4384:, 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
466:
311:
299:
323:
4580:
4623:
2176:
171:
4567:. 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
156:
126:
141:
4485:
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.
1664:
4644:
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
4667:
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
4484:
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
4613:
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
4643:
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
4775:
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
439:
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
2179:
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
448:
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
3405:
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
3373:
1964:(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
218:
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
2571:
380:) 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
210:
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
1665:
1305:
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.
2718:
3363:
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.
2322:
1667:
2103:
1440:
4209:
5574:'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
3033:
1958:
1668:
3615:
979:
2453:
55:
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
1617:
2911:
1968:. 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.
1775:
3113:
784:
563:
4724:
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
4008:
2420:
403:, 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.
2590:
2202:
3830:
4636:
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
1974:
3117:
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
3450:
1960:
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
1320:
1971:
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:
4097:
4760:, 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
1666:
1195:
44:
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
3170:
1800:
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).
4547:'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.
2926:
4243:
3897:
1872:
4415:, 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.
4090:
3499:
2815:
3508:
1144:
3667:
1051:
267:) 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
4473:
4301:
1647:
1029:
1003:
4517:
4413:
4382:
4331:
3941:
3638:
3358:
3311:
3264:
3217:
2159:
2132:
1528:
1501:
1470:
1303:
1276:
1249:
1222:
1109:
1082:
888:
861:
700:
619:
593:
3737:
310:
4050:
4030:
3917:
3850:
3759:
3711:
3689:
3475:
3331:
3284:
3237:
3190:
1839:
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
831:
807:
667:
645:
3379:
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
420:, 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 (
322:
4648:. Transonic compressibility drag increases significantly as the speed of flight increases towards Mach 1.0, dominating other forms of drag at those speeds.
97:
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.
1533:
2826:
483:, 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.
1703:
1146:, 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
3051:
720:
494:
5571:'Improved Empirical Model for Base Drag Prediction on Missile Configurations, based on New Wind Tunnel Data', Frank G Moore et al. NASA Langley Center
239:, 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.
3957:
4683:
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
2356:
4273:
From the body's perspective (near-field approach), the drag results from forces due to pressure distributions over the body surface, symbolized
896:
4734:
298:
5577:'Base Drag and Thick Trailing Edges', Sighard F. Hoerner, Air Materiel Command, in: Journal of the Aeronautical Sciences, Oct 1950, pp 622â628
4445:
normal forces on the body. Those forces can be added together and the component of that force that acts downstream represents the drag force,
5148:
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
291:
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.
4551:'s boundary layer theory in the 1920s provided the impetus to minimise skin friction. A further major call for streamlining was made by Sir
4056:
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.
4698:
theoretical concept is not subject to wave drag when operated at its design speed, but is incapable of generating lift in this condition.
4563:
was seminal. He proposed an ideal aircraft that would have minimal drag which led to the concepts of a 'clean' monoplane and retractable
1309:
It can be demonstrated that drag force can be expressed as a function of a dimensionless number, which is dimensionally identical to the
487:
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
5405:
4659:
formed at the leading and trailing edges of the body. In highly supersonic flows, or in bodies with turning angles sufficiently large,
3411:
5115:
Encyclopedia of
Automotive Engineering, David Crolla, Paper "Fundamentals, Basic principles in Road vehicle Aerodynamics and Design",
231:
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
5120:
4337:
Alternatively, calculated from the flow field perspective (far-field approach), the drag force results from three natural phenomena:
3360:â9 m/s, and so on. Terminal velocity for very small objects (pollen, etc.) at low Reynolds numbers is determined by Stokes law.
4866:
1811:. Therefore, the reference for a wing is often the lifting area, sometimes referred to as "wing area" rather than the frontal area.
5220:
4981:
4955:
5241:
4609:, and is important to pilots because it shows that, below a certain airspeed, maintaining airspeed counterintuitively requires
2566:{\displaystyle v(t)=v_{t}\tanh \left(t{\frac {g}{v_{t}}}+\operatorname {arctanh} \left({\frac {v_{i}}{v_{t}}}\right)\right).\,}
206:
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
3477:
is a constant that depends on both the material properties of the object and fluid, as well as the geometry of the object; and
5724:
5695:
5660:
5641:
5618:
5597:
5466:
1153:
3768:
3131:
5351:
5162:
5136:
4059:
The drag coefficient of a sphere can be determined for the general case of a laminar flow with
Reynolds numbers less than
4531:
The idea that a moving body passing through air or another fluid encounters resistance had been known since the time of
5756:
5738:
5321:
5236:
5388:
3866:
1796:
on a plane perpendicular to the direction of motion. For objects with a simple shape, such as a sphere, this is the
4757:
4605:
airspeed can be plotted as a characteristic curve, illustrated here. In aviation, this is often referred to as the
1313:. Consequently, drag force and drag coefficient can be a function of Bejan number. In fact, from the expression of
2713:{\displaystyle v(t)=v_{t}\coth \left(t{\frac {g}{v_{t}}}+\coth ^{-1}\left({\frac {v_{i}}{v_{t}}}\right)\right).\,}
372:
of an airplane. Induced drag consists primarily of two components: drag due to the creation of trailing vortices (
2775:
1251:
is more or less constant, but drag will vary as the square of the speed varies. The graph to the right shows how
465:
5007:
4764:
solutions to the Euler equations, other than the potential flow solutions, did not result in realistic results.
2317:{\displaystyle v(t)={\sqrt {\frac {2mg}{\rho AC_{d}}}}\tanh \left(t{\sqrt {\frac {g\rho C_{d}A}{2m}}}\right).\,}
2187:
as a function of time for an object falling through a non-dense medium, and released at zero relative-velocity
5773:
4841:
2098:{\displaystyle P_{d}=\mathbf {F} _{d}\cdot \mathbf {v_{o}} ={\tfrac {1}{2}}C_{d}A\rho (v_{w}+v_{o})^{2}v_{o}}
5608:
85:: Drag acting opposite to the direction of movement of a solid object such as cars, aircraft and boat hulls.
5199:
5031:
4806:
4726:
1435:{\displaystyle F_{\rm {d}}=\Delta _{p}A_{w}={\frac {1}{2}}C_{D}A_{f}{\frac {\nu \mu }{l^{2}}}Re_{L}^{2}}
5687:
4713:
4707:
4560:
4488:
The friction drag force, which is a tangential force on the aircraft surface, depends substantially on
1865:
Under the assumption that the fluid is not moving relative to the currently used reference system, the
48:
surface. Drag forces tend to decrease fluid velocity relative to the solid object in the fluid's path.
4519:, is calculated as the downstream projection of the viscous forces evaluated over the body's surface.
4216:
4204:{\displaystyle C_{D}={\frac {24}{Re}}+{\frac {4}{\sqrt {Re}}}+0.4~{\text{;}}~~~~~Re<2\cdot 10^{5}}
5215:
4555:
who provided the theoretical concepts to demonstrate emphatically the importance of streamlining in
4062:
1797:
670:
3482:
215:
has on the relative proportions of skin friction, and pressure difference between front and back.
5788:
4881:
1853:
is, in general, a function of the orientation of the flow with respect to the object (apart from
1789:
369:
1114:
3645:
278:
236:
4742:
4622:
4544:
3860:
2820:
1034:
20:
4448:
4276:
1622:
1012:
986:
391:
generated by a body increases, so does the lift-induced drag. This means that as the wing's
5705:
5274:
5259:
5075:
4495:
4391:
4360:
4309:
4265:, is the fluid drag force that acts on any moving solid body in the direction of the air's
3926:
3623:
3336:
3289:
3242:
3195:
2584:
2137:
2110:
1506:
1479:
1448:
1281:
1254:
1227:
1200:
1087:
1060:
866:
839:
707:
678:
604:
571:
450:
428:). Additionally, the presence of multiple bodies in relative proximity may incur so called
5733:, Fourth Edition, McGraw Hill Higher Education, Boston, Massachusetts, USA. 8th ed. 2015,
5467:
https://archive.org/details/Flight_International_Magazine_1913-02-01-pdf/page/n19/mode/2up
4213:
For
Reynolds numbers less than 1, Stokes' law applies and the drag coefficient approaches
3716:
3028:{\displaystyle {\frac {1}{m}}\sum F(v)-{\frac {\rho AC_{d}}{2m}}v^{2}={\frac {dv}{dt}}.\,}
8:
5502:
5366:
5175:
4801:
4756:
In the limit of high
Reynolds numbers, the NavierâStokes equations approach the inviscid
4738:
4640:, wave drag consists of multiple components depending on the speed regime of the flight.
