4395:, 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. Another drag component, namely
477:
322:
310:
334:
4591:
4634:
4578:. The aspect of Jones's paper that most shocked the designers of the time was his plot of the horse power required versus velocity, for an actual and an ideal plane. By looking at a data point for a given aircraft and extrapolating it horizontally to the ideal curve, the velocity gain for the same power can be seen. When Jones finished his presentation, a member of the audience described the results as being of the same level of importance as the
2187:
182:
4496:
the body does on the airflow is reversible and is recovered as there are no frictional effects to convert the flow energy into heat. Pressure recovery acts even in the case of viscous flow. Viscosity, however results in pressure drag and it is the dominant component of drag in the case of vehicles with regions of separated flow, in which the pressure recovery is infective.
167:
137:
152:
4655:
as it accelerates over the body to speeds above Mach 1.0. However, full supersonic flow over the vehicle will not develop until well past Mach 1.0. Aircraft flying at transonic speed often incur wave drag through the normal course of operation. In transonic flight, wave drag is commonly referred to as
4678:
will instead form. Additionally, local areas of transonic flow behind the initial shockwave may occur at lower supersonic speeds, and can lead to the development of additional, smaller shockwaves present on the surfaces of other lifting bodies, similar to those found in transonic flows. In supersonic
4495:
of the fluid has a major effect on drag. In the absence of viscosity, the pressure forces acting to hinder 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
4624:
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
4654:
In transonic flight, wave drag is the result of the formation of shockwaves in the fluid, formed when local areas of supersonic (Mach number greater than 1.0) flow are created. In practice, supersonic flow occurs on bodies traveling well below the speed of sound, as the local speed of air increases
4786:
in 1904, founded on both theory and experimentsâexplained the causes of drag at high
Reynolds numbers. The boundary layer is the thin layer of fluid close to the object's boundary, where viscous effects remain important even when the viscosity is very small (or equivalently the Reynolds number is
450:
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
2190:
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
459:
enters the picture. Each of these forms of drag 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 at or close to its optimal efficiency. Pilots will use this speed to maximize
3416:
is appropriate for objects or particles moving through 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
1975:(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
229:
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 the definition of
2582:
391:) that is not present when lift is zero. The trailing vortices in 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
221:
The effect of streamlining on the relative proportions of skin friction and form drag is shown for two different body sections: An airfoil, which is a streamlined body, and a cylinder, which is a bluff body. Also shown is a flat plate illustrating the effect that
1316:
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.
2729:
3374:
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.
2333:
1675:
2114:
1451:
4220:
3384:
5585:'Computational Investigation of Base Drag Reduction for a Projectile at Different Flight Regimes', M A Suliman et al. Proceedings of 13th International Conference on Aerospace Sciences & Aviation Technology, ASAT- 13, May 26 â 28, 2009
3044:
1969:
3626:
990:
2464:
66:
depends on velocity. This is because drag force is proportional to the velocity of low-speed flow, and the squared velocity for high-speed flow. This distinction between low and high-speed flow is measured by the
1628:
2922:
1979:. 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.
1786:
3124:
795:
574:
4735:
theory amenable to mathematical solutions, resulted in the prediction of zero drag. This was in contradiction with experimental evidence, and became known as d'Alembert's paradox. In the 19th century the
4019:
2431:
414:, 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.
2601:
2213:
3841:
4647:
Wave drag, sometimes referred to as compressibility drag, is drag that is created when a body moves in a compressible fluid and at the speed that is close to the speed of sound in that fluid. In
1985:
3128:
For objects of water-like density (raindrops, hail, live objectsâmammals, birds, insects, etc.) falling in air near Earth's surface at sea level, the terminal velocity is roughly equal to with
3461:
1676:
1971:
The power needed to push an object through 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
1678:
1331:
1982:
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:
4108:
4771:, of which the potential-flow solutions considered by d'Alembert are solutions. However, all experiments at high Reynolds numbers showed there is drag. Attempts to construct inviscid
1206:
55:
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
3181:
1811:
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).
4558:'s paper of 1922 began efforts to reduce drag by streamlining. Breguet went on to put his ideas into practice by designing several record-breaking aircraft in the 1920s and 1930s.
321:
2937:
333:
4254:
3908:
1883:
4426:, 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.
4101:
1679:
3510:
2826:
3519:
1155:
3678:
1062:
278:) is caused by the presence of shockwaves and first appears at subsonic aircraft speeds when local flow velocities become supersonic. The wave drag of the supersonic
4484:
4312:
1658:
1040:
1014:
4745:
4528:
4424:
4393:
4342:
3952:
3649:
3369:
3322:
3275:
3228:
2170:
2143:
1539:
1512:
1481:
1314:
1287:
1260:
1233:
1120:
1093:
899:
872:
711:
630:
604:
3748:
309:
4061:
4041:
3928:
3861:
3770:
3722:
3700:
3486:
3342:
3295:
3248:
3201:
1850:
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
842:
818:
678:
656:
3390:
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
431:, or profile drag, is drag caused by moving a solid object through a fluid. Parasitic drag is made up of multiple components including viscous pressure drag (
4659:. Transonic compressibility drag increases significantly as the speed of flight increases towards Mach 1.0, dominating other forms of drag at those speeds.
108:
In the physics of sports, drag force is necessary to explain the motion of balls, javelins, arrows and frisbees and the performance of runners and swimmers.
1544:
2837:
494:, as obtained from laboratory experiments. The dark line is for a sphere with a smooth surface, while the lighter line is for the case of a rough surface.
5131:
1714:
1157:, 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
3062:
731:
505:
5582:'Improved Empirical Model for Base Drag Prediction on Missile Configurations, based on New Wind Tunnel Data', Frank G Moore et al. NASA Langley Center
250:, 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.
1677:
3968:
4694:
The closed form solution for the minimum wave drag of a body of revolution with a fixed length was found by Sears and Haack, and is known as the
2367:
4284:
From the body's perspective (near-field approach), the drag results from forces due to pressure distributions over the body surface, symbolized
907:
5588:'Base Drag and Thick Trailing Edges', Sighard F. Hoerner, Air Materiel Command, in: Journal of the Aeronautical Sciences, Oct 1950, pp 622â628
4456:
normal forces on the body. Those forces can be added together and the component of that force that acts downstream represents the drag force,
5735:
5706:
5671:
5652:
5629:
5608:
5159:
A Case Study By
Aerospatiale And British Aerospace On The Concorde By Jean Rech and Clive S. Leyman, AIAA Professional Study Series, Fig. 3.6
302:
boat-tail drag on an aircraft is caused by the angle with which the rear fuselage, or engine nacelle, narrows to the engine exhaust diameter.
5173:
5147:
4562:'s boundary layer theory in the 1920s provided the impetus to minimise skin friction. A further major call for streamlining was made by Sir
4067:
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.
476:
4709:
theoretical concept is not subject to wave drag when operated at its design speed, but is incapable of generating lift in this condition.
4574:
was seminal. He proposed an ideal aircraft that would have minimal drag which led to the concepts of a 'clean' monoplane and retractable
1320:
It can be demonstrated that drag force can be expressed as a function of a dimensionless number, which is dimensionally identical to the
498:
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
5416:
4670:
formed at the leading and trailing edges of the body. In highly supersonic flows, or in bodies with turning angles sufficiently large,
3422:
5749:
5126:
Encyclopedia of
Automotive Engineering, David Crolla, Paper "Fundamentals, Basic principles in Road vehicle Aerodynamics and Design",
242:
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
4348:
Alternatively, calculated from the flow field perspective (far-field approach), the drag force results from three natural phenomena:
3371:â9 m/s, and so on. Terminal velocity for very small objects (pollen, etc.) at low Reynolds numbers is determined by Stokes law.
5399:
1822:. Therefore, the reference for a wing is often the lifting area, sometimes referred to as "wing area" rather than the frontal area.
5231:
4992:
4966:
5252:
4768:
4620:, and is important to pilots because it shows that, below a certain airspeed, maintaining airspeed counterintuitively requires
2577:{\displaystyle v(t)=v_{t}\tanh \left(t{\frac {g}{v_{t}}}+\operatorname {arctanh} \left({\frac {v_{i}}{v_{t}}}\right)\right).\,}
217:
due to the friction between the fluid and a surface which may be the outside of an object, or inside such as the bore of a pipe
3488:
is a constant that depends on both the material properties of the object and fluid, as well as the geometry of the object; and
5477:
1164:
4852:
3779:
3142:
5362:
4070:
The drag coefficient of a sphere can be determined for the general case of a laminar flow with
Reynolds numbers less than
4542:
The idea that a moving body passing through air or another fluid encounters resistance had been known since the time of
5767:
4737:
5332:
5247:
4817:
3877:
1807:
on a plane perpendicular to the direction of motion. For objects with a simple shape, such as a sphere, this is the
5698:
4724:
4718:
4616:
airspeed can be plotted as a characteristic curve, illustrated here. In aviation, this is often referred to as the
4571:
1324:. Consequently, drag force and drag coefficient can be a function of Bejan number. In fact, from the expression of
4633:
2724:{\displaystyle v(t)=v_{t}\coth \left(t{\frac {g}{v_{t}}}+\coth ^{-1}\left({\frac {v_{i}}{v_{t}}}\right)\right).\,}
383:
of an airplane. Induced drag consists primarily of two components: drag due to the creation of trailing vortices (
2786:
1262:
is more or less constant, but drag will vary as the square of the speed varies. The graph to the right shows how
5018:
4775:
solutions to the Euler equations, other than the potential flow solutions, did not result in realistic results.
