961:
1004:). An aircraft flying at this speed is operating at its optimal aerodynamic efficiency. According to the above equations, the speed for minimum drag occurs at the speed where the induced drag is equal to the parasitic drag. This is the speed at which for unpowered aircraft, optimum glide angle is achieved. This is also the speed for greatest range (although V
1074:
The engine specific fuel consumption is normally expressed in units of fuel flow rate per unit of thrust or per unit of power depending on whether the engine output is measured in thrust, as for a jet engine, or shaft horsepower, as for a propeller engine. To convert fuel rate per unit thrust to fuel
1016:
since this gives 3-5% greater speed for only 1% less range. Flying higher where the air is thinner will raise the speed at which minimum drag occurs, and so permits a faster voyage for the same amount of fuel. If the plane is flying at the maximum permissible speed, then there is an altitude at which
483:
From this equation it is clear that the induced drag varies with the square of the lift; and inversely with the square of the equivalent airspeed; and inversely with the square of the wingspan. Deviation from the non-planar wing with elliptical lift distribution are taken into account by dividing the
203:
at a high angle of attack will generate an aerodynamic reaction force with a high drag component. By increasing the speed and reducing the angle of attack, the lift generated can be held constant while the drag component is reduced. At the optimum angle of attack, total drag is minimised. If speed is
1020:
The speed for maximum endurance (i.e. time in the air) is the speed for minimum fuel flow rate, and is always less than the speed for greatest range. The fuel flow rate is calculated as the product of the power required and the engine specific fuel consumption (fuel flow rate per unit of power). The
220:
The vortices reduce the wing's ability to generate lift, so that it requires a higher angle of attack for the same lift, which tilts the total aerodynamic force rearwards and increases the drag component of that force. The angular deflection is small and has little effect on the lift. However, there
216:
When producing lift, air below the wing is at a higher pressure than the air pressure above the wing. On a wing of finite span, this pressure difference causes air to flow from the lower surface, around the wingtip, towards the upper surface. This spanwise flow of air combines with chordwise flowing
153:
191:
Lift is produced by the changing direction of the flow around a wing. The change of direction results in a change of velocity (even if there is no speed change), which is an acceleration. To change the direction of the flow therefore requires that a force be applied to the fluid; the total
1446:
Winglets, which are small, nearly vertical, winglike surfaces mounted at the tips of a wing, are intended to provide, for lifting conditions and subsonic Mach numbers, reductions in drag coefficient greater than those achieved by a simple wing-tip extension with the same structural weight
1512:
936:
the wing area is held constant, then induced drag will be inversely proportional to aspect ratio. However, since wingspan can be increased while decreasing aspect ratio, or vice versa, the apparent relationship between aspect ratio and induced drag does not always hold.
641:
164:" is the actual lift on the wing; it is perpendicular to the effective relative airflow in the vicinity of the wing. The lift generated by the wing has been tilted rearwards through an angle equal to the downwash angle in three-dimensional flow. The component of "L
995:
Induced drag must be added to the parasitic drag to find the total drag. Since induced drag is inversely proportional to the square of the airspeed (at a given lift) whereas parasitic drag is proportional to the square of the airspeed, the combined overall
135:
For a constant amount of lift, induced drag can be reduced by increasing airspeed. A counter-intuitive effect of this is that, up to the speed-for-minimum-drag, aircraft need less power to fly faster. Induced drag is also reduced when the
339:
221:
is an increase in the drag equal to the product of the lift force and the angle through which it is deflected. Since the deflection is itself a function of the lift, the additional drag is proportional to the square of the lift.
1008:
will decrease as the plane consumes fuel and becomes lighter). The speed for greatest range (i.e. distance travelled) is the speed at which a straight line from the origin is tangent to the fuel flow rate curve.
