60 Drag Forces on the Body

A skydiver maintains a horizontal (flat) body position with arms and legs spread, which reduces the terminal velocity and increases the fall time. Image Credit: “Gabriel Skydiving” By Gabriel Christian Brown, via Wikimedia Commons


Correct and thoughtful body orientation is an important part of  skydiving because the orientation of the body affects the amount of air resistance experienced by the body. In turn, the air resistance affects the terminal speed, as we will see in the next chapter.


Fluid moves around a sphere and curls toward the sphere on the back side before forming a vortex that detaches from the sphere and swirls away downstream.
Simulation of fluid flowing around a sphere. “Drag of a Sphere” by Glenn Research Center Learning Technologies ProjectNASA, via GIPHY is in the Public Domain, CC0


Air resistance limits the terminal speed that a falling body can reach. Air resistance is an example of  the drag force, which is force that objects feel when they move through a fluid (liquid or gas).  Similar to kinetic friction, drag force is reactive because it only exists when the object is moving and it points in the opposite direction to the object’s motion through the fluid. Drag force can be broken into two types: form drag and skin drag. Form drag is caused by the resistance of  fluids (liquids or gases) to being pushed out of the way by an object in motion through the fluid. Form drag is similar to the normal force provided by the resistance of solids to being deformed, only the fluid actually moves instead of just deforming. Skin drag is essentially a kinetic frictional force caused by the sliding of the fluid along the surface of the object.

The drag force  depends the density of the fluid (ρ), the maximum cross-sectional area of the object(A_x), and the drag coefficient (C_d), which accounts for the shape of the object. Objects with a low drag coefficient are often referred to as having an aerodynamic or streamlined shape. Finally, the drag force depends on the on the speed (v) of the object through the fluid. If the fluid is not not very viscous then drag depends on v2, but for viscous fluids the force depends just on v. In typical situations air is not very viscous so the complete formula for air resistance force is:

(1)   \begin{equation*} F_d = \frac{1}{2}C_d \rho A_x v^2 \end{equation*}

The image below illustrates how the shape of  an object, in this case a car, affects the drag coefficient. The table that follows provides drag coefficient values for a variety of objects.

A graph with drag coefficient on the vertical axis and year on the horizontal axis. The drag coefficients of of vehicles manufactures in various years are plotted. 0.6 in 1925, 0.5 in 1945, and 0.3 in 1975. The shapes of the vehicles and the shapes that would have a similar cross sectional area are also shown: A plate for 1925, a cylinder for 1945 and an oval for 1975.
Drag coefficients of cars (vertical axis on left) have changed over time (horizontal axis). Image Credit: Drag of Car by Eshaan 1992 via Wikimedia Commons


Drag Coefficients of Some Common Objects
Object Drag Coefficient (C)
Airfoil 0.05
Toyota Camry 0.28
Ford Focus 0.32
Honda Civic 0.36
Ferrari Testarossa 0.37
Dodge Ram pickup 0.43
Sphere 0.45
Hummer H2 SUV 0.64
Skydiver (feet first) 0.70
Bicycle 0.90
Skydiver (horizontal) 1.0
Circular flat plate 1.12

Reinforcement Exercises


  1. "Gabriel Skydiving" By Gabriel Christian Brown [CC BY-SA 4.0 (https://creativecommons.org/licenses/by-sa/4.0)], from Wikimedia Commons
  2. "Drag of a Sphere" by Glenn Research Center Learning Technologies ProjectNASA, via GIPHY is in the Public Domain, CC0
  3. Drag of Car By Eshaan 1992 [CC BY-SA 3.0 (https://creativecommons.org/licenses/by-sa/3.0)], from Wikimedia Commons
  4. OpenStax, College Physics. OpenStax CNX. Jan 17, 2019 http://cnx.org/contents/031da8d3-b525-429c-80cf-6c8ed997733a@14.5


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