Wingtip vorticesA vortex is a spinning, often turbulent,flow of fluid. Any spiral motion with closed streamlines is vortex flow. The motion of the fluid swirling rapidly around a center is called a vortex...
are tubes of circulating air which are left behind a
wingA wing is a surface used to produce lift for flight through the air or another gaseous or fluid medium. The wing shape is usually an airfoil. The word originally referred only to the foremost limbs of birds, but has been extended to include the wings of insects , bats, pterosaurs, and aircraft.A...
as it generates
liftA fluid flowing past the surface of a body exerts a force on it. Lift is defined to be the component of this force that is perpendicular to the oncoming flow direction. It contrasts with the drag force, which is defined to be the component of the fluid-dynamic force parallel to the flow...
. One wingtip
vortexA vortex is a spinning, often turbulent,flow of fluid. Any spiral motion with closed streamlines is vortex flow. The motion of the fluid swirling rapidly around a center is called a vortex...
trails from the
tipA wing tip is the part of the wing that is most distant from the fuselage of a fixed-wing aircraft.Because the wing tip shape influences the size and drag of the wingtip vortices, tip design has produced a diversity of shapes, including:* Squared-off...
of each wing. The cores of vortices spin at very high speed and are regions of very low pressure. To
first approximationIn science, engineering, and other quantitative disciplines, orders of approximation refer to formal or informal terms for how precise an approximation is, and to indicate progressively more refined approximations: in increasing order of precision, a zeroth order approximation, a first order...
, these low-pressure regions form with little exchange of heat with the neighboring regions (i.e.
adiabaticallyIn thermodynamics, an adiabatic process or an isocaloric process is a thermodynamic process in which no heat is transferred to or from the working fluid. The term "adiabatic" literally means impassable, coming from the Greek roots ἀ- , διὰ- , and βαῖνειν ; this etymology corresponds here to an...
), so the local temperature in the low-pressure regions drops, too. If it drops below the local
dew pointThe dew point is the temperature to which a given parcel of air must be cooled, at constant barometric pressure, for water vapor to condense into water. The condensed water is called dew. The dew point is a saturation point...
, there results a condensation of water vapor present in the cores of wingtip vortices, making them visible. The local temperature may even drop below the local
freezing pointFreezing Point is a news journal in the People's Republic of China which has been the subject of controversy over its criticism of Communist Party officials and the sympathetic ear it lent to a Chinese historian who had criticized official history textbooks...
, in which case ice crystals will form inside the cores.
Wingtip vortices are associated with induced drag, an essentially unavoidable side-effect of the wing generating lift. Managing induced drag and wingtip vortices by selecting the best
wing planformA planform or plan view is a vertical orthographic projection of an object on a horizontal plane, like a map.In aviation, a planform is the shape and layout of an airplane's wing and fuselage...
for the mission is critically important in
aerospace engineeringAerospace engineering is the branch of engineering behind the design, construction and science of aircraft and spacecraft. It is broken into two major and overlapping branches: aeronautical engineering and astronautical engineering...
.
Wingtip vortices form the major component of
wake turbulenceWake turbulence is turbulence that forms behind an aircraft as it passes through the air. This turbulence includes various components, the most important of which are wingtip vortices and jetwash. Jetwash refers simply to the rapidly moving gases expelled from a jet engine; it is extremely...
.
Migratory birds take advantage of each others' wingtip vortices by flying in a V formation so that all but the leader are flying in the
upwashthumb|right|300px|The effect of downwash from a hovering helicopter is clearly visible on the surface of water below.The term downwash has two meanings within the field of aerodynamics....
from the wing of the bird ahead. This upwash makes it a bit easier for the bird to support its own weight, reducing fatigue on migration flights.
Some technical writers use the alternative expression "trailing vortices" because these vortices also occur at points other than at the wing tips. They are induced at the outboard tip of the wing flaps and other abrupt changes in
wing planformA planform or plan view is a vertical orthographic projection of an object on a horizontal plane, like a map.In aviation, a planform is the shape and layout of an airplane's wing and fuselage...
.
Cause and effects
A wing generates
aerodynamic liftA fluid flowing past the surface of a body exerts a force on it. Lift is defined to be the component of this force that is perpendicular to the oncoming flow direction. It contrasts with the drag force, which is defined to be the component of the fluid-dynamic force parallel to the flow...
by creating a region of lower air pressure above it. Fluids are forced to flow from high to low pressure and the air below the wing tends to migrate toward the top of the wing via the wingtips. The air does not escape around the leading or trailing edge of the wing due to airspeed, but it can flow around the tip. Consequently, air flows from below the wing and out around the tip to the top of the wing in a circular fashion. This leakage will raise the pressure on top of the wing and reduce the lift that the wing can generate. It also produces an emergent flow pattern with low pressure in the center surrounded by fast-moving air with curved streamlines.
