Demo — RCS Aspect Explorer

Demo — RCS Aspect Explorer#

RCS is a pattern, not a number, and the whole of Block 3’s signature reasoning turns on one gap: a handful of narrow specular spikes drag the linear mean far above the median, while a search radar sweeping past sees the floor most of the time. The demo builds that picture in three tabs, in the lesson’s order. Scattering shapes traces rays off a flat plate, a corner reflector and a sphere as you turn each one, so you can see where each sends the energy. Aspect pattern puts a notional 360° aspect pattern on a polar plot and lets you sweep a sector across it, watching the three summary numbers — max, median, and linear-mean — disagree in exactly the way that matters for detection range. IADS exposure lays that same pattern on the ground as four radars’ detection footprints around an aircraft you can turn.

What the numbers mean#

The pattern is a low, noisy floor (roughly −12 to −27 dBsm) punctuated by four specular spikes at the facet normals 45°, 135°, 225°, and 315°, each reaching +15 dBsm across only a couple of degrees. To summarize a sector honestly, average in the linear domain, then convert back:

\[ \bar{\sigma}_\text{dBsm} = 10\log_{10}\!\left(\frac{1}{N}\sum_i 10^{\,\sigma_i/10}\right). \]

The median tracks the floor; the linear mean is pulled up by whatever spikes fall inside the sector. Detection range keys off the floor, because \(R_\text{max} \propto \sigma^{1/4}\) — so the median is the number a mission planner feeds in.

Interactive demo#

Open in full screen

Dataset · L25_RCSPattern.csv (360 aspect samples)↓

Walkthrough#

  1. Start on “Scattering shapes.” A plane wave arrives from the radar on the left. Pick each shape in turn and drag the incidence angle \(\theta\) from −60° to +60°. The rays are geometric optics, where the energy goes: red rays leave within 2° of straight back to the radar, and the first card counts the share that does. The curve under the picture is physical optics, how much comes back, as \(\sigma\) in dBsm for stated sizes at X-band (\(\lambda\) = 3 cm): a 0.5 m square plate, a dihedral of two 0.5 m square faces, and a sphere of the same 0.25 m² projected area. The selected shape is drawn bold and the other two faint, so slide 7’s table becomes one picture. The flat plate sends every ray home at \(\theta = 0\) and none past \(|\theta| = 1^\circ\), because a tilted plate throws the echo off at \(2\theta\); on the curve that is a +29.4 dBsm lobe (\(4\pi A^2/\lambda^2\)) that reaches its first null by 1.7°, then sidelobes falling to about −15 dBsm near 60°: loud but narrow. The corner reflector (a dihedral seen edge-on) bounces each ray off both faces and straight back, so it peaks at +32.4 dBsm and holds a broad double-bounce plateau, only 3 dB down at 15° and 10 dB down at 32°; at ±45° one face is square to the radar and flashes on its own at the plate’s +29.4 dBsm. The sphere returns the same sliver of rays (about 1.7%) and the same \(\pi r^2\) = −6.0 dBsm at every angle: the calibrator. The model ignores shadowing and edge diffraction.

  2. Open “Aspect pattern” and read the polar plot. Aspect runs clockwise with 0° nose-on. The deep, noisy ring is the floor; the four sharp petals at 45°, 135°, 225°, and 315° are the specular spikes where a facet normal faces the radar.

  3. Sweep the nose sector (±30°). With no spike in view, median and linear-mean agree near −19 dBsm and the max is only −13.5 dBsm of speckle, not a flash. This is the quiet the shaped nose bought.

  4. Sweep the quartering sector (30°–60°). One narrow spike now sits inside a narrow 31-sample window. The max jumps to +15 dBsm and the linear-mean climbs to ~+8 dBsm, while the median resists — it rises only to ~−7 dBsm, still far below the mean, leaving ~15 dB of mean-vs-median gap.

  5. Select the full 360°. All four spikes are in view. Max +15.0, median −18.8, linear-mean +3.4 dBsm: a 22.3 dB gap, manufactured entirely by four narrow petals over a wide quiet floor.

  6. Watch the readouts fight. The demo highlights the median-vs-mean gap as you drag. The question to keep asking: which number would you hand a mission planner, and why?

  7. Open the “IADS exposure” tab. The same 360-point pattern feeds a top-down plan view of four notional radars, one in each quadrant. Each sees the aspect bearing − heading, and detects out to \(R_\text{det} = k\,(\sigma/\sigma_\text{ref})^{1/4}\) with \(\sigma_\text{ref}\) the pattern’s full-360° median (−18.8 dBsm). Each site is drawn as its detection footprint, the familiar bugsplat: the ground where that radar would detect you if you flew the current heading from anywhere on the map. You sit at the center, so a site holds a track exactly when you are inside its footprint. Rotate the heading and every footprint turns rigidly with you; the pattern’s spikes stretch into needles that run out to the 300 km plot edge, and a site whose \(R_\text{det}\) toward you runs past the edge is tagged with its true value. The Show chips draw one radar’s footprint at a time (the table and summary still count all four), and the Pattern RCS change slider cuts \(\sigma\) by up to 30 dB everywhere on this tab, shrinking every footprint by \(10^{-N/40}\): at −30 dB each keeps 18% of its reach, slide 13’s collapsing rings.

Key observations#

  • The companion script’s table. Nose ±30°: max −13.5, median −19.1, linear-mean −18.9. Quartering 30°–60°: max +15.0, median −7.2, linear-mean +8.1. Full 360°: max +15.0, median −18.8, linear-mean +3.4. The demo reproduces these live.

  • A few spikes distort the mean. Because averaging is linear, a couple of degrees of +15 dBsm outweigh hundreds of degrees of floor. The median ignores them by construction.

  • The median prices detection range. A search radar spends its dwell on the floor, so via \(R_\text{max} \propto \sigma^{1/4}\) the median sets the practical detection ring. The spikes are brief real flashes — hard to detect on, harder to track on.

  • Neither number is wrong. They answer different questions: total-energy (builder), worst-case flash (buyer), and usual-case detection (mission planner). The lesson is to say which one you mean.

  • Orientation is survivability. Sweep the heading through all 360° on the third tab at 0 dB and the four sites hold anywhere from zero tracks (231 headings) to all four (20 headings). Each footprint is the pattern itself drawn on the ground. The three outer sites’ quiet floors stop short of you, so what reaches you from them is a spike’s needle swinging across; the close-in TTR also catches you on a loud patch of its floor. The fourth root does the rest: \(R_\text{det}\) toward the aircraft runs from 40 km (the TTR at a quiet aspect) to 841 km (the EW radar with a spike on it), and at 104 of the 360 headings at least one site’s \(R_\text{det}\) toward you runs past the plot edge. Cutting the pattern’s RCS shrinks the exposure: at least one radar tracks you on 129 headings at 0 dB, 108 at −10 dB, 92 at −20 dB and 4 at −30 dB, where only the close-in TTR still catches a spike at its peak. Stealth shrinks the footprints; it does not make you invisible.

Source#

MATLAB bundle · L25_RCSAspectPattern.m↓

The companion script reads L25_RCSPattern.csv, plots the pattern on a polar axis (with a +30 dB radial offset so polarplot accepts the negative radii), then masks three sectors — nose (±30°), quartering (30°–60°), and full 360° — and prints max, median, and the linear-domain mean for each. That linear-then-dB conversion for the mean is the load-bearing step: it is what makes the mean-vs-median gap appear.

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