Understanding Terminal Velocity: The Physics and Factors Involved

Terminal velocity is a fascinating concept in the physics of free fall, where an object reaches a constant speed due to the balance between gravitational force and air resistance. This article delves into the details of how terminal velocity is achieved and the factors that influence it, along with common misconceptions and real-world examples.

What is Terminal Velocity?

Terminal velocity is the maximum velocity that an object can achieve when falling through the air. It occurs when the force of gravity pulling the object downward is exactly balanced by the drag force (air resistance) acting upward. At this point, the object stops accelerating and continues to fall at a constant speed.

Physics Behind Terminal Velocity

The equilibrium of forces is critical in achieving terminal velocity. The force of gravity (Fg) is given by the mass (m) of the object multiplied by the acceleration due to gravity (g), i.e., Fg mg. The drag force (Fd) is determined by the object’s speed (v), the density of the air (ρ), the shape of the object (A), and a drag coefficient (Cd). The equation for drag force is:

Fd 1/2 * ρ * v^2 * A * Cd

When the gravitational force (Fg) equals the drag force (Fd), the object’s velocity is at terminal velocity (vT):

Fg Fd > mg 1/2 * ρ * vT^2 * A * Cd

Terminal Velocity for a Typical Human Skydiver

The terminal velocity for a typical human skydiver in a belly-to-earth position is approximately 120 miles per hour (193 kilometers per hour). This velocity is reached after a fall of about 1500 feet (approximately 457 meters). The specific altitude at which terminal velocity is reached can vary depending on factors such as body position, mass, and clothing. However, it is generally achieved within the first few seconds of free fall.

Misconceptions About Terminal Velocity

One common misconception is that achieving terminal velocity requires a specific height. In reality, terminal velocity is dependent on the balance between gravitational force and air resistance rather than the altitude. Another misconception is that the speed can be achieved at 100 feet during a skydive. This is not true, as the forces have already balanced out and terminal velocity is reached after a certain distance, typically within the first few seconds of free fall.

Gravitational Pressure and Atmospheric Factors

It is important to note that gravitational pressure and atmospheric conditions can vary over time. For example, the Earth’s gravitational field is slightly different at different points on the planet due to the planet’s shape and density variations. Additionally, the atmosphere’s density changes with altitude, which can affect the drag force experienced by an object in free fall. Over very long periods, these changes could theoretically impact terminal velocity, but such changes occur over geological timescales, far beyond human lifespans.

Conclusion

Despite changes in gravitational pressure and atmospheric conditions, terminal velocity is primarily determined by the balance of gravitational force and air resistance. The key factors influencing terminal velocity are the object’s mass, shape, and air density. Therefore, to reach terminal velocity, an object must fall a certain distance, not a specific height.