Wishart distribution: Difference between revisions

From formulasearchengine
Jump to navigation Jump to search
en>BeyondNormality
en>Trappist the monk
m →‎Marginal distribution of matrix elements: Remove redundant |year= parameter from CS1 citations; using AWB
 
Line 1: Line 1:
{{Refimprove|date=March 2013}}
<br><br>Bryan is actually a superstar during the building plus the vocation progress first second to his third hotel recording, And , is the proof. He burst to the picture in 2004 together with his funny mixture of straight down-house convenience, motion picture celebrity fantastic appearance and words, is set t inside a significant way. The newest a in the land graph and #2 on the pop charts, earning it the second highest first appearance during those times of 2008 for any country performer. <br><br>The son of your  [http://www.banburycrossonline.com cheap tickets to luke bryan] , knows perseverance and willpower are important elements in relation to an effective  career- . His  [http://www.museodecarruajes.org kenny chesney tickets] initial recording,  Remain Me, produced the most notable  reaches “All My Girlfriends Say” and “Country Gentleman,when his  work, Doin’  Factor, found the artist-three straight No. 8 single people:  Different Contacting Is often a Good Point.<br><br>Within the   [http://www.senatorwonderling.com cheap luke bryan concert tickets] tumble of 2010, Tour: Bryan  & which in fact had an outstanding set of , which includes Downtown. “It’s almost like you are getting a  acceptance to travel one stage further, states those designers that have been a part  [http://lukebryantickets.pyhgy.com luke bryan tickets klipsch] of the Concert toursaround right into a greater amount of designers.” It covered as among the most successful  trips in their 10-season historical past.<br><br>Here is my website: [http://lukebryantickets.iczmpbangladesh.org eagles concert tickets]
[[Image:Drag Curve 2.jpg|right]]
'''Parasitic drag''' is [[Drag (physics)|drag]] that results when an object is moved through a fluid medium (in the case of [[aerodynamics]], a gaseous medium, more specifically, the atmosphere). Parasitic drag is a combination of '''form drag''', '''skin friction''' and '''interference drag'''. '''Induced drag''' and '''wave drag''' are separate components of total drag, and are NOT components of parasitic drag.
 
In flight, [[induced drag]] results from the need to maintain [[Lift (force)|lift]]. It is greater at lower speeds where a high [[angle of attack]] is required. As speed increases, the induced drag decreases, but parasitic drag increases because the fluid is striking the object with greater force, and is moving across the object's surfaces at higher speed. As speed continues to increase into the [[transonic]] and [[Supersonic speed|supersonic]] regimes, [[wave drag]] enters the picture. Each of these drag components changes in proportion to 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 close to its optimal efficiency. Pilots will use this speed to maximize the gliding range in case of an engine failure. However, to maximize the gliding endurance, the aircraft's speed would have to be at the point of minimum power, which occurs at lower speeds than minimum drag.
 
At the point of minimum drag, C<sub>D,o</sub> (drag coefficient of aircraft when lift equals zero) is equal to C<sub>D,i</sub> (induced drag coefficient, or coefficient of drag created by lift). At the point of minimum power, C<sub>D,o</sub> is equal to one third times C<sub>D,i</sub>. This can be proven by deriving the following equations:
 
:<math>F_{drag} = \frac{1}{2} \rho V^2 A_s C_D </math>
and
:<math>C_{D} = C_{D,o} + C_{D,i}</math>
where
:<math>C_{D,i} = K C_L^2</math>
 
==Form drag==
'''Form drag''' or '''pressure drag''' arises because of the [[shape]] of the object. The general size and shape of the body are the most important factors in form drag; bodies with a larger presented cross-section will have a higher drag than thinner bodies; sleek ("streamlined") objects have lower form drag. Form drag follows the [[drag equation]], meaning that it increases with the square of velocity, and thus becomes more important for high-speed aircraft.
 
Form drag depends on the longitudinal section of the body. A prudent choice of body profile is essential for a low [[drag coefficient]]. [[Streamlines, streaklines and pathlines|Streamlines]] should be continuous, and [[Flow separation|separation of the boundary layer]] with its attendant [[vortex|vortices]] should be avoided.
 
==Profile drag==
Profile drag is usually defined as the sum of '''form drag''' and '''skin friction'''.<ref>[http://www.collinsdictionary.com/dictionary/english/profile-drag Collins Dictionary]</ref> However, the term is often used synonymously with '''form drag'''.
 
