|
|
| Line 1: |
Line 1: |
| [[Image:14ilf1l.svg|thumb]]
| | For the offense, you might experience Gunboats which can handily shoot at enemy defenses coming from a too long range and Landing Products which you must seal when you train types for example Rifleman, Heavy, Zooka, Warrior and Dive bombs. To your village defenses, you might possess structures like Mortar, Bike Gun, Sniper Tower, Cannon, Flamethrower, Mine, Tank Mine, Boom Cannon and Catapult Launcher to assist families eradicate enemies.<br><br>The underside line is, this is worth exploring if you want strategy games, especially while you are keen on Clash among Clans. Want conscious of what opinions you possess, when you do.<br><br>Located in clash of clans Cheats (a secret popular social architecture because arresting bold by Supercell) participants can acceleration high accomplishments for example building, [http://www.google.com/search?q=advance&btnI=lucky advance] or training militia with gems that are being sold for absolute finances. They're basically monetizing this player's . anxiety. Every amusing architecture vibrant I apperceive of manages to do it.<br><br>Till now, there exists a minimum of social options / attributes with this game my spouse and i.e. there is not any chat, attempting to team track at friends, etc but manage we could expect this excellent to improve soon being Boom Beach continues to be their Beta Mode.<br><br>We can can use this approach to acquisition the discount of any time anywhere between 1hr and one day. For archetype to emplette the majority of dispatch up 4 a good time, acting x equals 15, 400 abnormal and as well , you receive y = 51 gems.<br><br>If you have any questions pertaining to in which and how to use [http://prometeu.net how to hack clash of clans], you can make contact with us at our web page. Conserve lots of some money on your company's games, think about following into a assistance you simply can rent payments games from. The charge of these lease accords for the year is now normally under the amount of two video games. You can preserve the online titles until you control them and simply upload out them back after more and purchase another one in particular.<br><br>And all our options are considered and approved from the best virus recognition software not to mention anti-virus in the market to ensure a security-level as large as you can, in case you fear for protection of your computer or your cellular device, no hardships. In case you nevertheless have numerous doubts, take a evaluate the movie and you'll warning it operates and everyone 100% secure! It will only take a few moments of one's! |
| | |
| In [[fluid dynamics]], the '''drag coefficient''' (commonly denoted as: ''c<sub>d</sub>'', ''c<sub>x</sub>'' or ''c<sub>w</sub>'') is a [[dimensionless quantity]] that is used to quantify the [[drag (physics)|drag]] or resistance of an object in a fluid environment such as air or water. It is used in the [[drag equation]], where a lower drag coefficient indicates the object will have less [[Aerodynamics|aerodynamic]] or [[Hydrodynamics|hydrodynamic]] drag. The drag coefficient is always associated with a particular surface area.<ref>McCormick, Barnes W. (1979): ''Aerodynamics, Aeronautics, and Flight Mechanics''. p. 24, John Wiley & Sons, Inc., New York, ISBN 0-471-03032-5</ref>
| |
| | |
| The drag coefficient of any object comprises the effects of the two basic contributors to [[Fluid dynamics|fluid dynamic]] drag: [[skin friction]] and [[form drag]]. The drag coefficient of a lifting [[airfoil]] or [[hydrofoil]] also includes the effects of [[lift-induced drag]].<ref>Clancy, L. J.: ''Aerodynamics''. Section 5.18</ref><ref>[[Ira H. Abbott|Abbott, Ira H.]], and Von Doenhoff, Albert E.: ''Theory of Wing Sections''. Sections 1.2 and 1.3</ref> The drag coefficient of a complete structure such as an aircraft also includes the effects of [[interference drag]].<ref>{{cite web|url=http://wright.nasa.gov/airplane/drageq.html |title=NASA’s Modern Drag Equation |publisher=Wright.nasa.gov |date=2010-03-25 |accessdate=2010-12-07}}</ref><ref>Clancy, L. J.: ''Aerodynamics''. Section 11.17</ref>
| |
| | |
| ==Definition==
| |
| The drag coefficient <math>c_\mathrm d\,</math> is defined as:
| |
| | |
| :<math>c_\mathrm d = \dfrac{2 F_\mathrm d}{\rho v^2 A}\, </math>
| |
| | |
| where:
| |
| :<math>F_\mathrm d\,</math> is the [[drag (physics)|drag force]], which is by definition the force component in the direction of the flow velocity,<ref>See [[lift force]] and [[vortex induced vibration]] for a possible force components transverse to the flow direction.</ref>
| |
| :<math>\rho\,</math> is the [[mass density]] of the fluid,<ref>Note that for the [[Earth's atmosphere]], the air density can be found using the [[barometric formula]]. Air is 1.293 kg/m<sup>3</sup> at 0 °C and 1 [[atmosphere (unit)|atmosphere]].</ref>
| |
| :<math>v\,</math> is the [[speed]] of the object relative to the fluid and
| |
| :<math>A\,</math> is the reference [[area]].
