Technical Note: Analytical Linearization of the Biot–Savart Equations in Free-Vortex Wake Models

This technical note presents the analytical linearization of the induced velocity components of a free-vortex wake model with applications to rotary wings. The free-vortex wake model features a vortex-lattice near wake and a tip-vortex far wake. Both are formed by vortex line segments. The linearization is obtained through a first-order Taylor expansion of the Biot–Savart law applied to vortex line segments. Analytical linearization results are validated against exact solutions and linearized solutions obtained via finite differencing.