720:
987:
His experiments were carried out at relatively low airspeeds, slower than the speed for minimum drag. He observed that, at these low airspeeds, increasing speed required reducing power. (At higher airspeeds,
932:
wing will produce less induced drag than a wing of low aspect ratio. While induced drag is inversely proportional to the square of the wingspan, not necessarily inversely proportional to aspect ratio,
1017:
the air density will be sufficient to keep it aloft while flying at the angle of attack that minimizes the drag. The optimum altitude will increase during the flight as the plane becomes lighter.
774:
516:
1395:
With infinite span, fluid motion is 2-D and in the direction of flow perpendicular to the span. Infinite span can, for example, be simulated using a foil completely spanning a wind tunnel.
397:
884:
segment (or a 2D wing) would experience no induced drag. The drag characteristics of a wing with infinite span can be simulated using an airfoil segment the width of a
91:
427:
454:
217:
air, which twists the airflow and produces vortices along the wing trailing edge. Induced drag is the cause of the vortices; the vortices do not cause induced drag.
855:
130:
824:
801:
477:
367:
504:
176:
acting on a body is usually thought of as having two components, lift and drag. By definition, the component of force parallel to the oncoming flow is called
250:
160:
in the vicinity of the wing. The grey vertical line labeled "L" is the force required to counteract the weight of the aircraft. The red vector labeled "L
899:
to reduce the induced drag. Winglets also provide some benefit by increasing the vertical height of the wing system. Wingtip mounted fuel tanks and wing
895:
used curved trailing edges on their rectangular wings. Some early aircraft had fins mounted on the tips. More recent aircraft have wingtip-mounted
1365:
952:
is the largest component of total drag, at almost 48%. Reducing induced drag can therefore significantly reduce cost and environmental impact.
648:
976:
published the results of his experiments on various flat plates. At the same airspeed and the same angle of attack, plates with higher
876:
According to the equations above, for wings generating the same lift, the induced drag is inversely proportional to the square of the
914:
wing of a given span. A small number of aircraft have a planform approaching the elliptical — the most famous examples being the
868:. Similar methods can also be used to compute the minimum induced drag for non-planar wings or for arbitrary lift distributions.
1122:
1678:
1644:
1602:
1346:
1254:
510:
To compare with other sources of drag, it can be convenient to express this equation in terms of lift and drag coefficients:
636:{\displaystyle C_{D,i}={\frac {D_{\text{i}}}{{\frac {1}{2}}\rho _{0}V_{E}^{2}S}}={\frac {C_{L}^{2}}{\pi A\!\!{\text{R}}e}}}
731:
1300:
1716:
1547:
1459:
1410:
1388:
1324:
1202:
1182:
948:
speed, induced drag is the second-largest component of total drag, accounting for approximately 37% of total drag.
1100:
193:
1770:
830:
This indicates how, for a given wing area, high aspect ratio wings are beneficial to flight efficiency. With
1012:
The curve of range versus airspeed is normally very shallow and it is customary to operate at the speed for
1780:
1438:
A design approach and selected wind-tunnel results at high subsonic speeds for wing-tip mounted winglets
1436:
1013:
1755:
977:
1453:
1040:
891:
An increase in wingspan or a solution with a similar effect is one way to reduce induced drag. The
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404:
438:
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833:
8:
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For a two-dimensional wing at low Mach numbers, the drag contains no induced or wave drag
865:
808:
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777:
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351:
102:
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1734:
Invariant
Formulation for the Minimum Induced Drag Conditions of Nonplanar Wing Systems
1726:
1359:
1226:
949:
941:
911:
900:
489:
334:{\displaystyle D_{\text{i}}={\frac {L^{2}}{{\frac {1}{2}}\rho _{0}V_{E}^{2}\pi b^{2}}}}
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Marine rudders and control surfaces : principles, data, design and applications
992:
came to dominate, causing the power required to increase with increasing airspeed.)
1636:
Taking Flight: Inventing the Aerial Age, from
Antiquity Through the First World War
1590:
1490:
1055:
922:
225:
39:
1704:
1668:
1634:
1170:
925:. For modern wings with winglets, the ideal lift distribution is not elliptical.
