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72-418: Laminar-flow control is a technology that offers the potential for significant improvement in drag coefficient which would provide improvements in aircraft fuel usage, range or endurance that far exceed any known single aeronautical technology. In principle, if 80% of wing is laminar, then overall drag could be reduced by 25%. The frictional force between the air and the aircraft surface, known as viscous drag,

144-1826: A c d {\displaystyle c_{\mathrm {d} }} . The force between a fluid and a body, when there is relative motion, can only be transmitted by normal pressure and tangential friction stresses. So, for the whole body, the drag part of the force, which is in-line with the approaching fluid motion, is composed of frictional drag (viscous drag) and pressure drag (form drag). The total drag and component drag forces can be related as follows: c d = 2 F d ρ v 2 A = c p + c f = 2 ρ v 2 A ∫ S d S ( p − p o ) ( n ^ ⋅ i ^ ) ⏟ c p + 2 ρ v 2 A ∫ S d S ( t ^ ⋅ i ^ ) T w ⏟ c f {\displaystyle {\begin{aligned}c_{\mathrm {d} }&={\dfrac {2F_{\mathrm {d} }}{\rho v^{2}A}}\\&=c_{\mathrm {p} }+c_{\mathrm {f} }\\&=\underbrace {{\dfrac {2}{\rho v^{2}A}}\displaystyle \int _{S}\mathrm {d} S(p-p_{o})\left({\hat {\mathbf {n} }}\cdot {\hat {\mathbf {i} }}\right)} _{c_{\mathrm {p} }}+\underbrace {{\dfrac {2}{\rho v^{2}A}}\displaystyle \int _{S}\mathrm {d} S\left({\hat {\mathbf {t} }}\cdot {\hat {\mathbf {i} }}\right)T_{\rm {w}}} _{c_{\mathrm {f} }}\end{aligned}}} where: Therefore, when

216-476: A limit value of one, for large time t . In other words, velocity asymptotically approaches a maximum value called the terminal velocity v t : v t = 2 m g ρ A C D . {\displaystyle v_{t}={\sqrt {\frac {2mg}{\rho AC_{D}}}}.\,} For an object falling and released at relative-velocity v  = v i at time t  = 0, with v i < v t ,

288-665: A limit value of one, for large time t . Velocity asymptotically tends to the terminal velocity v t , strictly from above v t . For v i = v t , the velocity is constant: v ( t ) = v t . {\displaystyle v(t)=v_{t}.} These functions are defined by the solution of the following differential equation : g − ρ A C D 2 m v 2 = d v d t . {\displaystyle g-{\frac {\rho AC_{D}}{2m}}v^{2}={\frac {dv}{dt}}.\,} Or, more generically (where F ( v ) are

360-528: A blunt body. Cylinders and spheres are taken as blunt bodies because the drag is dominated by the pressure component in the wake region at high Reynolds number . To reduce this drag, either the flow separation could be reduced or the surface area in contact with the fluid could be reduced (to reduce friction drag). This reduction is necessary in devices like cars, bicycle, etc. to avoid vibration and noise production. Drag (physics) In fluid dynamics , drag , sometimes referred to as fluid resistance ,

432-409: A case where all of the fluid approaching the object is brought to rest, building up stagnation pressure over the whole front surface. The top figure shows a flat plate with the fluid coming from the right and stopping at the plate. The graph to the left of it shows equal pressure across the surface. In a real flat plate, the fluid must turn around the sides, and full stagnation pressure is found only at

504-462: A central fuselage bay underneath the wing. In initial testing there were significant problems with the porous materials and surface slots getting plugged with debris, bugs, and even rain. In certain conditions, ice crystals would form due to the rapid cooling of air over the laminar surfaces. This would abruptly disrupt laminar flow, causing rapid melting and rapid transition back to turbulent flow. Maximum achievement of 95% laminar flow over those areas

576-456: A completely new wing of increased span and area, with a sweep reduced from 35° to 30°. The wing had a multiple series of span-wise slots (800,000 in total) through which turbulent boundary-layer was "sucked in," resulting in a smoother laminar flow. Theoretically, reduced drag, better fuel economy and longer range could be achieved. The forward cockpit carried a pilot and two flight engineers while two additional flight test engineers were housed in

648-809: A fluid at relatively slow speeds (assuming there is no turbulence). 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: F D = − b v {\displaystyle \mathbf {F} _{D}=-b\mathbf {v} \,} where: 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})\,V\,g}{b}}\left(1-e^{-b\,t/m}\right)} where: The velocity asymptotically approaches

