A sailplane design team is sizing a new wing of area

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 sailplane design team is sizing a new wing of area S=12 m2S = 12\,\mathrm{m^2}. Wind-tunnel tests of the aerofoil section and fuselage give a zero-lift drag coefficient CD0=0.012C_{D0} = 0.012, and the wing is to have elliptic loading, so that CD=CD0+CL2π AR.C_D = C_{D0} + \frac{C_L^2}{\pi\,AR}. The team wants a best glide ratio (L/D)max⁡=32(L/D)_{\max} = 32. ((a)) Find the aspect ratio ARAR that gives this best glide ratio. ((b)) Find the required wingspan bb, using AR=b2/SAR = b^2/S. ((c)) Find the lift coefficient CL∗C_L^* at which this best glide ratio is achieved, and state briefly why it is an achievable cruise condition for a wing (typical maximum lift coefficients for such sections are 1.21.2 to 1.51.5).

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