Wingtip vortices only affect the portion of the wing closest to the tip. Thus, the longer the wing, the smaller the affected fraction of it will be. As well, the shorter the
chordIn aeronautics, chord refers to the imaginary straight line joining the trailing edge and the center of curvature of the leading edge of the cross-section of an airfoil...
of the wing, the less opportunity air will have to form vortices. This means that for an aircraft to be most efficient, it should have a very high
aspect ratiothumb|The low aspect ratio wing of a [[Piper PA-28 Cherokee]].In aerodynamics, the aspect ratio of a wing is defined as the square of the wing span divided by the wing area....
. This is evident in the design of
gliderUnpowered aircraft are a group of aerial vehicles that can fly without propulsion. They can be classified as gliders, balloons and kites. In this instance, 'flight' means a trajectory that is not merely a vertical descent such as a parachute. In the case of kites, the flight is not free, but...
s. It is also evident in long-range
airlinerAn airliner is a large fixed-wing aircraft for transporting passengers and cargo. Such planes are owned by airlines....
s, where fuel efficiency is of critical importance. However, increasing the
wingspanThe wingspan of an airplane or a bird, is the distance from the left wingtip to the right wingtip. For example, the Boeing 777 has a wingspan of about ; and a Wandering Albatross caught in 1965 had a wingspan of , the official record for a living bird.The term wingspan, more technically extent,...
reduces the maneuverability of the aircraft, which is why
combatA fighter aircraft is a military aircraft designed primarily for air-to-air combat with other aircraft, as opposed to a bomber, which is designed primarily to attack ground targets by dropping bombs. Fighters are small, fast, and maneuverable...
and
aerobaticAerobatics is the practice of flying maneuvers involving aircraft attitudes that are not used in normal flight. Aerobatics are performed in airplanes and gliders for training, recreation, entertainment and sport...
planes usually feature short, stubby wings despite the efficiency losses.
Another method of reducing fuel consumption is the use of winglets, as seen on some modern airliners such as the
Airbus A340The Airbus A340 is a long-range four-engined wide-body commercial passenger airliner manufactured by Airbus, a subsidiary of EADS. It seats between 261 and 380 passengers, and has a range between 6,700 and 9,000 NM . It is similar in design to the twin-engined A330...
. Winglets work by forcing the vortex to move to the very tip of the wing and allowing the entire span to produce lift, thereby effectively increasing the aspect ratio of the wing. Winglets also change the pattern of
vorticityVorticity is a concept used in fluid dynamics. In the simplest sense, vorticity is the tendency for elements of the fluid to "spin."More formally, vorticity can be related to the amount of "circulation" or "rotation" in a fluid.The average vorticity in a small region of fluid flow is equal to the...
in the core of the vortex pattern, spreading it out and reducing the kinetic energy in the circular air flow, which reduces the amount of fuel expended to perform work by the wing upon the spinning air. Winglets can yield worthwhile economy improvements on long-distance flights.
Visibility of vortices due to water condensation and freezing
The cores of the vortices are sometimes visible because water present in them
condensesCondensation is the change of the physical state of aggregation of matter from gaseous phase into liquid phase and the reverse of evaporation. When the transition happens from the gaseous phase into the solid phase directly, bypassing the liquid phase, the change is called deposition...
from
gasThis page is about the physical properties of gas as a state of matter. For the uses of gases, and other meanings, see Gas .A gas is one of four states of matter. Near absolute zero, a substance exists as a solid...
(
vaporA vapor or vapour is a substance in the gas phase at a temperature lower than its critical temperature....
) to
liquidLiquid is one of the principal states of matter. A liquid is a fluid that has the particles loose and can freely form a distinct surface at the boundaries of its bulk material. The surface is a free surface where the liquid is not constrained by a container....
, and sometimes even freezes, forming ice particles.
The
phaseIn the physical sciences, a phase is a region of space , throughout which all physical properties of a material are essentially uniform. Examples of physical properties include density, index of refraction, and chemical composition...
of water (i.e. whether it assumes the form of a solid, liquid, or gas) is determined by its
temperatureIn physics, temperature is a physical property of a system that underlies the common notions of hot and cold; something that feels hotter generally has the higher temperature. Temperature is one of the principal parameters of thermodynamics...
and
pressurePressure is the force per unit area applied in a direction perpendicular to the surface of an object. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure.- Definition :...