2328:{\displaystyle v(t)={\sqrt {\frac {2mg}{\rho AC_{d}}}}\tanh \left(t{\sqrt {\frac {g\rho C_{d}A}{2m}}}\right).\,}
2198:
as a function of time for an object falling through a non-dense medium, and released at zero relative-velocity
1808:
681:
5784:
2109:{\displaystyle P_{d}=\mathbf {F} _{d}\cdot \mathbf {v_{o}} ={\tfrac {1}{2}}C_{d}A\rho (v_{w}+v_{o})^{2}v_{o}}
5799:
5619:
4892:
1800:
380:
96:: Drag acting opposite to the direction of movement of a solid object such as cars, aircraft and boat hulls.
5210:
5042:
289:
247:
4753:
4555:
3871:
2831:
2186:
1446:{\displaystyle F_{\rm {d}}=\Delta _{p}A_{w}={\frac {1}{2}}C_{D}A_{f}{\frac {\nu \mu }{l^{2}}}Re_{L}^{2}}
31:
4590:
4499:
The friction drag force, which is a tangential force on the aircraft surface, depends substantially on
1876:
Under the assumption that the fluid is not moving relative to the currently used reference system, the
59:
surface. Drag forces tend to decrease fluid velocity relative to the solid object in the fluid's path.
4530:, is calculated as the downstream projection of the viscous forces evaluated over the body's surface.
4227:
5285:
5086:
4215:{\displaystyle C_{D}={\frac {24}{Re}}+{\frac {4}{\sqrt {Re}}}+0.4~{\text{;}}~~~~~Re<2\cdot 10^{5}}
2595:
718:
461:
5226:
4566:
who provided the theoretical concepts to demonstrate emphatically the importance of streamlining in
5186:
4812:
4749:
4551:
4073:
2734:
2339:
1017:
3493:
226:
has on the relative proportions of skin friction, and pressure difference between front and back.
5301:
5190:
5102:
5076:
2207:
1864:
is, in general, a function of the orientation of the flow with respect to the object (apart from
1844:
297:
210:
4547:
1125:
3656:
5745:
5731:
5702:
5667:
5648:
5625:
5604:
5395:
5194:
5169:
5143:
5127:
4902:
4877:
4802:
4365:
4064:
2746:
2354:
2181:
355:
254:
86:
1045:
5690:
5293:
5094:
4867:
4862:
4837:
4827:
4706:
4459:
4287:
1633:
1023:
997:
714:
407:
402:
generated by a body increases, so does the lift-induced drag. This means that as the wing's
5716:
5270:
4506:
4402:
4371:
4320:
4276:, is the fluid drag force that acts on any moving solid body in the direction of the air's
3937:
3634:
3347:
3300:
3253:
3206:
2148:
2121:
1517:
1490:
1459:
1292:
1265:
1238:
1211:
1098:
1071:
877:
850:
689:
615:
582:
439:). Additionally, the presence of multiple bodies in relative proximity may incur so called
5744:, Fourth Edition, McGraw Hill Higher Education, Boston, Massachusetts, USA. 8th ed. 2015,
5712:
5478:
https://archive.org/details/Flight_International_Magazine_1913-02-01-pdf/page/n19/mode/2up
5366:
5256:
5235:
4887:
4807:
4757:
4224:
For
Reynolds numbers less than 1, Stokes' law applies and the drag coefficient approaches
3727:
3395:
3039:{\displaystyle {\frac {1}{m}}\sum F(v)-{\frac {\rho AC_{d}}{2m}}v^{2}={\frac {dv}{dt}}.\,}
1976:
1877:
1826:
1700:
726:
488:
447:
403:
181:
68:
5513:
5377:
4767:
In the limit of high
Reynolds numbers, the NavierâStokes equations approach the inviscid
4651:, wave drag consists of multiple components depending on the speed regime of the flight.
3962:
1829:(like a sphere or circular cylinder), the drag coefficient may vary with Reynolds number
5289:
5090:
1964:{\displaystyle P_{d}=\mathbf {F} _{d}\cdot \mathbf {v} ={\tfrac {1}{2}}\rho v^{3}AC_{d}}
5804:
5773:
5664:
Physics for
Scientists and Engineers: Mechanics, Oscillations and Waves, Thermodynamics
4996:
4970:
4897:
4872:
4822:
4783:
4779:
4761:
4728:
4559:
4500:
4046:
4026:
3913:
3846:
3755:
3707:
3685:
3471:
3403:
3391:
3327:
3280:
3233:
3186:
2742:
2350:
827:
803:
663:
641:
423:
411:
286:
which extended the rear fuselage 3.73 m (12.2 ft) on the production aircraft.
231:
40:
5098:
5793:
5641:
5106:
5064:
4842:
4732:
4666:
is the result of shockwaves present in the fluid and attached to the body, typically
4563:
3931:
1789:
1692:
1669:
499:
204:
90:
5305:
5723:
4882:
4857:
4847:
4648:
4579:
4575:
4265:
3621:{\displaystyle v(t)={\frac {(\rho -\rho _{0})\,V\,g}{b}}\left(1-e^{-b\,t/m}\right)}
1819:
1818:, the reference areas are the same, and the drag force is in the same ratio as the
1484:
1321:
399:
392:
372:
368:
275:
262:
258:
243:
214:
100:
4488:
shock wave effects, vortex system generation effects, and wake viscous mechanisms.
5454:
4932:
5359:
4832:
4772:
1454:
465:
103:: Drag force on the immobile pipe decreases fluid velocity relative to the pipe.
5271:"Experiments on the flow past a circular cylinder at very high Reynolds number"
5297:
4797:
4607:
4349:
4277:
3387:
1972:
1325:
1158:
266:
246:
has an equivalent parasite area of 2.20 m (23.7 sq ft) and the
4043:= 0.5 micrometre (diameter = 1.0 ÎŒm) moving through water at a velocity
446:
In aviation, induced drag tends to be greater at lower speeds because a high
4907:
4741:
4642:
4543:
4492:
4396:
4353:
3867:
821:
456:
452:
293:
283:
271:
200:
83:
17:
3383:
985:{\displaystyle D_{e}=1.30\cdot {\frac {(a\cdot b)^{0.625}}{(a+b)^{0.25}}}}
4567:
4532:
The sum of friction drag and pressure (form) drag is called viscous drag.
4449:
2195:
1865:
845:
279:
5762:
5338:
4698:. Similarly, for a fixed volume, the shape for minimum wave drag is the
3866:
For the special case of small spherical objects moving slowly through a
166:
4912:
633:
410:
also increases, and so too does the lift-induced drag. At the onset of
296:
occurs when a solid object is moving along a fluid boundary and making
136:
4570:
design. In 1929 his paper 'The
Streamline Airplane' presented to the
151:
4317:
Forces due to skin friction, which is a result of viscosity, denoted
2191:
constant acceleration for a larger fraction of its accelerating time.
1623:{\displaystyle C_{D}=2{\frac {A_{w}}{A_{f}}}{\frac {Be}{Re_{L}^{2}}}}
5380:, from Department of Physics and Astronomy, Georgia State University
2917:{\displaystyle g-{\frac {\rho AC_{d}}{2m}}v^{2}={\frac {dv}{dt}}.\,}
725:
The drag coefficient depends on the shape of the object and on the
196:
Types of drag are generally divided into the following categories:
5780:
Smithsonian
National Air and Space Museum's How Things Fly website
5081:
4632:
4589:
3955:
3382:
2185:
1781:{\displaystyle F_{D}\,=\,{\tfrac {1}{2}}\,\rho \,v^{2}\,C_{d}\,A,}
1696:
475:
93:
56:
52:
5211:
Analysis of triangular sharkskin profiles according to second law
5019:"Calculating Viscous Flow: Velocity Profiles in Rivers and Pipes"
4364:
When the airplane produces lift, another drag component results.
3119:{\displaystyle v_{t}={\sqrt {gd{\frac {\rho _{obj}}{\rho }}}}.\,}
1695:
with a constant drag coefficient gives the force moving through
790:{\displaystyle R_{e}={\frac {vD}{\nu }}={\frac {\rho vD}{\mu }},}
569:{\displaystyle F_{D}\,=\,{\tfrac {1}{2}}\,\rho \,v^{2}\,C_{D}\,A}
443:, which is sometimes described as a component of parasitic drag.
282:
prototype aircraft was reduced at Mach 2 by 1.8% by applying the
4878:
Projectile motion#Trajectory of a projectile with air resistance
4637:
Qualitative variation in Cd factor with Mach number for aircraft
1684:
376:
2461:, is also defined in terms of the hyperbolic tangent function:
904:
For a rectangular shape cross-section in the motion direction,
234:. Parasite drag is often expressed in terms of a hypothetical.
5770:
and its effect on the acceleration and top speed of a vehicle.
5063:
Hernandez-Gomez, J J; Marquina, V; Gomez, R W (25 July 2013).