| |
| | |
| The reference area depends on what type of drag coefficient 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 <math>A = \pi r^2\,</math> (note this is not the surface area = <math>\!\ 4 \pi r^2</math>).
| |
| | |
| For [[airfoil]]s, the reference area is the [[planform]] area. Since this tends to be a rather large area compared to the projected frontal area, the resulting drag coefficients tend to be low: much lower than for a car with the same drag and frontal area, and at the same speed.
| |
| | |
| [[Airship]]s and some [[Solid of revolution|bodies of revolution]] use the volumetric drag coefficient, in which the reference area is the [[square (algebra)|square]] of the [[cube root]] of the airship volume. 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.
| |
| | |
| ==Background==
| |
| [[Image:Cd flat plate.svg|thumb|right|200px|Flow around a plate, showing stagnation.]] | |
| {{Main|Drag equation}}
| |
| | |
| The drag equation:
| |
| | |
| :<math>F_d\, =\, \tfrac12\, \rho\, v^2\, c_d\, A</math>
| |
| | |
| is essentially a statement that the [[Drag (physics)|drag]] [[force]] on any object is proportional to the density of the fluid and proportional to the square of the relative [[speed]] between the object and the fluid.
| |
| | |
| ''C<sub>d</sub>'' is not a constant but varies as a function of 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]] or <math>\scriptstyle Re\,</math>. <math>\scriptstyle C_\mathrm d\,</math> is thus a function of <math>\scriptstyle Re\, </math>. In compressible flow, the speed of sound is relevant and <math>\scriptstyle C_\mathrm d\,</math> is also a function of [[Mach number]] <math>\scriptstyle Ma\, </math>.
| |
| | |
| For a certain body shape the drag coefficient <math>\scriptstyle C_\mathrm d\,</math> only depends on the Reynolds number <math>\scriptstyle Re\,</math>, Mach number <math>\scriptstyle Ma\,</math> and the direction of the flow. For low Mach number <math>\scriptstyle Ma\,</math>, the drag coefficient is independent of Mach number. Also the variation with Reynolds number <math>\scriptstyle Re\,</math> within a practical range of interest is usually small, while for cars at highway speed and aircraft at cruising speed the incoming flow direction is as well more-or-less the same. So the drag coefficient <math>\scriptstyle C_\mathrm d\,</math> can often be treated as a constant.<ref>Clancy, L. J.: ''Aerodynamics''. Sections 4.15 and 5.4</ref>
| |
| | |
| For a streamlined body to achieve a low drag coefficient the [[boundary layer]] around 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 providing the Reynolds number of the flow around the body is high enough. Larger velocities, larger objects, and lower [[viscosity|viscosities]] contribute to larger Reynolds numbers.<ref name=Clancy_4.17>Clancy, L. J.: ''Aerodynamics''. Section 4.17</ref>
| |
| | |
| [[File:Drag sphere nasa.svg|right|thumb|Drag coefficient ''C''<sub>d</sub> for a sphere as a function of [[Reynolds number]] ''Re'', as obtained from laboratory experiments. The solid line is for a sphere with a smooth surface, while the dashed line is for the case of a rough surface. The numbers along the line indicate several flow regimes and associated changes in the drag coefficient:<br>
| |
| •2: attached flow ([[Stokes flow]]) and [[steady flow|steady]] [[flow separation|separated flow]],<br>
| |
| •3: separated unsteady flow, having a [[laminar flow]] [[boundary layer]] upstream of the separation, and producing a [[vortex street]],<br>
| |
| •4: separated unsteady flow with a laminar boundary layer at the upstream side, before flow separation, with downstream of the sphere a chaotic [[turbulence|turbulent]] [[wake]],<br>
| |
| •5: post-critical separated flow, with a turbulent boundary layer.]]