. For example, in the case of liquid-gas transition, at each pressure there is a special “transition temperature” such that if the sample temperature is even a little above , the sample will be a gas, but if the sample temperature is even a little below , the sample will be a liquid; see
phase transitionA phase transition is a natural physical process. It has the characteristic of taking a given medium with given properties and transforming some or all of that medium, into a new medium with new properties. Phase transitions occur frequently and are found everywhere in the natural world...
. For example, at the standard atmospheric pressure, is 100 °C = 212 °F. The transition temperature decreases with decreasing pressure (which explains why water boils at lower temperatures at higher altitudes and at higher temperatures in a pressure cooker; see here for more information). In the case of water vapor in air, the corresponding to the
partial pressureIn a mixture of ideal gases, each gas has a partial pressure which is the pressure which the gas would have if it alone occupied the volume. The total pressure of a gas mixture is the sum of the partial pressures of each individual gas in the mixture....
of water vapor is called the
dew pointThe dew point is the temperature to which a given parcel of air must be cooled, at constant barometric pressure, for water vapor to condense into water. The condensed water is called dew. The dew point is a saturation point...
. (The solid-liquid transition also happens around a specific transition temperature called the
melting pointThe melting point of a solid is the temperature range at which it changes state from solid to liquid. At the melting point the solid and liquid phase exist in equilibrium. When considered as the temperature of the reverse change from liquid to solid, it is referred to as the freezing point...
. For most substances, the melting point also decreases with decreasing pressure, although water ice in particular---in its
Ih formIce I
h is the hexagonal crystal form of ordinary ice, or frozen water. Virtually all ice in the biosphere is ice I
h, with the exception only of a small amount of ice I
c which is occasionally present in the upper atmosphere...
, which is the most familiar one---is a prominent
exception to this ruleWater is the most abundant molecule on Earth's surface, constituting about 70% of the planet's surface. In nature it exists in liquid, solid, and gaseous states. It is in dynamic equilibrium between the liquid and gas states at standard temperature and pressure. At room temperature, it is a nearly...
.)
Vortex cores are regions of low pressure. As a vortex core begins to form, the water in the air (in the region that is about to become the core) is in vapor phase, which means that the local temperature is above the local dew point. After the vortex core forms, the pressure inside it has decreased from the ambient value, and so the local dew point has dropped from the ambient value. Thus,
in and of itself, a drop in pressure would tend to keep water in vapor form: the initial dew point was already below the ambient air temperature, and the formation of the vortex has made the local dew point even lower. However, as the vortex core forms, its pressure (and so its dew point) is not the only property that is dropping: the vortex-core temperature is dropping also, and in fact it can drop by much more than the dew point does, as we now explain.
Here we follow the discussion in Ref. . To
first approximationIn science, engineering, and other quantitative disciplines, orders of approximation refer to formal or informal terms for how precise an approximation is, and to indicate progressively more refined approximations: in increasing order of precision, a zeroth order approximation, a first order...
, the formation of vortex cores is
thermodynamicallyIn physics, thermodynamics is the study of the conversion of energy into work and heat and its relation to macroscopic variables such as temperature, volume and pressure...
an
adiabatic processIn thermodynamics, an adiabatic process or an isocaloric process is a thermodynamic process in which no heat is transferred to or from the working fluid. The term "adiabatic" literally means impassable, coming from the Greek roots ἀ- , διὰ- , and βαῖνειν ; this etymology corresponds here to an...
, i.e. one with no exchange of heat. In such a process, the drop in pressure is accompanied by a drop in temperature, according to the equation
Here and are the
absolute temperatureThermodynamic temperature is the absolute measure of temperature and is one of the principal parameters of thermodynamics. Thermodynamic temperature is an “absolute” scale because it is the measure of the fundamental property underlying temperature: its null or zero point, absolute zero, is the...
and pressure at the beginning of the process (here equal to the ambient air temperature and pressure), and are the absolute temperature and pressure in the vortex core (which is the end result of the process), and the constant is about 7/5 = 1.4 for air (see here).
Thus, even though the local dew point inside the vortex cores is even lower than in the ambient air, the water vapor may nevertheless condense—if the formation of the vortex brings the local temperature below the new local dew point. Let us verify that this can indeed happen under realistic conditions.
For a typical transport aircraft landing at an airport, these conditions are as follows: we may take and to have values corresponding to the so-called standard conditions, i.e. = 1
atmThe standard atmosphere is an international reference pressure defined as 101,325 Pa and formerly used as unit of pressure . For practical purposes it has been replaced by the bar which is 100,000 Pa...
= 1013.25
mbThe bar is a unit of pressure equal to 100 kilopascals, and rougly equal to the atmospheric pressure on Earth at sea level. Other units derived from the bar are the decibar , centibar , and millibar...
