# Demo — Loudest Band
Give one aircraft four signature bands — radar, IR, visual, and acoustic — each detected by a matched threat with its own range law. Detection is a union: if any band crosses its threshold you are found, so the range that matters is the largest one. This demo lets you pour signature reduction into each band and watch the fused detection range refuse to move until you finally hit the limiter.
## The fusion rule
Each band has its own detection range at its baseline signature, and each shrinks under investment along a different law:
$$
R_\text{radar} = 45\left(\tfrac{\sigma}{0.1}\right)^{1/4}, \quad
R_\text{IR} = 30\sqrt{\tfrac{J}{500}}, \quad
R_\text{visual} = 12\sqrt{\tfrac{C}{1}}, \quad
R_\text{acoustic} = 4 .
$$
Because the defender needs only one band to cross its threshold, the fused detection range is the maximum, not the average:
$$
R_\text{det} = \max_b R_b .
$$
At baseline the ranges are radar 45 km, IR 30 km, visual 12 km, acoustic 4 km — so $R_\text{det} = 45$ km and the loudest band is **radar**. Everything interesting follows from what happens when you attack one band at a time.
## Interactive demo
Open in full screen
## Walkthrough
1. **Read the baseline.** Four bands, four ranges — radar 45, IR 30, visual 12, acoustic 4 km. The fused detection range is the maximum, 45 km, and the loudest band is radar. That single number is what a fused defender achieves.
2. **Spend on the wrong band.** Pour 10 dB of reduction into IR alone. Watch $R_\text{det}$ *not move* — it stays pinned at 45 km, because radar was always the limiter. A non-dominant band buys nothing.
3. **Spend on the loudest band.** Now pour reduction into radar. $R_\text{det}$ falls — then **flattens** at 30 km when IR inherits the limit. More radar reduction past that point is wasted; the defender simply leans on IR.
4. **Spend on both.** Only cutting radar *and* IR together drives $R_\text{det}$ down to the 12 km visual floor. Below that, no coating helps — a contrail is a contrail.
## Key observations
- **Your worst band decides your range.** $R_\text{det} = \max_b R_b$ means the loudest band alone sets how close a fused defender can get. The average signature is irrelevant.
- **Reduction on a quiet band is invisible.** Until a band becomes the limiter, cutting it changes nothing — this is the single most common way to waste weight, money, and maintenance.
- **The limiter moves.** Each cut hands the lead to the next band, so the range curve falls in steps and flattens between them. Attack the limiter, expect it to jump, re-plan, repeat.
- **Some floors resist coatings.** The eyeball (contrail, glint) and, tail-on, the plume set floors no material buys below. This is the loudest-first budget of L26, now spanning the whole spectrum — and it is the analytical core of Project 3.
## Source
MATLAB bundle · L28_LoudestBand.m↓
The companion script builds one aircraft with four bands, computes each band's detection range under its own law, and takes the maximum for the fused $R_\text{det}$. It then sweeps signature reduction into the wrong band (nothing moves), into the loudest band (the range falls, then flattens as IR takes over at 30 km), and into both (reaching the 12 km visual floor no coating can hide).