Lift-induced drag - Citizendia

In aerodynamics, lift-induced drag, induced drag, vortex drag, or sometimes drag due to lift, is a drag force which occurs whenever a lifting body or a wing of finite span generates lift. In Fluid dynamics, drag (sometimes called fluid resistance) is the force that resists the movement of a Solid object through a Fluid (a In Physics, a force is whatever can cause an object with Mass to Accelerate. The lifting body is an Aircraft configuration where the body itself produces lift. WING "ESPN 1410" is a commercial AM radio station in Dayton Ohio operating with 5000 watts at 1410 kHz with studios offices and transmitter located on David In the context of a Fluid flow relative to a body the lift force is the component of the Aerodynamic force that is Perpendicular to the flow With other parameters remaining the same, as the angle of attack increases, induced drag increases. Angle of attack ( AOA, \alpha Greek letter alpha) is a term used in Aerodynamics to describe the Angle between the

1 Source of induced drag
2 Reducing Induced drag
3 Calculation of Induced drag
- 3.1 Combined effect with other drag sources
4 See also

Source of induced drag

There is no possible wing of infinite span. The wingspan (or just span) of an airplane or a Bird, is the distance from the left wingtip to the right wingtip However, the characteristics of such a wing can be measured on a section of wing spanning the width of a wind tunnel, since the walls block spanwise flow and create an effectively 2-D flow. A wind tunnel is a research tool developed to assist with studying the effects of air moving over or around solid objects By definition, the reaction force is resolved into two components. That parallel to the incident airflow is the drag and that normal to the incident airflow is the lift. At practical angles of incidence the lift greatly exceeds the drag.

An airfoil produces lift by turning incident airflow around the wing in a "downwards" direction. An airfoil (in American English) or aerofoil (in British English) is the shape of a Wing or blade (of a Propeller, rotor In the context of a Fluid flow relative to a body the lift force is the component of the Aerodynamic force that is Perpendicular to the flow On a wing of finite span some air 'leaks' around the wingtip from the lower surface to the upper surface producing a wingtip vortex. Wingtip vortices are tubes of circulating air which are left behind by the Wing as it generates lift. The vortices created trail behind the wingtips for some distance and can be powerful, producing hazardous conditions for following aircraft flying into them. The deflection of the airflow by the bottom of the wing produces a down flow or 'downwash' behind the wing. The term downwash has two meanings within the field of Aerodynamics. The tip vortices also modify the airflow around the wing, relative to that on a wing of infinite span, reducing the effectiveness of the wing to generate lift, thus requiring a higher angle of attack to compensate and therefore tilting the total reaction force rearwards. The angular deflection is small and has little effect on the lift as defined above. However, there 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. Unlike parasitic drag, induced drag is inversely proportional to the square of the airspeed. Parasitic drag (also called parasite drag) is drag caused by moving a solid object through a fluid

Reducing Induced drag

Induced drag can be minimized by the following means:

Increase the wing span. The effect of the wingtip vortices is greatest near the wing tips. With increased wingspan a lesser portion of the wing is in the most affected region. Increasing span with no other change would increase wing area. In practice, the wing area is kept constant by increasing the aspect ratio rather than the span. In Aerodynamics, the aspect ratio of a wing is defined as the square of the wing span divided by the wing area

Optimise the spanwise load distribution. If the lift is diminished towards the wingtips there is less pressure differential near the wingtips to create wingtip vortices. Minimum induced drag is achieved when the spanwise lift distribution is elliptical. The parameter with greatest effect on lift distribution is the wing planform. A planform or Plan view is a vertical Orthographic projection of an object on a horizontal plane like a Map. Thus, a wing with elliptical planform would have low induced drag. Few aircraft have this planform because of manufacturing complications — the most famous example is the World War II Spitfire. World War II, or the Second World War, (often abbreviated WWII) was a global military conflict which involved a majority of the world's nations, including WikipediaWikiProject Aircraft. Please see WikipediaWikiProject Aircraft/page content for recommended layout Tapered wings with straight leading and trailing edges can approximate to elliptical lift distribution. Typically, straight wings produce between 5–15% more induced drag than an elliptical wing. The lift distribution may also be modified by the use of washout, a spanwise twist of the wing to reduce the incidence towards the wingtips, and by changing the airfoil section near the wingtips. Washout refers to a feature of wing design to deliberately reduce the lift distribution across the span of the Wing of an Aircraft. An airfoil (in American English) or aerofoil (in British English) is the shape of a Wing or blade (of a Propeller, rotor