907:
892:
858:
185:
1594:
1670:
The Bird Is on the Wing: Aerodynamics and the
Progress of the American Airplane
1045:
1035:
989:
973:
965:
896:
141:
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1612:
1269:
16:
Type of aerodynamic resistance against the motion of a wing or other airfoil
1480:
by Daniel O. Dommasch, Sydney S. Sherby, Thomas F. Connolly, 3rd ed. (1961)
1197:, Figure 3.29, Ninth edition. Longman Scientific & Technical, England.
981:
915:
205:
55:
51:
35:
1732:
Luciano Demasi, Antonio Dipace, Giovanni
Monegato, and Rauno Cavallaro.
885:
200:
1383:(1st ed.). Amsterdam: Elsevier/Butterworth-Heinemann. p. 41.
1234:. 2005 Boeing Performance and Flight Operations Engineering Conference.
997:
224:
The vortices created are unstable, and they quickly combine to produce
204:
increased beyond this, total drag will increase again due to increased
152:
1050:
63:
1737:
1379:
Molland, Anthony F. (2007). "Physics of control surface operation".
715:{\displaystyle C_{L}={\frac {L}{{\frac {1}{2}}\rho _{0}V_{E}^{2}S}}}
1249:(Sixth ed.). New York, NY: McGraw-Hill Education. p. 20.
877:
857:
being a function of angle of attack, induced drag increases as the
157:
137:
881:
180:; and the component perpendicular to the oncoming flow is called
59:
43:
1405:
1403:
1673:. College Station: Texas A&M University Press. p. 23.
984:
and experienced lower drag than those with lower aspect ratio.
168:" parallel to the free stream is the induced drag on the wing.
1536:"Control of Turbulent Flows for Skin Friction Drag Reduction"
1520:
1400:
1736:, AIAA Journal, Vol. 52, No. 10 (2014), pp. 2223–2240.
1286:
1284:
1282:
1000:
shows a minimum at some airspeed - the minimum drag speed (V
1123:"Why Aspect Ratio doesn't Matter – Understanding Aerospace"
47:
955:
456:
is the ratio of circumference to diameter of a circle, and
1293:
1279:
240:
wing with an elliptical lift distribution, induced drag D
46:
coming at it. This drag force occurs in airplanes due to
42:
force that occurs whenever a moving object redirects the
1534:
Coustols, Eric (1996). Meier, GEA; Schnerr, GH (eds.).
105:
72:
1021:
power required is equal to the drag times the speed.
836:
811:
788:
734:
651:
519:
492:
464:
441:
407:
377:
354:
253:
1721:
Abbott, Ira H., and Von
Doenhoff, Albert E. (1959),
769:{\displaystyle A\!\!{\text{R}}={\frac {b^{2}}{S}}\,}
156:
Induced drag is related to the angle of the induced
1434:
1751:Doug McLean, Common Misconceptions in Aerodynamics
1444:(Technical report). NASA. 19760019075. p. 1:
849:
818:
795:
768:
714:
635:
498:
471:
448:
421:
391:
361:
333:
124:
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1101:"Bjorn's Corner: Aircraft drag reduction, Part 3"
1075:rate per unit power one must divide by the speed.
739:
738:
621:
620:
1762:
1540:Control of Flow Instabilities and Unsteady Flows
1228:Wingtip Devices: What They Do and How They Do It
1517:Special Course on Skin Friction Drag Reduction
231:
1639:. Oxford University Press, USA. p. 147.
1511:Robert, JP (March 1992). Cousteix, J (ed.).
1474:The Elements of Aerofoil and Airscrew Theory
908:the elliptical spanwise distribution of lift
399:is the standard density of air at sea level,
1575:"Drag Reduction: A Major Task for Research"
1341:(Sixth ed.). Waltham, MA. p. 61.
1098:
1364:: CS1 maint: location missing publisher (
1513:"Drag reduction: an industrial challenge"
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910:produces the minimum induced drag for a
871:
864:The above equation can be derived using
151:
1632:
1626:
1579:Aerodynamic Drag Reduction Technologies
1378:
1372:
1238:
1120:
1094:
1092:
956:Combined effect with other drag sources
1763:
1711:, Pitman Publishing Limited, London.
