Section slicing spreads stations by leading-edge arc length, which collapses to nothing in span at a raked tip

[1-Bart-1]

Summary

station_indices (src/obj_adapter/obj_slice.jl:465) spreads its section targets
over equal leading-edge arc length:

return [argmin(abs.(arclen .- t)) for t in range(inner + d, outer - d, n)]

Near a closed or raked tip the leading edge runs almost straight downstream, so arc
length and span decouple completely. On a 16.3 m ram-air kite (SK100, 44 panels,
6.3 m max chord) the march_edges stations closest to the tip read:

station 251 | y=8.132 | d_arc=0.0816  d_span=0.0032  d_x=0.0807 | arc/span=25.87
station 252 | y=8.135 | d_arc=0.0816  d_span=0.0032  d_x=0.0807 | arc/span=25.87
station 255 | y=8.145 | d_arc=0.0816  d_span=0.0032  d_x=0.0807 | arc/span=25.87

Identical rows: the march has settled into walking along the tip cap, spending
25.87 m of arc per metre of span. That is faithful to the geometry — the min-x
crossing really does race aft as a section closes — but it means equal arc-length
targets are not equal anything in span.

What it does to the sections and panels

Sections bunch into the cap. With wingtip_distance = 0.05:

sec 40: y=7.607   sec 43: y=8.113
sec 41: y=7.893   sec 44: y=8.132
sec 42: y=8.069   sec 45: y=8.151

Four sections in the outermost 8 cm; sections 40->41 alone span 29 cm.

These are the panels, not just the sections. With n_panels = 44 and
n_sections = 45, refine! takes the length(unrefined_sections) == n_panels + 1
branch and calls copy_sections_to_refined!, so the declared BILLOWING
distribution is never reached and the mapping is 1:1 — measured
max |panel corner - section point| = 0.000e+00. Per panel:

panel |  y_1     y_2   | d_span
    1 |  8.121   8.110 | 0.0110      <- 1.1 cm
   22 |    ...         | 0.5440      <- 54.4 cm
   44 | -8.110  -8.121 | 0.0110

widest/narrowest = 49.5

The 1.1 cm panels are geometrically degenerate. Measured on the undeformed CAD wing
in a uniform freestream:

panel |  sweep from freestream | x_airf . y_airf
    1 |               10.7 deg |           0.996
    2 |               24.5 deg |           0.935
   21 |               88.5 deg |           0.028
   44 |               10.7 deg |           0.996

The outermost panel's bound vortex sits 10.7 deg from the freestream and its
chordwise and spanwise axes are nearly parallel. 6 of 44 panels are below 45 deg.

Why it matters beyond those panels

q_dyn = 0.5*rho*|v x y_airf|^2 correctly gives such a panel sin^2(10.7) = 3.4%
of freestream, so it carries almost no load — that part is fine and should not be
"fixed" by orthogonalising y_airf, which would fabricate a factor of 29 in tip
force. The problem is conditioning. z_airf = normalize(x_airf x span_vec) is the
normalised cross product of two vectors 5 deg apart, so on this panel 1 cm of
corner motion swings z_airf by 33 deg and its angle of attack by 2.44 deg
(mid-span: 0.05 deg). Since the LOOP iteration solves

gamma_new[i] = 0.5 * v_a_dist[i]^2 / va_magw[i] * cl(alpha_i) * chord[i]

a panel with negligible force still injects a wildly swinging circulation into every
other panel's induced velocity. On a flexible wing this shows up downstream as all
panels going non-finite at once.

The existing workaround, and why it is a poor one

wingtip_distance does help, but being in arc length it inherits the same problem.
Measured panel-level through obj_to_yaml on the same mesh:

 wtd  | worst sweep | x.y   | panels<45 | span ratio | half-span lost
 0.05 |    10.7 deg | 0.996 |         6 |       49.5 |  0.0%
 1.0  |    41.7 deg | 0.780 |         2 |        2.7 |  1.7%
 1.4  |    66.0 deg | 0.449 |         0 |        2.7 |  4.2%
 1.8  |    69.5 deg | 0.397 |         0 |        2.7 |  9.1%
 2.0  |    70.7 deg | 0.377 |         0 |        2.5 |  9.1%
 2.4  |    72.8 deg | 0.343 |         0 |        2.5 | 14.2%

It is strongly non-linear (0 -> 1.2 is nearly inert, because it is eating cap arc)
and it has plateaus (1.8 and 2.0 snap to the same march station). A user asking for
"1.2 m of tip inset" gets 4.9 cm of span.

Suggested fix

Place the targets by spanwise position rather than leading-edge arc length — either
march.le[i][2] directly, or the arc length of the quarter-chord line projected
into the span direction, which is also what refine_mesh_for_linear_cosine_distribution!
already uses for LINEAR/COSINE (src/wing_geometry.jl:1347). That makes the
section distribution mean the same thing on a raked tip as on a rectangular wing,
and makes wingtip_distance a predictable control.

Smaller and independent: station_indices takes min_chord_frac (default 0.01,
i.e. 1% of max chord = 6 cm here, which is why a 0.5 m-chord section survives), but
perpendicular_sections calls it as station_indices(m, n_sections; wingtip_distance)
and never passes it through, so it is unreachable from WingSettings. Plumbing it
would give a direct, geometrically meaningful way to drop degenerate tip stations.

Version

main @ v4.3.1 with #273 applied (quarter-chord normal), src/obj_adapter/obj_slice.jl.
Related: #272.