By E. van Spiegel
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Extra info for Boundary Value Problems in Lifting Surface Theory
The mathematical treatment of the anti-symmetric problem follows the same lines as in the symmetric case. The weight-functions @)and %(a) are written in the form . I The acceleration potentials reads in this case or on substituting the Fourier expansion (2,10,11) of wherein and u cosy I The Condition, that the normal velocity at the wing surface which corresponds to the acceleration’pctentialil. ) , p d taking thereupon the integral overs from -1 to t 1 , yields the system . or written in a simDler way where Ll Quite similar as in the symmetric case, approximate values of the unknown are found by truncating the infinite system (2,10,23) and coefficients 4, solving the resulting finite system of linear algebraic equations.
L-q)+(ltg:) . _ I 4 = , , (l-/+X (2 9 8,471 In the Appendix this-formula (2,8,47) expression for Green's function. , will be derived from the closed . Determination of the final acceleration potential. the wing surface that is infinite along the whole edge of the wing. a. ' .. normal acceleration U zUT. which vanishes along the whole edge. Nevertheless none of these two pressure distributions agrees with the actual pressure distribution. In linearized aerofoil theory it is always required that the flow over the wing satisfies the Kutta condition, which implies that no velocity discontinuity occurs at the trailing edge of the wing.
The system (2,10,17) represents an infinite set of linear algebraic equations In order to arrive at numerical results for the unknown coefficients an it is necessary to truncate the infinite series in (2,10,17) to get a finite system of linear equations, which can be solved. The mathematical treatment of the anti-symmetric problem follows the same lines as in the symmetric case. The weight-functions @)and %(a) are written in the form . I The acceleration potentials reads in this case or on substituting the Fourier expansion (2,10,11) of wherein and u cosy I The Condition, that the normal velocity at the wing surface which corresponds to the acceleration’pctentialil.