4540:
2723:
2328:
1818:(like a sphere or circular cylinder), the drag coefficient may vary with Reynolds number
1006:
5278:
5079:
1953:{\displaystyle P_{d}=\mathbf {F} _{d}\cdot \mathbf {v} ={\tfrac {1}{2}}\rho v^{3}AC_{d}}
1778:
5762:
5653:
Physics for
Scientists and Engineers: Mechanics, Oscillations and Waves, Thermodynamics
5290:
5179:
5091:
5065:
4985:
4959:
4536:
4035:
4015:
3902:
3835:
3744:
3696:
3674:
3460:
3316:
3269:
3222:
3175:
2196:
1833:
816:
792:
652:
630:
286:
275:
which extended the rear fuselage 3.73 m (12.2 ft) on the production aircraft.
199:
5087:
2175:
5734:
5720:
5691:
5656:
5637:
5630:
5614:
5593:
5384:
5183:
5158:
5132:
5116:
5095:
5053:
4891:
4791:
4655:
is the result of shockwaves present in the fluid and attached to the body, typically
4579:
4354:
4053:
2735:
2343:
2170:
344:
243:
75:
5294:
5679:
5282:
5083:
4856:
4851:
4826:
4695:
3610:{\displaystyle v(t)={\frac {(\rho -\rho _{0})\,V\,g}{b}}\left(1-e^{-b\,t/m}\right)}
1807:, the reference areas are the same, and the drag force is in the same ratio as the
703:
396:
4816:
4477:
shock wave effects, vortex system generation effects, and wake viscous mechanisms.
5701:
5443:
5355:
5245:
5224:
4921:
4876:
4796:
4746:
3951:
3384:
1965:
1866:
1815:
1689:
715:
477:
436:
392:
57:
5348:
92:: Drag force on the immobile pipe decreases fluid velocity relative to the pipe.
5793:
5260:"Experiments on the flow past a circular cylinder at very high Reynolds number"
4886:
4861:
4811:
4772:
4768:
4750:
4717:
4548:
4489:
3392:
3380:
2731:
2339:
412:
400:
220:
29:
5286:
235:
has an equivalent parasite area of 2.20 m (23.7 sq ft) and the
5782:
4831:
4721:
4552:
4032:= 0.5 micrometre (diameter = 1.0 ÎŒm) moving through water at a velocity
3920:
1681:
1658:
488:
435:
In aviation, induced drag tends to be greater at lower speeds because a high
193:
79:
5712:
4871:
4846:
4836:
4637:
4568:
4564:
4254:
1808:
1473:
1310:
388:
381:
361:
357:
264:
251:
247:
232:
203:
170:
89:
974:{\displaystyle D_{e}=1.30\cdot {\frac {(a\cdot b)^{0.625}}{(a+b)^{0.25}}}}
4821:
4761:
4521:
The sum of friction drag and pressure (form) drag is called viscous drag.
1443:
454:
5751:
5327:
4687:. Similarly, for a fixed volume, the shape for minimum wave drag is the
3855:
For the special case of small spherical objects moving slowly through a
4786:
4596:
4338:
4266:
3376:
1961:
1314:
1147:
399:
also increases, and so too does the lift-induced drag. At the onset of
285:
occurs when a solid object is moving along a fluid boundary and making
255:
4559:
design. In 1929 his paper 'The
Streamline Airplane' presented to the
4896:
4730:
4631:
4532:
4481:
4385:
4342:
4306:
Forces due to skin friction, which is a result of viscosity, denoted
3856:
2180:
constant acceleration for a larger fraction of its accelerating time.
1612:{\displaystyle C_{D}=2{\frac {A_{w}}{A_{f}}}{\frac {Be}{Re_{L}^{2}}}}
810:
445:
441:
282:
272:
260:
189:
72:
5369:, from Department of Physics and Astronomy, Georgia State University
2906:{\displaystyle g-{\frac {\rho AC_{d}}{2m}}v^{2}={\frac {dv}{dt}}.\,}
4556:
4438:
2184:
1854:
834:
714:
The drag coefficient depends on the shape of the object and on the
268:
185:
Types of drag are generally divided into the following categories:
5769:
Smithsonian
National Air and Space Museum's How Things Fly website
5070:
1770:{\displaystyle F_{D}\,=\,{\tfrac {1}{2}}\,\rho \,v^{2}\,C_{d}\,A,}
5627:
5200:
Analysis of triangular sharkskin profiles according to second law
5008:"Calculating Viscous Flow: Velocity Profiles in Rivers and Pipes"
4901:
4353:
When the airplane produces lift, another drag component results.
3108:{\displaystyle v_{t}={\sqrt {gd{\frac {\rho _{obj}}{\rho }}}}.\,}
1684:
with a constant drag coefficient gives the force moving through
779:{\displaystyle R_{e}={\frac {vD}{\nu }}={\frac {\rho vD}{\mu }},}
622:
558:{\displaystyle F_{D}\,=\,{\tfrac {1}{2}}\,\rho \,v^{2}\,C_{D}\,A}
432:, which is sometimes described as a component of parasitic drag.
271:
prototype aircraft was reduced at Mach 2 by 1.8% by applying the
4867:
Projectile motion#Trajectory of a projectile with air resistance
4626:
Qualitative variation in Cd factor with Mach number for aircraft
3372:
2450:, is also defined in terms of the hyperbolic tangent function:
893:
For a rectangular shape cross-section in the motion direction,
223:. Parasite drag is often expressed in terms of a hypothetical.
5759:
and its effect on the acceleration and top speed of a vehicle.
5052:
Hernandez-Gomez, J J; Marquina, V; Gomez, R W (25 July 2013).
155:
5768:
4617:
3944:
3765:
The velocity asymptotically approaches the terminal velocity
2819:
These functions are defined by the solution of the following
1685:
328:
Hawk aircraft showing base area above circular engine exhaust
316:
Concorde with 'low' wave drag tail (N.B. rear fuselage spike)
125:
82:
45:
41:
5590:
Newtonian Mechanics (The M.I.T. Introductory Physics Series)
5485:
A History of Aerodynamics: And Its Impact On Flying Machines
5051:
4003:{\displaystyle \mathbf {F} _{d}=-6\pi \eta r\,\mathbf {v} .}
140:
5131:
Fundamentals of Flight, Second Edition, Richard S. Shevell,
2415:{\displaystyle v_{t}={\sqrt {\frac {2mg}{\rho AC_{d}}}}.\,}
2195: = 0, is roughly given by a function involving a
1673:
395:
increases (up to a maximum called the stalling angle), the
365:
5592:(1st ed.). W. W. White & Company Inc., New York.
4432:
5529:
Bennett Melvill Jones. 28 January 1887 -- 31 October 1975
226:
2424:
For an object falling and released at relative-velocity
1846: > 3,500. The further the drag coefficient
356:) is drag which occurs as the result of the creation of
4745:. Stokes derived the drag around a sphere at very low
1869:
required to overcome the aerodynamic drag is given by:
1649:
is the Reynolds number related to fluid path length L.
333:
5054:"On the performance of Usain Bolt in the 100 m sprint"
4651:
In supersonic flight (Mach numbers greater than 1.0),
4418:
Therefore, there are three ways of categorizing drag.
3825:{\displaystyle v_{t}={\frac {(\rho -\rho _{0})Vg}{b}}}
3713:
is the acceleration due to gravity (i.e., 9.8 m/s
2022:
1913:
1723:
514:
4498:
4451:
4394:
4363:
4312:
4279:
4219:
4100:
4065:
4038:
4018:
3960:
3929:
3905:
3869:
3838:
3771:
3747:
3719:
3699:
3677:
3648:
3626:
3511:
3505:
When an object falls from rest, its velocity will be
3485:
3463:
3414:
3367:
3339:
3319:
3292:
3272:
3245:
3225:
3198:
3178:
3134:
3054:
2929:
2829:
2778:
2593:
2456:
2359:
2205:
2140:
2113:
1977:
1875:
1706:
1625:
1536:
1509:
1482:
1451:
1323:
1284:
1257:
1230:
1203:
1156:
1117:
1090:
1063:
1037:
1015:
989:
899:
869:
842:
819:
795:
723:
681:
655:
633:
607:
574:
497:
5532:. Vol. 23. The Royal Society. pp. 252â282.
5526:
Biographical Memoirs of Fellows of the Royal Society
5523:
Sir Morien Morgan, Sir Arnold Hall (November 1977).
4492:
configuration and viscosity. The net friction drag,
2923:) are the forces acting on the object beyond drag):
2583:, the velocity function is defined in terms of the
1814:For an object with a smooth surface, and non-fixed
5765:based on drag coefficient, frontal area and speed.
5629:
4511:
4467:
4407:
4376:
4325:
4295:
4237:
4203:
4084:
4044:
4024:
4002:
3950:The resulting expression for the drag is known as
3935:
3911:
3891:
3844:
3824:
3753:
3731:
3705:
3683:
3661:
3632:
3609:
3493:
3469:
3444:
3352:
3325:
3305:
3278:
3258:
3231:
3211:
3184:
3164:
3107:
3027:
2905:
2809:
2712:
2565:
2414:
2316:
2153:
2126:
2097:
1952:
1769:
1641:
1611:
1522:
1495:
1464:
1434:
1297:
1270:
1243:
1216:
1189:
1138:
1103:
1076:
1045:
1023:
997:
973:
882:
855:
825:
801:
778:
694:
661:
639:
613:
587:
557:
5686:. Cambridge Mathematical Library (2nd ed.).
