Terminal Velocity

Terminal Velocity

What exactly is terminal velocity? How is it calculated? Read to find all the answers...
Friction is a potent force at work in this world, manifesting itself in any situation where there is relative motion between matter particles. While studying physics and fluid mechanics in particular, one of the most important phenomena you will come across is the attainment of terminal velocity, when solid objects move through fluids.

The concept of terminal velocity is related to the motion of objects in fluids and therefore, it's necessary that you have a background in this matter before discussing specifics. One of the specialized topics of study in fluid mechanics is motion of a solid object through a fluid. It encompasses aerodynamics of all aerial vehicles, projectiles and objects in free fall through air, pulled down by gravity. Imagine a small metal bead falling through a long, transparent and cylindrical container filled with clear water. The dropped bead starts traveling towards the bottom under the force of gravity and water offers resistance to its flow.

The force that comes into play in such phenomena (opposing the force of gravity which incessantly pulls everything down), is 'Drag' or 'Fluid Resistance'. Two components that contribute to the total resistance offered by an object in free fall under gravity are skin friction and form drag. Drag and friction both work in a direction, which is exactly opposite to that of object's motion under influence of gravity, in the fluid. Drag is the causative agent, which makes the falling object attain terminal velocity.

Definition
Terminal velocity is the constant speed attained by an object in free fall, when the drag force exerted by the fluid layers on it, equals the gravitational force pulling it downwards. Every force exerted on an object causes acceleration and the fact that the object is in free fall, without being accelerated, means that there is a resistive force working against it, nullifying it in the process. If there would have been no air on Earth, an object in free fall would have accelerated at an approximate rate of 9.8 m/s2, but since the Earth has a dense atmosphere, the layers of air that the object pierces through, exert a drag force on it, leading to a progressive reduction in the acceleration rate, eventually nullifying it, causing the object to attain a constant velocity.

Actual experimental measurements have revealed that a sky diver in free fall, in the belly down position, will attain an approximate terminal velocity of 195 km/hr (which is about 55 m/s) in about 15 seconds after jumping!

Formula
The terminal velocity attained by an object depends on many factors related to the geometry and physical properties of the object and the fluid properties. The shape of the object, its mass and the surface area which is subjected to fluid resistance during free fall, influences the velocity value. The density of fluid and its 'Drag coefficient' are other two factors which determine terminal velocity. Here is the formula:

Terminal Velocity (VT) = √[(2Mg)/(ρCdA)]
Here
  • M is mass of the object
  • g is the acceleration due to gravity
  • ρ is the density of fluid
  • A is the projected area of the object, subjected to drag
  • Cd is the drag coefficient
In calculation of this formula, the upward force of buoyancy exerted by fluid layers hasn't been taken into consideration. As you can see in the above formula, greater the projected area subjected to drag, lesser is the velocity. That's why, parachutes with their large surface area, reduce the free fall speed of a sky diver and help him land smoothly.

To summarize, terminal velocity is the constant speed an object falling through a fluid attains when the forces acting on it nullify each other. If you want to experience what it feels like to be moving at terminal velocity, sky diving is particularly recommended. Oh yes, don't forget to have a parachute strapped to your back, or else landing might be kind of messy and ironically terminal ;-)!