Terminal Velocity Calculator
Calculate terminal velocity and related parameters for objects falling through air
Terminal velocity is the constant speed reached by an object falling through a fluid (like air) when the drag force equals the gravitational force. At this point:
- The net force on the object becomes zero
- Acceleration stops
- The object continues falling at a constant speed
Understanding terminal velocity is crucial in various applications, from meteorology to sports science and engineering.
Object Properties
- Mass and weight
- Cross-sectional area
- Shape (affecting drag coefficient)
- Surface texture
Environmental Conditions
- Air density (varies with altitude)
- Temperature
- Humidity
- Atmospheric pressure
Fluid Properties
- Viscosity
- Reynolds number
- Flow regime (laminar or turbulent)
Terminal Velocity Equation
v_t = √((2mg)/(ρAC_d))
Where:
- v_t = Terminal velocity
- m = Mass of object
- g = Acceleration due to gravity
- ρ = Air density
- A = Cross-sectional area
- C_d = Drag coefficient
Drag Force
F_d = ½ρv²AC_d
At terminal velocity, this equals the weight (mg)
Reynolds Number
Re = (ρvL)/μ
Where:
- ρ = Fluid density
- v = Velocity
- L = Characteristic length
- μ = Dynamic viscosity
Example 1: Skydiver
- Mass: 75 kg
- Cross-sectional area: 0.7 m²
- Drag coefficient: 1.0 (spread position)
- Altitude: 3000 m
- Terminal velocity: ~56 m/s
Example 2: Raindrop
- Mass: 0.1 g
- Cross-sectional area: 12.6 mm²
- Drag coefficient: 0.47 (sphere)
- Altitude: 1000 m
- Terminal velocity: ~9 m/s
How does altitude affect terminal velocity?
As altitude increases, air density decreases, resulting in less drag force and higher terminal velocity. This is why skydivers fall faster at higher altitudes.
Why do heavier objects not always fall faster?
Terminal velocity depends on the ratio of weight to drag force. While weight increases with mass, drag force depends on shape and size. A larger surface area can offset the effect of greater mass.
What is the significance of the Reynolds number?
Reynolds number indicates the flow regime (laminar or turbulent) around the object, which affects the drag coefficient. Higher Reynolds numbers typically indicate turbulent flow and can change how air moves around the object.