Flow-Field Idealization

The objective now will be to simplify the lift, drag, and sideforce components of the far-field force expres­sion (5.13) into forms which involve only the wake trailing from the lifting body. This will provide physical insight into the links between forces and flow-field properties, and will also result in practical calculation methods for the forces which will enhance aerodynamic configuration design and optimization procedures.

Consider the rather complicated but typical vortex wake shed by an aerodynamic body, sketched in Fig­ure 5.4. The following simplifications and idealizations of the wake vortex sheet will be made:

• The wake vortex sheet is assumed to trail straight back from the trailing edge where it is shed, along the freestream direction (i. e. along the x-axis). The yz cross-sectional shapes of the sheet will therefore be the yz-shape of the wing trailing edge. In effect this neglects the roll-up of the vortex sheet which typically begins at the sheet edges and eventually involves the entire sheet. The straight-wake assumption will be modified slightly in Section 5.9 where a fuselage affects the wake trajectory.

• Only the streamwise vorticity wx is assumed to have a nonzero lumped vortex sheet strength 7. This will be used to construct the perturbation velocity field Vp outside of the sheet, which is associated with the lift, sideforce, and induced drag. The transverse vorticity ws is associated with the viscous velocity defect within the sheet which determines the remaining profile drag component.