Flight Path Navigation

Calculus 3 · Axiom Academy

A plane never flies quite where it points — the wind is a vector too. Add the two and you get where you actually go. You're flying 300 knots and you point the nose due east — but a crosswind is pushing you the whole way. Where you actually end up is the vector sum of your heading and the wind. Three things you can do with it. Heading plus wind — where you actually go Your nose points east at 300 knots, but the wind adds its own vector. Drag the crosswind and watch the two arrows add tip-to-tail — the green resultant is your real ground track. Crab into the wind to hold your course A 60-knot crosswind is shoving you north. To actually track due east, you have to aim into the wind. Drag your heading until the green ground-track arrow snaps onto the target line. Headwind or tailwind — the time it costs Now the wind is straight down your route. Same airspeed, same 600-mile leg — drag the wind and watch the two clocks. Notice the headwind steals more time than the tailwind ever gives back. One idea, three moves: add the vectors to see your real path, solve for the heading to hold a course, and weigh the wind to know its cost. Any time one motion rides on top of another — a boat crossing a current , a swimmer in a river , a drone in a gust — the true velocity is the vector sum , and these same three moves work.

This is the written version of the interactive lesson above. See the full Calculus 3 course.