: 4.9įor a given wing area, a high aspect ratio wing will produce less induced drag than a wing of low aspect ratio. For modern wings with winglets, the ideal lift distribution is not elliptical. A small number of aircraft have a planform approaching the elliptical - the most famous examples being the World War II Spitfire and Thunderbolt. Typically, the elliptical spanwise distribution of lift produces the minimum induced drag for a planar wing of a given span. : 4.10 Wingtip mounted fuel tanks and wing washout may also provide some benefit. Winglets also provide some benefit by increasing the vertical height of the wing system. More recent aircraft have wingtip-mounted winglets to reduce the induced drag. Some early aircraft had fins mounted on the tips. : 4.10 The Wright brothers used curved trailing edges on their rectangular wings. Īn increase in wingspan or a solution with a similar effect is only way to reduce induced drag. The drag characteristics of a wing with infinite span can be simulated using an airfoil segment the width of a wind tunnel. A wing of infinite span and uniform airfoil segment (or a 2D wing) would experience no induced drag. Reducing induced drag Īccording to the equations above, for wings generating the same lift, the induced drag is inversely proportional to the square of the wingspan. Similar methods can also be used to compute the minimum induced drag for non-planar wings or for arbitrary lift distributions.
The above equation can be derived using Prandtl's lifting-line theory. : Section 5.14 Calculation of induced drag įor a planar wing with an elliptical lift distribution, induced drag D i can be calculated as follows:ĭ i = L 2 1 2 ρ 0 V E 2 π b 2 being a function of angle of attack, induced drag increases as the angle of attack increases. The vortices created are unstable, and they quickly combine to produce wingtip vortices which trail behind the wingtip. Since the deflection is itself a function of the lift, the additional drag is proportional to the square of the lift. However, there is an increase in the drag equal to the product of the lift force and the angle through which it is deflected. The angular deflection is small and has little effect on the lift. 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. Induced drag is the cause of the vortices the vortices do not cause induced drag. : 8.1.1 This spanwise flow of air combines with chordwise flowing air, which twists the airflow and produces vortices along the wing trailing edge. On a wing of finite span, this pressure difference causes air to flow from the lower surface, around the wingtip, towards the upper surface. When producing lift, air below the wing is at a higher pressure than the air pressure above the wing. If speed is increased beyond this, total drag will increase again due to increased profile drag. At the optimum angle of attack, total drag is minimised. By increasing the speed and reducing the angle of attack, the lift generated can be held constant while the drag component is reduced. To change the direction of the flow therefore requires that a force be applied to the fluid the total aerodynamic force is simply the reaction force of the fluid acting on the wing.Īn aircraft in slow flight at a high angle of attack will generate an aerodynamic reaction force with a high drag component. The change of direction results in a change of velocity (even if there is no speed change), which is an acceleration. Lift is produced by the changing direction of the flow around a wing. : Section 5.3 At practical angles of attack the lift greatly exceeds the drag. By definition, the component of force parallel to the oncoming flow is called drag and the component perpendicular to the oncoming flow is called lift. The total aerodynamic force acting on a body is usually thought of as having two components, lift and drag.
Drag airplane free#
The component of "L eff" parallel to the free stream is the induced drag on 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 red vector labeled "L eff" is the actual lift on the wing it is perpendicular to the effective relative airflow in the vicinity of the wing. The grey vertical line labeled "L" is the force required to counteract the weight of the aircraft. Induced drag is related to the angle of the induced downwash in the vicinity of the wing.
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