The rolled-up vortex wake downstream of a wing is schematically represented by two semi-infinite, parallel, horizontal...

 

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The rolled-up vortex wake downstream of a wing is schematically represented by two semi-infinite, parallel, horizontal line vortices. The vortex lines have opposed vorticity and equal strength (which equals the circulation of the wing). a. Calculate the vertical velocity component w, which is induced by the two vortices in point P which is located exactly midway between the two vortices and far downstream of the wing, as well as the corresponding induced downwash angle , for the following two cases: i. the vortices are at a large distance above the ground plane. ii. the vortices are at a height of h = 6 m above the ground plane. Hint: use 'mirror vortices' to bring the ground effect into account. Further data: flight speed V = 120 m/s; circulation strength = 72 m/s; the separation distance between the vortices b = 32 m. b. Determine, for this point P, the general expression for the reduction of the downwash in ground effect, by calculating Wground effect/Wno ground effect as a function of the vortex separation distance b and the ground clearance h. The rolled-up vortex wake downstream of a wing is schematically represented by two semi-infinite, parallel, horizontal line vortices. The vortex lines have opposed vorticity and equal strength (which equals the circulation of the wing). a. Calculate the vertical velocity component w, which is induced by the two vortices in point P which is located exactly midway between the two vortices and far downstream of the wing, as well as the corresponding induced downwash angle , for the following two cases: i. the vortices are at a large distance above the ground plane. ii. the vortices are at a height of h = 6 m above the ground plane. Hint: use 'mirror vortices' to bring the ground effect into account. Further data: flight speed V = 120 m/s; circulation strength = 72 m/s; the separation distance between the vortices b = 32 m. b. Determine, for this point P, the general expression for the reduction of the downwash in ground effect, by calculating Wground effect/Wno ground effect as a function of the vortex separation distance b and the ground clearance h.