Throughout Section 4.2, the pitching moment is calculated using the distance between the bound vortices and a datum (quarter chord or pitching axis). What differencewould it make if the pitching moment was calculated using the distance between the control points and the datum?

Data from Section 4.2

.........................

Transcribed Image Text:

The lumped vortex method is essentially a discrete unsteady thin airfoil theory. Recall that the finite state theory of Section 3.6 represents the flow using continuous bound and wake vorticity distributions, leading to the integral equation (3.219), which is then solved analyt- ically by expressing these vorticity distributions as finite series. The numerical alternative is to place a finite number of vortices both on the airfoil's surface and in the wake and thus replace the integral impermeability equation by a sum. Both approaches ignore the thick- ness of the airfoil, but the lumped vortex method imposes impermeability near the camber line while thin airfoil theory (see Section 3.2) imposes it on the chord line, modelling the camber by means of the upwash it generates.