| |
| For other objects, such as small particles, one can no longer consider that the drag coefficient <math>\scriptstyle C_\mathrm d\,</math> is constant, but certainly is a function of Reynolds number.<ref>Clift R., Grace J. R., Weber M. E.: ''Bubbles, drops, and particles''. Academic Press NY (1978).</ref><ref>Briens C. L.: ''Powder Technology''. 67, 1991, 87-91.</ref><ref>Haider A., Levenspiel O.: ''Powder Technology''. 58, 1989, 63-70.</ref>
| |
| 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, the drag force <math>\scriptstyle F_\mathrm d\,</math> is proportional to <math>\scriptstyle v\,</math> instead of <math>\scriptstyle v^2\,</math>; for a sphere this is known as [[Stokes law]]. Reynolds number will be low for small objects, low velocities, and high viscosity fluids.<ref name=Clancy_4.17/>
| |
| | |
| A <math>\scriptstyle C_\mathrm d\,</math> equal to 1 would be obtained in 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 the center, dropping off toward the edges as in the lower figure and graph. Only considering the front side, the <math>\scriptstyle C_\mathrm d\,</math> of a real flat plate would be less than 1; except that there will be suction on the back side: a negative pressure (relative to ambient). The overall <math>\scriptstyle C_\mathrm d\,</math> of a real square flat plate perpendicular to the flow is often given as 1.17.{{Citation needed|date=March 2013}} Flow patterns and therefore <math>\scriptstyle C_\mathrm d\,</math> for some shapes can change with the Reynolds number and the roughness of the surfaces.
| |
| <!-- and there should be examples of other simple shapes -->
| |
| | |
| ==Drag coefficient ''c''<sub>d</sub> examples==
| |
| | |
| ===General===
| |
| In general, <math>c_\mathrm d\,</math> is not an absolute constant for a given body shape. It varies with the speed of airflow (or more generally with [[Reynolds number]] <math>Re</math>). A smooth sphere, for example, has a <math>c_\mathrm d\,</math> that varies from high values for laminar flow to 0.47 for turbulent flow.
| |
| {| class="wikitable sortable" style="font-size:98%; width:400px;"
| |
| |+[http://web.archive.org/web/20070715171817/http://aerodyn.org/Drag/tables.html Shapes]<!-- [http://aerodyn.org/Drag/tables.html] (link broken, archived page: -->
| |
| ! ''c''<sub>d</sub>
| |
| ! class="unsortable"| Item
| |
| |-
| |
| | 0.001 || laminar flat plate parallel to the flow (<math>\!\ Re < 10^5</math>)
| |
| |-
| |
| | 0.005 || turbulent flat plate parallel to the flow (<math>\!\ Re > 10^5</math>)
| |
| |-
| |
| | 0.075 || [[Pac-car]]
| |
| |-
| |
| | 0.1 || smooth sphere (<math>\!\ Re = 10^6</math>)
| |
| |-
| |
| | 0.15 || Schlörwagen 1939 <ref>{{cite web|url=http://www.nast-sonderfahrzeuge.de/MB-Exotenforum/forum_entry.php?id=25942 |title=MB-Exotenforum |accessdate=2012-01-07}}</ref>
| |
| |-
| |
| | 0.186-0.189 || [[Volkswagen XL1]] 2014
| |
| |-
| |
| | 0.19 || [[General Motors EV1]] 1996<ref>[http://www.motortrend.com/auto_news/112_9606_general_motors_ev1/viewall.html MotorTrend: General Motors EV1 - Driving impression], June 1996</ref>
| |
| |-
| |
| | 0.25 || [[Toyota Prius (XW30)|Toyota Prius]] (3rd Generation)
| |
| |-
| |
| | 0.26 || [[BMW i8]]
| |
| |-
| |
| | 0.28 || [[Mercedes-Benz CLA-Class]] Type C 117.<ref>{{cite web|url=http://www.mbusa.com/mercedes/vehicles/model/class-CLA/model-CLA250C#!layout=/vehicles/model/specs&class=CLA&model=CLA250C&waypoint=model-specs}}</ref>
| |
| |-
| |
| | 0.295 || bullet (not [[ogive]], at subsonic velocity)
| |
| |-
| |
| | 0.3 ||[[Audi 100]] C3 (1982)
| |
| |-
| |
| | 0.48 || rough sphere (<math>\!\ Re = \!\ 10^6</math>),<br>[[Volkswagen Beetle]]<ref>{{cite web|url=http://www.maggiolinoweb.it/technique.html |title=Technique of the VW Beetle |publisher=Maggiolinoweb.it |date= |accessdate=2009-10-24}}</ref><ref>{{cite web|url=http://www.mayfco.com/dragcd~1.htm |title=The Mayfield Homepage - Coefficient of Drag for Selected Vehicles |publisher=Mayfco.com |date= |accessdate=2009-10-24}}</ref>
