Lesson 8: Dead Reckoning & Vector Physics: Speed, Heading & Leeway Drift
Exploring physical phenomena—waves, forces, vectors, optics, and relativity—through traditional Polynesian navigation and ocean science.
🎯 Ngā Whāinga Akoranga | Learning Intentions
Dead reckoning navigation mathematics, vector addition (), speed distance time calculations (), and estimating knots without mechanical logs.
Perform vector addition calculations for waka course over ground, measure waka speed using bubbles/drift objects and counting seconds, and correct for current drift.
🎥 Media Anchor & Pedagogical Scaffold
Dead Reckoning - Intro to Physics — Udacity
Video (Udacity): An introduction to dead reckoning navigation, including the mathematics of vector addition when multiple forces (heading, current, wind) affect an object's actual path.
🧠 1. Before Viewing (Activate & Predict)
If your waka sails North at 6 knots, but a 2-knot ocean current pushes East, where will you actually end up after 24 hours?
👁️ 2. During Viewing (Watch With a Job)
Watch the full 5-minute clip and collect evidence for how dead reckoning works:
- What is dead reckoning: What does it mean to navigate using dead reckoning?
- Vector addition: How do you add multiple velocity vectors (heading, current, wind) to find actual path?
- Speed and distance: What is the relationship between speed, distance, and time?
- Practical application: How can a navigator use these calculations to determine where a vessel will actually go?
🗣️ 3. After Viewing & Kaiako Move (Process & Apply)
Kaiako Move: Lead an outdoor field activity timing students running a fixed distance to calculate speed in m/s and convert to knots.
Immediate Task: Complete Section 8 of your Navigation Physics Logbook: Vector Addition Navigation Calculations.
⚡ Whakaoho | Do Now: Measure Your Speed With a Piece of Driftwood
You have a waka, a known hull length, a floating object and the ability to count seconds. Two minutes: describe the method for finding your speed.
You have just reinvented a real technique. Now write down what it cannot tell you — and that gap is exactly why leeway has to be corrected for separately.
📖 Activity 1: Add the Vectors, Then Run the Reckoning
Course over ground (13 min). Your waka holds a bearing at a set speed. A current runs across it and leeway pushes you further off. Draw all three vectors to scale, tip to tail, and measure the resultant. That resultant is your course over ground — and it is not the direction you are pointing.
Then project it (12 min). Using d = v t, plot your position after six hours, then twelve. Now introduce a one-degree heading error and re-plot. Record how far off you finish after twelve hours. That distance is why no navigator trusts reckoning alone.
📝 Activity 2: Navigation Physics Logbook & Problem Solving (20 mins)
Portfolio Section 8. Submit: (1) a scale vector diagram giving course over ground from heading, current and leeway; (2) your twelve-hour reckoned position with full working; (3) the error produced by a one-degree heading mistake in kilometres, with one sentence naming which independent check would catch it soonest.
🏫 Kaiako Planning & Pedagogy Notes
Year 10 Curriculum Alignment: NZ Curriculum Science Phase 4 — Physical World & Earth/Space Systems. Integrates traditional Polynesian wayfinding (Mātauranga Waka) with foundational NCEA Level 1 Physics mechanics, wave behaviour, and optics.