Drag equation
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In physics, the drag equation gives the drag experienced by an object moving through a fluid.
- <math>D={1 \over 2}C_d \rho A v^2<math>
where
- D is the force of drag,
- Cd is the drag coefficient (a dimensionless constant, e.g. 0.25 to 0.45 for a car, 1 for a cylinder)
- ρ is the density of the fluid*,
- v is the velocity of the object relative to the fluid, and
- A is the reference area.
* Note that for the Earth's atmosphere, the density can be found using the Barometric formula
Of particular importance is the V² dependence on velocity, meaning that fluid drag increases with the square of velocity. A car cruising on a highway at 50 mph (80 km/h) may require only 10 horsepower (7 kW) to overcome air drag, but that same car at 100 mph (160 km/h) requires 80 hp (60 kW). In other words, doubling the car's velocity increases the power needed to overcome air resistance by a factor of eight. This is because the force exerted by drag quadruples (2² = 4), and the power required equals force times velocity. Contrast this with other types of friction that generally do not vary at all with velocity.
The reference area A is related to, but not exactly equal to, the area of the projection of the object on a plane perpendicular to the direction of motion (ie cross-sectional area). Sometimes different reference areas are given for the same object in which case a drag coefficient corresponding to each of these different areas must be given. These numbers are determined by experiment.
It should also be noted that this equation is an empirical equation, and does not necessarily accurately reflect the air drag in all situations. Because drag is the result of many very complex interactions between the object and fluid in which it is moving, the drag equation is grossly simplified. However, for many common situations this simple equation provides a very good approximation for the objects behavior. One notable exception to this is when the object is moving fast enough to produce turbulence in the fluid, at which point the accuracy of the equation decreases. These inaccuracies can be overcome by providing different coefficients of drag for various speeds.
See also: terminal velocity
