Terminal Velocity Calculator

Understanding Terminal Velocity Calculator

Terminal velocity is reached when drag force equals gravitational force. A skydiver in spread position reaches about 55 m/s (200 km/h).

How to use this calculator

1. Enter the object mass, usually in kilograms, as well as the cross-sectional area, drag coefficient, and fluid density.
2. Make sure the units match the formula, so the result comes out in meters per second.
3. Use the calculator to compute the terminal velocity, which is the speed where forces balance.
4. Check whether the value is reasonable for the object and the fluid, because larger area or drag gives a smaller terminal velocity.

The formula explained

The formula computes terminal velocity, the constant falling speed when gravity is balanced by drag. It shows that heavier objects fall faster, while denser fluids, larger cross-sectional area, and higher drag coefficient reduce the terminal speed.

• \(v_t\) = terminal velocity in meters per second
• m = mass of the object in kilograms
• g = acceleration due to gravity, about \(9.8\) meters per second squared
• \(\rho\) = fluid density in kilograms per cubic meter
• A = cross-sectional area in square meters
• \(C_d\) = drag coefficient, a unitless measure of shape and drag

Step by step method

1. Start with the formula \(v_t = \sqrt{\frac{2mg}{\rho A C_d}}\).
2. Substitute the given values for \(m\), \(g\), \(\rho\), \(A\), and \(C_d\).
3. Compute the product in the denominator, divide, and then take the square root.
4. Report the result in meters per second, since that is the terminal velocity.

Worked example

Problem. Find the terminal velocity of a \(2\) kg object with cross-sectional area \(0.05\) m\(^2\), drag coefficient \(0.8\), in air with density \(1.2\) kg/m\(^3\). Use \(g = 9.8\) m/s\(^2\).

1. Substitute into the formula, \(v_t = \sqrt{\frac{2(2)(9.8)}{(1.2)(0.05)(0.8)}}\).
2. Simplify inside the square root, \(v_t = \sqrt{\frac{39.2}{0.048}}\).
3. Compute the value, \(v_t = \sqrt{816.666\ldots} \approx 28.6\).

Tips and common mistakes

• A bigger cross-sectional area or drag coefficient makes the terminal velocity smaller.
• Be careful with units, especially converting area to square meters and mass to kilograms.

Frequently asked questions