In fluid dynamics, drag (sometimes called air resistance, a type of friction, or fluid resistance, another type of friction or fluid friction) is a force acting opposite to the relative motion of any object moving with respect to a surrounding fluid.[1] This can exist between two fluid layers (or surfaces) or a fluid and a solid surface. Unlike other resistive forces, such as dry friction, which are nearly independent of velocity, drag forces depend on velocity.[2][3] Drag force is proportional to the velocity for a laminar flow and the squared velocity for a turbulent flow. Even though the ultimate cause of a drag is viscous friction, the turbulent drag is independent of viscosity.[4] Drag forces always decrease fluid velocity relative to the solid object in the fluid's path. Contents 1 Examples of drag 2 Types of drag 3 Drag at high velocity 3.1 Power 3.2 Velocity of a falling object 4 Very low Reynolds numbers: Stokes' drag 5 Aerodynamics 5.1 Overview
5.2 History
5.3 Lift-induced drag
5.4 Parasitic drag
5.5 Power curve in aviation
5.6
6 d'Alembert's paradox 7 See also 8 References 9 Bibliography 10 External links Examples of drag[edit] Examples of drag include the component of the net aerodynamic or hydrodynamic force acting opposite to the direction of movement of a solid object such as cars, aircraft[3] and boat hulls; or acting in the same geographical direction of motion as the solid, as for sails attached to a down wind sail boat, or in intermediate directions on a sail depending on points of sail.[5][6][7] In the case of viscous drag of fluid in a pipe, drag force on the immobile pipe decreases fluid velocity relative to the pipe.[8][9] In physics of sports, the drag force is necessary to explain the performance of runners, particularly of sprinters.[10] Types of drag[edit] Types of drag are generally divided into the following categories: parasitic drag, consisting of form drag, skin friction, interference drag, lift-induced drag, and wave drag (aerodynamics) or wave resistance (ship hydrodynamics). The phrase parasitic drag is mainly used in aerodynamics, since for lifting wings drag it is in general small compared to lift. For flow around bluff bodies, form and interference drags often dominate, and then the qualifier "parasitic" is meaningless.[citation needed] Further, lift-induced drag is only relevant when wings or a lifting body are present, and is therefore usually discussed either in aviation or in the design of semi-planing or planing hulls. Wave drag occurs either when a solid object is moving through a fluid at or near the speed of sound or when a solid object is moving along a fluid boundary, as in surface waves.
Drag depends on the properties of the fluid and on the size, shape, and speed of the object. One way to express this is by means of the drag equation: F D = 1 2 ρ v 2 C D A displaystyle F_ D ,=, tfrac 1 2 ,rho ,v^ 2 ,C_ D ,A where F D displaystyle F_ D is the drag force, ρ displaystyle rho is the density of the fluid,[11] v displaystyle v is the speed of the object relative to the fluid, A displaystyle A is the cross sectional area, and C D displaystyle C_ D is the drag coefficient – a dimensionless number. The drag coefficient depends on the shape of the object and on the Reynolds number R e = v D ν displaystyle R_ e = frac vD nu , where D displaystyle D is some characteristic diameter or linear dimension and ν displaystyle nu is the kinematic viscosity of the fluid (equal to the viscosity μ displaystyle mu divided by the density). At low R e displaystyle R_ e , C D displaystyle C_ D is asymptotically proportional to R e − 1 displaystyle R_ e ^ -1 , which means that the drag is linearly proportional to the speed. At high R e displaystyle R_ e , C D displaystyle C_ D is more or less constant and drag will vary as the square of the speed. The graph to the right shows how C D displaystyle C_ D varies with R e displaystyle R_ e for the case of a sphere. Since the power needed to overcome the drag force is the product of the force times speed, the power needed to overcome drag will vary as the square of the speed at low Reynolds numbers and as the cube of the speed at high numbers. Drag at high velocity[edit] Main article: Drag equation Explanation of drag by NASA. As mentioned, the drag equation with a constant drag coefficient gives the force experienced by an object moving through a fluid at relatively large velocity (i.e. high Reynolds number, Re > ~1000). This is also called quadratic drag. The equation is attributed to Lord Rayleigh, who originally used L2 in place of A (L being some length). F D = 1 2 ρ v 2 C d A , displaystyle F_ D ,=, tfrac 1 2 ,rho ,v^ 2 ,C_ d ,A, see derivation
The reference area A is often orthographic projection of the object
(frontal area)—on a plane perpendicular to the direction of
motion—e.g. for objects with a simple shape, such as a sphere, this
is the cross sectional area. Sometimes a body is a composite of
different parts, each with a different reference areas, in which case
a drag coefficient corresponding to each of those different areas must
be determined.