720-450: A fluid increases as the cube of the velocity increases. For example, a car cruising on a highway at 50 mph (80 km/h) may require only 10 horsepower (7.5 kW) to overcome aerodynamic drag, but that same car at 100 mph (160 km/h) requires 80 hp (60 kW). With a doubling of speeds, the drag/force quadruples per the formula. Exerting 4 times the force over a fixed distance produces 4 times as much work . At twice

792-406: A fluid. Parasitic drag is made up of multiple components including viscous pressure drag ( form drag ), and drag due to surface roughness ( skin friction drag ). Additionally, the presence of multiple bodies in relative proximity may incur so called interference drag , which is sometimes described as a component of parasitic drag. In aviation, induced drag tends to be greater at lower speeds because

SECTION 10

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864-423: A high angle of attack is required to maintain lift, creating more drag. However, as speed increases the angle of attack can be reduced and the induced drag decreases. Parasitic drag, however, increases because the fluid is flowing more quickly around protruding objects increasing friction or drag. At even higher speeds ( transonic ), wave drag enters the picture. Each of these forms of drag changes in proportion to

936-693: A human body ( d {\displaystyle d} ≈0.6 m) v t {\displaystyle v_{t}} ≈70 m/s, for a small animal like a cat ( d {\displaystyle d} ≈0.2 m) v t {\displaystyle v_{t}} ≈40 m/s, for a small bird ( d {\displaystyle d} ≈0.05 m) v t {\displaystyle v_{t}} ≈20 m/s, for an insect ( d {\displaystyle d} ≈0.01 m) v t {\displaystyle v_{t}} ≈9 m/s, and so on. Terminal velocity for very small objects (pollen, etc.) at low Reynolds numbers

1008-527: A pair of 9,490 lb f (42 kN) static thrust General Electric XJ79-GE-13 non-afterburning turbojets mounted in pods attached to the rear of the fuselage sides. Bleed air from the J79 engines was fed into a pair of underwing fairings, each of which housed a "bleed-burn" turbine which sucked the boundary layer air out through the wing slots. The X-21A test vehicles ( 55-0408 and 55-0410 ) also incorporated sophisticated laminar flow control systems built into

1080-405: A practical range of interest is usually small, while for cars at highway speed and aircraft at cruising speed, the incoming flow direction is also more-or-less the same. Therefore, the drag coefficient c d {\displaystyle c_{\mathrm {d} }} can often be treated as a constant. For a streamlined body to achieve a low drag coefficient, the boundary layer around

1152-483: A real square flat plate perpendicular to the flow is often given as 1.17. Flow patterns and therefore c d {\displaystyle c_{\mathrm {d} }} for some shapes can change with the Reynolds number and the roughness of the surfaces. In general, c d {\displaystyle c_{\mathrm {d} }} is not an absolute constant for a given body shape. It varies with

1224-468: A small sphere with radius r {\displaystyle r} = 0.5 micrometre (diameter = 1.0 μm) moving through water at a velocity v {\displaystyle v} of 10 μm/s. Using 10 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 drag coefficient of

1296-623: A sphere can be determined for the general case of a laminar flow with Reynolds numbers less than 2 ⋅ 10 5 {\displaystyle 2\cdot 10^{5}} using the following formula: C D = 24 R e + 4 R e + 0.4   ;           R e < 2 ⋅ 10 5 {\displaystyle C_{D}={\frac {24}{Re}}+{\frac {4}{\sqrt {Re}}}+0.4~{\text{;}}~~~~~Re<2\cdot 10^{5}} For Reynolds numbers less than 1, Stokes' law applies and

1368-403: Is a force acting opposite to the relative motion of any object moving with respect to a surrounding fluid . This can exist between two fluid layers, two solid surfaces, or between a fluid and a solid surface. Drag forces tend to decrease fluid velocity relative to the solid object in the fluid's path. Unlike other resistive forces, drag force depends on velocity. This is because drag force

1440-483: Is a streamlined body, and a cylinder, which is a bluff body. Also shown is a flat plate illustrating the effect that orientation has on the relative proportions of skin friction, and pressure difference between front and back. A body is known as bluff or blunt when the source of drag is dominated by pressure forces, and streamlined if the drag is dominated by viscous forces. For example, road vehicles are bluff bodies. For aircraft, pressure and friction drag are included in

