An object moving through a gas or liquid experiences a force in direction opposite to its motion. Terminal velocity is achieved when the drag force is equal in magnitude but opposite in direction to the force propelling the object.

In fluid dynamics, drag (sometimes called resistance) is the force that resists the movement of a solid object through a fluid (a liquid or gas). Drag is made up of friction forces, which act in a direction parallel to the object's surface (primarily along its sides, as friction forces at the front and back cancel themselves out), plus pressure forces, which act in a direction perpendicular to the object's surface. For a solid object moving through a fluid or gas, the drag is the sum of all the aerodynamic or hydrodynamic forces in the direction of the external fluid flow. (Forces perpendicular to this direction are considered lift). It therefore acts to oppose the motion of the object, and in a powered vehicle it is overcome by thrust. Image File history File links Terminal_Velocity. ... Image File history File links Terminal_Velocity. ... For other uses, see Force (disambiguation). ... For other uses, see Terminal velocity (disambiguation). ... Fluid dynamics is the sub-discipline of fluid mechanics dealing with fluids (liquids and gases) in motion. ... This box:      For other uses, see Solid (disambiguation). ... A fluid is defined as a substance that continually deforms (flows) under an applied shear stress regardless of the magnitude of the applied stress. ... For other uses, see Liquid (disambiguation). ... For other uses, see Gas (disambiguation). ... For other uses, see Friction (disambiguation). ... This article is about pressure in the physical sciences. ... A fluid is defined as a substance that continually deforms (flows) under an applied shear stress regardless of the magnitude of the applied stress. ... For other uses, see Gas (disambiguation). ... For the Daft Punk song, see Aerodynamic (song). ... Hydrodynamics is fluid dynamics applied to liquids, such as water, alcohol, oil, and blood. ... For other uses, see Force (disambiguation). ... The lift force, lifting force or simply lift is a mechanical force generated by solid objects as they move through a fluid. ... Thrust is a reaction force described quantitatively by Newtons Second and Third Laws. ...

In astrodynamics, depending on the situation, atmospheric drag can be regarded as inefficiency requiring expense of additional energy during launch of the space object or as a bonus simplifying return from orbit. Astrodynamics is the study of the motion of rockets, missiles, and space vehicles, as determined from Sir Isaac Newtons laws of motion and his law of universal gravitation. ... Rockets (including missiles) can be launched from the following: for a launch into an orbital spaceflight and beyond: a launch pad, including a floating platform (see San Marco platform, Sea Launch) for the launch into a suborbital flight also: a missile silo a mobile launcher vehicle a submarine air launch...

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 wings or a lifting body are present, and is therefore usually discussed either in the aviation perspective of drag, or in the design of either semi-planing or planing hulls. Wave drag occurs when a solid object is moving through a 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 the specified item, and the square of the velocity. Parasitic drag (also called parasite drag) is drag caused by moving a solid object through a fluid. ... In aerodynamics, lift-induced drag, induced drag, or sometimes drag due to lift, is a drag force which occurs whenever a lifting body or a wing of finite span generates lift. ... Wave drag is an aerodynamics term that refers to a sudden and very powerful form of drag that appears on aircraft flying at high-subsonic speeds. ... In aerodynamics, form drag, profile drag, or pressure drag, is a component of parasitic drag. ... In Aerodynamics, skin friction is the component of parasitic drag arising from the friction of the fluid against the skin of the object that is moving through it. ... In aerodynamics, interference drag is a component of parasitic drag which is caused by vortices. ... For other uses, see Wing (disambiguation). ... The lifting body is an aircraft configuration where the body itself produces lift. ... Wave drag is an aerodynamics term that refers to a sudden and very powerful form of drag that appears on aircraft flying at high-subsonic speeds. ... This page is about the physical speed of sound waves in a medium. ... In dimensional analysis, a dimensionless number (or more precisely, a number with the dimensions of 1) is a pure number without any physical units. ... The drag coefficient (Cd, Cx or Cw, depending on the country) is a dimensionless quantity that describes a characteristic amount of aerodynamic drag caused by fluid flow, used in the drag equation. ... In physics, the drag equation gives the drag experienced by an object moving through a fluid. ... This article is about velocity in physics. ... Area is a physical quantity expressing the size of a part of a surface. ...

Wind resistance or air 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). This article is about the sport. ... This article does not cite any references or sources. ... Squash racquet and ball Players in a glass-backed squash court International Squash Singles Court, as specified by the World Squash Federation Squash is an indoor racquet sport that was formerly called Squash racquets, a reference to the squashable soft ball used in the game (compared with the harder ball...

