Some of you asked me to elaborate on how the vortex lattice method actually works, so we’re going to get technical.
As I mentioned before, the vortex lattice method (VLM for short) is a bit unique compared to some other aerodynamic analysis methods. In many methods, it’s the fluid that is analyzed, while your aircraft geometry is treated as a solid wall for the fluid to act on. VLM is the opposite: it’s the geometry itself that is analyzed.
One critical part of understanding VLM is understanding something called a horseshoe vortex. Greatly simplified, this is a construct used to talk about fluid flows mathematically.
Imagine a strand of fishing line that somehow has air circling around it endlessly in the exact same direction. Now take that fishing line and bend it so you have one horizontal piece of a finite length, and two ends extending far into the distance in an upside-down U shape. That air is still circling around the fishing line, but because you’ve turned it into the U shape, now it appears that the air is coming from the outside, spilling over the top, and then going back under the line. This is a horseshoe vortex.
Let’s now apply this. Within VLM software, aircraft geometry is defined using a handful of surfaces. Typically there is one for every major lifting component; this includes both wings, as well as any tails or fins.
Each surface is then divided up into a grid of panels. A wing might have, say, five panels across its span, and four panels from the leading edge to trailing edge, for a total of twenty panels.
When you run the software to analyze this wing, it assigns a single horseshoe vortex to each of the panels. The top “bar” of each horseshoe is the exact width of its panel, with the other two sides extending straight out behind the model. This creates the “lattice” of the vortex lattice method.
Each panel now also gets a control point somewhere behind each horseshoe’s top bar. This point is where we can measure that panel’s local velocity, as induced by all of the swirling horseshoe vortices near it.
This type of theoretical flow requires that at every control point, the velocity is only ever tangential to that point—that is, there is no flow moving up out of the wing, only alongside it. The software then solves for the strength of each individual horseshoe vortex that also maintains the tangential flow condition for each control point.
Once a vortex strength is known, the software can calculate the resulting force generated by the vortex. And if we know the force generated by each vortex, we now know the total force generated by the surface itself. That’s where the aerodynamic forces and moments come from.
A VLM model usually has way more panels across a wing than just four. As you might guess, your panel density and distribution have a big impact on how precise the calculations and results are. But that’s a discussion for another day.