59 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

[1]

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

Drag

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

[2]

Air resistance limits the that a falling body can reach. Air resistance is an example of  the , which is force that objects feel when they move through a fluid (liquid or gas).  Similar to , drag force is 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: and . 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 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  of the object(A_x), and the (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 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 . 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

[3]

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

Which body orientation would put the largest on a human body moving vertically through a fluid?

  • body horizontal and sideways (side first)
  • body vertical with arms in (feet first)
  • body flat with arms out (front first)

 


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