Understanding Terminal Velocity: Factors and Real-World Examples

Terminal velocity is an important concept in both physics and everyday applications, especially in fields like skydiving. It's the speed at which the force of gravity acting on an object is balanced by the drag force acting against it, resulting in zero net acceleration. This occurs when the object falls through a fluid like air at a constant speed. Although it is often an abstract concept in theoretical contexts, its implications are quite practical in real-world scenarios.

Factors Affecting Terminal Velocity

The specific speed at which terminal velocity is reached depends on several factors including the mass of the object, its cross-sectional area, the drag coefficient, and the density of the fluid. For example, a skydiver can reach a terminal velocity of about 53 m/s (approximately 120 mph) in a belly-to-earth position, which is significantly lower than the 90 m/s (approximately 200 mph) they can achieve in a head-down position. This higher speed in the head-down position is due to the reduced drag experienced by the skydiver.

The mass of the object plays a crucial role in determining the terminal velocity. Heavier objects generally have a higher terminal velocity because they are harder to slow down by air resistance. Conversely, objects with a larger cross-sectional area experience more air resistance, leading to lower terminal velocities. The drag coefficient, a dimensionless number dependent on the shape of the object, further influences terminal velocity by quantifying how streamlined the object is. A more streamlined object has a lower drag coefficient, allowing it to reach terminal velocity faster.

The Role of Atmospheric Conditions

Atmospheric conditions also impact terminal velocity, as the density of the fluid can vary with changes in altitude. In the atmosphere, the density of air decreases with increasing altitude, which can affect terminal velocity. For instance, a skydiver at lower altitudes will experience a higher terminal velocity than at higher altitudes due to the denser air. This is why high-altitude skydiving requires careful planning and equipment to manage the lower air density.

A Practical Example: Skydiving

I, as a skydiver, have firsthand experience with terminal velocity. To achieve a specific position during a jump, we often use the principles of aerodynamics. In a flat position relative to the ground, an average-weight skydiver can reach a speed of about 120 mph. In a head-down dive, skydivers can typically achieve a higher speed of around 200 mph. This increased speed is due to the optimized aerodynamic shape and reduced drag experienced in a head-down position.

Formation Flying in Skydiving

A recent skydiving mission where we exited the plane individually and formed a specific formation in freefall exemplifies the application of these principles. In the picture below, all the skydivers used the principles of terminal velocity to achieve our desired formation. The image showcases how we strategically positioned ourselves based on our terminal velocities to achieve a visually stunning group formation mid-air.

All the skydivers exited the airplane individually and used the principles of terminal velocity to form a specific group formation in freefall.

Conclusion

Terminal velocity is reached when the gravitational force equals the drag force, allowing an object to fall at a constant speed. This speed depends on the object's mass, cross-sectional area, drag coefficient, and the density of the fluid through which it falls. While terminal velocity can be calculated for specific objects under specific conditions, the actual time it takes to reach terminal velocity varies and is generally beyond precise prediction. Understanding these factors is crucial for fields such as skydiving and other aerodynamic applications.

For more information on terminal velocity and related topics, please refer to the following resources:

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