Terminal Velocity Calculator
Calculate the terminal velocity of a falling object.
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Table of Contents
Terminal Velocity Formula
Terminal velocity is the maximum velocity attainable by an object as it falls through a fluid (air in this case).
Where:
- v = Terminal velocity (m/s)
- m = Mass of the object (kg)
- g = Acceleration due to gravity (9.81 m/s²)
- ρ = Air density (kg/m³)
- A = Cross-sectional area (m²)
- Cd = Drag coefficient
How to Calculate
To calculate terminal velocity, follow these steps:
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1Measure the mass of the object
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2Determine the cross-sectional area
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3Find the drag coefficient for the object's shape
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4Use the formula to calculate terminal velocity
Drag Coefficients
Common drag coefficients for different shapes:
- Sphere: 0.47
- Circular flat plate: 1.17
- Streamlined body: 0.04
- Cube: 1.05
The drag coefficient can vary based on the Reynolds number and surface roughness. For most practical applications, using the standard values is sufficient.
Practical Examples
Example 1 Skydiver
Calculate the terminal velocity of a skydiver with a mass of 80 kg and a cross-sectional area of 0.7 m².
m = 80 kg
A = 0.7 m²
Cd = 1.0 (approximate for a human body)
ρ = 1.225 kg/m³
v = √(2 × 80 × 9.81 / (1.225 × 0.7 × 1.0)) ≈ 42.7 m/s
Example 2 Raindrop
Calculate the terminal velocity of a raindrop with a diameter of 2 mm and a mass of 0.0042 g.
m = 0.0000042 kg
A = π × (0.001)² ≈ 3.14 × 10⁻⁶ m²
Cd = 0.47 (sphere)
ρ = 1.225 kg/m³
v = √(2 × 0.0000042 × 9.81 / (1.225 × 3.14 × 10⁻⁶ × 0.47)) ≈ 6.8 m/s