= 101325
PaThe pascal is the SI derived unit of pressure, stress, Young's modulus and tensile strength. It is a measure of force per unit area, defined as one newton per square metre...
and = 293.15 K (which is 20 °C = 68 °F). We will take the
relative humidityRelative humidity is a term used to describe the amount of water vapor that exists in a gaseous mixture of air and water vapor.- Definition :...
to be a comfortable 35% (dew point of 4.1 °C = 39.4 °F). This corresponds to a
partial pressureIn a mixture of ideal gases, each gas has a partial pressure which is the pressure which the gas would have if it alone occupied the volume. The total pressure of a gas mixture is the sum of the partial pressures of each individual gas in the mixture....
of water vapor of 820 Pa = 8.2 mb. We will assume that in a vortex core, the pressure drops to about 80% of the ambient pressure, i.e. to about 80 000 Pa.
Let us first determine the temperature in the vortex core. It is given by the equation above as or 0.86 °C = 33.5 °F.
Next, we determine the dew point in the vortex core. The partial pressure of water in the vortex core drops in proportion to the drop in the total pressure (i.e. by the same percentage), to about 650 Pa = 6.5 mb. According to a dew point calculator at
this site (alternatively one may use the
Antoine equationThe Antoine equationis a vapor pressure equation and describes the relation between vapour pressure and temperature for pure components. The Antoine equation is derived from the Clausius-Clapeyron relation.-The equation:...
to obtain an approximate value), that partial pressure results in the local dew point of about 0.86 °C; in other words, the new local dew point is about equal to the new local temperature.
Therefore, the case we have been considering is a marginal case; if the relative humidity of the ambient air were even a bit higher (with the total pressure and temperature remaining as above), then the local dew point inside the vortices would rise, while the local temperature would remain the same as what we have just found. Thus the local temperature would now be
lower than the local dew point, and so the water vapor inside the vortices would indeed condense. Under right conditions, the local temperature in vortex cores may drop below the local
freezing pointFreezing Point is a news journal in the People's Republic of China which has been the subject of controversy over its criticism of Communist Party officials and the sympathetic ear it lent to a Chinese historian who had criticized official history textbooks...
, in which case ice particles will form inside the vortex cores.
We have just seen that the water-vapor condensation mechanism in wingtip vortices is driven by local changes in air pressure and temperature. This is to be contrasted to what happens in another well-known case of water condensation related to airplanes: the
contrailContrails or vapour trails are visible trails of condensed water vapour made by the exhaust of aircraft engines. As the hot exhaust gases cool in the surrounding air they may precipitate a cloud of microscopic water droplets...
s from airplane engine exhausts. In the case of contrails, the local air pressure and temperature do not change significantly; what matters instead is that the exhaust contains both water vapor (which increases the local water-vapor
concentrationIn chemistry, concentration is the measure of how much of a given substance there is mixed with another substance. This can apply to any sort of chemical mixture, but most frequently the concept is limited to homogeneous solutions, where it refers to the amount of solute in the solvent.To...
and so its partial pressure, resulting in elevated dew point and freezing point) as well as
aerosolsTechnically, an aerosol is a suspension of fine solid particles or liquid droplets in a gas. Examples are smoke, oceanic haze, air pollution, smog and CS gas. In general conversation, aerosol usually refers to an aerosol spray can or the output of such a can...
(which provide
nucleation centersNucleation is the extremely localized budding of a distinct thermodynamic phase. Some examples of phases that may form via nucleation in liquids are gaseous bubbles, crystals, or glassy regions. Creation of liquid droplets in saturated vapor is also characterized by nucleation...
for the condensation and freezing).
Condensation of water vapor in wing tip vortices is most common on aircraft flying at high
angles of attackAngle of attack is a term used in fluid dynamics to describe the angle between a reference line on a body and the vector representing the relative motion between the body and the fluid through which it is moving. In general, the reference line could be any line on any arbitrarily shaped body in...
, such as fighter aircraft in high
gThe g-force experienced by an object is its acceleration relative to free-fall. The term g-force is considered a misnomer, as g-force is not a force but an acceleration....
maneuvers, or
airlinerAn airliner is a large fixed-wing aircraft for transporting passengers and cargo. Such planes are owned by airlines....
s taking off and landing on humid days.
