L34 Pre-flight

L34 Pre-flight#

Block 4: Aircraft Survivability and Mission Planning — Lesson 34: Optimal Path Planning Work this before L34. Pre-flights are never collected — in class, anyone may be cold-called to present any question at the board, and that recitation is the participation grade.

Assumed pre-class reading#

  • L31’s survival metric (independent encounters multiply; \(-\ln P_S\) adds) and L32’s detection contours and MEZ rings.

  • The Jupyter Book Reading page for L34 — routes as shortest paths on a graph, Dijkstra’s algorithm (settle the cheapest frontier node, relax its edges), why exposure is written as \(-\ln(1-p)\), the weight sweep and the fuel limit, and why aspect makes the route graph directed.

Quiz questions (5 items, ~5 minutes)#

Q1. (Multiple choice) A planner’s graph has five nodes, from the start S to the target T, and seven legs, each flyable in either direction, with these costs: S–A 4, S–B 2, A–B 1, A–C 5, B–C 8, B–T 11, C–T 3. Which route, at what total cost, does Dijkstra return?

  • [ ] (a) S–A–B–C–T, cost 16

  • [ ] (b) S–A–C–T, cost 12

  • [ ] (c) S–B–A–C–T, cost 11

  • [ ] (d) S–B–T, cost 13

Q2. (Multiple choice) In Q1’s graph a pop-up SAM raises the cost of leg A–B from 1 to 4; every other leg is unchanged. What does Dijkstra return now?

  • [ ] (a) S–B–A–C–T, cost 14

  • [ ] (b) S–A–C–T, cost 12

  • [ ] (c) S–B–C–T, cost 13

  • [ ] (d) S–B–T, cost 13

Q3. (Multiple choice) A weight sweep on one threat map returns five routes:

w (km)

Route length (km)

\(P_S\)

0

412

0.38

60

437

0.66

150

468

0.84

400

503

0.93

1500

548

0.99

The fuel limit allows at most 490 km of route. Which route do you fly?

  • [ ] (a) The w = 400 route: 503 km at \(P_S\) 0.93

  • [ ] (b) The w = 150 route: 468 km at \(P_S\) 0.84

  • [ ] (c) The w = 1500 route: 548 km at \(P_S\) 0.99

  • [ ] (d) The w = 0 route: 412 km at \(P_S\) 0.38

Q4. (Multiple choice) Route X crosses one threat leg with kill probability 0.50. Route Y crosses three independent threat legs at 0.20 each. Which route survives better, and which one does a planner pick if its edge weights are the raw \(p\)’s?

  • [ ] (a) Y survives better (0.512 vs 0.500); the raw-\(p\) planner picks X instead

  • [ ] (b) X survives better (0.500 vs 0.400); the raw-\(p\) planner picks X too

  • [ ] (c) Y survives better (0.800 vs 0.500); the raw-\(p\) planner picks X

  • [ ] (d) Y survives better (0.512 vs 0.500); the raw-\(p\) planner picks Y too

Q5. (Short answer) In one or two sentences, explain why an aspect-aware planner must use a directed graph (digraph): why can the leg from node a to node b cost something different from the same leg flown from b to a?

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