Air Resistance

in direction opposite to its motion. Terminal Velocity is achieved when the drag force is equal to force of gravity pulling it down.]]
For a solid object moving through a Fluid or Gas , drag is the sum of all the Aerodynamic or Hydrodynamic Force s in the direction of the external fluid flow. It therefore acts to oppose the motion of the object, and in a powered vehicle it is overcome by Thrust .

DETAILS

Types of drag are generally divided into three categories: Parasitic Drag , Lift-induced Drag and Wave Drag . Parasitic drag includes Form Drag , Skin Friction and Interference Drag . Lift-induced drag is only relevant when Wing s or a Lifting Body are present, and is therefore usually discussed only in the aviation perspective of drag. Beyond these two kinds of drag there is a third kind of drag, called Wave Drag , that occurs when the solid object is moving through the fluid at or near the Speed Of Sound in that fluid. The overall drag of an object is characterized by a Dimensionless Number called the Drag Coefficient , and is calculated using the Drag Equation . Assuming a constant drag coefficient, drag will vary as the square of Velocity . Thus, the resultant power needed to overcome this drag will vary as the cube of velocity. The standard equation for drag is one half the coefficient of drag multiplied by the fluid density, the cross sectional area of your specified item, and the square of the velocity

''Wind resistance'' is a layman's term used to describe drag. Its use is often vague, and is usually used in a relative sense (e.g. A Badminton shuttlecock has more ''wind resistance'' than a Squash ball).

DRAG AT SMALL VELOCITY

For objects moving through a fluid at relatively slow speeds the force of drag is approximately proportional to velocity, but opposite in direction:
:

F_d = - b v \,

where

b

v

DRAG AT LARGE VELOCITY

In Physics , the magnitude of the force experienced by an object moving through a Fluid is given by

:

F_d=rac{1}{2} 
ho C_d A v^2

where
:

F_d

is the Force of drag,
:

ho

is the Density of the fluid (about

1.29 kg/m^3

for air),
:

C_d

is the Drag Coefficient (a Dimensionless Constant , e.g. 0.25 to 0.45 for a car).
:

A

is the reference Area , and
:

v

is the Velocity of the object relative to the fluid,

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-section al 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. The reference for a wing would be the plane area rather than the frontal area.

The equation is based on an idealized situation where all of the fluid impinges on the reference area and comes to a complete stop, building up Stagnation Pressure over the whole area. No real object exactly corresponds to this behavior. ''C_d'' is the ratio of drag for any real object to that of the ideal object. In practice a rough unstreamlined body (a bluff body) will have a ''C_d'' around 1, more or less. Smoother objects can have much lower values of ''C_d''. The equation is precise, it is the ''C_d'' ( Drag Coefficient ) that can vary and is found by experiment.

Of particular importance is the ''v''² dependence on velocity, meaning that fluid drag increases with the square of velocity. When velocity is doubled, for example, not only does the fluid strike with twice the velocity, but twice the Mass of fluid strikes per second. Therefore the change of Momentum per second is multiplied by four. Force is equivalent to the change of momentum divided by time. This is in contrast with solid-on-solid Friction , which generally has very little velocity dependance.

Another interesting relation, though it is not part of the equation, is that the power needed to push an object through a fluid increases as the cube of the 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). With a doubling of speed the drag (force) quadruples per the formula. Since Power is the rate of doing Work , exerting four times the force at twice the speed requires eight times the power. However, with a doubling of velocity, the time taken to cover a given distance also halves. This means that the total Energy used to overcome drag over a given distance only increases with the square of velocity.

VELOCITY OF FALLING OBJECT

We'd like to find an equation for velocity as a function of time for a falling object.
So, to keep things simple, let us consider an object only experiencing only two forces: gravitational force, and a large-velocity drag force. The additon of these two forces results in:

:

F = mg - qv^2 \,

:where

m

g

q

which, when you plug in

F = ma

results in a differential equation:

:

m rac{dv}{dt} = mg - q v^2 \,

Rearange to see
:

rac{dv}{dt} + rac{q}{m} v^2 = g \,

The solution to this differential equation involves a Hyperbolic Tangent , and is
:

v(t) = \sqrt{ rac{gm}{q} } 	anh \left(\sqrt{rac{gq}{m}} t 
ight) \,

Plug ''q'' back in and you get the full solution:

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Air Resistance