Terminal Velocity Calculator
Calculate the maximum velocity of a falling object when drag force equals gravitational force
Calculate Terminal Velocity
Object Properties
Drag coefficient: 0.47
Mass of the falling object
Area facing the direction of motion
Environment Properties
kg/m³ (Air at 20°C: 1.2041, Water: 1000)
m/s² (Earth: 9.81, Moon: 1.62, Mars: 3.71)
Terminal Velocity Results
Formula used: vt = √((2 × m × g) / (ρ × A × Cd))
Input values: m = 0.000 kg, A = 0.000000 m², Cd = 0.47
At terminal velocity: Drag force = Weight = mg = 0.00 N
Physics Analysis
Example Calculations
Skydiver Example
Mass: 75 kg
Cross-sectional area: 0.18 m² (spread eagle)
Drag coefficient: 1.0 (person spread eagle)
Air density: 1.2041 kg/m³ (sea level, 20°C)
Gravity: 9.81 m/s²
Calculation
vt = √((2 × 75 × 9.81) / (1.2041 × 0.18 × 1.0))
vt = √(1471.5 / 0.217)
vt = √6782.9
vt = 82.4 m/s or 184 mph
Baseball Example
Mass: 0.145 kg (5.1 oz)
Cross-sectional area: 0.00426 m² (diameter 7.3 cm)
Drag coefficient: 0.3275
Terminal velocity: ≈ 40.7 m/s or 91 mph
Forces in Free Fall
Weight (mg)
Gravitational force downward
Constant throughout fall
Drag Force
Air resistance upward
Increases with velocity²
Equilibrium
Forces balance at vt
Zero acceleration
Common Drag Coefficients
Physics Tips
Terminal velocity occurs when drag force equals weight
Streamlined shapes have lower drag coefficients
Larger cross-sectional area reduces terminal velocity
Higher mass increases terminal velocity
At terminal velocity, acceleration = 0
Understanding Terminal Velocity
What is Terminal Velocity?
Terminal velocity is the maximum velocity reached by a falling object when the drag force equals the gravitational force. At this point, the net force becomes zero, and the object continues to fall at a constant velocity with zero acceleration.
Physical Process
- •Object starts falling under gravity
- •Velocity increases, drag force increases
- •Eventually drag force = weight
- •Acceleration becomes zero
- •Constant velocity achieved
Formula Derivation
At terminal velocity: Fdrag = Fweight
½ρvt²ACd = mg
vt = √((2mg)/(ρACd))
- vt: Terminal velocity (m/s)
- m: Mass of object (kg)
- g: Gravitational acceleration (m/s²)
- ρ: Fluid density (kg/m³)
- A: Cross-sectional area (m²)
- Cd: Drag coefficient (dimensionless)
Note: The drag force formula assumes turbulent flow and quadratic drag
Factors Affecting Terminal Velocity
Object-Dependent Factors
- • Mass: Heavier objects have higher terminal velocity
- • Shape: Streamlined shapes reduce drag coefficient
- • Size: Larger cross-sectional area reduces terminal velocity
- • Surface texture: Affects drag coefficient
Environment-Dependent Factors
- • Fluid density: Denser fluids reduce terminal velocity
- • Gravity: Stronger gravity increases terminal velocity
- • Temperature: Affects fluid density and viscosity
- • Pressure: Affects fluid density