1666:
1660:
1510:
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1224:
1111:
880:. A wing of infinite span and uniform
1572:
1563:
1504:
1339:Aerodynamics for engineering students
1207:
1177:. Pitman Publishing Limited, London.
1153:
1089:
188:the lift greatly exceeds the drag.
62:wings that redirect air to cause a
13:
1729:, Standard Book Number 486-60586-8
1476:(1926); referenced in Fig. 5.4 of
14:
1792:
1743:
1435:Richard T. Whitcomb (July 1976).
196:of the fluid acting on the wing.
1150:, Figure 1.30, NAVWEPS 00-80T-80
1121:Illsley, Michael (4 July 2017).
228:which trail behind the wingtip.
192:aerodynamic force is simply the
1698:
1633:Hallion, Richard (8 May 2003).
1483:
1466:
1428:
1337:Houghton, E. L. (2012). "1.6".
1309:
1272:, and Von Doenhoff, Albert E.,
1148:Aerodynamics for Naval Aviators
1068:
903:may also provide some benefit.
1263:
1245:Anderson, John D. Jr. (2017).
1187:
1140:
928:For a given wing area, a high
826:is the span efficiency factor.
244:can be calculated as follows:
147:
1:
1458:: CS1 maint: date and year (
1276:, Section 1.2 and Appendix IV
1082:
866:Prandtl's lifting-line theory
140:is higher, or for wings with
96:lift-induced drag coefficient
1581:. Springer. pp. 17–27.
1247:Fundamentals of aerodynamics
7:
1595:10.1007/978-3-540-45359-8_3
1099:Bjorn Fehrm (Nov 3, 2017).
1024:
392:{\displaystyle \rho _{0}\,}
232:Calculation of induced drag
211:
10:
1797:
1411:"Induced Drag Coefficient"
1315:Anderson, John D. (2005),
940:For a typical twin-engine
1667:Hansen, James R. (2004).
1577:. In Peter Thiede (ed.).
803:is a reference wing area,
484:induced drag by the span
86:{\textstyle D_{\text{i}}}
54:redirecting air to cause
1491:"Skybrary: Induced Drag"
1061:
1041:Oswald efficiency number
1723:Theory of Wing Sections
1274:Theory of Wing Sections
1127:Understanding Aerospace
422:{\displaystyle V_{E}\,}
1738:doi: 10.2514/1.J052837
1317:Introduction to Flight
1193:Kermode, A.C. (1972).
969:
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637:
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450:
449:{\displaystyle \pi \,}
423:
393:
363:
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126:
87:
66:. It is symbolized as
58:and also in cars with
1771:Aircraft aerodynamics
1573:Marec, J.-P. (2001).
1478:Airplane Aerodynamics
1291:McLean, Doug (2012).
1225:McLean, Doug (2005).
963:
872:Reducing induced drag
852:
850:{\displaystyle C_{L}}
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1519:. AGARD Report 786.
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125:{\textstyle C_{D,i}}
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1587:2001adrt.conf...17M
1195:Mechanics of Flight
1146:Hurt, H. H. (1965)
819:{\displaystyle e\,}
796:{\displaystyle S\,}
705:
612:
586:
472:{\displaystyle b\,}
431:equivalent airspeed
362:{\displaystyle L\,}
314:
1781:Gliding technology
1727:Dover Publications
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950:Skin friction drag
942:wide-body aircraft
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1680:978-1-58544-243-0
1646:978-0-19-516035-2
1604:978-3-642-07541-4
1348:978-0-08-096632-8
1256:978-1-259-12991-9
1031:Aerodynamic force
980:produced greater
968:plus induced drag
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499:{\displaystyle e}
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174:aerodynamic force
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32:drag due to lift,
20:Lift-induced drag
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1744:External links
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1014:99% best range
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974:Samuel Langley
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1699:Bibliography
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1669:
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1578:
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148:Explanation
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172:The total
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1447:penalty.
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1025:See also
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