A twelve-per-cent aerofoil section is fitted to a wing of planform area

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

Fluid Dynamics, Ch Separation, wakes, jets and free shear flows

Problem

A twelve-per-cent aerofoil section is fitted to a wing of planform area S=20 m2S = 20\,\mathrm{m^2}. Its measured stall behaviour is CL,max⁡≈1.5C_{L,\max} \approx 1.5 at an angle of attack of about 15∘15^\circ. At low angles the lift coefficient follows thin-aerofoil theory, CL=2πβC_L = 2\pi\beta with β\beta in radians. The aircraft weighs W=60000 NW = 60000\,\mathrm{N} and is approaching to land at sea level (ρ=1.2 kg m−3\rho = 1.2\,\mathrm{kg\,m^{-3}}) at an angle of attack of 10∘10^\circ. ((a)) Find CLC_L at 10∘10^\circ from thin-aerofoil theory and confirm that the wing has not stalled. ((b)) Find the minimum airspeed at which this wing can support the aircraft's weight at 10∘10^\circ.

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