Provide a physical barrier to vortex formation. Such a barrier might take several forms. Some early aircraft had fins mounted on the tips of the tailplane which served as endplates. More recent aircraft have wingtip mounted winglets to oppose the formation of vortices. Wingtip devices are usually intended to improve the efficiency of Fixed-wing aircraft. Wingtip mounted fuel tanks may also provide some benefit.

Calculation of Induced drag

For a wing with an elliptical lift distribution, induced drag is calculated as follows:

$D_i = \frac{1}{2} \rho V^2 S C_{Di} = \frac{1}{2} \rho_0 V_e^2 S C_{Di}$

where

$C_{Di} = \frac{k C_L^2}{ \pi AR}$ and

$C_L = \frac{L}{ \frac{1}{2} \rho_0 V_e^2 S}$

Thus

$C_{Di} = \frac{k L^2}{\frac{1}{4} \rho_0^2 V_e^4 S^2 \pi AR}$

Hence

$D_i = \frac{k L^2}{\frac{1}{2} \rho_0 V_e^2 S \pi AR}$

Where:

$AR \,$ is the aspect ratio,

$C_{Di} \,$ is the induced drag coefficient,

$C_L \,$ is the lift coefficient,

$D_i \,$ is the induced drag,

$k \,$ is the factor by which the induced drag exceeds that of an elliptical lift distribution, typically 1. In Aerodynamics, the aspect ratio of a wing is defined as the square of the wing span divided by the wing area The drag coefficient ( Cd, Cx or Cw) is a Dimensionless quantity that describes how streamlined an The lift coefficient ( CL or CZ) is a non-dimensional coefficient that relates the lift generated by an Airfoil, the 05 to 1. 15,

$L \,$ is the lift,

$S \,$ is the gross wing area,

$V \,$ is the true airspeed,

$V_e \,$ is the equivalent airspeed,

$\rho \,$ is the air density and

$\rho_0 \,$ is 1. Equivalent airspeed (EAS is the airspeed at sea level which represents the same Dynamic pressure as that flying at the True airspeed (TAS at altitude 225 kg/m³, the air density at sea level, ISA conditions. The International Standard Atmosphere (ISA is an atmospheric model of how the Pressure, Temperature, Density, and Viscosity

Combined effect with other drag sources

Curves showing induced, parasitic, and combined drag vs. airspeed

Induced drag must be added to the parasitic drag to find the total drag. Parasitic drag (also called parasite drag) is drag caused by moving a solid object through a fluid Since induced drag is inversely proportional to the square of the airspeed whereas parasitic drag is proportional to the square of the airspeed, the combined overall drag curve shows a minimum at some airspeed - the minimum drag speed. An aircraft flying at this speed is at its optimal aerodynamic efficiency. The minimum drag speed occurs at the speed where the induced drag is equal to the parasitic drag. This is the speed at which the best gradient of climb, or for unpowered aircraft, minimum gradient of descent, is achieved.

The speed for best endurance, i. e. time in the air, is the speed for minimum fuel flow rate. The fuel flow rate is calculated as the product of the drag or power required and the engine specific fuel consumption. The engine specific fuel consumption will be expressed in units of fuel flow rate per unit of thrust or per unit of power depending on whether the engine generates thrust e. g. a jet engine, or power e. g. a turbo-prop engine.

The speed for best range, i. e. distance travelled, occurs at the speed at which a tangent from the origin touches the fuel flow rate curve. The curve of range versus airspeed is normally very flat and it is customary to operate at the speed for 99% best range since this gives about 5% greater speed for only 1% less range.

Contents

Source of induced drag

Reducing Induced drag

Calculation of Induced drag

Combined effect with other drag sources

See also