1512-558: 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 with d in metre and v t in m/s. v t = 90 d , {\displaystyle v_{t}=90{\sqrt {d}},\,} For example, for

SECTION 20

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1584-448: Is also defined in terms of the hyperbolic tangent function: v ( t ) = v t tanh ⁡ ( t g v t + arctanh ⁡ ( v i v t ) ) . {\displaystyle v(t)=v_{t}\tanh \left(t{\frac {g}{v_{t}}}+\operatorname {arctanh} \left({\frac {v_{i}}{v_{t}}}\right)\right).\,} For v i > v t ,

1656-625: Is asymptotically proportional to R e − 1 {\displaystyle \mathrm {Re} ^{-1}} , which means that the drag is linearly proportional to the speed, i.e. the drag force on a small sphere moving through a viscous fluid is given by the Stokes Law : F d = 3 π μ D v {\displaystyle F_{\rm {d}}=3\pi \mu Dv} At high R e {\displaystyle \mathrm {Re} } , C D {\displaystyle C_{\rm {D}}}

1728-500: Is being measured. For automobiles and many other objects, the reference area is the projected frontal area of the vehicle. This may not necessarily be the cross-sectional area of the vehicle, depending on where the cross-section is taken. For example, for a sphere A = π r 2 {\displaystyle A=\pi r^{2}} (note this is not the surface area = 4 π r 2 {\displaystyle 4\pi r^{2}} ). For airfoils ,

1800-399: Is determined by Stokes law. In short, terminal velocity is higher for larger creatures, and thus potentially 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. The equation for viscous resistance or linear drag is appropriate for objects or particles moving through

1872-401: Is drag which occurs as the result of the creation of lift on a three-dimensional lifting body , such as the wing or propeller of an airplane. Induced drag consists primarily of two components: drag due to the creation of trailing vortices ( vortex drag ); and the presence of additional viscous drag ( lift-induced viscous drag ) that is not present when lift is zero. The trailing vortices in

1944-457: Is essentially a statement that the drag force on any object is proportional to the density of the fluid and proportional to the square of the relative flow speed between the object and the fluid. The factor of 1 / 2 {\displaystyle 1/2} comes from the dynamic pressure of the fluid, which is equal to the kinetic energy density. The value of c d {\displaystyle c_{\mathrm {d} }}

2016-479: Is more natural to write the drag force as being proportional to a drag coefficient multiplied by the speed of the object (rather than the square of the speed of the object). An example of such a regime is the study of the mobility of aerosol particulates, such as smoke particles. This leads to a different formal definition of the "drag coefficient," of course. In the non dimensional form of the Cauchy momentum equation,

2088-428: Is more or less constant, but drag will vary as the square of the speed varies. The graph to the right shows how C D {\displaystyle C_{\rm {D}}} varies with R e {\displaystyle \mathrm {Re} } 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

2160-437: Is much larger in a turbulent boundary layer than in a laminar one. The principal type of active laminar-flow control is removal of a small amount of the boundary-layer air by suction through porous materials, multiple narrow surface slots, or small perforations ( boundary layer suction ). Two major modifications were required, the first involving the standard underwing podded Allison J71 engines being removed and replaced by

2232-488: Is not a constant but varies as a function of flow speed, flow direction, object position, object size, fluid density and fluid viscosity . Speed, kinematic viscosity and a characteristic length scale of the object are incorporated into a dimensionless quantity called the Reynolds number R e {\displaystyle \mathrm {Re} } . c d {\displaystyle c_{\mathrm {d} }}

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2304-472: Is presented at Drag equation § Derivation . The reference area A is often the orthographic projection of the object, or the frontal area, on a plane perpendicular to the direction of motion. 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 area (drag coefficient corresponding to each of those different areas must be determined). In

2376-429: Is proportional to the velocity for low-speed flow and the velocity squared for high-speed flow. This distinction between low and high-speed flow is measured by the Reynolds number . Examples of drag include: Types of drag are generally divided into the following categories: The effect of streamlining on the relative proportions of skin friction and form drag is shown for two different body sections: An airfoil, which

2448-527: Is the Reynolds number related to fluid path length L. As mentioned, the drag equation with a constant drag coefficient gives the force moving through fluid a relatively large velocity, i.e. high Reynolds number , Re > ~1000. This is also called quadratic drag . F D = 1 2 ρ v 2 C D A , {\displaystyle F_{D}\,=\,{\tfrac {1}{2}}\,\rho \,v^{2}\,C_{D}\,A,} The derivation of this equation