5779:
3776:
The velocity asymptotically approaches the terminal velocity
2830:
These functions are defined by the solution of the following
339:
Hawk aircraft showing base area above circular engine exhaust
327:
Concorde with 'low' wave drag tail (N.B. rear fuselage spike)
5601:
Newtonian Mechanics (The M.I.T. Introductory Physics Series)
5496:
A History of Aerodynamics: And Its Impact On Flying Machines
4014:{\displaystyle \mathbf {F} _{d}=-6\pi \eta r\,\mathbf {v} .}
5142:
Fundamentals of Flight, Second Edition, Richard S. Shevell,
2426:{\displaystyle v_{t}={\sqrt {\frac {2mg}{\rho AC_{d}}}}.\,}
2206: = 0, is roughly given by a function involving a
406:
increases (up to a maximum called the stalling angle), the
5603:(1st ed.). W. W. White & Company Inc., New York.
5540:
Bennett Melvill Jones. 28 January 1887 -- 31 October 1975
2435:
For an object falling and released at relative-velocity
1857: > 3,500. The further the drag coefficient
367:) is drag which occurs as the result of the creation of
4756:. Stokes derived the drag around a sphere at very low
1880:
required to overcome the aerodynamic drag is given by:
1660:
is the Reynolds number related to fluid path length L.
5065:"On the performance of Usain Bolt in the 100 m sprint"
4662:
In supersonic flight (Mach numbers greater than 1.0),
4429:
Therefore, there are three ways of categorizing drag.
3836:{\displaystyle v_{t}={\frac {(\rho -\rho _{0})Vg}{b}}}
3724:
is the acceleration due to gravity (i.e., 9.8 m/s
2033:
1924:
1734:
525:
4509:
4462:
4405:
4374:
4323:
4290:
4230:
4111:
4076:
4049:
4029:
3971:
3940:
3916:
3880:
3849:
3782:
3758:
3730:
3710:
3688:
3659:
3637:
3522:
3516:
When an object falls from rest, its velocity will be
3496:
3474:
3425:
3350:
3330:
3303:
3283:
3256:
3236:
3209:
3189:
3145:
3065:
2940:
2840:
2789:
2604:
2467:
2370:
2216:
2151:
2124:
1988:
1886:
1717:
1636:
1547:
1520:
1493:
1462:
1334:
1295:
1268:
1241:
1214:
1167:
1128:
1101:
1074:
1048:
1026:
1000:
910:
880:
853:
830:
806:
734:
692:
666:
644:
618:
585:
508:
5543:. Vol. 23. The Royal Society. pp. 252â282.
5537:
Biographical Memoirs of Fellows of the Royal Society
5534:
Sir Morien Morgan, Sir Arnold Hall (November 1977).
4503:
configuration and viscosity. The net friction drag,
2934:) are the forces acting on the object beyond drag):
2594:, the velocity function is defined in terms of the
1825:For an object with a smooth surface, and non-fixed
5776:based on drag coefficient, frontal area and speed.
5640:
4522:
4478:
4418:
4387:
4336:
4306:
4248:
4214:
4095:
4055:
4035:
4013:
3961:The resulting expression for the drag is known as
3946:
3922:
3902:
3855:
3835:
3764:
3742:
3716:
3694:
3672:
3643:
3620:
3504:
3480:
3455:
3363:
3336:
3316:
3289:
3269:
3242:
3222:
3195:
3175:
3118:
3038:
2916:
2820:
2723:
2576:
2425:
2327:
2164:
2137:
2108:
1963:
1780:
1652:
1622:
1533:
1506:
1475:
1445:
1308:
1281:
1254:
1227:
1200:
1149:
1114:
1087:
1056:
1034:
1008:
984:
893:
866:
836:
812:
789:
705:
672:
650:
624:
598:
568:
5697:. Cambridge Mathematical Library (2nd ed.).
4023:For example, consider a small sphere with radius
3456:{\displaystyle \mathbf {F} _{d}=-b\mathbf {v} \,}
658:is the speed of the object relative to the fluid,
398:With other parameters remaining the same, as the
5514:"University of Cambridge Engineering Department"
5205:
5203:
1788:The derivation of this equation is presented at
387:); and the presence of additional viscous drag (
5621:Fluid Mechanics (A short course for physicists)
5417:"Drag coefficient (friction and pressure drag)"
3048:For a potato-shaped object of average diameter
2172:is the object speed (both relative to ground).
1703:, Re > ~1000. This is also called
5456:Influence of Attachment Line Flow on Form Drag
4612:The interaction of parasitic and induced drag
4486:. The nature of these normal forces combines
3874:derived an expression for the drag constant:
3230:â70 m/s, for a small animal like a cat (
1453:and consequently allows expressing the drag
1020:of the fluid (equal to the dynamic viscosity
8:
5639:Serway, Raymond A.; Jewett, John W. (2004).
5571:
5569:
5567:
5508:
5506:
5488:
5486:
5317:
5315:
4683:is commonly separated into two components,
3870:fluid (and thus at small Reynolds number),
27:Retarding force on a body moving in a fluid
5785:Effect of dimples on a golf ball and a car
5209:Liversage, P., and Trancossi, M. (2018). "
4629:Wave drag in transonic and supersonic flow
4534:This drag component is due to viscosity.
820:is some characteristic diameter or linear
116:
5189:, the air density can be found using the
5080:
4514:
4508:
4467:
4461:
4410:
4404:
4379:
4373:
4328:
4322:
4295:
4289:
4231:
4229:
4206:
4167:
4143:
4125:
4116:
4110:
4087:
4075:
4048:
4028:
4003:
4002:
3978:
3973:
3970:
3939:
3915:
3899:
3879:
3848:
3812:
3796:
3787:
3781:
3757:
3734:
3729:
3709:
3687:
3664:
3658:
3636:
3603:
3599:
3592:
3567:
3563:
3554:
3538:
3521:
3497:
3495:
3473:
3452:
3447:
3432:
3427:
3424:
3355:
3349:
3329:
3308:
3302:
3282:
3261:
3255:
3235:
3214:
3208:
3188:
3172:
3162:
3150:
3144:
3115:
3093:
3087:
3079:
3070:
3064:
3035:
3012:
3003:
2982:
2969:
2941:
2939:
2913:
2890:
2881:
2860:
2847:
2839:
2809:
2788:
2720:
2700:
2690:
2684:
2668:
2653:
2644:
2624:
2603:
2573:
2553:
2543:
2537:
2516:
2507:
2487:
2466:
2422:
2409:
2384:
2375:
2369:
2324:
2295:
2281:
2257:
2232:
2215:
2156:
2150:
2129:
2123:
2100:
2090:
2080:
2067:
2048:
2032:
2022:
2017:
2008:
2003:
1993:
1987:
1955:
1942:
1923:
1915:
1906:
1901:
1891:
1885:
1771:
1765:
1760:
1754:
1749:
1745:
1733:
1732:
1728:
1722:
1716:
1644:
1635:
1611:
1606:
1588:
1580:
1570:
1564:
1552:
1546:
1525:
1519:
1498:
1492:
1467:
1461:
1437:
1432:
1417:
1403:
1397:
1387:
1373:
1364:
1354:
1340:
1339:
1333:
1300:
1294:
1273:
1267:
1246:
1240:
1219:
1213:
1173:
1172:
1166:
1138:
1133:
1127:
1106:
1100:
1079:
1073:
1049:
1047:
1027:
1025:
1001:
999:
973:
949:
930:
915:
909:
885:
879:
858:
852:
829:
805:
766:
748:
739:
733:
697:
691:
665:
643:
617:
590:
584:
562:
556:
551:
545:
540:
536:
524:
523:
519:
513:
507:
4452:distribution acting on a body's surface
1673:
992:, where a and b are the rectangle edges.
464:(minimum fuel consumption), or maximize
5763:Educational materials on air resistance
5557:Oxford Dictionary of National Biography
4924:
4598:: parasitic drag and lift-induced drag
4444:Additional information for aerodynamics
1699:a relatively large velocity, i.e. high
1201:{\displaystyle F_{\rm {d}}=3\pi \mu Dv}
305:
5730:, Pitman Publishing Limited, London.
4063:of 10 Όm/s. Using 10 Pa·s as the
3176:{\displaystyle v_{t}=90{\sqrt {d}},\,}
2353:approaches a maximum value called the
435:), and drag due to surface roughness (
238:Parasitic drag experienced by aircraft
5394:. Butterworth-Heinemann. p. 30.
5390:Collinson, Chris; Roper, Tom (1995).
4689:supersonic volume-dependent wave drag
261:in aviation and with semi-planing or
7:
5643:Physics for Scientists and Engineers
5215:Modelling, Measurement and Control B
5168:Design For Air Combat, Ray Whitford,
4731:, the 18th century state-of-the-art
4439:Vortex drag, wave drag and wake drag
3863:, denser objects fall more quickly.
2733:The hyperbolic cotangent also has a
345:Lift-induced drag and parasitic drag
5774:Vehicle Aerodynamic Drag calculator
5453:Gowree, Erwin Ricky (20 May 2014).
4685:supersonic lift-dependent wave drag
468:in the event of an engine failure.
315:Concorde with 'high' wave drag tail
207:due to the size and shape of a body
5259:, from NASA Glenn Research Center.
5238:, from NASA Glenn Research Center.
3379:Low Reynolds numbers: Stokes' drag
1351:
1341:
1174:
1122:is asymptotically proportional to
25:
5695:An introduction to fluid dynamics
5193:. It is 1.293 kg/m at 0 °C and 1
4760:, the result of which is called
4712:
4249:{\displaystyle {\frac {24}{Re}}}
4004:
3974:
3498:
3448:
3428:
3277:â40 m/s, for a small bird (
2023:
2019:
2004:
1916:
1902:
332:
320:
308:
180:
165:
150:
135:
5740:Anderson, John D. Jr. (2000);
5666:(5th ed.). W. H. Freeman.
