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Drag force
Intermediate
Fluid resistance grows with speed.
F = ½ρC_dAv²Drag opposes motion through a fluid: F = ½ρC_dAv² at high speed (turbulent), growing with the square of speed. It depends on shape (C_d), frontal area A and density ρ.
Doubling the speed of a cyclist increases drag fourfold and the power needed eightfold.
At low speeds drag is closer to linear in v.
In more detail
Drag is a resistive force from a fluid acting on a moving object. At low speeds it is roughly proportional to velocity, and at high speeds it is roughly proportional to velocity squared.
Real-world uses
- Car designers reduce drag to improve fuel efficiency.
- Cyclists and swimmers adopt streamlined positions to reduce drag.
- A cyclist or a skydiver faces air drag that grows with speed, which limits how fast they can go.
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Frequently asked questions
Why does drag increase so quickly with speed?
At high speeds the air must be pushed aside, and the force depends on the square of speed in the simple model.
How can drag be reduced?
By streamlining the shape and reducing the cross-sectional area presented to the flow.
Does drag depend on the shape of the object?
Yes. The drag coefficient depends on shape, so a streamlined car has less drag than a flat-fronted van at the same speed.
Related topics in Newton's Laws & Forces
Loop-the-loop · Centrifugal force · Pseudo forces · Stokes' law · Terminal velocity of a sphere · Spring force