2520-755: Is the wind speed and v o {\displaystyle v_{o}} is the object speed (both relative to ground). 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 {g\rho C_{D}A}{2m}}}\right).\,} The hyperbolic tangent has

2592-473: Is thus a function of R e {\displaystyle \mathrm {Re} } . In a compressible flow, the speed of sound is relevant, and c d {\displaystyle c_{\mathrm {d} }} is also a function of Mach number M a {\displaystyle \mathrm {Ma} } . For certain body shapes, the drag coefficient c d {\displaystyle c_{\mathrm {d} }} only depends on

2664-433: Is used in the drag equation in which a lower drag coefficient indicates the object will have less aerodynamic or hydrodynamic drag. The drag coefficient is always associated with a particular surface area. The drag coefficient of any object comprises the effects of the two basic contributors to fluid dynamic drag: skin friction and form drag . The drag coefficient of a lifting airfoil or hydrofoil also includes

2736-476: Is very small and drag is dominated by the friction component. Therefore, such a body (here an airfoil) is described as streamlined, whereas for bodies with fluid flow at high angles of attack, boundary layer separation takes place. This mainly occurs due to adverse pressure gradients at the top and rear parts of an airfoil . Due to this, wake formation takes place, which consequently leads to eddy formation and pressure loss due to pressure drag. In such situations,

2808-405: The drag coefficient (commonly denoted as: c d {\displaystyle c_{\mathrm {d} }} , c x {\displaystyle c_{x}} or c w {\displaystyle c_{\rm {w}}} ) is a dimensionless quantity that is used to quantify the drag or resistance of an object in a fluid environment, such as air or water. It

2880-413: The order 10 ). For an object with well-defined fixed separation points, like a circular disk with its plane normal to the flow direction, the drag coefficient is constant for Re  > 3,500. The further the drag coefficient C d is, in general, a function of the orientation of the flow with respect to the object (apart from symmetrical objects like a sphere). Under the assumption that

2952-452: The Reynolds number R e {\displaystyle \mathrm {Re} } , Mach number M a {\displaystyle \mathrm {Ma} } and the direction of the flow. For low Mach number M a {\displaystyle \mathrm {Ma} } , the drag coefficient is independent of Mach number. Also, the variation with Reynolds number R e {\displaystyle \mathrm {Re} } within

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3024-413: 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

3096-416: The airfoil is stalled and has higher pressure drag than friction drag. In this case, the body is described as a blunt body. A streamlined body looks like a fish ( tuna ), Oropesa , etc. or an airfoil with small angle of attack, whereas a blunt body looks like a brick, a cylinder or an airfoil with high angle of attack. For a given frontal area and velocity, a streamlined body will have lower resistance than

3168-407: 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

3240-466: The body must remain attached to the surface of the body for as long as possible, causing the wake to be narrow. A high form drag results in a broad wake. The boundary layer will transition from laminar to turbulent if Reynolds number of the flow around the body is sufficiently great. Larger velocities, larger objects, and lower viscosities contribute to larger Reynolds numbers. For other objects, such as small particles, one can no longer consider that

3312-453: The case of a wing , the reference areas are the same, and the drag force is in the same ratio as the lift force . Therefore, the reference for a wing is often the lifting area, sometimes referred to as "wing area" rather than the frontal area. For an object with a smooth surface, and non-fixed separation points (like a sphere or circular cylinder), the drag coefficient may vary with Reynolds number Re , up to extremely high values ( Re of

3384-420: The center, dropping off toward the edges as in the lower figure and graph. Only considering the front side, the c d {\displaystyle c_{\mathrm {d} }} of a real flat plate would be less than 1; except that there will be suction on the backside: a negative pressure (relative to ambient). The overall c d {\displaystyle c_{\mathrm {d} }} of

3456-685: The definition of parasitic drag . Parasite drag is often expressed in terms of a hypothetical. This is the area of a flat plate perpendicular to the flow. It is used when comparing the drag of different aircraft For example, the Douglas DC-3 has an equivalent parasite area of 2.20 m (23.7 sq ft) and the McDonnell Douglas DC-9 , with 30 years of advancement in aircraft design, an area of 1.91 m (20.6 sq ft) although it carried five times as many passengers. Lift-induced drag (also called induced drag )