4956:French (1970), p. 211, Eq. 7-20
4433:Pressure drag and friction drag
3903:{\displaystyle b=6\pi \eta r\,}
3183:For example, for a human body (
1836:, up to extremely high values (
1790:Drag equation § Derivation
1487:and the ratio between wet area
62:Unlike other resistive forces,
5624:. Cambridge University Press.
5575:Batchelor (2000), pp. 337â343.
4657:transonic compressibility drag
3818:
3799:
3560:
3541:
3532:
3526:
3512:is the velocity of the object.
2963:
2957:
2799:
2793:
2614:
2608:
2477:
2471:
2226:
2220:
2087:
2060:
970:
957:
946:
933:
901:is the D of the sphere itself.
487:for a sphere as a function of
1:
5647:(6th ed.). Brooks/Cole.
5493:Anderson, John David (1929).
4436:Profile drag and induced drag
4103:using the following formula:
4096:{\displaystyle 2\cdot 10^{5}}
3651:is the density of the object,
3324:â20 m/s, for an insect (
3059:, terminal velocity is about
2737:value of one, for large time
2342:value of one, for large time
2338:The hyperbolic tangent has a
874:of the object. For a sphere,
5334:Part 6: Speed and Horsepower
3702:is the volume of the object,
3505:{\displaystyle \mathbf {v} }
2926:Or, more generically (where
2783:, the velocity is constant:
2176:Velocity of a falling object
5415:tec-science (31 May 2020).
5099:10.1088/0143-0807/34/5/1227
4818:Automobile drag coefficient
4550:, this was named "drag" by
2821:{\displaystyle v(t)=v_{t}.}
47:, sometimes referred to as
5821:
5699:Cambridge University Press
5499:. University of Cambridge.
5278:Journal of Fluid Mechanics
4716:
4640:
4605:
4572:Royal Aeronautical Society
3401:
2179:
1667:
1150:{\displaystyle R_{e}^{-1}}
421:
353:
79:Examples of drag include:
29:
5360:"On Being the Right Size"
5321:Batchelor (1967), p. 341.
5298:10.1017/S0022112061000950
5249:Wing geometry definitions
4853:KeuleganâCarpenter number
3673:{\displaystyle \rho _{0}}
2349:In other words, velocity
389:lift-induced viscous drag
4696:Sears-Haack Distribution
4360:Overview of aerodynamics
3680:is density of the fluid,
1868:objects like a sphere).
292:(ship hydrodynamics) or
257:appears with wings or a
5681:Huntley, H. E. (1967).
5440:Anderson, John D. Jr.,
5269:Roshko, Anatol (1961).
4893:Stall (fluid mechanics)
4744:flow were developed by
4740:for the description of
4738:NavierâStokes equations
4586:Power curve in aviation
3394:, and the green object
2202: = 0 at time
1801:orthographic projection
1683:Explanation of drag by
1057:{\displaystyle {\rho }}
1042:divided by the density
371:on a three-dimensional
5742:Introduction to Flight
5599:French, A. P. (1970).
5442:Introduction to Flight
5331:Brian Beckman (1991),
4638:
4603:
4524:
4480:
4479:{\displaystyle D_{pr}}
4420:
4389:
4338:
4308:
4307:{\displaystyle D_{pr}}
4250:
4216:
4097:
4057:
4037:
4015:
3948:
3924:
3904:
3857:
3837:
3772:is mass of the object.
3766:
3744:
3718:
3696:
3674:
3645:
3622:
3506:
3482:
3457:
3399:
3365:
3338:
3318:
3291:
3271:
3244:
3224:
3197:
3177:
3120:
3040:
2918:
2822:
2755:, strictly from above
2725:
2578:
2427:
2329:
2192:
2166:
2145:is the wind speed and
2139:
2110:
1965:
1803:of the object, or the
1782:
1688:
1654:
1653:{\displaystyle Re_{L}}
1624:
1535:
1508:
1477:
1447:
1328:it has been obtained:
1310:
1283:
1256:
1229:
1202:
1151:
1116:
1089:
1058:
1036:
1035:{\displaystyle {\mu }}
1010:
1009:{\displaystyle {\nu }}
986:
895:
868:
838:
814:
791:
707:
674:
652:
626:
600:
570:
495:
248:McDonnell Douglas DC-9
5662:Tipler, Paul (2004).
5618:G. Falkovich (2011).
5043:"Viscous Drag Forces"
4672:unattached shockwaves
4636:
4593:
4556:Louis Charles Breguet
4525:
4523:{\displaystyle D_{f}}
4481:
4421:
4419:{\displaystyle D_{w}}
4390:
4388:{\displaystyle D_{i}}
4339:
4337:{\displaystyle D_{f}}
4309:
4251:
4217:
4098:
4058:
4038:
4016:
3949:
3947:{\displaystyle \eta }
3934:of the particle, and
3925:
3905:
3872:George Gabriel Stokes
3858:
3838:
3767:
3745:
3719:
3697:
3675:
3646:
3644:{\displaystyle \rho }
3623:
3507:
3483:
3458:
3386:
3366:
3364:{\displaystyle v_{t}}
3339:
3319:
3317:{\displaystyle v_{t}}
3292:
3272:
3270:{\displaystyle v_{t}}
3245:
3225:
3223:{\displaystyle v_{t}}
3198:
3178:
3121:
3041:
2919:
2832:differential equation
2823:
2726:
2579:
2447: = 0, with
2428:
2330:
2189:
2167:
2165:{\displaystyle v_{o}}
2140:
2138:{\displaystyle v_{w}}
2111:
1966:
1783:
1682:
1655:
1625:
1536:
1534:{\displaystyle A_{f}}
1509:
1507:{\displaystyle A_{w}}
1478:
1476:{\displaystyle C_{D}}
1448:
1311:
1309:{\displaystyle R_{e}}
1284:
1282:{\displaystyle C_{D}}
1257:
1255:{\displaystyle C_{D}}
1230:
1228:{\displaystyle R_{e}}
1203:
1152:
1117:
1115:{\displaystyle C_{D}}
1090:
1088:{\displaystyle R_{e}}
1059:
1037:
1011:
987:
896:
894:{\displaystyle D_{e}}
869:
867:{\displaystyle D_{e}}
839:
815:
792:
708:
706:{\displaystyle C_{D}}
675:
653:
627:
625:{\displaystyle \rho }
601:
599:{\displaystyle F_{D}}
571:
479:
5683:Dimensional Analysis
5480:Flight, 1913, p. 126
5228:Size effects on drag
4933:"Definition of DRAG"
4719:d'Alembert's paradox
4713:d'Alembert's paradox
4507:
4460:
4403:
4372:
4352:, vortex sheet, and
4321:
4288:
4228:
4109:
4074:
4047:
4027:
3969:
3938:
3914:
3878:
3847:
3780:
3756:
3743:{\displaystyle ^{2}}
3728:
3708:
3686:
3657:
3635:
3520:
3494:
3472:
3423:
3348:
3328:
3301:
3281:
3254:
3234:
3207:
3187:
3143:
3063:
2938:
2838:
2787:
2602:
2596:hyperbolic cotangent
2465:
2368:
2214:
2149:
2122:
1986:
1884:
1715:
1634:
1545:
1518:
1491:
1460:
1332:
1293:
1266:
1239:
1212:
1165:
1126:
1099:
1072:
1046:
1024:
998:
908:
878:
851:
828:
804:
732:
719:dimensionless number
690:
682:cross sectional area
664:
642:
616:
583:
506:
30:For other uses, see
5554:Mair, W.A. (1976).
5290:1961JFM....10..345R
5091:2013EJPh...34.1227H
4813:Atmospheric density
4582:in thermodynamics.
4552:Archibald Reith Low
3378:
1795:The reference area
1616:
1442:
1146:
1018:kinematic viscosity
5392:Particle Mechanics
5365:2011-08-22 at the
5255:2011-03-07 at the
5234:2016-11-09 at the
5191:barometric formula
5187:Earth's atmosphere
4668:oblique shockwaves
4639:
4604:
4520:
4476:
4416:
4385:
4334:
4304:
4246:
4212:
4093:
4053:
4033:
4011:
3944:
3920:
3900:
3853:
3833:
3762:
3740:
3714:
3692:
3670:
3641:
3618:
3502:
3478:
3453:
3410:viscous resistance
3400:
3361:
3334:
3314:
3287:
3267:
3240:
3220:
3193:
3173:
3116:
3036:
2914:
2818:
2721:
2574:
2423:
2325:
2208:hyperbolic tangent
2193:
2162:
2135:
2106:
2042:
1961:
1933:
1778:
1743:
1691:As mentioned, the
1689:
1650:
1620:
1602:
1531:
1504:
1473:
1443:
1428:
1306:
1279:
1252:
1225:
1198:
1147:
1129:
1112:
1085:
1054:
1032:
1006:
982:
891:
864:
844:is the equivalent
834:
810:
787:
703:
670:
648:
622:
596:
566:
534:
496:
437:skin friction drag
211:skin friction drag
5736:978-0-273-01120-0
5708:978-0-521-66396-0
5691:Batchelor, George
5673:978-0-7167-0809-4
5654:978-0-534-40842-8
5631:978-1-107-00575-4
5610:978-0-393-09958-4
5358:Haldane, J.B.S.,
5217:. 87(3), 188-196.
