Lifting line theory is a mathematical model used to analyze the aerodynamics of a wing during steady, level flight. It assumes that the wing can be represented as a straight, infinitely long line and uses mathematical equations to predict the lift and drag forces acting on the wing.
The main assumptions made in lifting line theory include:
Helmholtz theorems are used in lifting line theory to find the solution to the governing equations for lift and circulation. These theorems state that the lift and circulation can be expressed as a line integral of the velocity potential around the wing, and can be calculated using a closed contour integral.
Lifting line theory has several limitations, including:
Lifting line theory is commonly used in the design and analysis of aircraft wings, as it provides a simplified mathematical model for predicting lift and drag forces. It is also used in the study of fluid dynamics and aerodynamics, and has applications in other fields such as wind turbine design and sailboat performance.