5678:
5522:
4012:For example, consider a small sphere with radius
3445:{\displaystyle \mathbf {F} _{d}=-b\mathbf {v} \,}
647:is the speed of the object relative to the fluid,
387:With other parameters remaining the same, as the
5780:
5503:"University of Cambridge Engineering Department"
5194:
5192:
1777:The derivation of this equation is presented at
376:); and the presence of additional viscous drag (
5610:Fluid Mechanics (A short course for physicists)
5406:"Drag coefficient (friction and pressure drag)"
3037:For a potato-shaped object of average diameter
2164:
2161:is the object speed (both relative to ground).
1692:, Re > ~1000. This is also called
5445:Influence of Attachment Line Flow on Form Drag
5378:
4601:The interaction of parasitic and induced drag
5587:
5319:
5189:
4475:. The nature of these normal forces combines
3863:derived an expression for the drag constant:
3219:â70 m/s, for a small animal like a cat (
1442:and consequently allows expressing the drag
1009:of the fluid (equal to the dynamic viscosity
5650:
5628:Serway, Raymond A.; Jewett, John W. (2004).
5560:
5558:
5556:
5497:
5495:
5477:
5475:
5403:
5306:
5304:
4672:is commonly separated into two components,
4348:
3859:fluid (and thus at small Reynolds number),
16:Retarding force on a body moving in a fluid
5774:Effect of dimples on a golf ball and a car
5198:Liversage, P., and Trancossi, M. (2018). "
4618:Wave drag in transonic and supersonic flow
4574:
4523:This drag component is due to viscosity.
809:is some characteristic diameter or linear
5553:
5516:
5492:
5178:, the air density can be found using the
5069:
3991:
3888:
3588:
3556:
3552:
3441:
3161:
3104:
3024:
2902:
2709:
2562:
2411:
2313:
1760:
1749:
1738:
1734:
1721:
1717:
551:
540:
529:
525:
512:
508:
5481:
5472:
5301:
4974:
4948:
4621:
4578:
4441:distribution acting on a body's surface
3371:
2174:
1662:
981:, where a and b are the rectangle edges.
464:
453:(minimum fuel consumption), or maximize
5752:Educational materials on air resistance
5669:
5546:Oxford Dictionary of National Biography
4701:
4587:: parasitic drag and lift-induced drag
4433:Additional information for aerodynamics
1688:a relatively large velocity, i.e. high
1190:{\displaystyle F_{\rm {d}}=3\pi \mu Dv}
5781:
5719:, Pitman Publishing Limited, London.
5441:
5435:
5257:
5000:
4052:of 10 Όm/s. Using 10 Pa·s as the
3165:{\displaystyle v_{t}=90{\sqrt {d}},\,}
2342:approaches a maximum value called the
424:), and drag due to surface roughness (
227:Parasitic drag experienced by aircraft
5383:. Butterworth-Heinemann. p. 30.
5379:Collinson, Chris; Roper, Tom (1995).
4678:supersonic volume-dependent wave drag
250:in aviation and with semi-planing or
5632:Physics for Scientists and Engineers
5542:
5536:
5204:Modelling, Measurement and Control B
5157:Design For Air Combat, Ray Whitford,
4720:, the 18th century state-of-the-art
4428:Vortex drag, wave drag and wake drag
3852:, denser objects fall more quickly.
2722:The hyperbolic cotangent also has a
460:
338:
334:Lift-induced drag and parasitic drag
5763:Vehicle Aerodynamic Drag calculator
5442:Gowree, Erwin Ricky (20 May 2014).
4674:supersonic lift-dependent wave drag
1652:
457:in the event of an engine failure.
304:Concorde with 'high' wave drag tail
196:due to the size and shape of a body
13:
5248:, from NASA Glenn Research Center.
5227:, from NASA Glenn Research Center.
3368:Low Reynolds numbers: Stokes' drag
1340:
1330:
1163:
1111:is asymptotically proportional to
14:
5805:
5745:
5684:An introduction to fluid dynamics
5182:. It is 1.293 kg/m at 0 °C and 1
406:
4749:, the result of which is called
4238:{\displaystyle {\frac {24}{Re}}}
3993:
3963:
3487:
3437:
3417:
3266:â40 m/s, for a small bird (
2012:
2008:
1993:
1905:
1891:
321:
309:
297:
169:
154:
139:
124:
5729:Anderson, John D. Jr. (2000);
5655:(5th ed.). W. H. Freeman.
5581:
5460:
5423:
5397:
5372:
5360:
5341:
5313:
5251:
5230:
5209:
5168:
5151:
5142:
4945:French (1970), p. 211, Eq. 7-20
4422:Pressure drag and friction drag
4248:
3892:{\displaystyle b=6\pi \eta r\,}
3172:For example, for a human body (
1825:, up to extremely high values (
1779:Drag equation § Derivation
1476:and the ratio between wet area
51:Unlike other resistive forces,
5613:. Cambridge University Press.
5606:
5564:Batchelor (2000), pp. 337â343.
5125:
5109:
5045:
5024:
4939:
4914:
4646:transonic compressibility drag
3807:
3788:
3549:
3530:
3521:
3515:
3501:is the velocity of the object.
2952:
2946:
2788:
2782:
2603:
2597:
2466:
2460:
2215:
2209:
2076:
2049:
959:
946:
935:
922:
890:is the D of the sphere itself.
476:for a sphere as a function of
1:
5636:(6th ed.). Brooks/Cole.
5482:Anderson, John David (1929).
4908:
4425:Profile drag and induced drag
4092:using the following formula:
4085:{\displaystyle 2\cdot 10^{5}}
3640:is the density of the object,
3313:â20 m/s, for an insect (
3048:, terminal velocity is about
2726:value of one, for large time
2331:value of one, for large time
2327:The hyperbolic tangent has a
863:of the object. For a sphere,
5323:Part 6: Speed and Horsepower
3691:is the volume of the object,
3494:{\displaystyle \mathbf {v} }
2915:Or, more generically (where
2772:, the velocity is constant:
2165:Velocity of a falling object
7:
5404:tec-science (31 May 2020).
5088:10.1088/0143-0807/34/5/1227
4807:Automobile drag coefficient
4779:
4539:, this was named "drag" by
2810:{\displaystyle v(t)=v_{t}.}
63:
36:, sometimes referred to as
10:
5810:
5688:Cambridge University Press
5488:. University of Cambridge.
5267:Journal of Fluid Mechanics
4705:
4629:
4594:
4561:Royal Aeronautical Society
4526:
3390:
2168:
1656:
1139:{\displaystyle R_{e}^{-1}}
410:
342:
68:Examples of drag include:
18:
5349:"On Being the Right Size"
5310:Batchelor (1967), p. 341.
5287:10.1017/S0022112061000950
5238:Wing geometry definitions
4842:KeuleganâCarpenter number
3662:{\displaystyle \rho _{0}}
2338:In other words, velocity
378:lift-induced viscous drag
4685:Sears-Haack Distribution
4349:Overview of aerodynamics
3669:is density of the fluid,
1860:
1857:objects like a sphere).
281:(ship hydrodynamics) or
246:appears with wings or a
101:
5670:Huntley, H. E. (1967).
5429:Anderson, John D. Jr.,
5258:Roshko, Anatol (1961).
4882:Stall (fluid mechanics)
4733:flow were developed by
4729:for the description of
4727:NavierâStokes equations
4575:Power curve in aviation
3383:, and the green object
2191: = 0 at time
1790:orthographic projection
1672:Explanation of drag by
1046:{\displaystyle {\rho }}
1031:divided by the density
360:on a three-dimensional
5731:Introduction to Flight
5588:French, A. P. (1970).
5431:Introduction to Flight
5320:Brian Beckman (1991),
4627:
4592:
4513:
4469:
4468:{\displaystyle D_{pr}}
4409:
4378:
4327:
4297:
4296:{\displaystyle D_{pr}}
4239:
4205:
4086:
4046:
4026:
4004:
3937:
3913:
3893:
3846:
3826:
3761:is mass of the object.
3755:
3733:
3707:
3685:
3663:
3634:
3611:
3495:
3471:
3446:
3388:
3354:
3327:
3307:
3280:
3260:
3233:
3213:
3186:
3166:
3109:
3029:
2907:
2811:
2744:, strictly from above
2714:
2567:
2416:
2318:
2181:
2155:
2134:is the wind speed and
2128:
2099:
1954:
1792:of the object, or the
1771:
1677:
1643:
1642:{\displaystyle Re_{L}}
1613:
1524:
1497:
1466:
1436:
1317:it has been obtained:
1299:
1272:
1245:
1218:
1191:
1140:
1105:
1078:
1047:
1025:
1024:{\displaystyle {\mu }}
999:
998:{\displaystyle {\nu }}
975:
884:
857:
827:
803:
780:
696:
663:
641:
615:
589:
559:
484:
237:McDonnell Douglas DC-9
5651:Tipler, Paul (2004).