5132:978 0 470 97402 5
4903:Terminal velocity
4803:Aerodynamic force
4244:
4186:
4183:
4180:
4177:
4174:
4170:
4166:
4156:
4155:
4138:
4065:dynamic viscosity
4056:{\displaystyle v}
4036:{\displaystyle r}
3923:{\displaystyle r}
3856:{\displaystyle b}
3831:
3765:{\displaystyle m}
3717:{\displaystyle g}
3695:{\displaystyle V}
3575:
3481:{\displaystyle b}
3408:The equation for
3337:{\displaystyle d}
3290:{\displaystyle d}
3243:{\displaystyle d}
3196:{\displaystyle d}
3167:
3110:
3108:
3030:
2997:
2949:
2908:
2875:
2747:terminal velocity
2706:
2659:
2559:
2522:
2417:
2416:
2355:terminal velocity
2314:
2313:
2265:
2264:
2182:Terminal velocity
2041:
1932:
1827:separation points
1814:In the case of a
1742:
1680:
1618:
1586:
1483:as a function of
1423:
1381:
980:
837:{\displaystyle D}
813:{\displaystyle D}
782:
761:
673:{\displaystyle A}
651:{\displaystyle v}
533:
480:Drag coefficient
472:The drag equation
441:interference drag
361:Lift-induced drag
356:Lift-induced drag
350:Lift-induced drag
255:lift-induced drag
194:
193:
16:(Redirected from
5812:
5768:Aerodynamic Drag
5720:
5686:
5677:
5658:
5646:
5635:
5614:
5576:
5573:
5562:
5561:
5551:
5545:
5544:
5531:
5525:
5524:
5522:
5520:
5510:
5501:
5500:
5490:
5481:
5475:
5469:
5468:
5466:
5464:
5450:
5444:
5438:
5432:
5431:
5429:
5427:
5412:
5406:
5405:
5387:
5381:
5375:
5369:
5356:
5350:
5349:
5348:
5346:
5337:, archived from
5328:
5322:
5319:
5310:
5309:
5275:
5266:
5260:
5245:
5239:
5224:
5218:
5207:
5198:
5183:
5177:
5166:
5160:
5157:
5151:
5140:
5134:
5124:
5118:
5117:
5115:
5113:
5084:
5075:(5): 1227â1233.
5060:
5054:
5053:
5051:
5049:
5039:
5033:
5032:
5030:
5028:
5023:
5015:
5009:
5008:
5006:
5004:
4995:. Archived from
4989:
4983:
4982:
4980:
4978:
4969:. Archived from
4963:
4957:
4954:
4948:
4947:
4945:
4943:
4929:
4868:Nose cone design
4863:Morison equation
4838:Drag coefficient
4758:Reynolds numbers
4707:Busemann biplane
4700:Von Karman Ogive
4529:
4527:
4526:
4521:
4519:
4518:
4485:
4483:
4482:
4477:
4475:
4474:
4425:
4423:
4422:
4417:
4415:
4414:
4394:
4392:
4391:
4386:
4384:
4383:
4343:
4341:
4340:
4335:
4333:
4332:
4313:
4311:
4310:
4305:
4303:
4302:
4272:, also known as
4270:aerodynamic drag
4255:
4253:
4252:
4247:
4245:
4243:
4232:
4221:
4219:
4218:
4213:
4211:
4210:
4184:
4181:
4178:
4175:
4172:
4171:
4168:
4164:
4157:
4148:
4144:
4139:
4137:
4126:
4121:
4120:
4102:
4100:
4099:
4094:
4092:
4091:
4062:
4060:
4059:
4054:
4042:
4040:
4039:
4034:
4020:
4018:
4017:
4012:
4007:
3983:
3982:
3977:
3953:
3951:
3950:
3945:
3929:
3927:
3926:
3921:
3909:
3907:
3906:
3901:
3862:
3860:
3859:
3854:
3842:
3840:
3839:
3834:
3832:
3827:
3817:
3816:
3797:
3792:
3791:
3771:
3769:
3768:
3763:
3749:
3747:
3746:
3741:
3739:
3738:
3723:
3721:
3720:
3715:
3701:
3699:
3698:
3693:
3679:
3677:
3676:
3671:
3669:
3668:
3650:
3648:
3647:
3642:
3627:
3625:
3624:
3619:
3617:
3613:
3612:
3611:
3607:
3576:
3571:
3559:
3558:
3539:
3511:
3509:
3508:
3503:
3501:
3487:
3485:
3484:
3479:
3462:
3460:
3459:
3454:
3451:
3437:
3436:
3431:
3370:
3368:
3367:
3362:
3360:
3359:
3343:
3341:
3340:
3335:
3323:
3321:
3320:
3315:
3313:
3312:
3296:
3294:
3293:
3288:
3276:
3274:
3273:
3268:
3266:
3265:
3249:
3247:
3246:
3241:
3229:
3227:
3226:
3221:
3219:
3218:
3202:
3200:
3199:
3194:
3182:
3180:
3179:
3174:
3168:
3163:
3155:
3154:
3125:
3123:
3122:
3117:
3111:
3109:
3104:
3103:
3088:
3080:
3075:
3074:
3045:
3043:
3042:
3037:
3031:
3029:
3021:
3013:
3008:
3007:
2998:
2996:
2988:
2987:
2986:
2970:
2950:
2942:
2923:
2921:
2920:
2915:
2909:
2907:
2899:
2891:
2886:
2885:
2876:
2874:
2866:
2865:
2864:
2848:
2827:
2825:
2824:
2819:
2814:
2813:
2730:
2728:
2727:
2722:
2716:
2712:
2711:
2707:
2705:
2704:
2695:
2694:
2685:
2676:
2675:
2660:
2658:
2657:
2645:
2629:
2628:
2583:
2581:
2580:
2575:
2569:
2565:
2564:
2560:
2558:
2557:
2548:
2547:
2538:
2523:
2521:
2520:
2508:
2492:
2491:
2432:
2430:
2429:
2424:
2418:
2415:
2414:
2413:
2397:
2386:
2385:
2380:
2379:
2334:
2332:
2331:
2326:
2320:
2316:
2315:
2312:
2304:
2300:
2299:
2283:
2282:
2266:
2263:
2262:
2261:
2245:
2234:
2233:
2171:
2169:
2168:
2163:
2161:
2160:
2144:
2142:
2141:
2136:
2134:
2133:
2115:
2113:
2112:
2107:
2105:
2104:
2095:
2094:
2085:
2084:
2072:
2071:
2053:
2052:
2043:
2034:
2028:
2027:
2026:
2013:
2012:
2007:
1998:
1997:
1970:
1968:
1967:
1962:
1960:
1959:
1947:
1946:
1934:
1925:
1919:
1911:
1910:
1905:
1896:
1895:
1787:
1785:
1784:
1779:
1770:
1769:
1759:
1758:
1744:
1735:
1727:
1726:
1681:
1664:At high velocity
1659:
1657:
1656:
1651:
1649:
1648:
1629:
1627:
1626:
1621:
1619:
1617:
1615:
1610:
1597:
1589:
1587:
1585:
1584:
1575:
1574:
1565:
1557:
1556:
1540:
1538:
1537:
1532:
1530:
1529:
1513:
1511:
1510:
1505:
1503:
1502:
1482:
1480:
1479:
1474:
1472:
1471:
1452:
1450:
1449:
1444:
1441:
1436:
1424:
1422:
1421:
1412:
1404:
1402:
1401:
1392:
1391:
1382:
1374:
1369:
1368:
1359:
1358:
1346:
1345:
1344:
1315:
1313:
1312:
1307:
1305:
1304:
1288:
1286:
1285:
1280:
1278:
1277:
1261:
1259:
1258:
1253:
1251:
1250:
1234:
1232:
1231:
1226:
1224:
1223:
1207:
1205:
1204:
1199:
1179:
1178:
1177:
1156:
1154:
1153:
1148:
1145:
1137:
1121:
1119:
1118:
1113:
1111:
1110:
1094:
1092:
1091:
1086:
1084:
1083:
1063:
1061:
1060:
1055:
1053:
1041:
1039:
1038:
1033:
1031:
1015:
1013:
1012:
1007:
1005:
991:
989:
988:
983:
981:
979:
978:
977:
955:
954:
953:
931:
920:
919:
900:
898:
897:
892:
890:
889:
873:
871:
870:
865:
863:
862:
843:
841:
840:
835:
819:
817:
816:
811:
796:
794:
793:
788:
783:
778:
767:
762:
757:
749:
744:
743:
715:drag coefficient
712:
710:
709:
704:
702:
701:
679:
677:
676:
671:
657:
655:
654:
649:
631:
629:
628:
623:
605:
603:
602:
597:
595:
594:
575:
573:
572:
567:
561:
560:
550:
549:
535:
526:
518:
517:
408:lift coefficient
336:
324:
312:
184:
169:
154:
139:
117:
99:Viscous drag of
49:fluid resistance
21:
5820:
5819:
5815:
5814:
5813:
5811:
5810:
5809:
5790:
5789:
5759:
5709:
5689:
5685:. LOC 67-17978.