| |
| |-
| |
| | 0.75 || a typical [[model rocket]]<ref>{{cite web|url=http://exploration.grc.nasa.gov/education/rocket/termvr.html |title=Terminal Velocity |publisher=Goddard Space Center |date= |accessdate=2012-02-16}}</ref>
| |
| |-
| |
| | .8-.9 || coffee filter, face-up
| |
| |-
| |
| | 1.0 || [[road bicycle]] plus cyclist, touring position<ref>Wilson, David Gordon (2004): ''Bicycling Science, 3rd ed.''. p. 197, Massachusetts Institute of Technology, Cambridge, ISBN 0-262-23237-5</ref>
| |
| |-
| |
| | 1.0–1.1 || [[skier]]
| |
| |-
| |
| | 1.0–1.3 || wires and cables
| |
| |-
| |
| | 1.0–1.3 || man (upright position)
| |
| |-
| |
| | 1.1-1.3 || ski jumper<ref name=tool>{{cite web|url=http://www.engineeringtoolbox.com/drag-coefficient-d_627.html |title=Drag Coefficient |publisher=Engineeringtoolbox.com |date= |accessdate=2010-12-07}}</ref>
| |
| |-
| |
| | 1.28 || flat plate perpendicular to flow (3D) <ref>{{cite web|url=http://www.grc.nasa.gov/WWW/k-12/airplane/shaped.html | title=Shape Effects on Drag | publisher=NASA | accessdate=2013-03-11}}</ref>
| |
| |-
| |
| | 1.3–1.5 || [[Empire State Building]]
| |
| |-
| |
| | 1.8–2.0 || [[Eiffel Tower]]
| |
| |-
| |
| | 1.98–2.05 || flat plate perpendicular to flow (2D)
| |
| |-
| |
| | 2.1 || a smooth brick{{Citation needed|date=May 2010}}
| |
| |}
| |
| | |
| ==Aircraft==
| |
| As noted above, aircraft use wing area as the reference area when computing <math>c_\mathrm d\, ,</math> while automobiles (and many other objects) use frontal cross sectional 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 a <math>C_d</math>.<ref>Basha, W. A. and Ghaly, W. S., “Drag Prediction in Transitional Flow over Airfoils,” Journal of Aircraft, Vol. 44, 2007,p. 824–32.</ref>
| |
| | |
| {| class="wikitable" style="font-size:98%; width:200px;"
| |
| |+Aircraft<ref>{{cite web|url=http://www.aerospaceweb.org/question/aerodynamics/q0184.shtml |title=Ask Us - Drag Coefficient & Lifting Line Theory |publisher=Aerospaceweb.org |date=2004-07-11 |accessdate=2010-12-07}}</ref>
| |
| ! ''c''<sub>d</sub> !! Aircraft type
| |
| |-
| |
| | 0.021 || [[F-4 Phantom II]] (subsonic)
| |
| |-
| |
| | 0.022 || [[Learjet 24]]
| |
| |-
| |
| | 0.024 || [[Boeing 787]]<ref>{{cite web|url=http://www.lissys.demon.co.uk/samp1/index.html |title=Boeing 787 Dreamliner : Analysis |publisher=Lissys.demon.co.uk |date=2006-06-21 |accessdate=2010-12-07}}</ref>
| |
| |-
| |
| | 0.027 || [[Cessna 172]]/[[Cessna 182|182]]
| |
| |-
| |
| | 0.027 || [[Cessna 310]]
| |
| |-
| |
| | 0.031 || [[Boeing 747]]
| |
| |-
| |
| | 0.044 || F-4 Phantom II (supersonic)
| |
| |-
| |
| | 0.048 || [[F-104 Starfighter]]
| |
| |-
| |
| | 0.095 || [[X-15]] (Not confirmed)
| |
| |}
| |
| | |
| ==Bluff and streamlined body flows==
| |
| | |
| ===Concept===
| |
| | |
| [[Drag]], in context of [[fluid dynamics]] refers to forces which act on a solid object in the direction of the relative fluid flow velocity. The aerodynamic forces on a body come primarily from differences in pressure and viscous shearing stresses. Thereby, the drag force on a body could be divided into two components, namely frictional drag (viscous drag) and pressure drag (form drag). The net drag force could be decomposed as follows:
| |
| [[File:Aerodynamics of Airfoil.jpg|thumb|Flow across an airfoil showing the relative impact of drag force to the direction of motion of fluid over the body. This drag force gets divided into frictional drag and pressure drag. The same airfoil is considered as a streamlined body if friction drag (viscous drag) dominates pressure drag and is considered a bluff body when pressure drag (form drag) dominates friction drag.]]