Hazards
Wingtip vortices can also pose a severe hazard to light aircraft, especially during the
landingthumb|right|A [[Mute Swan]] alighting. Note the ruffled feathers on top of the wings indicate that the swan is flying at the [[Stall |stall]]ing speed...
and
take off"Take Off" is the first official single from Young Dro's second studio album P.O.L.O. . The song features Yung L.A. and is produced by Raz for Beat Billionaires. The song was leaked on November 11, 2008, but was officially released on iTunes on March 17, 2009.-Music Video:The video was shot on...
phases of flight. The intensity or strength of the vortex is a function of aircraft size, speed, and configuration (flap setting, etc.). The strongest vortices are produced by heavy aircraft, flying slowly, with
wing flapsFlaps are hinged surfaces on the trailing edge of the wings of a fixed-wing aircraft. As flaps are extended, the stalling speed of the aircraft is reduced, which means that the aircraft can fly safely at slower speeds...
retracted (Heavy, slow, and clean). Large
jet aircraftA jet aircraft is an aircraft propelled by jet engines. Jet aircraft generally fly much faster than propeller-powered aircraft and at higher altitudes — as high as 10,000 to 15,000 meters . At these altitudes, jet engines achieve maximum efficiency over long distances...
can generate vortices which are larger than an entire light aircraft. These vortices can persist for many minutes, drifting with the wind. The hazardous aspects of wingtip vortices are most often discussed in the context of
wake turbulenceWake turbulence is turbulence that forms behind an aircraft as it passes through the air. This turbulence includes various components, the most important of which are wingtip vortices and jetwash. Jetwash refers simply to the rapidly moving gases expelled from a jet engine; it is extremely...
. If a light aircraft is immediately preceded by a heavy aircraft, wake turbulence from the heavy aircraft can roll the light aircraft faster than can be resisted by use of ailerons. At low altitudes, particularly during takeoff and landing, this can lead to an upset from which recovery is not possible.
Air traffic controllerAir traffic controllers are the people who operate the air traffic control systems to expedite and maintain a safe and orderly flow of air traffic and help prevent mid-air collisions. They apply separation rules to keep aircraft apart from each other in their area of responsibility and move all...
s attempt to ensure an adequate separation between departing and arriving aircraft, particularly where a heavy aircraft is preceding a light aircraft by issuing wake turbulence cautions. For example, a controller may state, "Acey 5523 caution wake turbulence preceding heavy 767 departing. Position and hold runway 8R." The aircraft will then hold for approximately 3 minutes on the runway, and then will be issued a takeoff clearance, as in "Acey 5523, fly runway heading, cleared for takeoff runway 8R."
See also
- Aspect ratio
thumb|The low aspect ratio wing of a [[Piper PA-28 Cherokee]].In aerodynamics, the aspect ratio of a wing is defined as the square of the wing span divided by the wing area....
- Contrail
Contrails or vapour trails are visible trails of condensed water vapour made by the exhaust of aircraft engines. As the hot exhaust gases cool in the surrounding air they may precipitate a cloud of microscopic water droplets...
- Helmholtz's theorems
In fluid mechanics, Helmholtz's theorems describe the three-dimensional motion of fluid in the vicinity of vortex filaments. These theorems apply to inviscid flows and flows where the influence of viscous forces is small and can be ignored....
- Horseshoe vortex
The horseshoe vortex model is a simplified representation of the vortex system of a wing. In this model the wing vorticity is modelled by a bound vortex of constant circulation, travelling with the wing, and two trailing vortices, therefore having a shape vaguely reminiscent of a horseshoe...
- V formation
- Von Kármán vortex street
A Kármán vortex street is a term in fluid dynamics for a repeating pattern of swirling vortices caused by the unsteady separation of flow of a fluid over bluff bodies...
- Vortex
A vortex is a spinning, often turbulent,flow of fluid. Any spiral motion with closed streamlines is vortex flow. The motion of the fluid swirling rapidly around a center is called a vortex...
- Vortex shedding
Vortex shedding is an unsteady flow that takes place in special flow velocities . In this flow, vortices are created at the back of the body and detach periodically from either side of the body. See Von Kármán vortex street.Vortex shedding is caused when a fluid flows past a blunt object...
External links
- Video from NASA
The National Aeronautics and Space Administration is an agency of the United States government, responsible for the nation's public space program. NASA was established by the National Aeronautics and Space Act on July 29, 1958, replacing its predecessor, the National Advisory Committee for...
's Dryden Flight Research CenterThe Dryden Flight Research Center , located inside Edwards Air Force Base, is an aeronautical research center operated by NASA. On March 26, 1976 it was named in honor of the late Hugh L. Dryden, a prominent aeronautical engineer who at the time of his death in 1965 was NASA's deputy administrator...
tests on wingtip vortices:
- Wind prediction for analysis of vortex drift
- Flares released by an air force jet form a "smoke angel"