How does a Ferris wheel make a sine wave?
As the wheel turns steadily, a car's height rises and falls smoothly, tracing one sine cycle per full turn. The model is h(t) = R·sin(2πt/T − π/2) + R + clearance.
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Ferris Wheel Height
Find the height of a Ferris-wheel car at any time using h(t) = R·sin(2πt/T − π/2) + R + clearance, with the turning angle shown in degrees or radians.
h(t) = R·sin(2πt/T − π/2) + R + clearance
Angle unit
Frequently asked questions
What do the parts mean?
R is the wheel's radius, T the time for one turn, and clearance the gap from the ground to the lowest point. The −π/2 phase starts the car at the bottom.
Can you show a worked example?
With R = 10, T = 30 s, clearance 2, at t = 7.5 s (a quarter turn, 90°) the car is at axle height: h = 12. At the top (t = 15 s) it reaches 2R + clearance = 22.
Where is the highest and lowest point?
Lowest = clearance (the bottom), highest = 2R + clearance (the top), and the axle sits at R + clearance — the midline of the sine wave.
Does the angle work in radians?
Yes — the turned angle can be shown in degrees or radians via the toggle; 90° is π/2 ≈ 1.5708 rad.