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Terminal Velocity Calculator + Online Solver With Free Steps


The Terminal Velocity Calculator determines the terminal velocity of an object based on the parameters provided and calculates the problem using the general terminal velocity equation. Furthermore, the result is shown by using different units of conversions for ease of usage in other unit systems. 

The calculator requires each parameter, except for the drag coefficient, to have a unit designated to it when entering its required value. If they are missed out, the calculator calculates garbage or incorrect value. Hence it is necessary to write units. 

Moreover, real-life examples are used to compare it, such as the record speed on a 100m-dash or the speed of a falling raindrop.

What Is the Terminal Velocity Calculator?

The Terminal Velocity Calculator is an online tool that calculates the terminal velocity of an object using the parameters (mass, gravity, density, projected area, and drag coefficient) and inputs it into the general terminal velocity equation. 

The calculator interface comprises five separate text boxes labeled as mass, gravity, density, projected area, and drag coefficient. These five parameters require units at the end for the calculator to work correctly. 

Furthermore, the calculator compares this result with the real-life stats of different speeds, such as the speed of sound or a falling raindrop. It helps the user to get a better grasp of it.

How To Use the Terminal Velocity Calculator?

You can use the Terminal Velocity Calculator by simply entering the values of the parameters into their respective text boxes. A popup window will generate a detailed result for the user. 

Step 1

Enter the object parameters, which you want to calculate the terminal velocity into their respective text boxes. 

Step 2

Ensure that the parameter values are entered correctly with their respective units after entering it. Furthermore, ensure the appropriate usage of the prefix in the parameters. 

Step 3

Press the “Submit” button to get the results. 

Results

A pop-up window appears showing the detailed results in the sections explained below: 

  • Input Interpretation: This section shows the parameter values inputted into the general terminal velocity equation. You can use this section to verify whether or not you have entered the values as intended. 
  • Result: This section displays the object’s terminal velocity based on the entered parameters in the metric units(that is, meters per second).
  • Unit Conversions: The resulting terminal velocity is represented in different units or unit systems, such as miles per hour, kilometers per hour, feet per second, etc. The “More” button on the top right-hand shows further unit conversions for your requirements.
  • Comparisons as Speed: This section covers the comparisons of the result with facts and real-life stats of possible speeds (for example, the cruise speed of a Boeing 777) for you to comprehend the velocity.
  • Comparison as Sound Speed: The terminal velocity is compared with the speed of sound in different conditions, such as in dry at 26 degrees Celsius and at one atmospheric pressure.
  • Interpretations: This section defines how this terminal velocity can be interpreted. For example, this velocity can be a wave speed, phase speed, or kinematic mass flux. 
  • Basic Unit Dimensions: Dimensions of the terminal velocity in the form of primary dimensions, namely length and time. The terminal velocity is a product of length and the inverse of time.
  • Corresponding Quantities: The velocity is written in the form of time taken to cover 1 meter or 1 kilometer. Furthermore, it also calculates the effective rocket exhaust speed and the thrust speed fuel consumption from this terminal velocity.

Solved Examples

Example 1

Consider a skydiver diving from a plane. The skydiver has a mass of 75 kg and a projected area of 1.32 m². The air density is 1.225 kg/m³, and the head-first drag coefficient of the diver is 0.56. Find the terminal velocity of the diver. The value of gravity is supposed to be 9.81 m/s².

Solution

The parameters for finding the terminal velocity are explicitly shown in the above example. We can find the final terminal velocity of the skydiver using the following general equation:

\[V_T = \sqrt{\frac{2mg}{\rho A C_d}} \]

where m is the mass, g is the gravity, $\rho$ is the density of the medium, A is the Projected Area, and $C_d$ is the Coefficient of drag. 

Using the terminal velocity equation, we can find the terminal velocity by replacing the variables with their respective values. 

\[V_T = \sqrt{\frac{2 \times 75 \times 9.81}{1.225 \times 1.32 \times 0.56}} \]

\[V_T = \sqrt{\frac{1471.5}{0.90552}} \]

\[V_T = \sqrt{1625.03313}\]

\[\mathbf{V_T = 40.312 m/s}\]

Converting this to km/h for ease of usage:

\[V_T = 40.312\times \frac{3600}{1000} \,\text{km/h }\]

\[\mathbf{V_T = 145.122 \, \text{km/h}} \]

Hence, the terminal velocity is 145.122 km/h for the skydiver. 

Example 2

Consider a Boeing 777 crashing due to the loss of engine into the open sea. The plane has a mass of 201,840 kg and a projected area of 950 m². The air density is 1.225 kg/m³, and the drag coefficient of the plane is 0.96. Find the terminal velocity of the plane. The gravity is supposed to be 9.81 m/s².

Solution

Similar to Example 1 in the above example. We can find the final terminal velocity of the skydiver using the following general equation:

\[V_T = \sqrt{\frac{2mg}{\rho A C_d}} \]

\[V_T = \sqrt{\frac{2 \times 201840 \times 9.81}{1.225 \times 950 \times 0.96}} \]

\[V_T = \sqrt{\frac{3960100.8}{111.72}} \]

\[V_T = \sqrt{3544.6}\]

\[\mathbf{V_T = 59.53 m/s}\]

Converting this to km/h for ease of usage:

\[V_T = 188.27\times \frac{3600}{1000} \,\text{km/h }\]

\[\mathbf{V_T = 214.3  \, \text{km/h}} \]

Hence, the terminal velocity is 214.3 km/h for the Boeing 777. 

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