This program represents a subsonic aerodynamic method for determining the mean camber surface of trimmed noncoplaner planforms with minimum vortex drag. With this program, multiple surfaces can be designed together to yield a trimmed configuration with minimum induced drag at some specified lift coefficient. The method uses a vortex-lattice and overcomes previous difficulties with chord loading specification. A Trefftz plane analysis is used to determine the optimum span loading for minimum drag. The program then solves for the mean camber surface of the wing associated with this loading. Pitching-moment or root-bending-moment constraints can be employed at the design lift coefficient. Sensitivity studies of vortex-lattice arrangements have been made with this program and comparisons with other theories show generally good agreement. The program is very versatile and has been applied to isolated wings, wing-canard configurations, a tandem wing, and a wing-winglet configuration.

The design problem solved with this code is essentially an optimization one. A subsonic vortex-lattice is used to determine the span load distribution(s) on bent lifting line(s) in the Trefftz plane. A Lagrange multiplier technique determines the required loading which is used to calculate the mean camber slopes, which are then integrated to yield the local elevation surface. The problem of determining the necessary circulation matrix is simplified by having the chordwise shape of the bound circulation remain unchanged across each span, though the chordwise shape may vary from one planform to another. The circulation matrix is obtained by calculating the spanwise scaling of the chordwise shapes. A chordwise summation of the lift and pitching-moment is utilized in the Trefftz plane solution on the assumption that the trailing wake does not roll up and that the general configuration has specifiable chord loading shapes.

This program was released by NASA through COSMIC as LAR-15160. The italicized text above is from the official NASA release.

- Go to the page of references for the VLMD program.
- Go to the download page for vlmd.

From the report summary:

A new subsonic method has been developed by which the mean
camber surface can be determined for trimmed noncoplanar planforms
with minimum vortex drag. The method uses a vortex lattice and
overcomes previous difficulties with chord loading specification.
This method uses a Trefftz plane analysis to determine the optimum
span loading for minimum drag, then solves for the mean camber
surface of the wing, which will provide the required loading.
Pitching-moment or root-bending-moment constraints can be employed
as well at the design lift coefficient.