Theodorsen

Theodorsen refers to Theodore Theodorsen, an aerodynamics researcher whose work in the 1930s led to a foundational concept in unsteady aerodynamics. He is best known for introducing the Theodorsen function, a complex transfer function that describes how an oscillating, thin airfoil in incompressible, inviscid flow responds to harmonic motions. Theodorsen’s theory provides a linear, frequency-domain relationship between the airfoil’s motion (such as plunge and pitch) and the resulting aerodynamic loads.

Theodorsen function and definition

The Theodorsen function, C(k), relates unsteady lift and moment to the airfoil’s motion through a reduced frequency, k = ωc/(2U), where ω is the oscillation frequency, c is the mean aerodynamic chord, and U is the free-stream velocity. It is defined in terms of Hankel functions of the second kind: C(k) = H1^(2)(k) / H0^(2)(k). The function is complex, with both magnitude and phase varying with k. In the low-frequency limit (k → 0), C(k) approaches 1, recovering quasi-steady lift, while at higher reduced frequencies the lift shows lag and amplitude attenuation.

Applications and context

Theodorsen’s theory provides a practical framework for calculating unsteady aerodynamic forces on oscillating airfoils, useful in aeroelastic analysis, flutter studies, and gust response of wings and rotor blades. It is often used in conjunction with time-domain models such as the Wagner function to obtain transient lift responses. The Theodorsen function remains a foundational tool in classical unsteady aerodynamics and aeroelasticity.