==Interference drag==
Interference drag results when airflow around one part of an object (such as a fuselage) must occupy the same space as the airflow around another part (such as a wing). The two competing airflows must speed up in order to pass through the restricted area; this speeding-up process requires extra energy and creates turbulence, resulting in a measurable increase in the form drag. This velocity increase is present at all airspeeds, but becomes even more important in the transonic range when the resulting velocity becomes sonic, producing shock waves.
 
Interference drag plays a role throughout the entire aircraft (e.g., [[nacelle]]s, [[hardpoint|pylon]]s, [[empennage]]) and its detrimental effect is always kept in mind by designers. Ideally, the pressure distributions on the intersecting bodies should complement each other’s pressure distribution. If one body locally displays a negative pressure coefficient, the intersecting body should have a positive pressure coefficient. In reality, however, this is not always possible. Particular geometric characteristics on aircraft often show how designers have dealt with the issue of interference drag. A prime example is the wing-body fairing, which smooths the sharp angle between the wing and the fuselage. Another example is the junction between the horizontal and vertical tailplane in a T-tail. Often, an additional fairing (acorn) is positioned to reduce the added supervelocities. The position of the [[nacelle]] with respect to the wing is a third example of how interference-drag considerations dominate this geometric feature. For nacelles that are positioned beneath the wing, the lateral and longitudinal distance from the wing is dominated by interference-drag considerations. If there is little vertical space available between the wing and the nacelle (because of ground clearance) the nacelle is usually positioned much more in front of the wing. The NACA [[area rule]] is one approach to reducing transonic interference drag.
 
==Skin friction==
'''Skin friction''' arises from the friction of the fluid against the "skin" of the object that is moving through it. Skin friction arises from the interaction between the fluid and the skin of the body, and is directly related to the wetted surface, the area of the surface of the body that is in contact with the fluid. As with other components of parasitic drag, skin friction follows the [[drag equation]] and rises with the square of the [[velocity]].
 
The skin friction coefficient, <math>C_f</math>, is defined by
:<math>C_f \equiv \frac{\tau_w}{\frac{1}{2} \, \rho \, U_\infty^2},</math>
where <math>\tau_w</math> is the local [[wall shear stress]], <math>\rho</math> is the fluid density, and <math>U_\infty</math> is the free-stream velocity (usually taken outside of the boundary layer or at the inlet).<ref>[http://www.cfd-online.com/Wiki/Skin_friction_coefficient Skin friction coefficient] article in [http://www.cfd-online.com/Wiki CFD-Wiki]</ref>
It is related to the momentum thickness as
:<math>C_f = 2 \frac{d \theta}{d x}.</math>
For comparison, the [[turbulent flow|turbulent]] empirical relation known as the 1/7 Power Law (derived by [[von Karman|Theodore von Kármán]]) is:
:<math>C_f = \frac{0.0583}{Re^{0.2} },</math>
where <math>Re</math> is the [[Reynolds number]].
 
Skin friction is caused by [[viscosity|viscous drag]] in the [[boundary layer]] around the object. The boundary layer at the front of the object is usually laminar and relatively thin, but becomes turbulent and thicker towards the rear. The position of the [[transition point]] depends on the shape of the object. There are two ways to decrease friction drag: the first is to shape the moving body so that laminar flow is possible, like an airfoil. The second method is to decrease the length and cross-section of the moving object as much as practicable. To do so, a designer can consider the [[fineness ratio]], which is the length of the aircraft divided by its diameter at the widest point (L/D).
 
==See also==
* [[NACA duct]]
* [[Skin friction line]]
 
==References==
{{reflist}}
 
[[Category:Fluid dynamics]]
[[Category:Aerodynamics]]

Latest revision as of 19:44, 2 December 2014



Bryan is actually a superstar during the building plus the vocation progress first second to his third hotel recording, And , is the proof. He burst to the picture in 2004 together with his funny mixture of straight down-house convenience, motion picture celebrity fantastic appearance and words, is set t inside a significant way. The newest a in the land graph and #2 on the pop charts, earning it the second highest first appearance during those times of 2008 for any country performer.

The son of your cheap tickets to luke bryan , knows perseverance and willpower are important elements in relation to an effective career- . His kenny chesney tickets initial recording, Remain Me, produced the most notable reaches “All My Girlfriends Say” and “Country Gentleman,” when his work, Doin’ Factor, found the artist-three straight No. 8 single people: Different Contacting Is often a Good Point.”

Within the cheap luke bryan concert tickets tumble of 2010, Tour: Bryan & which in fact had an outstanding set of , which includes Downtown. “It’s almost like you are getting a acceptance to travel one stage further, states those designers that have been a part luke bryan tickets klipsch of the Concert toursaround right into a greater amount of designers.” It covered as among the most successful trips in their 10-season historical past.

Here is my website: eagles concert tickets