# 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.