Calculate terminal velocity of a falling object from its mass, frontal area and drag coefficient, with illustrative preset examples and optional fluid density and driving acceleration.

Constant quadratic drag model; neglects buoyancy, changing density and orientation. Object and shape presets are illustrative assumptions, not measured safe speeds.

Fluid and acceleration

Blank uses 1.225 kg/m³ for sea-level air.

Blank uses Earth gravity, 9.80665 m/s²; this is not net acceleration at terminal speed.

Maximum Velocity Formula

The following equation is used to calculate the Maximum Velocity.

Vmax = SQRT (2 × m × a / (p × A × C))
  • Where Vmax is the maximum velocity (m/s)
  • m is the mass of the object (kg)
  • a is the driving force per mass before drag (m/s^2); for free fall use gravity, not net acceleration
  • p is the density of the fluid (kg/m^3)
  • A is the cross-sectional area (m^2)
  • C is the coefficient of drag

To calculate the maximum velocity, divide the product of 2 times the acceleration times the mass by the product of the density, cross-sectional area, and coefficient of drag, then take the square root of the result.

What is a Maximum Velocity?

Definition:

This model estimates terminal speed under constant quadratic drag. Drag balances the driving force, so net acceleration is zero; the asymptotic speed may not be reached over a finite falling distance. Preset object values are illustrative assumptions rather than measured maximum speeds.

How to Calculate Maximum Velocity?

Example Problem:

The following example outlines the steps and information needed to calculate Maximum Velocity.

First, determine the mass of the object. In this example, the mass is found to be 20 kg.

In Custom object mode, enter the mass, frontal area and drag coefficient. Open Fluid and acceleration, then enter the driving force per mass. For this problem, the total acceleration is found to be 25 m/s^2.

Next, determine the density of the fluid. In this case, the density of the fluid is measured to be 1.2 kg/m^3.

Next, determine the cross-sectional area exposed to drag. In this problem, the area is 3 m^2.

Next, determine the coefficient of drag. This is determined to be .45.

Finally, calculate the Maximum Velocity using the formula above:

Vmax = SQRT ( 2*m*a / (p*A*C) )

Vmax = SQRT ( 2*20*25 / (1.2*3*.45) )

Vmax ≈ 24.845 m/s