3528-678: The drag coefficient C D {\displaystyle C_{\rm {D}}} as a function of Bejan number and the ratio between wet area A w {\displaystyle A_{\rm {w}}} and front area A f {\displaystyle A_{\rm {f}}} : C D = 2 A w A f B e R e L 2 {\displaystyle C_{\rm {D}}=2{\frac {A_{\rm {w}}}{A_{\rm {f}}}}{\frac {\mathrm {Be} }{\mathrm {Re} _{L}^{2}}}} where R e L {\displaystyle \mathrm {Re} _{L}}

3600-399: The drag coefficient c d {\displaystyle c_{\mathrm {d} }} is constant, but certainly is a function of Reynolds number. At a low Reynolds number, the flow around the object does not transition to turbulent but remains laminar, even up to the point at which it separates from the surface of the object. At very low Reynolds numbers, without flow separation,

3672-487: The drag coefficient approaches 24 R e {\displaystyle {\frac {24}{Re}}} ! In aerodynamics , aerodynamic drag , also known as air resistance , is the fluid drag force that acts on any moving solid body in the direction of the air's freestream flow. Alternatively, calculated from the flow field perspective (far-field approach), the drag force results from three natural phenomena: shock waves , vortex sheet, and viscosity . When

SECTION 50

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3744-479: The drag coefficient, there are other definitions that one may encounter in the literature. The reason for this is that the conventional definition makes the most sense when one is in the Newton regime, such as what happens at high Reynolds number, where it makes sense to scale the drag to the momentum flux into the frontal area of the object. But, there are other flow regimes. In particular at very low Reynolds number, it

3816-620: The drag constant: b = 6 π η r {\displaystyle b=6\pi \eta r\,} where r {\displaystyle r} is the Stokes radius of the particle, and η {\displaystyle \eta } is the fluid viscosity. The resulting expression for the drag is known as Stokes' drag : F D = − 6 π η r v . {\displaystyle \mathbf {F} _{D}=-6\pi \eta r\,\mathbf {v} .} For example, consider

3888-486: The drag force F d {\displaystyle F_{\mathrm {d} }} is proportional to v {\displaystyle v} instead of v 2 {\displaystyle v^{2}} ; for a sphere this is known as Stokes' law . The Reynolds number will be low for small objects, low velocities, and high viscosity fluids. A c d {\displaystyle c_{\mathrm {d} }} equal to 1 would be obtained in

3960-462: The drag force increases. As noted above, aircraft use their wing area as the reference area when computing c d {\displaystyle c_{\mathrm {d} }} , while automobiles (and many other objects) use projected frontal area; thus, coefficients are not directly comparable between these classes of vehicles. In the aerospace industry, the drag coefficient is sometimes expressed in drag counts where 1 drag count = 0.0001 of

4032-483: The drag is dominated by a frictional component, the body is called a streamlined body ; whereas in the case of dominant pressure drag, the body is called a blunt or bluff body . Thus, the shape of the body and the angle of attack determine the type of drag. For example, an airfoil is considered as a body with a small angle of attack by the fluid flowing across it. This means that it has attached boundary layers , which produce much less pressure drag. The wake produced

4104-548: The effects of lift-induced drag . The drag coefficient of a complete structure such as an aircraft also includes the effects of interference drag. The drag coefficient c d {\displaystyle c_{\mathrm {d} }} is defined as c d = 2 F d ρ u 2 A {\displaystyle c_{\mathrm {d} }={\dfrac {2F_{\mathrm {d} }}{\rho u^{2}A}}} where: The reference area depends on what type of drag coefficient

4176-411: The flow-field, present in the wake of a lifting body, derive from the turbulent mixing of air from above and below the body which flows in slightly different directions as a consequence of creation of lift . With other parameters remaining the same, as the lift generated by a body increases, so does the lift-induced drag. This means that as the wing's angle of attack increases (up to a maximum called

4248-441: The fluid is not moving relative to the currently used reference system, the power required to overcome the aerodynamic drag is given by: 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}} The power needed to push an object through

4320-448: The forces acting on the object beyond drag): 1 m ∑ F ( v ) − ρ A C D 2 m v 2 = d v d t . {\displaystyle {\frac {1}{m}}\sum F(v)-{\frac {\rho AC_{D}}{2m}}v^{2}={\frac {dv}{dt}}.\,} For a potato-shaped object of average diameter d and of density ρ obj , terminal velocity

4392-749: 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_{\mathrm {D} }\,=\,{\tfrac {1}{2}}\,\rho \,v^{2}\,C_{\mathrm {D} }\,A} where The drag coefficient depends on the shape of the object and on the Reynolds number R e = v D ν = ρ v D μ , {\displaystyle \mathrm {Re} ={\frac {vD}{\nu }}={\frac {\rho vD}{\mu }},} where At low R e {\displaystyle \mathrm {Re} } , C D {\displaystyle C_{\rm {D}}}

