The chordwise attached-trailed vortex segments carry no force, which is the swept-wing term

[1-Bort-1]

Each panel's horseshoe already has the two chordwise segments running from the quarter-chord line back to the trailing edge:

reinit!(panel.filaments[1], bound_point_2, bound_point_1, vec)   # spanwise, 1/4 chord
reinit!(panel.filaments[2], bound_point_1, panel.TE_point_1, vec)
reinit!(panel.filaments[3], panel.TE_point_2, bound_point_2, vec)

(src/panel.jl:120-122.) They carry the ring's circulation and induce velocity, but nothing computes a force on them: the panel force is assembled from cl, cd, cm alone (panel_loads, src/panel_aerodynamics.jl).

Gaunaa, Li & Pirrung, From thin airfoil theory to finite wings: consistent implementation of Lifting Line-based models, TORQUE 2026, J. Phys. Conf. Ser. 3224 042030 (OpenSourceAWE/Internal Papers/Gaunaa_2026.pdf) names those segments the attached trailed (AT) vortex and the force on them is the paper's headline contribution. p. 5, §3 — and note this is the alignment the code already uses:

we propose, in line with the Crossflow Principle, to align the bound part of the trailed vortex lines with the local chordwise direction up to the trailing edge, after which the trailed vortex follows the flow direction. […] This chordwise vortex segment remains attached to the wing and is therefore part of the bound vortex system.

p. 6, §3, the force (unnumbered in the paper):

ΔF{Γ,AT,j} = ρ Δa_j V{3D,rel,j} × Γ_{AT,j}

Here, Δa_j is the length of AT vortex element j, Γ{AT,j} is the circulation vector of the AT vortex, and V{3D,rel,j} is the total 3D velocity vector evaluated at the 3/4 chord point of the AT vortex line. This chordwise location is chosen because this is the point where the total velocity has no component through the wing, making it a physically sensible evaluation point.

Two things in that are easy to get wrong: V_3D,rel,j is the total 3D velocity, deliberately not the span-perpendicular V^⊥ or the self-induction-corrected V_inner that drive the 2D model; and it is sampled at the 3/4-chord point of the AT filament, not at the panel's control point.

Size

Straight wings do not need it — p. 9: "For straight wings, omitting the force due to AT vortex has only a very small effect on both the integrated force coefficients and the spanwise distributions." Swept wings do. Table 2, p. 9, elliptic wing with 10 % backward sweep and 25 % anhedral, α = 10°, against VLM (C_L 0.753, e_Osw,Blade 1.106):

	C_L	e_Osw,Blade
same method, AT force omitted	+2.14 %	−12.03 %
same method, AT force included	−0.04 %	−0.47 %

For LL-Gaunaa, the force contribution from the AT vortex is important because the blade is swept. If it is omitted, the C_L is overpredicted by about 2% and e_{Osw,Blade} is underestimated by about 12%. It is also noted that if the forces from the AT vortex is not included, the agreement between on-blade and Trefftz-plane drag estimations is bad.

The paper claims the term is "absent in all previous LL models known to the authors" (p. 2), which matches what is here.

What I would do

Add the Kutta–Joukowski force on filaments 2 and 3 to the panel force. The geometry, the circulation and the induction machinery all exist; what is missing is the force term, the choice of which panel a shared junction's contribution is attributed to — the paper gives the per-element force and does not say how it is summed into a section — and a test. The swept + anhedral elliptic wing of §5.2 against C_l = 2πα is reproducible here and would be the case to assert on.

Found while checking #273 against this paper. Related: #317, #318.