Optimum potential jump calculation

The above application of Calculus of Variations produced the optimum normal velocity distribution dp/dn(s). The one remaining step is to determine the corresponding Ap(s). A suitable numerical approach is to use the 2D panel method sketched in Figure 5.12. Using the AIC matrix Aj defined by (5.81), condition (5.98) is imposed at each panel control point.

N

^ Aij Apj — Л cos ві = 0 (i = 1 …N) (5.100)

j=1

The constant Л is one additional unknown in the problem. The appropriate additional equation is the specified-lift constraint, written by using the discrete lift expression (5.78).

N

P^VL^2 a pi cos ві Аві = Lspec (5.101)

i= 1

Equations (5.100) and (5.101) together constitute a (N+1) x(N+1) linear system for the unknowns Api, Л. The corresponding induced drag can then be computed by re-using the AIC matrix Aij to obtain dp/dni, and then using this in the discrete induced drag expression (5.82).