where [alpha] is the geometric angle of attack in an arbitrary spanwise section, [[delta].sub.1] and [[delta].sub.2] are the incidence angle of the fore wing and the hind wing, respectively, [[epsilon].sub.11]([[theta].sub.1]) and [[epsilon].sub.22]([[theta].sub.2]) are the induced angle of attack by its self-downwash effect, and [[epsilon].sub.12]([[theta].sub.1]) and [[epsilon].sub.21]([[theta].sub.2]) are the induced angle of attack by the upwash and downwash effect between the fore wing and the hind wing, respectively; the induced angle of attack is positive for the downwash effect.

Since the induced velocity is small compared to the freestream velocity, the induced angle of attack by its self-downwash effect, [[epsilon].sub.11]([[theta].sub.1]) and [[epsilon].sub.22]([[theta].sub.2]), would be approximated as the induced velocity divided by the freestream velocity, as

Hence, with the same approximation in calculating the induced angle of attack by its self-downwash effect, the induced angle of attack by the other lifting surface would be

Because of the wake-induced velocity, the freestream velocity vector will be rotated by the induced angle of attack, [[alpha].sub.i], as shown in Figure 4 and the induced angles of attack for the two wings can be obtained as

Moreover, the magnitude of the local velocity used in (10) and (14) to calculate the induced angle of attack should also be corrected by the local x-velocity component of each lifting surface composed of the freestream velocity and the induced x-velocity component, as shown in (21).

After replacing the magnitude of the freestream velocity with the corrected magnitude of the local velocity in the achievement of the section lift coefficient and the induced angle of attack, the classical Prandtl's lifting-line equation would be derived as a system of N (where N = [N.sub.1] + [N.sub.2]) nonlinear equation relating the N unknown coefficients (consists of {[A.sub.n]} and {[B.sub.n]}) of the distribution of the section circulation to known properties of the lifting surface.