5607:G. Falkovich (2011).
5032:"Viscous Drag Forces"
4661:unattached shockwaves
4625:
4582:
4545:Louis Charles Breguet
4514:
4512:{\displaystyle D_{f}}
4470:
4410:
4408:{\displaystyle D_{w}}
4379:
4377:{\displaystyle D_{i}}
4328:
4326:{\displaystyle D_{f}}
4298:
4240:
4206:
4087:
4047:
4027:
4005:
3938:
3936:{\displaystyle \eta }
3923:of the particle, and
3914:
3894:
3861:George Gabriel Stokes
3847:
3827:
3756:
3734:
3708:
3686:
3664:
3635:
3633:{\displaystyle \rho }
3612:
3496:
3472:
3447:
3375:
3355:
3353:{\displaystyle v_{t}}
3328:
3308:
3306:{\displaystyle v_{t}}
3281:
3261:
3259:{\displaystyle v_{t}}
3234:
3214:
3212:{\displaystyle v_{t}}
3187:
3167:
3110:
3030:
2908:
2821:differential equation
2812:
2715:
2568:
2436: = 0, with
2417:
2319:
2178:
2156:
2154:{\displaystyle v_{o}}
2129:
2127:{\displaystyle v_{w}}
2100:
1955:
1772:
1671:
1644:
1614:
1525:
1523:{\displaystyle A_{f}}
1498:
1496:{\displaystyle A_{w}}
1467:
1465:{\displaystyle C_{D}}
1437:
1300:
1298:{\displaystyle R_{e}}
1273:
1271:{\displaystyle C_{D}}
1246:
1244:{\displaystyle C_{D}}
1219:
1217:{\displaystyle R_{e}}
1192:
1141:
1106:
1104:{\displaystyle C_{D}}
1079:
1077:{\displaystyle R_{e}}
1048:
1026:
1000:
976:
885:
883:{\displaystyle D_{e}}
858:
856:{\displaystyle D_{e}}
828:
804:
781:
697:
695:{\displaystyle C_{D}}
664:
642:
616:
614:{\displaystyle \rho }
590:
588:{\displaystyle F_{D}}
560:
468:
5672:Dimensional Analysis
5469:Flight, 1913, p. 126
5217:Size effects on drag
4922:"Definition of DRAG"
4708:d'Alembert's paradox
4702:d'Alembert's paradox
4496:
4449:
4392:
4361:
4341:, vortex sheet, and
4310:
4277:
4217:
4098:
4063:
4036:
4016:
3958:
3927:
3903:
3867:
3836:
3769:
3745:
3732:{\displaystyle ^{2}}
3717:
3697:
3675:
3646:
3624:
3509:
3483:
3461:
3412:
3337:
3317:
3290:
3270:
3243:
3223:
3196:
3176:
3132:
3052:
2927:
2827:
2776:
2591:
2585:hyperbolic cotangent
2454:
2357:
2203:
2138:
2111:
1975:
1873:
1704:
1623:
1534:
1507:
1480:
1449:
1321:
1282:
1255:
1228:
1201:
1154:
1115:
1088:
1061:
1035:
1013:
987:
897:
867:
840:
817:
793:
721:
708:dimensionless number
679:
671:cross sectional area
653:
631:
605:
572:
495:
19:For other uses, see
5543:Mair, W.A. (1976).
5279:1961JFM....10..345R
5080:2013EJPh...34.1227H
4802:Atmospheric density
4571:in thermodynamics.
4541:Archibald Reith Low
1784:The reference area
1605:
1431:
1135:
1007:kinematic viscosity
5381:Particle Mechanics
5354:2011-08-22 at the
5244:2011-03-07 at the
5223:2016-11-09 at the
5180:barometric formula
5176:Earth's atmosphere
4657:oblique shockwaves
4628:
4593:
4509:
4465:
4405:
4374:
4323:
4293:
4235:
4201:
4082:
4042:
4022:
4000:
3933:
3909:
3889:
3842:
3822:
3751:
3729:
3703:
3681:
3659:
3630:
3607:
3491:
3467:
3442:
3399:viscous resistance
3389:
3350:
3323:
3303:
3276:
3256:
3229:
3209:
3182:
3162:
3105:
3025:
2903:
2807:
2710:
2563:
2412:
2314:
2197:hyperbolic tangent
2182:
2151:
2124:
2095:
2031:
1950:
1922:
1767:
1732:
1680:As mentioned, the
1678:
1639:
1609:
1591:
1520:
1493:
1462:
1432:
1417:
1295:
1268:
1241:
1214:
1187:
1136:
1118:
1101:
1074:
1043:
1021:
995:
971:
880:
853:
833:is the equivalent
823:
799:
776:
692:
659:
637:
611:
585:
555:
523:
485:
426:skin friction drag
200:skin friction drag
5725:978-0-273-01120-0
5697:978-0-521-66396-0
5680:Batchelor, George
5662:978-0-7167-0809-4
5643:978-0-534-40842-8
5620:978-1-107-00575-4
5599:978-0-393-09958-4
5347:Haldane, J.B.S.,
5206:. 87(3), 188-196.
5121:978 0 470 97402 5
4892:Terminal velocity
4792:Aerodynamic force
4233:
4175:
4172:
4169:
4166:
4163:
4159:
4155:
4145:
4144:
4127:
4054:dynamic viscosity
4045:{\displaystyle v}
4025:{\displaystyle r}
3912:{\displaystyle r}
3845:{\displaystyle b}
3820:
3754:{\displaystyle m}
3706:{\displaystyle g}
3684:{\displaystyle V}
3564:
3470:{\displaystyle b}
3397:The equation for
3326:{\displaystyle d}
3279:{\displaystyle d}
3232:{\displaystyle d}
3185:{\displaystyle d}
3156:
3099:
3097:
3019:
2986:
2938:
2897:
2864:
2736:terminal velocity
2695:
2648:
2548:
2511:
2406:
2405:
2344:terminal velocity
2303:
2302:
2254:
2253:
2171:Terminal velocity
2030:
1921:
1816:separation points
1803:In the case of a
1731:
1669:
1607:
1575:
1472:as a function of
1412:
1370:
969:
826:{\displaystyle D}
802:{\displaystyle D}
771:
750:
662:{\displaystyle A}
640:{\displaystyle v}
522:
469:Drag coefficient
461:The drag equation
430:interference drag
350:Lift-induced drag
345:Lift-induced drag
339:Lift-induced drag
244:lift-induced drag
183:
182:
5801:
5757:Aerodynamic Drag
5709:
5675:
5666:
5647:
5635:
5624:
5603:
5565:
5562:
5551:
5550:
5540:
5534:
5533:
5520:
5514:
5513:
5511:
5509:
5499:
5490:
5489:
5479:
5470:
5464:
5458:
5457:
5455:
5453:
5439:
5433:
5427:
5421:
5420:
5418:
5416:
5401:
5395:
5394:
5376:
5370:
5364:
5358:
5345:
5339:
5338:
5337:
5335:
5326:, archived from
5317:
5311:
5308:
5299:
5298:
5264:
5255:
5249:
5234:
5228:
5213:
5207:
5196:
5187:
5172:
5166:
5155:
5149:
5146:
5140:
5129:
5123:
5113:
5107:
5106:
5104:
5102:
5073:
5064:(5): 1227â1233.
