A Ferris Wheel Equation Calculator helps you easily find the height of a passenger at any given point during a ride. By using simple trigonometric formulas, it calculates how high above the ground a seat will be based on the wheel’s radius, its rotation speed, and the elapsed time. This is valuable for ride engineers, physics students, amusement park designers, and anyone curious about the physics of circular motion. The calculator ensures quick, accurate results for educational, design, or safety purposes.
formula of Ferris Wheel Equation Calculator
Basic Equation:
Height (h) = R × sin(θ) + C
Where:
- h = height above ground (meters or feet)
- R = radius of the Ferris wheel
- θ = angle in radians (can convert degrees to radians: θ(rad) = degrees × π/180)
- C = vertical offset to ground level (usually equal to the radius plus the axle height if the lowest point is above ground)
When the wheel rotates at constant speed:
θ = ω × t
Where:
- ω = angular speed (radians per second)
- t = time in seconds
So, the height as a function of time is:
h(t) = R × sin(ω × t) + C
This formula assumes the seat starts at the lowest point when t = 0.
Common Reference Table
| Term | Meaning | Typical Value or Unit |
|---|---|---|
| Radius (R) | Distance from center to seat | meters (m) or feet (ft) |
| Angle (θ) | Rotation angle | radians |
| Offset (C) | Center-to-ground distance | meters (m) or feet (ft) |
| Angular Speed (ω) | How fast the wheel turns | radians/sec |
| Time (t) | Elapsed ride time | seconds (s) |
| π | Pi | ≈ 3.14159 |
This quick table helps you match units and understand what each parameter means for your Ferris wheel calculation.
Example of Ferris Wheel Equation Calculator
Scenario:
You want to find the height of a seat on a Ferris wheel with:
- Radius, R = 20 meters
- Axle height above ground, axle = 2 meters
- Therefore, C = R + axle = 20 + 2 = 22 meters
- Angular speed, ω = 0.2 radians per second
- Time elapsed, t = 15 seconds
Step 1:
θ = ω × t = 0.2 × 15 = 3 radians
Step 2:
h(t) = R × sin(θ) + C
h(15) = 20 × sin(3) + 22
Step 3:
sin(3 radians) ≈ 0.1411
So, h ≈ 20 × 0.1411 + 22
h ≈ 2.822 + 22 = 24.822 meters
Therefore, after 15 seconds, the seat is about 24.8 meters above the ground.
Most Common FAQs
A: It calculates the passenger’s height at any moment during the ride, based on radius, axle height, and rotation speed.
A: Yes. Just ensure all inputs (radius, axle height, speed) use the same unit system (all meters or all feet).
A: Use θ(rad) = degrees × π/180. For example, 90° = 90 × π/180 = π/2 radians.