In the case of a wing the reference areas are the same and the drag
force is in the same ratio to the lift force as the ratio of drag
coefficient to lift coefficient.[12] Therefore, the reference for a
wing is often the lifting area ("wing area") rather than the frontal
area.[13]
For an object with a smooth surface, and non-fixed separation
points—like a sphere or circular cylinder—the drag coefficient may
vary with
P d = F d ⋅ v = 1 2 ρ v 3 A C d displaystyle P_ d =mathbf F _ d cdot mathbf v = tfrac 1 2 rho v^ 3 AC_ d 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).[16] With a doubling of speed the drag (force) quadruples per the formula. Exerting 4 times the force over a fixed distance produces 4 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, 4 times the work done in half the time requires 8 times the power. When the fluid is moving relative to the reference system (e.g. a car driving into headwind) the power required to overcome the aerodynamic drag is given by: P d = F d ⋅ v o = 1 2 C d A ρ ( v w + v o ) 2 v o displaystyle P_ d =mathbf F _ d cdot mathbf v_ o = tfrac 1 2 C_ d Arho (v_ w +v_ o )^ 2 v_ o Where v w displaystyle v_ w is the wind speed and v o displaystyle v_ o it the object speed (both relative to ground). Velocity of a falling object[edit] Main article: Terminal velocity An object falling through viscous medium accelerates quickly towards its terminal speed, approaching gradually as the speed gets nearer to the terminal speed. Whether the object experiences turbulent or laminar drag changes the characteristic shape of the graph with turbulent flow resulting in a constant acceleration for a larger fraction of its accelerating time. The velocity as a function of time for an object falling through a non-dense medium, and released at zero relative-velocity v = 0 at time t = 0, is roughly given by a function involving a hyperbolic tangent (tanh): v ( t ) = 2 m g ρ A C d tanh ( t g ρ C d A 2 m ) . displaystyle v(t)= sqrt frac 2mg rho AC_ d tanh left(t sqrt frac grho C_ d A 2m right)., The hyperbolic tangent has a limit value of one, for large time t. In other words, velocity asymptotically approaches a maximum value called the terminal velocity vt: v t = 2 m g ρ A C d . displaystyle v_ t = sqrt frac 2mg rho AC_ d ., For a potato-shaped object of average diameter d and of density ρobj, terminal velocity is about v t = g d ρ o b j ρ . displaystyle v_ t = sqrt gd frac rho _ obj rho ., For objects of water-like density (raindrops, hail, live objects—mammals, birds, insects, etc.) falling in air near Earth's surface at sea level, the terminal velocity is roughly equal to v t = 90 d , displaystyle v_ t =90 sqrt d ,, with d in metre and vt in m/s. For example, for a human body ( d displaystyle mathbf d ~ 0.6 m) v t displaystyle mathbf v_ t ~ 70 m/s, for a small animal like a cat ( d displaystyle mathbf d ~ 0.2 m) v t displaystyle mathbf v_ t ~ 40 m/s, for a small bird ( d displaystyle mathbf d ~ 0.05 m) v t displaystyle mathbf v_ t ~ 20 m/s, for an insect ( d displaystyle mathbf d ~ 0.01 m) v t displaystyle mathbf v_ t ~ 9 m/s, and so on.
Trajectories of three objects thrown at the same angle (70°). The black object does not experience any form of drag and moves along a parabola. The blue object experiences Stokes' drag, and the green object Newton drag. Main article: Stokes' law The equation for viscous resistance or linear drag is appropriate for objects or particles moving through a fluid at relatively slow speeds where there is no turbulence (i.e. low Reynolds number, R e < 1 displaystyle R_ e <1 ).[18] Note that purely laminar flow only exists up to Re = 0.1 under this definition. In this case, the force of drag is approximately proportional to velocity. The equation for viscous resistance is:[19] F d = − b v displaystyle mathbf F _ d =-bmathbf v , where: b displaystyle mathbf b is a constant that depends on the properties of the fluid and the dimensions of the object, and v displaystyle mathbf v is the velocity of the object When an object falls from rest, its velocity will be v ( t ) = ( ρ − ρ 0 ) V g b ( 1 − e − b t / m ) displaystyle v(t)= frac (rho -rho _ 0 )Vg b left(1-e^ -bt/m right) which asymptotically approaches the terminal velocity v t = ( ρ − ρ 0 ) V g b displaystyle mathbf v_ t = frac (rho -rho _ 0 )Vg b . For a given b displaystyle mathbf b , heavier objects fall more quickly. 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: b = 6 π η r displaystyle b=6pi eta r, where: r displaystyle mathbf r is the
η displaystyle mathbf eta is the fluid viscosity. The resulting expression for the drag is known as Stokes' drag:[20] F d = − 6 π η r v . displaystyle mathbf F _ d =-6pi eta r,mathbf v . For example, consider a small sphere with radius r displaystyle mathbf r = 0.5 micrometre (diameter = 1.0 µm) moving through water at a velocity v displaystyle mathbf 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. Aerodynamics[edit] In aerodynamics, aerodynamic drag is the fluid drag force that acts on any moving solid body in the direction of the fluid freestream flow.[21] From the body's perspective (near-field approach), the drag results from forces due to pressure distributions over the body surface, symbolized D p r displaystyle D_ pr , and forces due to skin friction, which is a result of viscosity, denoted D f displaystyle D_ f . Alternatively, calculated from the flowfield perspective (far-field approach), the drag force results from three natural phenomena: shock waves, vortex sheet, and viscosity. Overview[edit] The pressure distribution acting on a body's surface exerts normal forces on the body. Those forces can be summed and the component of that force that acts downstream represents the drag force, D p r displaystyle D_ pr , due to pressure distribution acting on the body. The nature of these
normal forces combines shock wave effects, vortex system generation
effects, and wake viscous mechanisms.