Stokes's drag

The equation for viscous resistance or linear drag is appropriate for small objects or particles moving through a fluid at relatively slow speeds where there is no turbulence (i.e. low Reynolds number, R_e < 1).^[1] In this case, the force of drag is approximately proportional to velocity, but opposite in direction. [1] The equation for viscous resistance is: In fluid mechanics, the Reynolds number may be described as the ratio of inertial forces (vsρ) to viscous forces (μ/L) and, consequently, it quantifies the relative importance of these two types of forces for given flow conditions. ...

where:

b is a constant that depends on the properties of the fluid and the dimensions of the object, and

v is the velocity of the object.

When an object falls from rest, its velocity will be

which asymptotically approaches the terminal velocity v_t = mg / b. For a given b, heavier objects fall faster.

For the special case of small spherical objects moving slowly through a viscous fluid (and thus at small Reynolds number), George Gabriel Stokes derived an expression for the drag constant, For other uses, see Viscosity (disambiguation). ... A fluid is defined as a substance that continually deforms (flows) under an applied shear stress regardless of the magnitude of the applied stress. ... Sir George Gabriel Stokes, 1st Baronet FRS (13 August 1819–1 February 1903), was an Irish mathematician and physicist, who at Cambridge made important contributions to fluid dynamics (including the Navier-Stokes equations), optics, and mathematical physics (including Stokes theorem). ...

where:

r is the Stokes radius of the particle, and η is the fluid viscosity.

For example, consider a small sphere with radius r = 0.5 micrometre (diameter = 1.0 µm) moving through water at a velocity v of 10 µm/s. Using 10⁻³ Pa·s as the dynamic viscosity of water in SI units, we find a drag force of 0.09 pN. This is about the drag force that a bacterium experiences as it swims through water. The Stokes radius or hydrodynamic diameter is the radius of a hydrated atom, but can also be applied to molecules. ... Viscosity is a measure of the resistance of a fluid to deformation under shear stress. ...

Drag at high velocity

The Drag equation calculates the force experienced by an object moving through a fluid at relatively large velocity (i.e. high Reynolds number, ), also called quadratic drag. The equation is attributed to Lord Rayleigh, who originally used in place of (L being some length). The force on a moving object due to a fluid is: In physics, the drag equation gives the drag experienced by an object moving through a fluid. ... A fluid is defined as a substance that continually deforms (flows) under an applied shear stress regardless of the magnitude of the applied stress. ... In fluid mechanics, the Reynolds number may be described as the ratio of inertial forces (vsρ) to viscous forces (μ/L) and, consequently, it quantifies the relative importance of these two types of forces for given flow conditions. ... See also Rayleigh fading Rayleigh scattering Rayleigh number Rayleigh waves Rayleigh-Jeans law External links Nobel website bio of Rayleigh About John William Strutt MacTutor biography of Lord Rayleigh Categories: People stubs | 1842 births | 1919 deaths | Nobel Prize in Physics winners | Peers | British physicists | Discoverer of a chemical element ...

    ^{see derivation}

where Derivation of the drag equation (See Huntley 1967) The drag equation may be derived to within a multiplicative constant by the method of dimensional analysis. ...

F_d is the force of drag,

ρ is the density of the fluid (Note that for the Earth's atmosphere, the density can be found using the barometric formula. It is 1.293 kg/m³ at 0 °C and 1 atmosphere.),

v is the speed of the object relative to the fluid,

A is the reference area,

C_d is the drag coefficient (a dimensionless constant, e.g. 0.25 to 0.45 for a car), and

is the unit vector indicating the direction of the velocity (the negative sign indicating the drag is opposite to that of 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 (i.e., 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. The reference for a wing would be the plane area rather than the frontal area. For other uses, see Force (disambiguation). ... For other uses, see Density (disambiguation). ... Air redirects here. ... The barometric formula, sometimes called the exponential atmosphere or isothermal atmosphere, is a formula used to model how the pressure (or density) of the air changes with altitude. ... Standard atmosphere (symbol: atm) is a unit of pressure. ... This article does not cite any references or sources. ... This article is about the physical quantity. ... The drag coefficient (Cd, Cx or Cw, depending on the country) is a dimensionless quantity that describes a characteristic amount of aerodynamic drag caused by fluid flow, used in the drag equation. ... In dimensional analysis, a dimensionless number (or more precisely, a number with the dimensions of 1) is a pure number without any physical units. ... In mathematics and the mathematical sciences, a constant is a fixed, but possibly unspecified, value. ... In mathematics, a unit vector in a normed vector space is a vector (often a spatial vector) whose length, (or magnitude) is 1. ... A 3-D view of a beverage-can stove with a cross section in yellow. ...

