Explain the horseshoe vortex model and how it relates to induced velocity on the wing.

Explain the horseshoe vortex model and how it relates to induced velocity on the wing.

• A. A bound vortex with trailing leg vortices models the wing's circulation; Biot-Savart integration yields the downwash and induced velocity that reduce effective angle and create induced drag.
• B. A simple point vortex model is used to approximate lift.
• C. The horseshoe vortex model describes boundary layer thickening.
• D. The horseshoe vortex model ignores induced drag.

Answer: (C)

Think of lift from a finite wing as being produced by circulation around the wing, represented geometrically by a bound vortex that runs along the wingspan with trailing leg vortices shooting downstream from the wingtips. The strength of that bound vortex corresponds to the lift per unit span the wing generates. To connect this to the flow field, you use the Biot-Savart law: the bound vortex and its trailing legs create a velocity field, and at any point near the wing there is an induced velocity component, primarily a downward one called the downwash. This induced downwash reduces the effective angle of attack that the wing “feels” because the freestream velocity is now more tilted relative to the wing surface. With a smaller effective angle of attack, the wing’s lift comes from the same circulation but the flight condition changes, and the flow must work to sustain that circulation, which shows up as induced drag—an energy cost due to the wake’s swirl. In short, the horseshoe vortex model links the wing’s lift to a specific wake structure: a bound vortex plus trailing legs produces an induced velocity field that lowers the wing’s effective angle of attack and tilts the lift vector backward, yielding induced drag. This model is useful because it lets us predict how downwash and induced drag vary with wing geometry and loading. Note that boundary-layer thickening is a viscous surface effect, not described by this vortex model, and while a simple point vortex can approximate some aspects of lift, the horseshoe representation captures the finite-wing downwash and induced drag more accurately.

Think of lift from a finite wing as being produced by circulation around the wing, represented geometrically by a bound vortex that runs along the wingspan with trailing leg vortices shooting downstream from the wingtips. The strength of that bound vortex corresponds to the lift per unit span the wing generates. To connect this to the flow field, you use the Biot-Savart law: the bound vortex and its trailing legs create a velocity field, and at any point near the wing there is an induced velocity component, primarily a downward one called the downwash. This induced downwash reduces the effective angle of attack that the wing “feels” because the freestream velocity is now more tilted relative to the wing surface. With a smaller effective angle of attack, the wing’s lift comes from the same circulation but the flight condition changes, and the flow must work to sustain that circulation, which shows up as induced drag—an energy cost due to the wake’s swirl.

In short, the horseshoe vortex model links the wing’s lift to a specific wake structure: a bound vortex plus trailing legs produces an induced velocity field that lowers the wing’s effective angle of attack and tilts the lift vector backward, yielding induced drag. This model is useful because it lets us predict how downwash and induced drag vary with wing geometry and loading. Note that boundary-layer thickening is a viscous surface effect, not described by this vortex model, and while a simple point vortex can approximate some aspects of lift, the horseshoe representation captures the finite-wing downwash and induced drag more accurately.