How to Calculate Drag Force

Wingtips on airplanes are designed to reduce drag forces.
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Everyone is intuitively familiar with the concept of drag force. When you wade through water or ride a bike, you notice that the more work you exert and the faster you move, the more resistance you get from the surrounding water or air, both of which are considered fluids by physicists. In the absence of drag forces, the world might be treated to 1,000-foot home runs in baseball, much faster world records in track and field, and cars with supernatural levels of fuel economy.

Drag forces, being restrictive rather than propulsive, are not as dramatic as other natural forces, but they are critical in mechanical engineering and related disciplines. Thanks to the efforts of mathematically-minded scientists, it is possible to not only identify drag forces in nature but also to calculate their numerical values in a variety of everyday situations.

The Drag Force Equation 

Pressure, in physics, is defined as force per unit area:


Using "D" to represent drag force specifically, this equation can be rearranged to


where C is a constant of proportionality that varies from object to object. The pressure on an object moving through a fluid can be expressed as (1/2) ρv, where ρ (the Greek letter rho) is the density of the fluid and v is the object's velocity.


D=\frac{1}{2}C\rho v^2A

Note several consequences of this equation: The drag force rises in direct proportion to density and surface area, and it rises with the square of the velocity. If you are running at 10 miles per hour, you experience four times the aerodynamic drag as you do at 5 miles per hour, with all else held constant.

Drag Force on a Falling Object

One of the equations of motion for an object in free fall from classical mechanics is


In it, v = velocity at time t, v0 is initial velocity (usually zero), a is acceleration due to gravity (9.8 m/s2 on Earth), and t is elapsed time in seconds. It is plain at a glance that an object dropped from a great height would fall at ever-increasing speed if this equation were strictly true, but it is not because it neglects drag force.

When the sum of the forces acting on an object is zero, it is no longer accelerating, although it may be moving at a high, constant speed. Thus, a skydiver attains her terminal velocity when drag force equals the force of gravity. She can manipulate this through her body posture, which affects A in the drag equation. Terminal velocity is around 120 miles per hour.

Drag Force on a Swimmer

Competitive swimmers face four distinct forces: gravity and buoyancy, which counteract one another in a vertical plane, and drag and propulsion, which act in opposite directions in a horizontal plane. In fact, the propulsive force is nothing more than a drag force applied by the swimmer's feet and hands to overcome the drag force of the water, which, as you have likely surmised, is significantly greater than that of air.

Until 2010, Olympic swimmers were permitted to use special aerodynamic suits that had only been around for a few years. Swimming's governing body banned the suits because their effect was so pronounced that world records were being broken by athletes who were otherwise unremarkable (but still world-class) without the suits.