Each graph is built from your waypoints. Notice that distance travelled only ever rises, while displacement can fall when you head back toward the start. Drag the speed slider on the map tab and watch the time axis stretch and squeeze.
The raw numbers behind the motion. Leg = each straight segment between two waypoints. Bearings are measured clockwise from north. Use to analyse in a spreadsheet.
Four challenges. Two are pencil-and-paper; two ask you to build a real route on the map and check it against a target.
You walk 300 m due east, then turn and walk 400 m due north. Work out the three quantities below (round to whole numbers; bearing to one decimal).
On the map, switch to Manual waypoints mode and build a route that travels at least 400 m but finishes with a displacement under 40 m — a journey that gets you almost nowhere. What kind of shape does that take?
Build a route whose displacement points due east — a final bearing within 10° of 090° — and whose displacement is at least 250 m. Either mode works: drop a start, then a finish to the east.
The physics behind the buttons. Everything in this lab comes from two GPS coordinates and a little spherical trigonometry.
Distance travelled is the full length of the path — a scalar, always positive, found by adding up every leg.
Displacement is the straight arrow from start to finish — a vector with size and direction. Walk a full lap of a track and your distance is 400 m but your displacement is zero.
Displacement can never exceed distance, so their ratio (the directness) lives between 0 and 1.
Average speed = distance ÷ time. Average velocity = displacement ÷ time, pointing along the displacement.
Because displacement ≤ distance, the magnitude of average velocity is always ≤ average speed. They're only equal for motion in a perfectly straight line.
Latitude runs 0° at the equator to ±90° at the poles (north–south). Longitude runs 0° at Greenwich to ±180° (east–west).
One degree of latitude ≈ 111 km everywhere. A degree of longitude shrinks toward the poles — it's 111 km × cos(latitude).
To get the real "great-circle" distance between two points on a sphere of radius R:
φ is latitude, λ is longitude, Δ means "the change in", all in radians.
The compass direction from one point to the next, measured clockwise from north:
0° = north, 90° = east, 180° = south, 270° = west.
Trace a route to a real destination, then compare the walk time the lab predicts against a maps app. Discuss why they differ — traffic lights, hills, and crossings aren't in the model.
Or build two routes between the same two points: same displacement, very different distances. Which has the higher average speed for the same walking pace?
Your in-class walk was one-dimensional. Every GPS reading is really two numbers. Read the latitude & longitude graphs point by point, work out the direction of each leg, then check your reading against the plotted route.
Which route produced these graphs?
Tip: latitude up = North, longitude up = East. Each leg is walked at a steady pace.Part 2 — about how far did they walk? (total path length)
Latitude is the North–South graph. Rising = walking North, falling = South.
Longitude is the East–West graph. Rising = walking East, falling = West.
Both graphs share one time axis. A turn is a single instant, so a slope change lines up vertically in both. Steeper slope = faster in that direction.