Demo — Thermal Crossover

Demo — Thermal Crossover#

An LWIR sensor does not measure how hot the target is; it measures how much hotter or colder the target is than whatever sits behind it. That contrast swings across the day and passes through zero twice — once after sunrise and once after sunset. This demo runs a simple diurnal model so you can watch the airframe’s LWIR contrast climb, cross zero, and flip sign, and read off the two crossover times.

The contrast that vanishes#

The LWIR signature lives on thermal contrast between the skin and the background:

\[ \Delta T = T_{\text{skin}} - T_{\text{bg}}. \]

The model gives each surface a sinusoidal diurnal swing about a daily mean of 15 °C. The terrain background swings hard (amplitude 18 °C, peaking mid-afternoon and bottoming out before dawn), while the aircraft skin swings less and lags a touch (amplitude 6 °C):

\[ T_{\text{bg}} = 15 + 18\sin\!\frac{2\pi(t-8)}{24}, \qquad T_{\text{skin}} = 15 + 6\sin\!\frac{2\pi(t-9)}{24}. \]

Because the terrain amplitude is the larger of the two, it overtakes the skin near midday (target reads cold) and falls below it at night (target reads warm). The sign changes of \(\Delta T\) are the crossover times.

Interactive demo#

Open in full screen

Walkthrough#

  1. Read the two temperature curves. The high-amplitude curve is the terrain background; the gentler, slightly lagging one is the aircraft skin. Both ride the same daily mean.

  2. Watch them cross. Twice a day the two curves intersect. Between the crossings the terrain is warmer; outside them the skin is warmer.

  3. Switch to the contrast plot. \(\Delta T = T_{\text{skin}} - T_{\text{bg}}\) is negative through midday (target colder than terrain) and positive overnight (target warmer). The dashed line marks \(\Delta T = 0\).

  4. Find the crossover markers. The black filled circles sit where \(\Delta T\) changes sign — about 7.5 h and 19.5 h, roughly one hour after sunrise and one hour after sunset.

  5. Reason about the ingress. An LWIR sensor loses the skin at those two instants. Ask what a stern-aspect MWIR seeker sees at the same moment — and note it does not care.

  6. Switch to the “IR signature by aspect” tab. Notional stacked bars re-weight five components by band: MWIR is dominated by plume/nozzle (worst from the stern), LWIR by skin/aero — the very term the crossover kills.

Key observations#

  • Contrast, not temperature, is what the LWIR sensor sees. A warm target on warmer terrain reads as a cold silhouette.

  • Crossover happens twice daily, about an hour after sunrise and after sunset, because the larger-amplitude terrain curve overtakes and then falls below the skin.

  • Midday is negative, night is positive. Sun-baked terrain beats the skin by day; terrain radiating to cold sky drops below the skin at night.

  • Crossover zeroes only the LWIR skin term. The plume and hot parts still shout in the MWIR — an ingress timed at crossover hides the skin, not the tailpipe. You do not disappear in every band at once.

Source#

MATLAB bundle · L22_ThermalCrossover.m↓

The companion script builds a 24-hour time axis at one-minute resolution, evaluates the two sinusoidal temperature curves, forms \(\Delta T\), and finds the sign changes to locate the two crossover times. It prints them near 7.5 h and 19.5 h and plots both the temperature curves and the contrast curve with the crossover instants marked.

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