60 Drag Forces on the Body
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.
Drag
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(), and the drag coefficient (), 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)
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.
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
- "Gabriel Skydiving" By Gabriel Christian Brown [CC BY-SA 4.0 (https://creativecommons.org/licenses/by-sa/4.0)], from Wikimedia Commons ↵
- "Drag of a Sphere" by Glenn Research Center Learning Technologies Project, NASA, via GIPHY is in the Public Domain, CC0 ↵
- Drag of Car By Eshaan 1992 [CC BY-SA 3.0 (https://creativecommons.org/licenses/by-sa/3.0)], from Wikimedia Commons ↵
- OpenStax, College Physics. OpenStax CNX. Jan 17, 2019 http://cnx.org/contents/031da8d3-b525-429c-80cf-6c8ed997733a@14.5 ↵
a force acting opposite to the relative motion of any object moving with respect to a surrounding fluid
the speed at which restive forces such as friction and drag balance driving forces and speed stops increasing, e.g. the gravitational force on a falling object is balanced by air resistance
a force applied by a fluid to any object moving with respect to the fluid, which acts opposite to the relative motion of the object relative to the fluid
a force that resists the sliding motion between two surfaces
a type of force supplied by an object in response to application of a different force on the object. Friction is a reactive force
that part of the drag on an object that arises from its shape and angle at which it moves the fluid and which can be decreased by streamlining
friction caused by the viscous nature of fluids
the outward force supplied by an object in response to being compressed from opposite directions, typically in reference to solid objects.
The cross-sectional area is the area of a two-dimensional shape that is obtained when a three-dimensional object - such as a cylinder - is sliced perpendicular to some specified axis at a point. For example, the cross-section of a cylinder - when sliced parallel to its base - is a circle
a number characterizing the effect of object shape and orientation on the drag force, usually determined experimentally
a fluid that exhibits a large degree of internal friction (between sections of the fluid moving with different speed or direction)