5680:
5674:
5661:
5655:
5638:
5632:
5617:
5611:
5598:
5595:
5579:
5574:
5565:
5553:
5552:
5548:
5533:
5532:
5528:
5518:
5516:
5512:
5511:
5504:
5492:
5491:
5484:
5476:
5472:
5462:
5460:
5452:
5451:
5447:
5439:
5435:
5425:
5423:
5414:
5413:
5409:
5402:
5389:
5388:
5384:
5376:
5372:
5367:Wayback Machine
5357:
5353:
5344:
5342:
5341:on 16 June 2019
5330:
5329:
5325:
5320:
5313:
5273:
5268:
5267:
5263:
5257:Wayback Machine
5246:
5242:
5236:Wayback Machine
5225:
5221:
5208:
5201:
5184:
5180:
5167:
5163:
5158:
5154:
5141:
5137:
5125:
5121:
5111:
5109:
5062:
5061:
5057:
5047:
5045:
5041:
5040:
5036:
5026:
5024:
5021:
5017:
5016:
5012:
5002:
5000:
4993:"What is Drag?"
4991:
4990:
4986:
4976:
4974:
4967:"What is Drag?"
4965:
4964:
4960:
4955:
4951:
4941:
4939:
4937:Merriam-Webster
4931:
4930:
4926:
4922:
4917:
4888:Reynolds number
4808:Angle of attack
4793:
4782:âintroduced by
4780:boundary layers
4769:Euler equations
4721:
4715:
4645:
4631:
4610:
4588:
4548:Mervyn O'Gorman
4546:. According to
4540:
4510:
4505:
4504:
4463:
4458:
4457:
4446:
4406:
4401:
4400:
4375:
4370:
4369:
4362:
4324:
4319:
4318:
4291:
4286:
4285:
4262:
4236:
4226:
4225:
4202:
4130:
4112:
4107:
4106:
4083:
4072:
4071:
4045:
4044:
4025:
4024:
3972:
3967:
3966:
3936:
3935:
3912:
3911:
3876:
3875:
3845:
3844:
3808:
3798:
3783:
3778:
3777:
3754:
3753:
3731:
3726:
3725:
3706:
3705:
3684:
3683:
3660:
3655:
3654:
3633:
3632:
3588:
3581:
3577:
3550:
3540:
3518:
3517:
3492:
3491:
3470:
3469:
3426:
3421:
3420:
3417:resistance is:
3406:
3381:
3351:
3346:
3345:
3326:
3325:
3304:
3299:
3298:
3279:
3278:
3257:
3252:
3251:
3232:
3231:
3210:
3205:
3204:
3185:
3184:
3146:
3141:
3140:
3137:
3089:
3066:
3061:
3060:
3057:
3052:and of density
3022:
3014:
2999:
2989:
2978:
2971:
2936:
2935:
2900:
2892:
2877:
2867:
2856:
2849:
2836:
2835:
2805:
2785:
2784:
2782:
2773:
2760:
2753:
2696:
2686:
2680:
2664:
2649:
2640:
2636:
2620:
2600:
2599:
2593:
2589:
2549:
2539:
2533:
2512:
2503:
2499:
2483:
2463:
2462:
2459:
2452:
2442:
2405:
2398:
2387:
2371:
2366:
2365:
2361:
2305:
2291:
2284:
2277:
2273:
2253:
2246:
2235:
2212:
2211:
2184:
2178:
2152:
2147:
2146:
2125:
2120:
2119:
2096:
2086:
2076:
2063:
2044:
2018:
2002:
1989:
1984:
1983:
1951:
1938:
1900:
1887:
1882:
1881:
1874:
1862:
1855:
1841:
1834:
1809:cross sectional
1761:
1750:
1718:
1713:
1712:
1701:Reynolds number
1674:
1672:
1666:
1640:
1632:
1631:
1598:
1590:
1576:
1566:
1548:
1543:
1542:
1521:
1516:
1515:
1514:and front area
1494:
1489:
1488:
1463:
1458:
1457:
1413:
1405:
1393:
1383:
1360:
1350:
1335:
1330:
1329:
1296:
1291:
1290:
1269:
1264:
1263:
1242:
1237:
1236:
1215:
1210:
1209:
1168:
1163:
1162:
1124:
1123:
1102:
1097:
1096:
1075:
1070:
1069:
1044:
1043:
1022:
1021:
996:
995:
969:
956:
945:
932:
911:
906:
905:
881:
876:
875:
854:
849:
848:
826:
825:
802:
801:
768:
750:
735:
730:
729:
727:Reynolds number
693:
688:
687:
662:
661:
640:
639:
614:
613:
586:
581:
580:
552:
541:
509:
504:
503:
489:Reynolds number
486:
474:
448:angle of attack
426:
420:
404:angle of attack
358:
352:
347:
340:
337:
328:
325:
316:
313:
290:wave resistance
240:
129:
124:
120:Shape and flow
115:
101:fluid in a pipe
77:
69:Reynolds number
35:
28:
23:
22:
15:
12:
11:
5:
5818:
5816:
5808:
5807:
5802:
5800:Drag (physics)
5792:
5791:
5788:
5787:
5782:
5777:
5771:
5765:
5758:
5757:External links
5755:
5754:
5753:
5750:978-0078027673
5738:
5721:
5707:
5687:
5678:
5672:
5659:
5653:
5636:
5630:
5615:
5609:
5594:
5591:
5590:
5589:
5586:
5583:
5578:
5577:
5563:
5546:
5526:
5502:
5482:
5470:
5445:
5433:
5407:
5400:
5382:
5370:
5351:
5323:
5311:
5284:(3): 345â356.
5261:
5240:
5219:
5199:
5178:
5161:
5152:
5135:
5119:
5055:
5034:
5010:
4999:on 24 May 2010
4984:
4973:on 24 May 2010
4958:
4949:
4923:
4921:
4918:
4916:
4915:
4910:
4905:
4900:
4895:
4890:
4885:
4880:
4875:
4873:Parasitic drag
4870:
4865:
4860:
4855:
4850:
4845:
4840:
4835:
4830:
4825:
4823:Boundary layer
4820:
4815:
4810:
4805:
4800:
4794:
4792:
4789:
4778:The notion of
4729:potential flow
4717:Main article:
4714:
4711:
4679:flow regimes,
4641:Main article:
4630:
4627:
4606:Main article:
4587:
4584:
4560:Ludwig Prandtl
4539:
4536:
4517:
4513:
4501:boundary layer
4473:
4470:
4466:
4445:
4442:
4441:
4440:
4437:
4434:
4413:
4409:
4382:
4378:
4361:
4358:
4346:
4345:
4331:
4327:
4315:
4301:
4298:
4294:
4274:air resistance
4261:
4258:
4242:
4239:
4235:
4209:
4205:
4201:
4198:
4195:
4192:
4189:
4163:
4160:
4154:
4151:
4147:
4142:
4136:
4133:
4129:
4124:
4119:
4115:
4090:
4086:
4082:
4079:
4052:
4032:
4010:
4006:
4001:
3998:
3995:
3992:
3989:
3986:
3981:
3976:
3943:
3919:
3898:
3895:
3892:
3889:
3886:
3883:
3852:
3843:. For a given
3830:
3826:
3823:
3820:
3815:
3811:
3807:
3804:
3801:
3795:
3790:
3786:
3774:
3773:
3761:
3751:
3737:
3733:
3713:
3703:
3691:
3681:
3667:
3663:
3652:
3640:
3616:
3610:
3606:
3602:
3598:
3595:
3591:
3587:
3584:
3580:
3574:
3570:
3566:
3562:
3557:
3553:
3549:
3546:
3543:
3537:
3534:
3531:
3528:
3525:
3514:
3513:
3500:
3489:
3477:
3450:
3446:
3443:
3440:
3435:
3430:
3402:Main article:
3380:
3377:
3358:
3354:
3333:
3311:
3307:
3286:
3264:
3260:
3239:
3217:
3213:
3192:
3171:
3166:
3161:
3158:
3153:
3149:
3135:
3114:
3107:
3102:
3099:
3096:
3092:
3086:
3083:
3078:
3073:
3069:
3055:
3034:
3028:
3025:
3020:
3017:
3011:
3006:
3002:
2995:
2992:
2985:
2981:
2977:
2974:
2968:
2965:
2962:
2959:
2956:
2953:
2948:
2945:
2912:
2906:
2903:
2898:
2895:
2889:
2884:
2880:
2873:
2870:
2863:
2859:
2855:
2852:
2846:
2843:
2817:
2812:
2808:
2804:
2801:
2798:
2795:
2792:
2778:
2769:
2758:
2751:
2743:asymptotically
2719:
2715:
2710:
2703:
2699:
2693:
2689:
2683:
2679:
2674:
2671:
2667:
2663:
2656:
2652:
2648:
2643:
2639:
2635:
2632:
2627:
2623:
2619:
2616:
2613:
2610:
2607:
2591:
2587:
2572:
2568:
2563:
2556:
2552:
2546:
2542:
2536:
2532:
2529:
2526:
2519:
2515:
2511:
2506:
2502:
2498:
2495:
2490:
2486:
2482:
2479:
2476:
2473:
2470:
2457:
2450:
2440:
2439: = v
2421:
2412:
2408:
2404:
2401:
2396:
2393:
2390:
2383:
2378:
2374:
2359:
2351:asymptotically
2323:
2319:
2311:
2308:
2303:
2298:
2294:
2290:
2287:
2280:
2276:
2272:
2269:
2260:
2256:
2252:
2249:
2244:
2241:
2238:
2231:
