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# Terminal Velocity Calculator

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

The terminal velocity calculator is useful to find the maximum terminal speed of an object. The speed can be variable due to the mass of an object and due to gravity, density, or a fluid viscosity. You may experience different terminal velocities of the same mass in different media.Different objects may have different terminal velocities due the fact various mediums have different friction coefficients.

### Terminal Velocity:

“The Terminal velocity is the highest velocity an object is going to attain when it is going to fall through the air.” The terminal velocity is the resultant force when the dragged force (Fd) and the downwards force of gravity (FG) acting on the body. When we are finding the terminal velocity, then at this point, the acceleration is equal to “Zero”. The terminal velocity calculator is efficiently able to find the terminal velocity of a falling object.

### Terminal Velocity Equation:

The simple terminal velocity equation is as follows:

Vt = √ ((2 x m x g) / (ρ x A x Cd))

Where:

Vt=Terminal velocity or maximum falling speed

m= The mass of the falling objects

g=Gravitational acceleration

ρ= Density of fluid

A=Projected area of the object

Cd=Drag Coefficient

### Dimension of Terminal Velocity:

The unit of terminal velocity is meter/seconds(m/s). We can find the dimension of any quantity by the dimension analysis calculator.

#### Practical Examples of the Terminal Velocity:

We are presenting the practical implementation of the terminal velocity:

Exp 1:

A man is falling 2000 m from the height. What is its terminal velocity?

Sol:

Given Data Height h=2000 m We can find the Terminal velocity by the given formula:

Vt= √2×g ×h Vt= √2×9.8 ×2000 = √39200 = 197.98 m/s.

Exp 2:

Find the height of the body if its terminal velocity is 100 m/s.

Sol:

Here we are having: Terminal velocity=Vt=100 m/s We can find the Terminal velocity by the given formula: h=v2/2g = 10000 / 9.8 x 2 h = 510.204 m. We can check the answer by using the terminal velocity calculator.

### Forces Affecting the Falling Object:

When an object is falling in the atmosphere, it is experiencing two types of external forces. These forces determine how fast is terminal velocity. The external forces are as follows:

1. The Gravitational Force
2. The Drag Force

### The Gravitational Force:

Consider an object of a force “F” and the mass “m”moving with the acceleration “a”. Then according to the Newton’s second law of motion, we have:

F = m * a

This can be solved for the acceleration of the object: We have the following acceleration, a = F / m-------------------(1)

In case of Earth, we take a=g, which is the gravitational force, so the “g” is:

g=F/m

On the surface of the earth gravitational pull or “g”=9.8 m/s2. The value of “g”is going to be changed by the changing altitude.

### The Drag Force:

The Drag force is different for various surfaces, this is the main reason there are various Drag coefficients for various surfaces. The terminal velocity calculator is available to find various terminal velocity coefficients for various surfaces. The Drag force is equal to:

F = W - D---------------------(2)

Where:

F = is drag force

W= is the weight of an object

D= is drag of an object

The terminal velocity m/s can’t be measured without finding the drag coefficient. We need to compare the equation (1) and (2): We can relate the gravitational force and the drag force to find the a relations between the two forces: Now put the values drag force, F into the equation (1) Now we know that:

F=W-D

Put the value in eq(1), we get The acceleration of a falling object:

a = (W - D) / m

We can find the n=magnitude of the drag by the drag equation, The drag “D” depends upon the drag coefficient “Cd”, the atmospheric density “r”. The square of the terminal velocity(air velocity) Vtand reference area “A” of an object.

D = Cd × r × Vt ^2 × A / 2

We can find the value of the terminal velocity(Vt) from the above equation. The terminal velocity calculator provides you the facility to enter the different drag coefficients for various surfaces for instant calculations.

### Drag coefficient for Various Surfaces:

The Drag coefficient for various surfaces are as follows:

 Various Surfaces Drag Coefficient Sphere 0.47 Golfball 0.389 Baseball 0.3275 Hemisphere 0.42 Cube 1.05 Angled Cube 0.8 Streamlined Body 0.04

### Working of Terminal Velocity Calculator:

The terminal velocity equation is simple to find if you have the information about the drag coefficient particular to a specific surface. Let’s have a look at working!

Input:

• Choose the desired shape from the list.
• Enter the mass of the object and cross sectional area.
• Hit the calculate button.

Output: The terminal velocity calculator is specifically designed to find the terminal velocity of various shapes:

• The separate result is represented for specific shape
• The terminal velocity and the drag force is displayed

### What is terminal velocity of a human?

The terminal velocity of the human is around 120 mph, and its horizontal position falls outward the earth surface.The max terminal velocity of humans is around 150-180 mph and 240-290 km/h. It is actually the head's own position of the human, and has less frictional area.

### Do heavy objects fall faster than lighter objects?

Yes, the heavier objects do fall quickly, it may be confusing for most of us but it is a fact. Consider the equation F=mg, when heavier objects fall they are experiencing more force due to their large or heavier mass as compared to the lighter mass.

Example:

The elephant continues to accelerate much faster due to its heavier mass as compared to the mouse .This is the main reason the elephant is going to hit much earlier than the mouse.

### What factors affect the rate of fall of an object and its speed?

The terminal velocity of an object depends on the following factors:

• Mass.
• Surface area.
• Acceleration due to gravity,”g”

### What is the effect of gravity on mass?

The gravity has a direct effect on mass, the greater the mass the more gravitational pull the object would experience.

### Can mass be zero of an object?

It is the mass of the matter in an object and it can never be Zero but weight can be Zero when there is no existence of gravity.

### Conclusion:

The terminal speed is essential to know when an object is falling in space or in air. We need the terminal velocity of various objects to know the aerodynamics of various shapes.We can find the terminal velocity of most of the Geometrical spades by the terminal velocity calculator.

### Reference:

From the source of Wikipedia: Terminal velocity , Physics, Derivation for terminal velocity From the source of concepts-of-physics.com : Stokes' Law and Terminal Velocity, Problem from IIT JEE 2016