5049:
5043:
5042:
5040:
5038:
5028:
5022:
5021:
5019:
5017:
5012:
5004:
4998:
4997:
4995:
4993:
4984:. Archived from
4978:
4972:
4971:
4969:
4967:
4958:. Archived from
4952:
4946:
4943:
4937:
4936:
4934:
4932:
4918:
4857:Nose cone design
4852:Morison equation
4827:Drag coefficient
4747:Reynolds numbers
4696:Busemann biplane
4689:Von Karman Ogive
4518:
4516:
4515:
4510:
4508:
4507:
4474:
4472:
4471:
4466:
4464:
4463:
4414:
4412:
4411:
4406:
4404:
4403:
4383:
4381:
4380:
4375:
4373:
4372:
4332:
4330:
4329:
4324:
4322:
4321:
4302:
4300:
4299:
4294:
4292:
4291:
4261:, also known as
4259:aerodynamic drag
4244:
4242:
4241:
4236:
4234:
4232:
4221:
4210:
4208:
4207:
4202:
4200:
4199:
4173:
4170:
4167:
4164:
4161:
4160:
4157:
4153:
4146:
4137:
4133:
4128:
4126:
4115:
4110:
4109:
4091:
4089:
4088:
4083:
4081:
4080:
4051:
4049:
4048:
4043:
4031:
4029:
4028:
4023:
4009:
4007:
4006:
4001:
3996:
3972:
3971:
3966:
3942:
3940:
3939:
3934:
3918:
3916:
3915:
3910:
3898:
3896:
3895:
3890:
3851:
3849:
3848:
3843:
3831:
3829:
3828:
3823:
3821:
3816:
3806:
3805:
3786:
3781:
3780:
3760:
3758:
3757:
3752:
3738:
3736:
3735:
3730:
3728:
3727:
3712:
3710:
3709:
3704:
3690:
3688:
3687:
3682:
3668:
3666:
3665:
3660:
3658:
3657:
3639:
3637:
3636:
3631:
3616:
3614:
3613:
3608:
3606:
3602:
3601:
3600:
3596:
3565:
3560:
3548:
3547:
3528:
3500:
3498:
3497:
3492:
3490:
3476:
3474:
3473:
3468:
3451:
3449:
3448:
3443:
3440:
3426:
3425:
3420:
3359:
3357:
3356:
3351:
3349:
3348:
3332:
3330:
3329:
3324:
3312:
3310:
3309:
3304:
3302:
3301:
3285:
3283:
3282:
3277:
3265:
3263:
3262:
3257:
3255:
3254:
3238:
3236:
3235:
3230:
3218:
3216:
3215:
3210:
3208:
3207:
3191:
3189:
3188:
3183:
3171:
3169:
3168:
3163:
3157:
3152:
3144:
3143:
3114:
3112:
3111:
3106:
3100:
3098:
3093:
3092:
3077:
3069:
3064:
3063:
3034:
3032:
3031:
3026:
3020:
3018:
3010:
3002:
2997:
2996:
2987:
2985:
2977:
2976:
2975:
2959:
2939:
2931:
2912:
2910:
2909:
2904:
2898:
2896:
2888:
2880:
2875:
2874:
2865:
2863:
2855:
2854:
2853:
2837:
2816:
2814:
2813:
2808:
2803:
2802:
2719:
2717:
2716:
2711:
2705:
2701:
2700:
2696:
2694:
2693:
2684:
2683:
2674:
2665:
2664:
2649:
2647:
2646:
2634:
2618:
2617:
2572:
2570:
2569:
2564:
2558:
2554:
2553:
2549:
2547:
2546:
2537:
2536:
2527:
2512:
2510:
2509:
2497:
2481:
2480:
2421:
2419:
2418:
2413:
2407:
2404:
2403:
2402:
2386:
2375:
2374:
2369:
2368:
2323:
2321:
2320:
2315:
2309:
2305:
2304:
2301:
2293:
2289:
2288:
2272:
2271:
2255:
2252:
2251:
2250:
2234:
2223:
2222:
2160:
2158:
2157:
2152:
2150:
2149:
2133:
2131:
2130:
2125:
2123:
2122:
2104:
2102:
2101:
2096:
2094:
2093:
2084:
2083:
2074:
2073:
2061:
2060:
2042:
2041:
2032:
2023:
2017:
2016:
2015:
2002:
2001:
1996:
1987:
1986:
1959:
1957:
1956:
1951:
1949:
1948:
1936:
1935:
1923:
1914:
1908:
1900:
1899:
1894:
1885:
1884:
1776:
1774:
1773:
1768:
1759:
1758:
1748:
1747:
1733:
1724:
1716:
1715:
1670:
1653:At high velocity
1648:
1646:
1645:
1640:
1638:
1637:
1618:
1616:
1615:
1610:
1608:
1606:
1604:
1599:
1586:
1578:
1576:
1574:
1573:
1564:
1563:
1554:
1546:
1545:
1529:
1527:
1526:
1521:
1519:
1518:
1502:
1500:
1499:
1494:
1492:
1491:
1471:
1469:
1468:
1463:
1461:
1460:
1441:
1439:
1438:
1433:
1430:
1425:
1413:
1411:
1410:
1401:
1393:
1391:
1390:
1381:
1380:
1371:
1363:
1358:
1357:
1348:
1347:
1335:
1334:
1333:
1304:
1302:
1301:
1296:
1294:
1293:
1277:
1275:
1274:
1269:
1267:
1266:
1250:
1248:
1247:
1242:
1240:
1239:
1223:
1221:
1220:
1215:
1213:
1212:
1196:
1194:
1193:
1188:
1168:
1167:
1166:
1145:
1143:
1142:
1137:
1134:
1126:
1110:
1108:
1107:
1102:
1100:
1099:
1083:
1081:
1080:
1075:
1073:
1072:
1052:
1050:
1049:
1044:
1042:
1030:
1028:
1027:
1022:
1020:
1004:
1002:
1001:
996:
994:
980:
978:
977:
972:
970:
968:
967:
966:
944:
943:
942:
920:
909:
908:
889:
887:
886:
881:
879:
878:
862:
860:
859:
854:
852:
851:
832:
830:
829:
824:
808:
806:
805:
800:
785:
783:
782:
777:
772:
767:
756:
751:
746:
738:
733:
732:
704:drag coefficient
701:
699:
698:
693:
691:
690:
668:
666:
665:
660:
646:
644:
643:
638:
620:
618:
617:
612:
594:
592:
591:
586:
584:
583:
564:
562:
561:
556:
550:
549:
539:
538:
524:
515:
507:
506:
397:lift coefficient
325:
313:
301:
173:
158:
143:
128:
106:
105:
88:Viscous drag of
38:fluid resistance
5809:
5808:
5804:
5803:
5802:
5800:
5799:
5798:
5779:
5778:
5748:
5698:
5674:. LOC 67-17978.
5663:
5644:
5621:
5600:
5584:
5568:
5563:
5554:
5541:
5537:
5521:
5517:
5507:
5505:
5501:
5500:
5493:
5480:
5473:
5465:
5461:
5451:
5449:
5440:
5436:
5428:
5424:
5414:
5412:
5402:
5398:
5391:
5377:
5373:
5365:
5361:
5356:Wayback Machine
5346:
5342:
5333:
5331:
5330:on 16 June 2019
5318:
5314:
5309:
5302:
5262:
5256:
5252:
5246:Wayback Machine
5235:
5231:
5225:Wayback Machine
5214:
5210:
5197:
5190:
5173:
5169:
5156:
5152:
5147:
5143:
5130:
5126:
5114:
5110:
5100:
5098:
5050:
5046:
5036:
5034:
5030:
5029:
5025:
5015:
5013:
5010:
5006:
5005:
5001:
4991:
4989:
4982:"What is Drag?"
4980:
4979:
4975:
4965:
4963:
4956:"What is Drag?"