Power

The power required to overcome the aerodynamic drag is given by:

Note 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 (7.5 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. Exerting four times the force over a fixed distance produces four times as much work. At twice the speed the work (resulting in displacement over a fixed distance) is done twice as fast. Since power is the rate of doing work, four times the work done in half the time requires eight times the power. This article is about a unit of measurement. ... In physics, mechanical work is the amount of energy transferred by a force. ... In physics, power (symbol: P) is the rate at which work is performed or energy is transmitted, or the amount of energy required or expended for a given unit of time. ...

It should be emphasized here that the drag equation is an approximation, and does not necessarily give a close approximation in every instance. Thus one should be careful when making assumptions using these equations.

Velocity of falling object

Main article: Terminal velocity

The velocity as a function of time for an object falling through a non-dense medium is roughly given by a function involving a hyperbolic tangent: For other uses, see Terminal velocity (disambiguation). ... In mathematics, the hyperbolic functions are analogs of the ordinary trigonometric, or circular, functions. ...

In other words, velocity asymptotically approaches a maximum value called the Terminal velocity: See also Asymptotic analysis but contrast asymptotic curve. ... For other uses, see Terminal velocity (disambiguation). ...

For a potato-shaped object of average diameter d and of density ρ_obj terminal velocity is about

For objects of water-like density (raindrops, hail, live objects - animals, birds, insects, etc.) falling in air near the surface of the Earth at sea level, terminal velocity is roughly equal to

For example, for human body (d~0.6 m) v_t ~70 m/s, for a small animal like a cat (d~0.2 m) v_t ~40 m/s, for a small bird (d~0.05 m) v_t ~20 m/s, for an insect (d~0.01 m) v_t ~9 m/s, for a fog droplet (d~0.0001 m) v_t ~0.9 m/s, for a pollen or bacteria (d~0.00001 m) v_t ~0.3 m/s and so on. Actual terminal velocity for very small objects (pollen, etc) is even smaller due to the viscosity of air.

Terminal velocity is higher for larger creatures, and thus more deadly. A creature such as a mouse falling at its terminal velocity is much more likely to survive impact with the ground than a human falling at its terminal velocity. A small animal such as a cricket impacting at its terminal velocity will probably be unharmed. This explains why small animals can fall from an arbitrarily large height and not be harmed. Subfamilies See Taxonomy section Crickets, family Gryllidae (also known as true crickets), are insects somewhat related to grasshoppers and more closely related to katydids or bush crickets (family Tettigoniidae). ...

See also

In physics, ram pressure is pressure exerted on a body which is moving at supersonic velocity through a fluid medium. ... Parasitic drag (also called parasite drag) is drag caused by moving a solid object through a fluid. ... Added mass is the weight added to a system due to the fact that an accelerating or decelerating body must move some volume of surrounding fluid with it as it moves. ... In this diagram, the black arrow represents the direction of the wind. ... Trident I first launch on 18 January 1977 at Cape Canaveral, showing the aerospike A drag-reducing aerospike is a device used to reduce the forebody pressure drag of blunt bodies at supersonic speeds. ... In astrodynamics, gravity drag is inefficiency encountered by a spacecraft thrusting while moving against a gravitational field. ... In aerodynamics, a stall is a condition in which an excessive angle of attack causes loss of lift due to disruption of airflow. ... For other uses, see Terminal velocity (disambiguation). ... In physics and fluid mechanics, a boundary layer is that layer of fluid in the immediate vicinity of a bounding surface. ... The Coanda effect is the tendency of a stream of fluid to stay attached to a convex surface, rather than follow a straight line in its original direction. ... The drag coefficient (Cd, Cx or Cw, depending on the country) is a dimensionless quantity that describes a characteristic amount of aerodynamic drag caused by fluid flow, used in the drag equation. ... In fluid mechanics, the Reynolds number may be described as the ratio of inertial forces (vsρ) to viscous forces (μ/L) and, consequently, it quantifies the relative importance of these two types of forces for given flow conditions. ... In 1851, George Gabriel Stokes derived an expression for the frictional force exerted on spherical objects with very small Reynolds numbers (e. ...

References

1. ^ Drag Force

• Serway, Raymond A.; Jewett, John W. (2004). Physics for Scientists and Engineers (6th ed.). Brooks/Cole. ISBN 0-534-40842-7. 
• Tipler, Paul (2004). Physics for Scientists and Engineers: Mechanics, Oscillations and Waves, Thermodynamics (5th ed.). W. H. Freeman. ISBN 0-7167-0809-4. 
• Huntley, H. E. (1967). Dimensional Analysis. Dover. LOC 67-17978. 

External links

• Educational materials on air resistance
• Aerodynamic Drag and its effect on the acceleration and top speed of a vehicle.