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EspañolLIFT (FORCE)
The 'lift force', 'lifting force' or simply 'lift' is a mechanical force generated by solid objects as they move through a fluid.[1]
While many types of objects can generate lift, the most common and familiar object in this category is the airfoil, a relatively flat object of which the common airplane wing is an example. For the sake of simplicity, this article will discuss lift primarily in the context of airfoils and wings.
Technically, lift is the sum of all the fluid dynamic forces on a body perpendicular to the direction of the external flow approaching that body. The mathematical equations describing lift have been well established since the Wright Brothers experimentally determined a reasonably precise value for the "Smeaton coefficient" more than 100 years ago,[2] but the practical explanation of what those equations mean is still controversial, with persistent misinformation and pervasive misunderstanding.[3]
Sometimes the term 'dynamic lift' or 'dynamic lifting force' is used for the perpendicular force resulting from motion of the body in the fluid, as in an aerodyne, in contrast to the static lifting force resulting from buoyancy, as in an aerostat. Lift is commonly associated with the wing of an aircraft. However there are many other examples of lift such as propellers on both aircraft and boats, rotors on helicopters, sails and keels on sailboats, hydrofoils, wings on auto racing cars, and wind turbines. While the common meaning of the term "lift" suggests an upward action, the lift force is not necessarily directed up with respect to gravity.
Lift is generated when an object turns a fluid away from its direction of flow. When the object and fluid move relative to each other, the object turns the fluid flow in a direction perpendicular to that flow, and the force required to do this creates an equal and opposite force that is lift. The object may be moving through a stationary fluid, or the fluid may be flowing past a stationary object—the effect is the same in both cases.
In the case of an aircraft wing, the wing turns the passing flow of air downward towards the ground as it passes. The force required to do this engenders an equal and opposite force that is lift, and this latter force supports the aircraft in the air.
The lift generated by an airfoil depends on such factors as the speed of the airflow, the density of the air, the total area of the airfoil, and the ''angle of attack.'' The angle of attack is the angle at which the airfoil meets the oncoming airflow (or vice versa). A symmetric airfoil must have a positive angle of attack to generate positive lift. At a zero angle of attack, no lift is generated. At a negative angle of attack, negative lift is generated. A cambered airfoil may produce positve lift at zero, or even small negative angles of attack.
The basic concept of lift is simple. However, the details of how the relative movement of air and airfoil interact to produce the turning action that generates lift are complex. Below are several explanations of lift, all of which are different but equivalent descriptions of the same phenomenon from different viewpoints.
Lift is created as the fluid flow is deflected by an airfoil or other body. The force created by this acceleration of the fluid creates an equal and opposite force according to Newton's third law of motion. Air deflected downward by an aircraft wing, or helicopter rotor, generating lift is known as downwash.
It is important to note that the acceleration of air flowing over an aircraft wing does not just involve the air molecules "bouncing off" the lower surface. Rather, air molecules closely follow both the top and bottom surfaces, and the airflow is deflected downward when the wing is producing lift. The acceleration of the air during the creation of lift can also been described as a "turning" of the airflow.
Many shapes, such as a flat plate set at an angle to the flow, will produce lift. This can be demonstrated simply by holding a sheet of paper at an angle in front of you as you move forward. However, lift generation by most shapes will be very inefficient and create a great deal of drag. One of the primary goals of airfoil design is to devise a shape that produces the most lift while producing the least Form drag.
It is possible to measure lift using the reaction model. The force acting on the wing is the negative of the time-rate-of-change of the momentum of the air. In a wind tunnel, the speed and direction of the air can be measured (using, for example, a Pitot tube or Laser Doppler velocimetry) and the lift calculated. Alternately, the force on the wind tunnel itself can be measured as the equal and opposite forces to those acting on the test body.
The force on the wing can also be examined in terms of the pressure differences above and below the wing, which can be related to velocity changes by
Bernoulli's principle.
The total force (Lift + Drag) is the integral of pressure over the contour of the wing:
where:
★ 'L' is the Lift,
★ 'D' is the Drag,
★ is the frontier of the domain,
★ ''p'' is the value of the pressure,
★ 'n' is the normal to the profile.
Since it is a two-dimensional vector equation, and since lift is perpendicular to drag, this equation suffices to predict both lift and drag. The drag component is Lift-induced drag rather than Form drag.
This equation is always exactly true, by the definition of force and pressure.
One method for calculating the pressure is Bernoulli's equation, which is the mathematical expression of Bernoulli's principle. This method ignores the effects of viscosity, which can be important in the boundary layer and to predict drag, though it has only a small effect on lift calculations.
Bernoulli's principle states that in fluid flow, an increase in velocity occurs simultaneously with decrease in pressure. It is named for the Dutch-Swiss mathematician and scientist Daniel Bernoulli, though it was previously understood by Leonhard Euler and others. In a fluid flow with no viscosity, and therefore one in which a pressure difference is the only accelerating force, it is equivalent to Newton's laws of motion.
