Here is a short guideline to contemporary LD airfoiling, to be used for boomerangs of the MegaQuirl, Voyager, Buzz Whip, Backdraft, etc. type.
If we think about what LD booms are supposed to do, i.e. go out far and come all the way back, we can identify two airfoil characteristics:
1. low lift
2. low drag
The boom must have a little bit more lift than required to keep it in the air. Because of the small forces and moments, inertia dominates the motion and the boom will go out far. The boomerang must be launched almost flat, so that the small lift force may counteract the weight of the boom.
Of utmost importance is low drag to maximize the conservation of energy, which the boom needs to come back to the thrower eventually.
Here is an airfoil, not too aggressive, for you to start with: I use it on the Offspring, which is not a top performer, but a steady boomerang with range 100-120
m. Compared to airfoils of shorter flying boomerangs, e.g. booms for Aussie Round, the leading and trailing edges are more pointed, reducing thereby lift and drag. An important feature is the undercut, meaning material is removed from underneath the trailing edge, which reduces lift dramatically. Be careful with undercuts - too much and your boom will just fly straight out and won't return.
Booms with airfoils like the one shown above (Offspring) fly considerably far, while still being quite forgiving and stable in flight. For throws going out much farther, the airfoils need to be more AGGRESSiVE. The Backdraft is my competition boom with a distance 120-170m. Compared to the previously shown airfoils, the faces are carved much further into the wing, with smooth transitions. Also, the leading edge is rather pointed. These features let the boom travel out much farther, but also render it less stable and prone
to crashing on the way back. You have to give the boomerang as much forward velocity and rotation as possible to keep it in stable flight.
Here is the airfoil Manuel Schütz uses for his Voyagers. It seems less aggressive than the Backdraft airfoil. But maybe he showed here a bit of a conservative airfoil, not his most aggressive one. Anyway, we can see that the undercut reaches up to half the material thickness, giving very low lift.
A special feature Manuel introduced is the concave trailing edge. He has booms with concave carving only on the top, and such where both sides are shaped concave. Manuel points out that this brings about a further reduction in drag, and judging from flights I have seen of Manuel's boomerangs, it appears that the ones with the concave trailing edge return with higher velocity.
In conclustion, it can be said that in order to attain a maximum distance, you have to go to the boundary of the stable to the unstable flight regime. The last bit of tweaking to approach this limit may be effectively achieved by tuning. Reducing drag is of primary importance. So use the thinnest material available that is still stiff and strong enough to withstand your throw without getting deformed or warped.