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4464-408: The others based on speed. The combined overall drag curve therefore shows a minimum at some airspeed - an aircraft flying at this speed will be at or close to its optimal efficiency. Pilots will use this speed to maximize endurance (minimum fuel consumption), or maximize gliding range in the event of an engine failure. Drag depends on the properties of the fluid and on the size, shape, and speed of

4536-400: The reference area is the nominal wing area. Since this tends to be large compared to the frontal area, the resulting drag coefficients tend to be low, much lower than for a car with the same drag, frontal area, and speed. Airships and some bodies of revolution use the volumetric drag coefficient, in which the reference area is the square of the cube root of the airship volume (volume to

4608-438: The skin drag coefficient or skin friction coefficient is referred to the transversal area (the area normal to the drag force, so the coefficient is locally defined as: c d = τ q = 2 τ ρ u 2 {\displaystyle c_{\mathrm {d} }={\dfrac {\tau }{q}}={\dfrac {2\tau }{\rho u^{2}}}} where: The drag equation

4680-448: The speed of airflow (or more generally with Reynolds number R e {\displaystyle \mathrm {Re} } ). A smooth sphere, for example, has a c d {\displaystyle c_{\mathrm {d} }} that varies from high values for laminar flow to 0.47 for turbulent flow . Although the drag coefficient decreases with increasing R e {\displaystyle \mathrm {Re} } ,

4752-808: 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, for example, a car driving into headwind, the power required to overcome the aerodynamic drag is given by the following formula: 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}A\rho (v_{w}+v_{o})^{2}v_{o}} Where v w {\displaystyle v_{w}}

4824-884: The square of the speed at low Reynolds numbers, and as the cube of the speed at high numbers. It can be demonstrated that drag force can be expressed as a function of a dimensionless number, which is dimensionally identical to the Bejan number . Consequently, drag force and drag coefficient can be a function of Bejan number. In fact, from the expression of drag force it has been obtained: F d = Δ p A w = 1 2 C D A f ν μ l 2 R e L 2 {\displaystyle F_{\rm {d}}=\Delta _{\rm {p}}A_{\rm {w}}={\frac {1}{2}}C_{\rm {D}}A_{\rm {f}}{\frac {\nu \mu }{l^{2}}}\mathrm {Re} _{L}^{2}} and consequently allows expressing

4896-407: The stalling angle), the lift coefficient also increases, and so too does the lift-induced drag. At the onset of stall , lift is abruptly decreased, as is lift-induced drag, but viscous pressure drag, a component of parasite drag, increases due to the formation of turbulent unattached flow in the wake behind the body. Parasitic drag , or profile drag, is drag caused by moving a solid object through

4968-482: The terminal velocity v t = ( ρ − ρ 0 ) V g b {\displaystyle v_{t}={\frac {(\rho -\rho _{0})Vg}{b}}} . For a given b {\displaystyle b} , denser 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

5040-419: The two-thirds power). Submerged streamlined bodies use the wetted surface area. Two objects having the same reference area moving at the same speed through a fluid will experience a drag force proportional to their respective drag coefficients. Coefficients for unstreamlined objects can be 1 or more, for streamlined objects much less. As a caution, note that although the above is the conventional definition for

5112-489: The velocity function is defined in terms of the hyperbolic cotangent function: v ( t ) = v t coth ⁡ ( t g v t + coth − 1 ⁡ ( v i v t ) ) . {\displaystyle v(t)=v_{t}\coth \left(t{\frac {g}{v_{t}}}+\coth ^{-1}\left({\frac {v_{i}}{v_{t}}}\right)\right).\,} The hyperbolic cotangent also has

5184-851: Was desired. However, the design effort was canceled due to the plugging problems. Pioneering data were obtained in the X-21 flight program, including the effects of surface irregularities, boundary-layer turbulence induced by three-dimensional span-wise flow effects in the boundary layer (referred to as span-wise contamination) and degrading environmental effects such as ice crystals in the atmosphere. Both X-21As ended up in storage at Edwards Air Force Base , California, where they gradually became derelicts, used primarily as photo targets. The remains can still be viewed, but no efforts have been made to recover either example for restoration or display. General characteristics Performance Related development Drag coefficient In fluid dynamics ,

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