Human Terminal Velocity Calculator

Terminal Velocity Equation:

\[ v_t = \sqrt{ \frac{2 m g}{\rho A C_d} } \approx 53 \text{ m/s for skydiver} \]

Mass (m):

Gravity (g):

m/s²

Air Density (ρ):

kg/m³

Cross-Sectional Area (A):

m²

Drag Coefficient (C_d):

(unitless)

Terminal Velocity (v_t):

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1. What is Terminal Velocity?

Terminal velocity is the maximum velocity attainable by an object as it falls through a fluid (like air). It occurs when the sum of the drag force and buoyancy equals the downward force of gravity, resulting in zero acceleration.

2. How Does the Calculator Work?

The calculator uses the terminal velocity equation:

\[ v_t = \sqrt{ \frac{2 m g}{\rho A C_d} } \]

Where:

\( v_t \) — Terminal velocity (m/s)
\( m \) — Mass of the falling object (kg)
\( g \) — Acceleration due to gravity (9.81 m/s² on Earth)
\( \rho \) — Density of the fluid (1.2 kg/m³ for air at sea level)
\( A \) — Projected cross-sectional area (m²)
\( C_d \) — Drag coefficient (dimensionless)

Explanation: The equation balances gravitational force with drag force to find the equilibrium falling speed.

3. Importance of Terminal Velocity

Details: Understanding terminal velocity is crucial for skydiving, parachute design, vehicle aerodynamics, and predicting the impact speed of falling objects.

4. Using the Calculator

Tips: For a typical human skydiver: mass ≈ 70 kg, area ≈ 0.7 m² (spread-eagle) to 0.2 m² (head-first), drag coefficient ≈ 1.0. Default values are provided for convenience.

5. Frequently Asked Questions (FAQ)

Q1: What's the terminal velocity of a human?
A: Typically 53-56 m/s (190-200 km/h or 120-130 mph) in stable, spread-eagle position. In head-down position, up to 90 m/s (320 km/h or 200 mph).

Q2: How does parachuting affect terminal velocity?
A: A deployed parachute dramatically increases cross-sectional area, reducing terminal velocity to about 5-7 m/s (18-25 km/h or 11-16 mph).

Q3: What factors affect terminal velocity most?
A: Cross-sectional area and drag coefficient have the greatest impact. Doubling area reduces terminal velocity by about 30%.

Q4: Can terminal velocity be dangerous?
A: Yes, human terminal velocity is typically fatal if impact occurs without deceleration. Survival is possible only with proper landing techniques or deceleration devices.

Q5: How does altitude affect terminal velocity?
A: Higher altitudes have lower air density, resulting in higher terminal velocities until reaching denser air layers.