L29 — Project 3 Work Day#
No new theory today. Your group is the B-21 signature-management cell, and the period belongs to Project 3: given a fixed budget, choose the package of investments that buys the B-21 the most survivability — across radar, IR, and the rest — against a three-band threat that will not let you hide in every band at once.
The ask#
Recommend a prioritized signature-management package for the B-21 that buys the most survivability against a three-band threat, inside a fixed budget. Everything you need is Block 3: the fourth-power RCS law (L25–L26), the IR emitters (L22) and the passive IR range rule (L23), radar-absorbing material (L27), and the multi-spectral fusion rule from L28 — detection is a union, so the range that matters is the loudest band, \(R_\text{det} = \max_b R_b\).
The threat mix#
Three threats, each with its own detection law and reference point:
Threat |
Band |
Detection law |
Reference |
|---|---|---|---|
VHF surveillance |
low-band radar |
\(R = 90\,(\sigma_\text{VHF}/2.0)^{1/4}\) |
90 km at 2 m² |
X-band fire-control |
high-band radar |
\(R = 45\,(\sigma_\text{X}/0.03)^{1/4}\) |
45 km at 0.03 m² |
IR MANPADS |
infrared |
\(R = \min\!\big(8\sqrt{J/300},\ 6\big)\) |
8 km at 300 W/sr, lethal to 6 km |
At baseline the B-21 is found at ≈ 90 km. The IR intensity \(J\) is two contributors — the skin, and the hot parts and plume — and each IR treatment on the menu cuts only one of them. DIRCM drives the MANPADS range to zero. There are no threat positions and no routes in this project: the radars look at the nose and the MANPADS at the tail, and “ingress” and “egress” are shorthand for the aspect the aircraft presents. Routes are the Final Project’s job, with this same signature pattern.
The method#
Signature → detection → loudest band. Apply your package’s decibel cuts to each band’s signature (for the IR, to each contributor), recompute the three ranges, and take the maximum — that is where you are found. Then attack that band — and check whether the limiter ever changes hands.
The budget — and the tension#
Every investment on the menu costs against two caps: total cost ≤ 10 and total weight ≤ 5. Every row cuts some bands and not others, and the budget cannot buy them all. The tension is the whole project: the threat that sets how early you are found is not the one that is lethal at the target. Decide what you give up, and defend it.
Your tasks#
Signature-to-detection pipeline — turn the baseline signature and a chosen package into the three threat ranges and \(R_\text{det}\); verify against the starter’s baseline (\(R_\text{det} \approx 90\) km) and its example package.
Budget search — score every package that fits the caps and find the one that minimizes \(R_\text{det}\); name the loudest band at baseline and after each purchase, and say what stops you from going lower.
The terminal threat — plot every feasible package, \(R_\text{det}\) against the MANPADS engagement range; mark the ones no other package beats, pick one, and say what you gave up in kilometers to get it.
Aspect — turn the aircraft: score the baseline and your packages with all three threats at the nose (0°), the beam (90°), and the tail (180°). Required; only a full aspect sweep is bonus.
Recommendation — one slide, prioritized: what to buy first, what it buys, what you left on the table, and the residual risk you accept.
The handout carries the full wording of each task and the rubric.
Materials#
Work the pre-flight before class — anyone can be called to the board.
MATLAB bundle · L29_Project3Starter.m↓
The starter reads B21_SignaturePattern.csv and SignatureMenu.csv, scores the baseline and one example package (X-band RAM + plume suppression) against the three threats, and shows the fourth-power trade. The package is an example, not a recommendation. The starter is the plumbing, so your group starts at the trade study, not the file I/O. Extending it to the full menu, the budget search, the terminal-threat plot, and the aspect check is the job. The Project 3 page has sample prompts for getting coding help from AI within the handout’s rules, and its interactive dashboard lets you explore packages before you write any code. (Both CSVs are bundled in the code zip beside the starter, which reads them from the current folder.)
How to use the work day#
First 10 minutes — groups assigned; read the handout together and score the baseline by hand.
Next 30 minutes — divide the work: the pipeline and budget search, the terminal-threat plot, the aspect check, the recommendation.
Last 10 minutes — regroup: best package so far, what’s blocked, who owns what before L30.
Plan the recommendation first — it tells you what to compute. Next lesson: L30 — Project 3 presentations. Slides and code due before class, HW3 due at the start of class, and Quiz 3 in class.