4954:
4953:
4949:
4944:
4940:
4930:
4928:
4926:Merriam-Webster
4920:
4919:
4915:
4911:
4906:
4877:Reynolds number
4797:Angle of attack
4782:
4771:âintroduced by
4769:boundary layers
4758:Euler equations
4710:
4704:
4634:
4620:
4599:
4577:
4537:Mervyn O'Gorman
4535:. According to
4529:
4503:
4499:
4497:
4494:
4493:
4456:
4452:
4450:
4447:
4446:
4435:
4399:
4395:
4393:
4390:
4389:
4368:
4364:
4362:
4359:
4358:
4351:
4317:
4313:
4311:
4308:
4307:
4284:
4280:
4278:
4275:
4274:
4251:
4225:
4220:
4218:
4215:
4214:
4195:
4191:
4156:
4132:
4119:
4114:
4105:
4101:
4099:
4096:
4095:
4076:
4072:
4064:
4061:
4060:
4037:
4034:
4033:
4017:
4014:
4013:
3992:
3967:
3962:
3961:
3959:
3956:
3955:
3928:
3925:
3924:
3904:
3901:
3900:
3868:
3865:
3864:
3837:
3834:
3833:
3801:
3797:
3787:
3785:
3776:
3772:
3770:
3767:
3766:
3746:
3743:
3742:
3723:
3720:
3718:
3715:
3714:
3698:
3695:
3694:
3676:
3673:
3672:
3653:
3649:
3647:
3644:
3643:
3625:
3622:
3621:
3592:
3581:
3577:
3570:
3566:
3543:
3539:
3529:
3527:
3510:
3507:
3506:
3486:
3484:
3481:
3480:
3462:
3459:
3458:
3436:
3421:
3416:
3415:
3413:
3410:
3409:
3406:resistance is:
3395:
3370:
3344:
3340:
3338:
3335:
3334:
3318:
3315:
3314:
3297:
3293:
3291:
3288:
3287:
3271:
3268:
3267:
3250:
3246:
3244:
3241:
3240:
3224:
3221:
3220:
3203:
3199:
3197:
3194:
3193:
3177:
3174:
3173:
3151:
3139:
3135:
3133:
3130:
3129:
3126:
3082:
3078:
3076:
3068:
3059:
3055:
3053:
3050:
3049:
3046:
3041:and of density
3011:
3003:
3001:
2992:
2988:
2978:
2971:
2967:
2960:
2958:
2930:
2928:
2925:
2924:
2889:
2881:
2879:
2870:
2866:
2856:
2849:
2845:
2838:
2836:
2828:
2825:
2824:
2798:
2794:
2777:
2774:
2773:
2771:
2762:
2749:
2742:
2689:
2685:
2679:
2675:
2673:
2669:
2657:
2653:
2642:
2638:
2633:
2629:
2625:
2613:
2609:
2592:
2589:
2588:
2582:
2578:
2542:
2538:
2532:
2528:
2526:
2522:
2505:
2501:
2496:
2492:
2488:
2476:
2472:
2455:
2452:
2451:
2448:
2441:
2431:
2398:
2394:
2387:
2376:
2373:
2364:
2360:
2358:
2355:
2354:
2350:
2294:
2284:
2280:
2273:
2270:
2266:
2262:
2246:
2242:
2235:
2224:
2221:
2204:
2201:
2200:
2173:
2167:
2145:
2141:
2139:
2136:
2135:
2118:
2114:
2112:
2109:
2108:
2089:
2085:
2079:
2075:
2069:
2065:
2056:
2052:
2037:
2033:
2021:
2011:
2007:
2006:
1997:
1992:
1991:
1982:
1978:
1976:
1973:
1972:
1944:
1940:
1931:
1927:
1912:
1904:
1895:
1890:
1889:
1880:
1876:
1874:
1871:
1870:
1863:
1851:
1844:
1830:
1823:
1798:cross sectional
1754:
1750:
1743:
1739:
1722:
1711:
1707:
1705:
1702:
1701:
1690:Reynolds number
1663:
1661:
1655:
1633:
1629:
1624:
1621:
1620:
1600:
1595:
1587:
1579:
1577:
1569:
1565:
1559:
1555:
1553:
1541:
1537:
1535:
1532:
1531:
1514:
1510:
1508:
1505:
1504:
1503:and front area
1487:
1483:
1481:
1478:
1477:
1456:
1452:
1450:
1447:
1446:
1426:
1421:
1406:
1402:
1394:
1392:
1386:
1382:
1376:
1372:
1362:
1353:
1349:
1343:
1339:
1329:
1328:
1324:
1322:
1319:
1318:
1289:
1285:
1283:
1280:
1279:
1262:
1258:
1256:
1253:
1252:
1235:
1231:
1229:
1226:
1225:
1208:
1204:
1202:
1199:
1198:
1162:
1161:
1157:
1155:
1152:
1151:
1127:
1122:
1116:
1113:
1112:
1095:
1091:
1089:
1086:
1085:
1068:
1064:
1062:
1059:
1058:
1038:
1036:
1033:
1032:
1016:
1014:
1011:
1010:
990:
988:
985:
984:
962:
958:
945:
938:
934:
921:
919:
904:
900:
898:
895:
894:
874:
870:
868:
865:
864:
847:
843:
841:
838:
837:
818:
815:
814:
794:
791:
790:
757:
755:
739:
737:
728:
724:
722:
719:
718:
716:Reynolds number
686:
682:
680:
677:
676:
654:
651:
650:
632:
629:
628:
606:
603:
602:
579:
575:
573:
570:
569:
545:
541:
534:
530:
513:
502:
498:
496:
493:
492:
478:Reynolds number
475:
463:
437:angle of attack
415:
409:
393:angle of attack
347:
341:
336:
329:
326:
317:
314:
305:
302:
279:wave resistance
229:
118:
113:
109:Shape and flow
104:
90:fluid in a pipe
66:
58:Reynolds number
24:
17:
12:
11:
5:
5807:
5797:
5796:
5791:
5789:Drag (physics)
5777:
5776:
5771:
5766:
5760:
5754:
5747:
5746:External links
5744:
5743:
5742:
5739:978-0078027673
5727:
5710:
5696:
5676:
5667:
5661:
5648:
5642:
5625:
5619:
5604:
5598:
5583:
5580:
5579:
5578:
5575:
5572:
5567:
5566:
5552:
5535:
5515:
5491:
5471:
5459:
5434:
5422:
5396:
5389:
5371:
5359:
5340:
5312:
5300:
5273:(3): 345â356.
5250:
5229:
5208:
5188:
5167:
5150:
5141:
5124:
5108:
5044:
5023:
4999:
4988:on 24 May 2010
4973:
4962:on 24 May 2010
4947:
4938:
4912:
4910:
4907:
4905:
4904:
4899:
4894:
4889:
4884:
4879:
4874:
4869:
4864:
4862:Parasitic drag
4859:
4854:
4849:
4844:
4839:
4834:
4829:
4824:
4819:
4814:
4812:Boundary layer
4809:
4804:
4799:
4794:
4789:
4783:
4781:
4778:
4767:The notion of
4718:potential flow
4706:Main article:
4703:
4700:
4668:flow regimes,
4630:Main article:
4619:
4616:
4595:Main article:
4576:
4573:
4549:Ludwig Prandtl
4528:
4525:
4506:
4502:
4490:boundary layer
4462:
4459:
4455:
4434:
4431:
4430:
4429:
4426:
4423:
4402:
4398:
4371:
4367:
4350:
4347:
4335:
4334:
4320:
4316:
4304:
4290:
4287:
4283:
4263:air resistance
4250:
4247:
4231:
4228:
4224:
4198:
4194:
4190:
4187:
4184:
4181:
4178:
4152:
4149:
4143:
4140:
4136:
4131:
4125:
4122:
4118:
4113:
4108:
4104:
4079:
4075:
4071:
4068:
4041:
4021:
3999:
3995:
3990:
3987:
3984:
3981:
3978:
3975:
3970:
3965:
3932:
3908:
3887:
3884:
3881:
3878:
3875:
3872:
3841:
3832:. For a given
3819:
3815:
3812:
3809:
3804:
3800:
3796:
3793:
3790:
3784:
3779:
3775:
3763:
3762:
3750:
3740:
3726:
3722:
3702:
3692:
3680:
3670:
3656:
3652:
3641:
3629:
3605:
3599:
3595:
3591:
3587:
3584:
3580:
3576:
3573:
3569:
3563:
3559:
3555:
3551:
3546:
3542:
3538:
3535:
3532:
3526:
3523:
3520:
3517:
3514:
3503:
3502:
3489:
3478:
3466:
3439:
3435:
3432:
3429:
3424:
3419:
3391:Main article:
3369:
3366:
3347:
3343:
3322:
3300:
3296:
3275:
3253:
3249:
3228:
3206:
3202:
3181:
3160:
3155:
3150:
3147:
3142:
3138:
3124:
3103:
3096:
3091:
3088:
3085:
3081:
3075:
3072:
3067:
3062:
3058:
3044:
3023:
3017:
3014:
3009:
3006:
3000:
2995:
2991:
2984:
2981:
2974:
2970:
2966:
2963:
2957:
2954:
2951:
2948:
2945:
2942:
2937:
2934:
2901:
2895:
2892:
2887:
2884:
2878:
2873:
2869:
2862:
2859:
2852:
2848:
2844:
2841:
2835:
2832:
2806:
2801:
2797:
2793:
2790:
2787:
2784:
2781:
2767:
2758:
2747:
2740:
2732:asymptotically
2708:
2704:
2699:
2692:
2688:
2682:
2678:
2672:
2668:
2663:
2660:
2656:
2652:
2645:
2641:
2637:
2632:
2628:
2624:
2621:
2616:
2612:
2608:
2605:
2602:
2599:
2596:
2580:
2576:
2561:
2557:
2552:
2545:
2541:
2535:
2531:
2525:
2521:
2518:
2515:
2508:
2504:
2500:
2495:
2491:
2487:
2484:
2479:
2475:
2471:
2468:
2465:
2462:
2459:
2446:
2439:
2429:
2428: = v
2410:
2401:
2397:
2393:
2390:
2385:
2382:
2379:
2372:
2367:
2363:
2348:
2340:asymptotically
2312:
2308:
2300:
2297:
2292:
2287:
2283:
2279:
2276:
2269:
2265:
2261:
2258:
2249:
2245:
2241:
2238:
2233:
2230:
2227:
2220:
2217:
2214:
2211:
2208:
2169:Main article:
2166:
2163:
2148:
2144:
2121:
2117:
2092:
2088:
2082:
2078:
2072:
2068:
2064:
2059:
2055:
2051:
2048:
2045:
2040:
2036:
2029:
2026:
2020:
2014:
2010:
2005:
2000:
1995:
1990:
1985:
1981:
1947:
1943:
1939:
1934:
1930:
1926:
1920:
1917:
1911:
1907:
1903:
1898:
1893:
1888:
1883:
1879:
1862:
1859:
1849:
1842:
1828:
1821:
1766:
1763:
1757:
1753:
1746:
1742:
1737:
1730:
1727:
1720:
1714:
1710:
1695:quadratic drag
1657:Main article:
1654:
1651:
1636:
1632:
1628:
1603:
1598:
1594:
1590:
1585:
1582:
1572:
1568:
1562:
1558:
1552:
1549:
1544:
1540:
1517:
1513:
1490:
1486:
1459:
1455:
1429:
1424:
1420:
1416:
1409:
1405:
1400:
1397:
1389:
1385:
1379:
1375:
1369:
1366:
1361:
1356:
1352:
1346:
1342:
1338:
1332:
1327:
1292:
1288:
1265:
1261:
1238:
1234:
1211:
1207:
1186:
1183:
1180:
1177:
1174:
1171:
1165:
1160:
1133:
1130:
1125:
1121:
1098:
1094:
1071:
1067:
1055:
1054:
1041:
1019:
993:
982:
965:
961:
957:
954:
951:
948:
941:
937:
933:
930:
927:
924:
918:
915:
912:
907:
903:
891:
877:
873:
850:
846:
822:
798:
775:
770:
766:
763:
760:
754:
749:
745:
742:
736:
731:
727:
712:
711:
689:
685:
674:
658:
648:
636:
626:
610:
600:
582:
578:
554:
548:
544:
537:
533:
528:
521:
518:
511:
505:
501:
473:
462:
459:
418:Parasitic drag
413:Parasitic drag
411:Main article:
408:
407:Parasitic drag
405:
364:, such as the
343:Main article:
340:
337:
335:
332:
331:
330:
327:
320:
318:
315:
308:
306:
303:
296:
293:
292:
289:
276:
258:
228:
225:
221:parasitic drag
208:
207:
197:
181:
180:
177:
174:
166:
165:
162:
159:
151:
150:
147:
144:
136:
135:
132:
129:
121:
120:
115:
110:
103:
100:
99:
98:
94:
93:
86:
65:
62:
30:fluid dynamics
15:
9:
6:
4:
3:
2:
5806:
5795:
5792:
5790:
5787:
5786:
5784:
5775:
5772:
5770:
5767:
5764:
5761:
5758:
5755:
5753:
5750:
5749:
5740:
5736:
5732:
5728:
5726:
5722:
5718:
5714:
5711:
5707:
5703:
5699:
5693:
5689:
5685:
5681:
5677:
5673:
5668:
5664:
5658:
5654:
5649:
5645:
5639:
5634:
5633:
5626:
5622:
5616:
5612:
5611:
5605:
5601:
5595:
5591:
5586:
5585:
5576:
5573:
5570:
5569:
5561:
5559:
5557:
5548:
5545:
5539:
5531:
5528:
5525:
5519:
5504:
5498:
5496:
5487:
5484:
5478:
5476:
5468:
5463:
5447:
5446:
5438:
5432:
5426:
5411:
5407:
5400:
5392:
5390:9780080928593
5386:
5382:
5375:
5368:
5363:
5357:
5353:
5350:
5344:
5329:
5325:
5324:
5316:
5307:
5305:
5296:
5292:
5288:
5284:
5280:
5276:
5272:
5268:
5261:
5254:
5247:
5243:
5240:
5239:
5233:
5226:
5222:
5219:
5218:
5212:
5205:
5201:
5195:
5193:
5185:
5181:
5177:
5171:
5164:
5163:0 7106 0426 2
5160:
5154:
5145:
5138:
5137:0 13 339060 8
5134:
5128:
5122:
5118:
5112:
5097:
5093:
5089:
5085:
5081:
5077:
5072:
5067:
5063:
5059:
5055:
5048:
5033:
5027:
5009:
5003:
4987:
4983:
4977:
4961:
4957:
4951:
4942:
4927:
4923:
4917:
4913:
4903:
4900:
4898:
4895:
4893:
4890:
4888:
4885:
4883:
4880:
4878:
4875:
4873:
4870:
4868:
4865:
4863:
4860:
4858:
4855:
4853:
4850:
4848:
4845:
4843:
4840:
4838:
4835:
4833:
4832:Drag equation
4830:
4828:
4825:
4823:
4820:
4818:
4817:CoandÄ effect
4815:
4813:
4810:
4808:
4805:
4803:
4800:
4798:
4795:
4793:
4790:
4788:
4785:
4784:
4777:
4776:very large).
4774:
4770:
4765:
4763:
4759:
4754:
4752:
4748:
4744:
4740:
4736:
4732:
4728:
4723:
4722:inviscid flow
4719:
4715:
4709:
4699:
4697:
4692:
4690:
4686:
4681:
4679:
4675:
4671:
4666:
4662:
4658:
4654:
4649:
4647:
4641:
4639:
4633:
4624:
4615:
4612:
4608:
4604:
4598:
4590:
4586:
4581:
4572:
4570:
4566:
4565:undercarriage
4562:
4558:
4554:
4553:Melvill Jones
4550:
4546:
4542:
4538:
4534:
4524:
4522:
4504:
4500:
4491:
4486:
4483:
4479:
4478:
4460:
4457:
4453:
4444:
4440:
4427:
4424:
4421:
4420:
4419:
4416:
4400:
4396:
4387:
4369:
4365:
4357:, symbolized
4356:
4346:
4344:
4340:
4318:
4314:
4305:
4288:
4285:
4281:
4272:
4271:
4270:
4268:
4264:
4260:
4256:
4246:
4229:
4226:
4222:
4211:
4196:
4192:
4188:
4185:
4182:
4179:
4176:
4150:
4147:
4141:
4138:
4134:
4129:
4123:
4120:
4116:
4111:
4106:
4102:
4093:
4077:
4073:
4069:
4066:
4057:
4055:
4039:
4019:
4010:
3997:
3988:
3985:
3982:
3979:
3976:
3973:
3968:
3953:
3948:
3946:
3930:
3922:
3921:Stokes radius
3906:
3885:
3882:
3879:
3876:
3873:
3870:
3862:
3858:
3853:
3839:
3817:
3813:
3810:
3802:
3798:
3794:
3791:
3782:
3777:
3773:
3748:
3741:
3724:
3721:
3700:
3693:
3678:
3671:
3654:
3650:
3642:
3627:
3620:
3619:
3618:
3603:
3597:
3593:
3589:
3585:
3582:
3578:
3574:
3571:
3567:
3561:
3557:
3553:
3544:
3540:
3536:
3533:
3524:
3518:
3512:
3479:
3464:
3457:
3456:
3455:
3452:
3433:
3430:
3427:
3422:
3407:
3404:
3400:
3394:
3386:
3382:
3378:
3374:
3365:
3361:
3345:
3341:
3320:
3298:
3294:
3273:
3251:
3247:
3226:
3204:
3200:
3179:
3158:
3153:
3148:
3145:
3140:
3136:
3127:
3121:in metre and
3120:
3115:
3101:
3094:
3089:
3086:
3083:
3079:
3073:
3070:
3065:
3060:
3056:
3047:
3040:
3035:
3021:
3015:
3012:
3007:
3004:
2998:
2993:
2989:
2982:
2979:
2972:
2968:
2964:
2961:
2955:
2949:
2943:
2940:
2935:
2932:
2922:
2918:
2913:
2899:
2893:
2890:
2885:
2882:
2876:
2871:
2867:
2860:
2857:
2850:
2846:
2842:
2839:
2833:
2830:
2822:
2817:
2804:
2799:
2795:
2791:
2785:
2779:
2770:
2766:
2761:
2757:
2752:
2750:
2743:
2737:
2734:tends to the
2733:
2729:
2725:
2720:
2706:
2702:
2697:
2690:
2686:
2680:
2676:
2670:
2666:
2661:
2658:
2654:
2650:
2643:
2639:
2635:
2630:
2626:
2622:
2619:
2614:
2610:
2606:
2600:
2594:
2586:
2573:
2559:
2555:
2550:
2543:
2539:
2533:
2529:
2523:
2519:
2516:
2513:
2506:
2502:
2498:
2493:
2489:
2485:
2482:
2477:
2473:
2469:
2463:
2457:
2449:
2442:
2435:
2427:
2422:
2408:
2399:
2395:
2391:
2388:
2383:
2380:
2377:
2370:
2365:
2361:
2353:
2351:
2345:
2341:
2336:
2334:
2330:
2324:
2310:
2306:
2298:
2295:
2290:
2285:
2281:
2277:
2274:
2267:
2263:
2259:
2256:
2247:
2243:
2239:
2236:
2231:
2228:
2225:
2218:
2212:
2206:
2198:
2194:
2190:
2186:
2177:
2172:
2162:
2146:
2142:
2119:
2115:
2105:
2090:
2086:
2080:
2070:
2066:
2062:
2057:
2053:
2046:
2043:
2038:
2034:
2027:
2024:
2018:
2003:
1998:
1988:
1983:
1979:
1969:
1967:
1963:
1945:
1941:
1937:
1932:
1928:
1924:
1918:
1915:
1909:
1901:
1896:
1886:
1881:
1877:
1868:
1858:
1856:
1852:
1845:
1837:
1835:
1831:
1824:
1817:
1812:
1810:
1806:
1801:
1799:
1795:
1794:frontal area,
1791:
1788:is often the
1787:
1782:
1780:
1764:
1761:
1755:
1751:
1744:
1740:
1735:
1728:
1725:
1718:
1712:
1708:
1699:
1698:
1696:
1691:
1687:
1683:
1682:drag equation
1675:
1660:
1659:Drag equation
1650:
1634:
1630:
1626:
1601:
1596:
1592:
1588:
1583:
1580:
1570:
1566:
1560:
1556:
1550:
1547:
1542:
1538:
1515:
1511:
1488:
1484:
1475:
1457:
1453:
1445:
1427:
1422:
1418:
1414:
1407:
1403:
1398:
1395:
1387:
1383:
1377:
1373:
1367:
1364:
1359:
1354:
1350:
1344:
1336:
1325:
1316:
1312:
1307:
1290:
1286:
1263:
1259:
1236:
1232:
1209:
1205:
1184:
1181:
1178:
1175:
1172:
1169:
1158:
1149:
1131:
1128:
1123:
1119:
1096:
1092:
1069:
1065:
1039:
1017:
1008:
991:
983:
963:
955:
952:
949:
939:
931:
928:
925:
916:
913:
910:
905:
901:
892:
875:
871:
848:
844:
836:
820:
812:
796:
789:
788:
787:
773:
768:
764:
761:
758:
752:
747:
743:
740:
734:
729:
725:
717:
709:
705:
687:
683:
675:
672:
656:
649:
634:
627:
625:of the fluid,
624:
608:
601:
598:
580:
576:
568:
567:
566:
552:
546:
542:
535:
531:
526:
519:
516:
509:
503:
499:
490:
489:drag equation
482:
479:
472:
467:
458:
456:
455:gliding range
452:
447:
443:
438:
433:
431:
427:
423:
419:
414:
404:
402:
398:
394:
390:
385:
383:
379:
375:
371:
367:
363:
359:
355:
352:(also called
351:
346:
324:
319:
312:
307:
300:
295:
294:
290:
288:
287:surface waves
284:
280:
277:
274:
270:
266:
262:
259:
257:
253:
252:planing hulls
249:
245:
242:
241:
240:
238:
234:
224:
222:
216:
214:
205:
201:
198:
195:
194:pressure drag
191:
188:
187:
186:
178:
175:
172:
168:
167:
163:
160:
157:
153:
152:
148:
145:
142:
138:
137:
133:
130:
127:
123:
122:
116:
111:
108:
107:
96:
95:
91:
87:
84:
81:
77:
74:
71:
70:
69:
61:
59:
54:
49:
47:
43:
39:
35:
31:
26:
22:
5730:
5717:Aerodynamics
5716:
5713:L. J. Clancy
5683:
5671:
5652:
5631:
5609:
5589:
5582:Bibliography
5547:
5544:
5538:
5530:
5527:
5524:
5518:
5506:. Retrieved
5486:
5483:
5462:
5450:. Retrieved
5444:
5437:
5430:
5425:
5413:. Retrieved
5409:
5399:
5380:
5374:
5367:Air friction
5362:
5343:
5332:, retrieved
5328:the original
5322:
5315:
5270:
5266:
5253:
5237:
5232:
5216:
5211:
5203:
5170:
5153:
5144:
5127:
5111:
5099:. Retrieved
5061:
5058:Eur. J. Phys
5057:
5047:
5035:. Retrieved
5026:
5014:. Retrieved
5002:
4990:. Retrieved
4986:the original
4976:
4964:. Retrieved
4960:the original
4950:
4941:
4929:. Retrieved
4925:
4916:
4872:Ram pressure
4847:Lift (force)
4837:Gravity drag
4766:
4755:
4735:Saint-Venant
4716:proved that
4711:
4693:
4688:
4684:
4682:
4677:
4673:
4669:
4664:
4660:
4656:
4652:
4650:
4645:
4642:
4638:aerodynamics
4635:
4610:
4606:
4602:
4600:
4588:
4584:
4569:Carnot cycle
4530:
4520:
4487:
4480:
4476:
4442:
4436:
4417:
4355:Induced drag
4352:
4336:
4262:
4258:
4255:aerodynamics
4252:
4249:Aerodynamics
4212:
4094:
4058:
4011:
3952:Stokes' drag
3949:
3854:
3764:
3504:
3453:
3408:
3402:
3398:
3396:
3381:Stokes' drag
3377:Trajectories
3362:
3122:
3118:
3116:
3042:
3038:
3036:
2920:
2916:
2914:
2818:
2768:
2764:
2759:
2755:
2753:
2745:
2738:
2727:
2721:
2574:
2444:
2437:
2433:
2425:
2423:
2346:
2337:
2332:
2326:
2325:
2192:
2188:
2183:
2106:
1970:
1864:
1847:
1840:
1838:
1826:
1819:
1813:
1804:
1802:
1793:
1785:
1783:
1700:
1694:
1693:
1679:
1474:Bejan number
1311:Bejan number
1308:
1278:varies with
1056:
813:. Actually,
713:
596:
486:
480:
470:
434:
429:
425:
421:
417:
416:
386:
377:
373:
362:lifting body
354:induced drag
353:
349:
348:
265:aerodynamics
248:lifting body
233:Douglas DC-3
230:
217:
212:
209:
204:viscous drag
184:
80:hydrodynamic
67:
52:
50:
37:
33:
27:
25:
5410:tec-science
4887:Stokes' law
4822:Drag crisis
4762:steady flow
4751:Stokes' law
4607:power curve
4585:power curve
4339:shock waves
3947:viscosity.
3403:linear drag
3393:Stokes' law
3385:Newton drag
2730:. Velocity
1855:symmetrical
1444:coefficient
374:vortex drag
213:orientation
76:aerodynamic
5783:Categories
5508:28 January
5448:(doctoral)
5184:atmosphere
5037:16 October
5016:16 October
4992:16 October
4966:16 October
4909:References
4787:Added mass
4714:d'Alembert
4597:Drag curve
4267:freestream
2587:function:
1962:horsepower
1809:lift force
1315:drag force
1148:Stokes Law
597:drag force
256:watercraft
53:drag force
5096:118693492
5071:1305.3947
4897:Wave drag
4670:wave drag
4665:bow waves
4653:wave drag
4632:Wave drag
4533:Aristotle
4482:Viscosity
4386:wave drag
4343:viscosity
4189:⋅
4070:⋅
3986:η
3983:π
3977:−
3931:η
3883:η
3880:π
3799:ρ
3795:−
3792:ρ
3651:ρ
3628:ρ
3583:−
3575:−
3541:ρ
3537:−
3534:ρ
3431:−
3333:â0.01 m)
3286:â0.05 m)
3128:in m/s.
3095:ρ
3080:ρ
2962:ρ
2956:−
2941:∑
2840:ρ
2834:−
2667:
2659:−
2623:
2520:
2486:
2389:ρ
2278:ρ
2260:
2237:ρ
2047:ρ
2004:⋅
1925:ρ
1902:⋅
1736:ρ
1399:μ
1396:ν
1341:Δ
1179:μ
1176:π
1129:−
1040:ρ
1018:μ
992:ν
929:⋅
917:⋅
811:dimension
769:μ
759:ρ
748:ν
609:ρ
527:ρ
451:endurance
446:wave drag
442:transonic
422:form drag
370:propeller
283:wave drag
273:area rule
261:wave drag
190:form drag
119:friction
5715:(1975),
5682:(2000).
5452:22 March
5352:Archived
5295:11816281
5242:Archived
5221:Archived
5101:23 April
4780:See also
4712:In 1752
4591:airspeed
4557:aircraft
4439:pressure
3239:â0.2 m)
3192:â0.6 m)
2432:at time
2199:(tanh):
2185:Velocity
1197:At high
835:diameter
269:Concorde
64:Examples
5706:1744638
5415:25 June
5275:Bibcode
5165:, p.212
5139:, p.185
5076:Bibcode
4902:Windage
4773:Prandtl
4731:viscous
4614:curve.
4527:History
4269:flow.
3943:is the
3919:is the
3857:viscous
3617:where:
3454:where:
2517:arctanh
1832:of the
1057:At low
1005:is the
702:is the
669:is the
623:density
621:is the
595:is the
40:, is a
5737:
5723:
5704:
5694:
5659:
5640:
5617:
5596:
5387:
5334:18 May
5293:
5161:
5135:
5119:
5094:
4743:Stokes
4739:Navier
4443:exerts
4174:
4171:
4168:
4165:
4162:
4154:
3899:where
3739:), and
2579:> v
2107:Where
1619:where
786:where
565:where
176:â100%
134:â100%
5794:Force
5291:S2CID
5263:(PDF)
5092:S2CID
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