study, a mathematical model is developed to simulate the takeoff of a wing near the ground using an Iterative Boundary Element Method （IBEM） and the finite difference scheme. Two stand-alone sub-codes and a mother code, which enables communication between the sub-codes, are developed to solve for the self-excitation of the Wing-In-Ground （WIG） effect. The aerodynamic force exerted on the wing is calculated by the first sub-code using the IBEM, and the vertical displacement of the wing is calculated by the second sub-code using the finite difference scheme. The mother code commands the two sub-codes and can solve for the aerodynamics of the wing and operating height within seconds. The developed code system is used to solve for the force, velocity, and displacement of an NACA6409 wing at a 4° Angle of Attack （AoA） which has various numerical and experimental studies in the literature. The effects of thickness and AoA are then investigated and conclusions were drawn with respect to generated results. The proposed model provides a practical method for understanding the flight dynamics and it is specifically beneficial at the pre-design stages of a WIG effect craft.