Ferris Wheel Modeling

Pre-Calculus · Axiom Academy

Your height on a spinning Ferris wheel rises and falls in a perfect wave — one cosine captures the whole ride. You board the Giant Sky Wheel at the bottom: a 40 ft radius, an axle 50 ft up, one full turn every 2 min — three things you can do with one height model. Ride the wheel, watch the wave Spin up the wheel and watch your height rise and fall. The dot on the wheel and the dot on the graph are the same height at every instant — that wave IS the model h(t) = 50 − 40·cos(πt). Read your height at any moment Stop fighting the clock — pick a time and let the model tell you the height. Drag the dial and read h(t) = 50 − 40·cos(πt) straight off: halfway up at the midline, peaking at the top. Every wheel has its own wave. Resize the radius, raise the axle, or change the spin time — and watch amplitude, midline, and period move in lockstep with the curve. That's A = radius, D = axle height, B = 2π ÷ period. One wheel, three moves: ride it , read it , build it . Anything that loops back on itself at a steady rate rides the same cosine — tides rising and falling, daylight hours over the year, a piston in an engine, an AC voltage . Find the midline, the amplitude, and the period, and you've got the model.

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