Demo — Planform Alignment

Demo — Planform Alignment#

Edges cannot be deleted, but you can choose which direction each one throws its spike. This demo builds a synthetic RCS-vs-azimuth pattern from six aircraft edges, then lets you collapse their orientations from six scattered normals down to two — watching the loud fraction of the compass fall while the surviving lobes grow taller.

The model#

Each edge of physical length \(L\) throws a specular lobe whose peak grows as \(L^2\), and it fires that lobe at its normal and at the mirror direction \(180^\circ\) away:

\[ \sigma_{\text{peak}} = 10\log_{10}\!\left(1.25\,L^2\right)\ \text{dBsm}, \qquad \sigma(d) = \sigma_{\text{peak}} - \tfrac{1}{2}\!\left(\frac{d}{w}\right)^2. \]

The lobe is a Gaussian in dB space against the signed angular distance \(d\) from the normal, with width \(w \approx 1^\circ\). Six edges of lengths \([6,6,5,5,3,3]\) m (wing leading edges 6 m, trailing edges 5 m, tail edges 3 m) sit on a \(-25\) dBsm shaping floor. The only thing that changes between the two presets is the orientation of those six edges — the lengths, the floor, and the lobe physics are identical.

Interactive demo#

Open in full screen

Walkthrough#

  1. Start on Conventional. Six edges point six different ways (normals near \(\pm25^\circ\), \(\pm10^\circ\), \(\pm60^\circ\)), so their lobes and mirrors sprinkle bright spikes all around the compass — including into the nose sector (\(\pm30^\circ\) about the nose).

  2. Read the scoreboard. Two metrics report the design: the loud fraction of the compass (percent of azimuths above \(-5\) dBsm) and the nose-sector maximum (the loudest return within \(\pm30^\circ\) of the nose).

  3. Switch to Aligned. The same six edges collapse onto two normals (\(\pm40^\circ\)). Watch the scattered spikes vanish and reassemble into four narrow butterfly lobes at \(\pm40^\circ\) and their mirrors \(\pm140^\circ\) — none of them in the nose sector.

  4. Compare the scoreboards. The loud fraction drops by about two-thirds and the nose-sector max falls to about \(-24\) dBsm — essentially the \(-25\) dBsm shaping floor. But the surviving lobes are taller than any single conventional spike.

  5. Read the trade. Aligning did not delete energy; it concentrated it. A few known-direction lobes off the mission axis are survivable in a way a bright nose-on flash never is.

Key observations#

  • Alignment stacks, it does not delete. Collapsing six normals to two concentrates the same energy into fewer azimuths, so the surviving butterfly lobes get taller even as most of the compass goes quiet.

  • The nose sector is the prize. Dropping the \(\pm30^\circ\) nose-sector max to the floor is what matters for a penetrating strike aircraft — the mission axis is the one direction the threat is looking from.

  • Longer edges are louder. Peak scales as \(L^2\), so the 6 m wing leading edges dominate the 3 m tail edges by 6 dB — a reason flying wings have so few, long, shared edges.

  • This is planform alignment. Real airframes take it further: the B-2 and B-21 share every planform angle, so nearly all diffracted energy lands in a handful of predictable lobes off-axis.

Source#

MATLAB bundle · L26_PlanformAlignment.m↓

The companion script builds the same six-edge pattern on a \(-25\) dBsm floor, runs it twice — once with six distinct normals, once with the aligned pair — overlays both on a polar plot, and prints the loud-compass fraction and the nose-sector max for each design so the class can read the trade out loud.

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