| |
| | |
| :<math>c_\mathrm d = \dfrac{2 F_\mathrm d}{\rho v^2 A}\ = c_\mathrm p + c_\mathrm f = \underbrace{ \dfrac{1}{\rho v^2 A}\ \textstyle \int\limits_{S} (p-p_o). \hat n. \hat i dA }_{ c_\mathrm p }+ \underbrace{ \dfrac{1}{\rho v^2 A}\ \textstyle \int\limits_{S} T_w . \hat t. \hat i dA }_{ c_\mathrm f} </math>
| |
| | |
| where:
| |
| :<math>c_\mathrm p\,</math> is the [[pressure]] drag coefficient,
| |
| :<math>c_\mathrm f\,</math> is the [[friction]] drag coefficient,
| |
| :<math>\hat t </math> = Tangential direction to the surface with area dA,
| |
| :<math>\hat n </math> = Normal direction to the surface with area dA,
| |
| :<math>T_\mathrm w\,</math> is the [[shear Stress]] acting on the surface dA,
| |
| :<math>p_\mathrm o\,</math> is the pressure far away from the surface dA,
| |
| :<math>p\,</math> is pressure at surface dA,
| |
| :<math>\hat i</math> is the unit vector in direction normal to the surface dA, forming a unit vector <math>d\hat A</math>
| |
| | |
| Therefore, when the [[drag]] is dominated by frictional component, the body is called as streamlined body whereas in case of dominant pressure drag, the body is called a 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 layer]]s which produce much less pressure drag.
| |
| [[File:Pressure Drag and Friction Drag.png|thumb|right|Trade-off relationship between pressure drag and friction drag]]
| |
| The [[wake]] produced is very small and drag is dominated by the friction component. Therefore, such a body (here an airfoil) is described as [[streamline]]d, whereas for bodies with fluid flow at high angles of attack [[boundary layer]] separation takes place. This mainly occurs due to adverse [[pressure gradient]]s 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, the [[airfoil]] is [[Stall (flight)|stall]]ed and has higher pressure drag than friction drag. In this case, the body is described as a bluff body.
| |
| A streamlined body looks like a fish ( [[Tuna]], [[Oropesa]], etc.) or an airfoil with small angle of attack whereas a bluff 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 a bluff body. Cylinders and spheres are taken as bluff bodies because the drag is dominated by pressure component in the wake region at high [[Reynolds number]].
| |
| | |
| To reduce this [[drag]], either flow separation could be reduced or 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.
| |
| | |
| ====Practical example====
| |
| [[Automotive aerodynamics|Aerodynamic]] design of cars has evolved from 1920s to the end of 20th century. This change in design from a bluff body to a more streamlined body reduced the drag coefficient from about 0.95 to 0.30.
| |
| | |
| [[File:Aerodynamic Drag of Car.jpg|centre|Time history of aerodynamic drag of cars in comparison with change in geometry of streamlined bodies (bluff to streamline).]]
| |
| | |
| <center>''Time history of [[Aerodynamic drag]] of cars in comparison with change in geometry of streamlined bodies (bluff to streamline).''</center>
| |
| | |
| ==See also==
| |
| * [[Automotive aerodynamics]]
| |
| * [[Automobile drag coefficient]]
| |
| * [[Drag crisis]]
| |
| * [[Zero-lift drag coefficient]]
| |
| | |
| ==Notes==
| |
| {{Reflist}}
| |
| | |
| ==References==
| |
| * Clancy, L. J. (1975): ''Aerodynamics''. Pitman Publishing Limited, London, ISBN 0-273-01120-0
| |
| * Abbott, Ira H., and Von Doenhoff, Albert E. (1959): ''Theory of Wing Sections''. Dover Publications Inc., New York, Standard Book Number 486-60586-8
| |
| * Hoerner, S. F. (1965): ''Fluid-Dynamic Drag''. Hoerner Fluid Dynamics, Brick Town, N. J., USA
| |
| * Bluff Body: http://www.engineering.uiowa.edu/~me_160/lecture.../Bluff%20Body2.pdf
| |
| * Drag of Blunt Bodies and Streamlined Bodies: http://www.princeton.edu/~asmits/Bicycle_web/blunt.html
| |
| * Hucho, W.H., Janssen, L.J., Emmelmann, H.J. 6(1975): ''The optimization of body details-A method for reducing the aerodynamics drag''. SAE 760185.
| |
| | |
| [[Category:Aerodynamics]]
| |
| [[Category:Aerospace engineering]]
| |
| [[Category:Dimensionless numbers of fluid mechanics]]
| |
| [[Category:Fluid dynamics]]
| |