A glider of mass and wingspan flies level at in air of density

PHYSICS · Multi-part · Fermi University Physics · Fluids & Continuum Physics · Kinematics, conservation laws and ideal flow · Kinematics, conservation laws and ideal flow

Fluid Dynamics, Ch Potential flow, conformal mapping and the finite wing

Problem

A glider of mass m=800 kgm=800\,\mathrm{kg} and wingspan b=10 mb=10\,\mathrm{m} flies level at U=50 m s−1U=50\,\mathrm{m\,s^{-1}} in air of density ρ=1.225 kg m−3\rho=1.225\,\mathrm{kg\,m^{-3}}, with elliptic spanwise loading. Well behind the wing the wake is modelled as a pair of straight trailing vortices separated by b0=πb/4b_0=\pi b/4 (the rolled-up separation for elliptic loading), each carrying the same circulation Γ0\Gamma_0 as the wing's centreline bound vortex, related to the lift by L=ρUΓ0b0L=\rho U\Gamma_0 b_0. Take g=9.8 m s−2g=9.8\,\mathrm{m\,s^{-2}}. ((a)) Find Γ0\Gamma_0 for level flight (L=mgL=mg). ((b)) Using the Biot-Savart law for the velocity one straight line vortex induces at the location of the other, find the speed at which the vortex pair sinks. ((c)) Find the time for the pair to descend a distance equal to one wingspan bb.

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