Terminal Velocity Calculator

Terminal Velocity Calculator

Enter the mass, cross-sectional area, and drag coefficient for the selected shape, and the calculator will determine its terminal velocity in the air.

Mass:

Select Shape:

kg ▾

Drag Coefficient (A):

m² ▾

Cross-section area:

Density of fluid (ρ):

kg/m³ ▾

Sphere (g):

m/s² ▾

The terminal velocity calculator is a tool used to estimate the highest speed an object can reach when falling through a fluid, such as air or water. Terminal velocity depends on the object's mass, the gravitational force, the fluid's density, and the fluid's resistance or viscosity. Objects of the same mass may fall at different speeds in different media, and different shapes experience different drag forces.

Terminal Velocity:

Terminal velocity is the constant speed a falling object reaches when the force of gravity pulling it downward is exactly counteracted by the drag force pushing upward. At this point, the object no longer accelerates and moves steadily through the fluid. Using a terminal velocity calculator allows you to find this speed for various objects and conditions.

Terminal Velocity Equation:

The equation to determine terminal velocity is:

Vt = √((2 × m × g) / (ρ × A × Cd))

Where:

Vt = Terminal velocity (maximum falling speed)

m = Mass of the object

g = Acceleration due to gravity

ρ = Density of the fluid

A = Cross-sectional area of the object

Cd = Drag coefficient

Dimension of Terminal Velocity:

Terminal velocity is measured in meters per second (m/s). Its dimensional formula can also be verified using dimensional analysis.

Practical Examples of Terminal Velocity:

Example 1:

A skydiver jumps from a height of 1500 m. What is the approximate terminal velocity?

Solution:

Vt = √(2 × g × h)
Vt = √(2 × 9.8 × 1500)
Vt = √29400
Vt ≈ 171.5 m/s

Example 2:

Find the height from which an object falls if its terminal velocity is 50 m/s.

Solution:

h = Vt² / (2 × g)
h = 50² / (2 × 9.8)
h = 2500 / 19.6
h ≈ 127.55 m

Forces Acting on a Falling Object:

Two main forces influence a falling object:

Gravitational Force: The downward pull caused by gravity.
Drag Force: The upward resistance provided by the fluid opposing motion.

Gravitational Force:

According to Newton's second law:

F = m × a

Here, F is the net force, m is mass, and a is acceleration. Near the Earth's surface, a = g = 9.8 m/s².

Drag Force:

Drag depends on the object's shape and the medium it moves through. The drag force can be expressed as:

D = (Cd × ρ × Vt² × A) / 2

Where Cd is the drag coefficient. At terminal velocity, drag balances weight:

W = D

Drag Coefficients for Different Shapes:

Shape	Drag Coefficient (Cd)
Sphere	0.47
Golf Ball	0.39
Baseball	0.33
Hemisphere	0.42
Cube	1.05
Streamlined Body	0.04

Using the Terminal Velocity Calculator:

Steps:

Select the object's shape.
Enter the mass and cross-sectional area.
Click "Calculate" to get the terminal velocity.

Output:

The terminal velocity for the selected shape is displayed.
The corresponding drag force is also shown.

FAQs:

What is the terminal velocity of a human?

In a stable belly-down position, a human reaches about 193 km/h (120 mph). In a head-down dive, speeds can reach 240–290 km/h (150–180 mph).

Do heavy objects fall faster?

In a vacuum, all objects fall at the same rate. In air, heavier objects may fall faster if shape and air resistance allow it.

Factors affecting terminal velocity:

Mass of the object
Surface area
Gravitational acceleration
Drag coefficient and fluid density

Conclusion:

Terminal velocity is essential for understanding how objects fall through fluids. It depends on mass, shape, and fluid properties. A terminal velocity calculator allows for quick and accurate predictions for a wide range of objects.

References:

Sources: Wikipedia: Terminal Velocity, Concepts of Physics: Stokes' Law and Terminal Velocity