2228:
2225:
2222:
2219:
2180:Main article:
2177:
2174:
2159:
2155:
2132:
2128:
2103:
2099:
2093:
2089:
2083:
2079:
2075:
2070:
2066:
2062:
2059:
2056:
2051:
2047:
2040:
2037:
2031:
2025:
2021:
2016:
2011:
2006:
2001:
1996:
1992:
1958:
1954:
1950:
1945:
1941:
1937:
1931:
1928:
1922:
1918:
1914:
1909:
1904:
1899:
1894:
1890:
1873:
1870:
1860:
1853:
1839:
1832:
1777:
1774:
1768:
1764:
1757:
1753:
1748:
1741:
1738:
1731:
1725:
1721:
1706:quadratic drag
1668:Main article:
1665:
1662:
1647:
1643:
1639:
1614:
1609:
1605:
1601:
1596:
1593:
1583:
1579:
1573:
1569:
1563:
1560:
1555:
1551:
1528:
1524:
1501:
1497:
1470:
1466:
1440:
1435:
1431:
1427:
1420:
1416:
1411:
1408:
1400:
1396:
1390:
1386:
1380:
1377:
1372:
1367:
1363:
1357:
1353:
1349:
1343:
1338:
1303:
1299:
1276:
1272:
1249:
1245:
1222:
1218:
1197:
1194:
1191:
1188:
1185:
1182:
1176:
1171:
1144:
1141:
1136:
1132:
1109:
1105:
1082:
1078:
1066:
1065:
1052:
1030:
1004:
993:
976:
972:
968:
965:
962:
959:
952:
948:
944:
941:
938:
935:
929:
926:
923:
918:
914:
902:
888:
884:
861:
857:
833:
809:
786:
781:
777:
774:
771:
765:
760:
756:
753:
747:
742:
738:
723:
722:
700:
696:
685:
669:
659:
647:
637:
621:
611:
593:
589:
565:
559:
555:
548:
544:
539:
532:
529:
522:
516:
512:
484:
473:
470:
429:Parasitic drag
424:Parasitic drag
422:Main article:
419:
418:Parasitic drag
416:
375:, such as the
354:Main article:
351:
348:
346:
343:
342:
341:
338:
331:
329:
326:
319:
317:
314:
307:
304:
303:
300:
287:
269:
239:
236:
232:parasitic drag
219:
218:
208:
192:
191:
188:
185:
177:
176:
173:
170:
162:
161:
158:
155:
147:
146:
143:
140:
132:
131:
126:
121:
114:
111:
110:
109:
105:
104:
97:
76:
73:
41:fluid dynamics
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
5817:
5806:
5803:
5801:
5798:
5797:
5795:
5786:
5783:
5781:
5778:
5775:
5772:
5769:
5766:
5764:
5761:
5760:
5756:
5751:
5747:
5743:
5739:
5737:
5733:
5729:
5725:
5722:
5718:
5714:
5710:
5704:
5700:
5696:
5692:
5688:
5684:
5679:
5675:
5669:
5665:
5660:
5656:
5650:
5645:
5644:
5637:
5633:
5627:
5623:
5622:
5616:
5612:
5606:
5602:
5597:
5596:
5592:
5587:
5584:
5581:
5580:
5572:
5570:
5568:
5564:
5559:
5556:
5550:
5547:
5542:
5539:
5536:
5530:
5527:
5515:
5509:
5507:
5503:
5498:
5495:
5489:
5487:
5483:
5479:
5474:
5471:
5458:
5457:
5449:
5446:
5443:
5437:
5434:
5422:
5418:
5411:
5408:
5403:
5401:9780080928593
5397:
5393:
5386:
5383:
5379:
5374:
5371:
5368:
5364:
5361:
5355:
5352:
5340:
5336:
5335:
5327:
5324:
5318:
5316:
5312:
5307:
5303:
5299:
5295:
5291:
5287:
5283:
5279:
5272:
5265:
5262:
5258:
5254:
5251:
5250:
5244:
5241:
5237:
5233:
5230:
5229:
5223:
5220:
5216:
5212:
5206:
5204:
5200:
5196:
5192:
5188:
5182:
5179:
5175:
5174:0 7106 0426 2
5171:
5165:
5162:
5156:
5153:
5149:
5148:0 13 339060 8
5145:
5139:
5136:
5133:
5129:
5123:
5120:
5108:
5104:
5100:
5096:
5092:
5088:
5083:
5078:
5074:
5070:
5066:
5059:
5056:
5044:
5038:
5035:
5020:
5014:
5011:
4998:
4994:
4988:
4985:
4972:
4968:
4962:
4959:
4953:
4950:
4938:
4934:
4928:
4925:
4919:
4914:
4911:
4909:
4906:
4904:
4901:
4899:
4896:
4894:
4891:
4889:
4886:
4884:
4881:
4879:
4876:
4874:
4871:
4869:
4866:
4864:
4861:
4859:
4856:
4854:
4851:
4849:
4846:
4844:
4843:Drag equation
4841:
4839:
4836:
4834:
4831:
4829:
4828:CoandÄ effect
4826:
4824:
4821:
4819:
4816:
4814:
4811:
4809:
4806:
4804:
4801:
4799:
4796:
4795:
4790:
4788:
4787:very large).
4785:
4781:
4776:
4774:
4770:
4765:
4763:
4759:
4755:
4751:
4747:
4743:
4739:
4734:
4733:inviscid flow
4730:
4726:
4720:
4710:
4708:
4703:
4701:
4697:
4692:
4690:
4686:
4682:
4677:
4673:
4669:
4665:
4660:
4658:
4652:
4650:
4644:
4635:
4628:
4626:
4623:
4619:
4615:
4609:
4601:
4597:
4592:
4585:
4583:
4581:
4577:
4576:undercarriage
4573:
4569:
4565:
4564:Melvill Jones
4561:
4557:
4553:
4549:
4545:
4537:
4535:
4533:
4515:
4511:
4502:
4497:
4494:
4490:
4489:
4471:
4468:
4464:
4455:
4451:
4443:
4438:
4435:
4432:
4431:
4430:
4427:
4411:
4407:
4398:
4380:
4376:
4368:, symbolized
4367:
4359:
4357:
4355:
4351:
4329:
4325:
4316:
4299:
4296:
4292:
4283:
4282:
4281:
4279:
4275:
4271:
4267:
4259:
4257:
4240:
4237:
4233:
4222:
4207:
4203:
4199:
4196:
4193:
4190:
4187:
4161:
4158:
4152:
4149:
4145:
4140:
4134:
4131:
4127:
4122:
4117:
4113:
4104:
4088:
4084:
4080:
4077:
4068:
4066:
4050:
4030:
4021:
4008:
3999:
3996:
3993:
3990:
3987:
3984:
3979:
3964:
3959:
3957:
3941:
3933:
3932:Stokes radius
3917:
3896:
3893:
3890:
3887:
3884:
3881:
3873:
3869:
3864:
3850:
3828:
3824:
3821:
3813:
3809:
3805:
3802:
3793:
3788:
3784:
3759:
3752:
3735:
3732:
3711:
3704:
3689:
3682:
3665:
3661:
3653:
3638:
3631:
3630:
3629:
3614:
3608:
3604:
3600:
3596:
3593:
3589:
3585:
3582:
3578:
3572:
3568:
3564:
3555:
3551:
3547:
3544:
3535:
3529:
3523:
3490:
3475:
3468:
3467:
3466:
3463:
3444:
3441:
3438:
3433:
3418:
3415:
3411:
3405:
3397:
3393:
3389:
3385:
3376:
3372:
3356:
3352:
3331:
3309:
3305:
3284:
3262:
3258:
3237:
3215:
3211:
3190:
3169:
3164:
3159:
3156:
3151:
3147:
3138:
3132:in metre and
3131:
3126:
3112:
3105:
3100:
3097:
3094:
3090:
3084:
3081:
3076:
3071:
3067:
3058:
3051:
3046:
3032:
3026:
3023:
3018:
3015:
3009:
3004:
3000:
2993:
2990:
2983:
2979:
2975:
2972:
2966:
2960:
2954:
2951:
2946:
2943:
2933:
2929:
2924:
2910:
2904:
2901:
2896:
2893:
2887:
2882:
2878:
2871:
2868:
2861:
2857:
2853:
2850:
2844:
2841:
2833:
2828:
2815:
2810:
2806:
2802:
2796:
2790:
2781:
2777:
2772:
2768:
2763:
2761:
2754:
2748:
2745:tends to the
2744:
2740:
2736:
2731:
2717:
2713:
2708:
2701:
2697:
2691:
2687:
2681:
2677:
2672:
2669:
2665:
2661:
2654:
2650:
2646:
2641:
2637:
2633:
2630:
2625:
2621:
2617:
2611:
2605:
2597:
2584:
2570:
2566:
2561:
2554:
2550:
2544:
2540:
2534:
2530:
2527:
2524:
2517:
2513:
2509:
2504:
2500:
2496:
2493:
2488:
2484:
2480:
2474:
2468:
2460:
2453:
2446:
2438:
2433:
2419:
2410:
2406:
2402:
2399:
2394:
2391:
2388:
2381:
2376:
2372:
2364:
2362:
2356:
2352:
2347:
2345:
2341:
2335:
2321:
2317:
2309:
2306:
2301:
2296:
2292:
2288:
2285:
2278:
2274:
2270:
2267:
2258:
2254:
2250:
2247:
2242:
2239:
2236:
2229:
2223:
2217:
2209:
2205:
2201:
2197:
2188:
2183:
2175:
2173:
2157:
2153:
2130:
2126:
2116:
2101:
2097:
2091:
2081:
2077:
2073:
2068:
2064:
