2.19. The trailing vortex wake left behind by an airplane can be a safety hazard to following aircraft as illustrated in Figure P2.19. The most likely place to encounter the wake of another aircraft is in the vicinity of the airport during takeoff or landing. To minimize References 95 From the simple analysis presented here it is clear that the vortex strength is proportional to the weight of the generating aircraft and inversely proportional to its speed. Therefore large heavy transports flying at approach or takeoff speeds will create the strongest wakes and the greatest hazard to following aircraft. Wake vortices decay slowly in calm atmospheric conditions. Because the wake vortices decay very slowly in a calm atmosphere we will neglect vortex decay in this problem. Develop an expression for estimating the roll moment induced on an air- plane wing when the wing is centered in the vortex core of another aircraft's trailing vortex wake. Upwash Imposed roll Downwash Loss of altitude rate of climb Upwash X Structural load factors FIGURE P2.19 the possibility of a wake encounter the FAA has developed a separation criteria between aircraft of different sizes. If an elliptic wing loading is assumed, the strength of the trailing wake can be shown to be related to the size and speed of the generating aircraft. L= W = pVTb where Llift W = weight p = air density V = velocity of the airplane I = vortex strength b' = effective span of vortices. The effective span of the wing tip vortices for an elliptic load distribution can be shown to be T b' = b where b is the wingspan of the generating aircraft. Solving for the circulation (i.e.. vortex strength) yields W pVb' The tangential velocity field at some point downstream created by one of the vortices is given by = rsa 2 ra 2r