The viscosity of the fluid has a major effect on drag. In the absence
of viscosity, the pressure forces acting to retard the vehicle are
canceled by a pressure force further aft that acts to push the vehicle
forward; this is called pressure recovery and the result is that the
drag is zero. That is to say, the work the body does on the airflow,
is reversible and is recovered as there are no frictional effects to
convert the flow energy into heat.
D f displaystyle D_ f , is calculated as the downstream projection of the viscous forces evaluated over the body's surface. The sum of friction drag and pressure (form) drag is called viscous drag. This drag component is due to viscosity. In a thermodynamic perspective, viscous effects represent irreversible phenomena and, therefore, they create entropy. The calculated viscous drag D v displaystyle D_ v use entropy changes to accurately predict the drag force. When the airplane produces lift, another drag component results. Induced drag, symbolized D i displaystyle D_ i , is due to a modification of the pressure distribution due to the
trailing vortex system that accompanies the lift production. An
alternative perspective on lift and drag is gained from considering
the change of momentum of the airflow. The wing intercepts the airflow
and forces the flow to move downward. This results in an equal and
opposite force acting upward on the wing which is the lift force. The
change of momentum of the airflow downward results in a reduction of
the rearward momentum of the flow which is the result of a force
acting forward on the airflow and applied by the wing to the air flow;
an equal but opposite force acts on the wing rearward which is the
induced drag.
D w displaystyle D_ w , results from shock waves in transonic and supersonic flight speeds.
The shock waves induce changes in the boundary layer and pressure
distribution over the body surface.
History[edit]
The idea that a moving body passing through air or another fluid
encounters resistance had been known since the time of Aristotle.
Louis Charles Breguet's paper of 1922 began efforts to reduce drag by
streamlining.[22] Breguet went on to put his ideas into practice by
designing several record-breaking aircraft in 1920s and 1930s. Ludwig
Prandtl's boundary layer theory in the 1920s provided the impetus to
minimise skin friction. A further major call for streamlining was made
by Sir
The power curve: form and induced drag vs. airspeed The interaction of parasitic and induced drag vs. airspeed can be
plotted as a characteristic curve, illustrated here. In aviation, this
is often referred to as the power curve, and is important to pilots
because it shows that, below a certain airspeed, maintaining airspeed
counterintuitively requires more thrust as speed decreases, rather
than less. The consequences of being "behind the curve" in flight are
important and are taught as part of pilot training. At the subsonic
airspeeds where the "U" shape of this curve is significant, wave drag
has not yet become a factor, and so it is not shown in the curve.
Qualitative variation in Cd factor with Mach number for aircraft Main article: wave drag
Added mass Aerodynamic force Angle of attack Boundary layer Coandă effect Drag crisis Drag coefficient Drag equation Gravity drag Keulegan–Carpenter number Lift (force) Morison equation Nose cone design Parasitic drag Ram pressure Reynolds number Stall (fluid mechanics) Stokes' law Terminal velocity Wave drag Windage References[edit] ^ "Definition of DRAG". www.merriam-webster.com.
^ French (1970), p. 211, Eq. 7-20
^ a b "What is Drag?".
^ G. Falkovich (2011).
Bibliography[edit] French, A. P. (1970). Newtonian Mechanics (The M.I.T. Introductory
Physics Series) (1st ed.). W. W. Norton & Company Inc., New York.
ISBN 978-0-393-09958-4.
G. Falkovich (2011).
External links[edit] Educational materials on air resistance Aerodynamic Drag and its effect on the acceleration and top speed of a vehicle. Vehicle Aerodynamic Drag calculator based on drag coefficient, frontal area and speed. Smithsonian National Air and Space Museum's How Things Fly website Effect of dimples on a g |