2057:
2054:
2049:
2045:
2038:
2035:
2029:
2014:
2009:
1999:
1994:
1990:
1980:
1978:
1974:
1956:
1952:
1948:
1943:
1939:
1935:
1929:
1926:
1920:
1912:
1907:
1897:
1892:
1888:
1879:
1871:
1869:
1867:
1863:
1856:
1848:
1846:
1842:
1835:
1828:
1823:
1821:
1817:
1812:
1810:
1806:
1805:frontal area,
1802:
1799:is often the
1798:
1793:
1791:
1775:
1772:
1766:
1762:
1755:
1751:
1746:
1739:
1736:
1729:
1723:
1719:
1710:
1709:
1707:
1702:
1698:
1694:
1693:drag equation
1686:
1671:
1670:Drag equation
1663:
1661:
1645:
1641:
1637:
1612:
1607:
1603:
1599:
1594:
1591:
1581:
1577:
1571:
1567:
1561:
1558:
1553:
1549:
1526:
1522:
1499:
1495:
1486:
1468:
1464:
1456:
1438:
1433:
1429:
1425:
1418:
1414:
1409:
1406:
1398:
1394:
1388:
1384:
1378:
1375:
1370:
1365:
1361:
1355:
1347:
1336:
1327:
1323:
1318:
1301:
1297:
1274:
1270:
1247:
1243:
1220:
1216:
1195:
1192:
1189:
1186:
1183:
1180:
1169:
1160:
1142:
1139:
1134:
1130:
1107:
1103:
1080:
1076:
1050:
1028:
1019:
1002:
994:
974:
966:
963:
960:
950:
942:
939:
936:
927:
924:
921:
916:
912:
903:
886:
882:
859:
855:
847:
831:
823:
807:
800:
799:
798:
784:
779:
775:
772:
769:
763:
758:
754:
751:
745:
740:
736:
728:
720:
716:
698:
694:
686:
683:
667:
660:
645:
638:
636:of the fluid,
635:
619:
612:
609:
591:
587:
579:
578:
577:
563:
557:
553:
546:
542:
537:
530:
527:
520:
514:
510:
501:
500:drag equation
493:
490:
483:
478:
471:
469:
467:
466:gliding range
463:
458:
454:
449:
444:
442:
438:
434:
430:
425:
417:
415:
413:
409:
405:
401:
396:
394:
390:
386:
382:
378:
374:
370:
366:
363:(also called
362:
357:
349:
344:
335:
330:
323:
318:
311:
306:
301:
299:
298:surface waves
295:
291:
288:
285:
281:
277:
273:
270:
268:
264:
263:planing hulls
260:
256:
253:
252:
251:
249:
245:
237:
235:
233:
227:
225:
216:
212:
209:
206:
205:pressure drag
202:
199:
198:
197:
189:
186:
183:
179:
178:
174:
171:
168:
164:
163:
159:
156:
153:
149:
148:
144:
141:
138:
134:
133:
127:
122:
119:
118:
112:
107:
106:
102:
98:
95:
92:
88:
85:
82:
81:
80:
74:
72:
70:
65:
60:
58:
54:
50:
46:
42:
37:
33:
19:
5741:
5728:Aerodynamics
5727:
5724:L. J. Clancy
5694:
5682:
5663:
5642:
5620:
5600:
5593:Bibliography
5558:
5555:
5549:
5541:
5538:
5535:
5529:
5517:. Retrieved
5497:
5494:
5473:
5461:. Retrieved
5455:
5448:
5441:
5436:
5424:. Retrieved
5420:
5410:
5391:
5385:
5378:Air friction
5373:
5354:
5343:, retrieved
5339:the original
5333:
5326:
5281:
5277:
5264:
5248:
5243:
5227:
5222:
5214:
5181:
5164:
5155:
5138:
5122:
5110:. Retrieved
5072:
5069:Eur. J. Phys
5068:
5058:
5046:. Retrieved
5037:
5025:. Retrieved
5013:
5001:. Retrieved
4997:the original
4987:
4975:. Retrieved
4971:the original
4961:
4952:
4940:. Retrieved
4936:
4927:
4883:Ram pressure
4858:Lift (force)
4848:Gravity drag
4777:
4766:
4746:Saint-Venant
4727:proved that
4722:
4704:
4699:
4695:
4693:
4688:
4684:
4680:
4675:
4671:
4667:
4663:
4661:
4656:
4653:
4649:aerodynamics
4646:
4621:
4617:
4613:
4611:
4599:
4595:
4580:Carnot cycle
4541:
4531:
4498:
4491:
4487:
4453:
4447:
4428:
4366:Induced drag
4363:
4347:
4273:
4269:
4266:aerodynamics
4263:
4260:Aerodynamics
4223:
4105:
4069:
4022:
3963:Stokes' drag
3960:
3865:
3775:
3515:
3464:
3419:
3413:
3409:
3407:
3392:Stokes' drag
3388:Trajectories
3373:
3133:
3129:
3127:
3053:
3049:
3047:
2931:
2927:
2925:
2829:
2779:
2775:
2770:
2766:
2764:
2756:
2749:
2738:
2732:
2585:
2455:
2448:
2444:
2436:
2434:
2357:
2348:
2343:
2337:
2336:
2203:
2199:
2194:
2117:
1981:
1875:
1858:
1851:
1849:
1837:
1830:
1824:
1815:
1813:
1804:
1796:
1794:
1711:
1705:
1704:
1690:
1485:Bejan number
1322:Bejan number
1319:
1289:varies with
1067:
824:. Actually,
724:
607:
497:
491:
481:
445:
440:
436:
432:
428:
427:
397:
388:
384:
373:lifting body
365:induced drag
364:
360:
359:
276:aerodynamics
259:lifting body
244:Douglas DC-3
241:
228:
223:
220:
215:viscous drag
195:
91:hydrodynamic
78:
63:
61:
48:
44:
38:
36:
18:Drag (force)
5421:tec-science
4898:Stokes' law
4833:Drag crisis
4773:steady flow
4762:Stokes' law
4618:power curve
4596:power curve
4350:shock waves
3958:viscosity.
3414:linear drag
3404:Stokes' law
3396:Newton drag
2741:. Velocity
1866:symmetrical
1455:coefficient
385:vortex drag
224:orientation
87:aerodynamic
5794:Categories
5519:28 January
5459:(doctoral)
5195:atmosphere
5048:16 October
5027:16 October
5003:16 October
4977:16 October
4920:References
4798:Added mass
4725:d'Alembert
4608:Drag curve
4278:freestream
2598:function:
1973:horsepower
1820:lift force
1326:drag force
1159:Stokes Law
608:drag force
267:watercraft
64:drag force
5107:118693492
5082:1305.3947
4908:Wave drag
4681:wave drag
4676:bow waves
4664:wave drag
4643:Wave drag
4544:Aristotle
4493:Viscosity
4397:wave drag
4354:viscosity
4200:⋅
4081:⋅
3997:η
3994:π
3988:−
3942:η
3894:η
3891:π
3810:ρ
3806:−
3803:ρ
3662:ρ
3639:ρ
3594:−
3586:−
3552:ρ
3548:−
3545:ρ
3442:−
3344:â0.01 m)
3297:â0.05 m)
3139:in m/s.
3106:ρ
3091:ρ
2973:ρ
2967:−
2952:∑
2851:ρ
2845:−
2678:
2670:−
2634:
2531:
2497:
2400:ρ
2289:ρ
2271:
2248:ρ
2058:ρ
2015:⋅
1936:ρ
1913:⋅
1747:ρ
1410:μ
1407:ν
1352:Δ
1190:μ
1187:π
1140:−
1051:ρ
1029:μ
1003:ν
940:⋅
928:⋅
822:dimension
780:μ
770:ρ
759:ν
620:ρ
538:ρ
462:endurance
457:wave drag
453:transonic
433:form drag
381:propeller
294:wave drag
284:area rule
272:wave drag
201:form drag
130:friction
5726:(1975),
5693:(2000).
5463:22 March
5363:Archived
5306:11816281
5253:Archived
5232:Archived
5112:23 April
4791:See also
4723:In 1752
4602:airspeed
4568:aircraft
4450:pressure
3250:â0.2 m)
3203:â0.6 m)
2443:at time
2210:(tanh):
2196:Velocity
1208:At high
846:diameter
280:Concorde
75:Examples
5717:1744638
5426:25 June
5286:Bibcode
5176:, p.212
5150:, p.185
5087:Bibcode
4913:Windage
4784:Prandtl
4742:viscous
4625:curve.
4538:History
4280:flow.
3954:is the
3930:is the
3868:viscous
3628:where:
3465:where:
2528:arctanh
1843:of the
1068:At low
1016:is the
713:is the
680:is the
634:density
632:is the
606:is the
51:, is a
5748:
5734:
5715:
5705:
5670:
5651:
5628:
5607:
5398:
5345:18 May
5304:
5172:
5146:
5130:
5105:
4754:Stokes
4750:Navier
4454:exerts
4185:
4182:
4179:
4176:
4173:
4165:
3910:where
3750:), and
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