Bernoulli's principle also describes the Venturi effect that is used in carburetors and elsewhere. In a carburetor, air is passed through a Venturi tube in order to decrease its pressure. This happens because the air velocity has to increase as it flows through the constriction.
In order to solve for the velocity of inviscid flow around a wing, the Kutta condition must be applied to simulate the effects of inertia and viscosity. The Kutta condition allows for the correct choice among an infinite number of flow solutions that otherwise obey the laws of conservation of mass and conservation of momentum.
Some lay versions of this explanation use false information due to lack of understanding the Kutta condition, such as the incorrect assumption that the two parcels of air which separate at the leading edge of a wing must meet again at the trailing edge. There is no reason that a parcel of air on one side of the wing must rejoin a neighboring parcel with which it was originally synchronized on the other side. In fact, the requirement for circulation (see below) in order to generate non-zero lift specifies that parcels must never meet.
A third way to calculate lift is to determine the mathematical quantity called circulation; (this concept is sometimes applied approximately to wings of large aspect ratio as "lifting-line theory"). Again, it is mathematically equivalent to the two explanations above. It is often used by practising aerodynamicists as a convenient quantity in calculations, see say thin-airfoil theory.
The circulation is the line integral of the velocity of the air, in a closed loop around the boundary of an airfoil. It can be understood as the total amount of "spinning" (or vorticity) of air around the airfoil. When the circulation is known, the section lift can be calculated using the following equation:
:
where is the air density, is the free-stream airspeed, and is the circulation. This is sometimes known as the 'Kutta-Joukowski Theorem.'
A similar equation applies to the sideways force generated around a spinning object, the Magnus effect, though here the necessary circulation is induced by the mechanical rotation, rather than aerofoil action.
The Helmholtz theorem states that circulation is conserved; put simply this is conservation of the air's angular momentum. When an aircraft is at rest, there is no circulation. As the flow speed increases (that is, the aircraft accelerates in the air-body-fixed frame), a vortex, called the starting vortex, forms at the trailing edge of the airfoil, due to viscous effects in the boundary layer. Eventually the vortex detaches from the airfoil and gets swept away from it rearward. The circulation in the starting vortex is equal in magnitude and opposite in direction to the circulation around the airfoil. Theoretically, the starting vortex remains connected to the vortex bound in the airfoil, through the wing-tip vortices, forming a closed circuit. In reality, the starting vortex is dissipated by a number of effects, as are the wing-tip vortices far behind the aircraft. However, the net circulation in "the world" is still zero as the circulation from the vortices is transferred to the surroundings as they dissipate. (Note that despite being an idealisation of the real world, the 'vortex system' set up round a wing is both real and observable, and is one of the reasons that a light aircraft cannot take off immediately after a jumbo jet.)
One misconception encountered in a number of explanations of lift is the "equal transit time" fallacy. This fallacy states that the parcels of air which are divided by an airfoil must rejoin again; because of the greater curvature (and hence longer path) of the upper surface of an airfoil, the air going over the top must go faster in order to "catch up" with the air flowing around the bottom.
Although it is true that the air moving over the top of the wing is moving faster (when the effective angle of attack is positive) there is no requirement for equal transit time. In fact if the air above and below an airfoil has equal transit time, there is no circulation, and therefore no lift. Only if the air flowing above has a ''shorter'' transit time than the air flowing below, is upward lift produced, along with downward deflection of the air behind the wing and a vortex at each wing tip. Wind tunnel smoke streamline pictures reveal these flow features.[4][5]
A further flaw in this explanation is that it requires an airfoil to have a curvature in order to create lift. In fact, a thin, flat plate inclined to a flow of fluid also generates lift.[6][7]
It is unclear why this explanation has gained such currency, except by repetition by authors of populist (rather than rigorously scientific) books and perhaps the fact that the explanation is easiest to grasp intuitively without mathematics. At least one common flight training book depicts the equal transit fallacy, adding to the confusion.[8]
Albert Einstein, in attempting to design a practical aircraft based on this principle, came up with an airfoil section that featured a large hump on its upper surface, on the basis that an even longer path must aid lift if the principle is true. Its performance was terrible. Herr Dr Prof Albert Who? Einstein the Aerodynamicist, That's Who!, , Peter, Grosz, WWI Aero,
There are two techniques for increasing the lift on an airfoil. One is to decrease the pressure on the side of the airfoil normal to the direction of the desired lift and the other is to increase the pressure on the other side. (The latter is the primary cause of the lift of a paper airplane.) In order to generate lift one must create a pressure differential between the top and bottom of the airfoil.
The Coandă effect is the name given to the tendency of an airflow, under some conditions, to deflect toward a surface that curves away from the flow direction. This effect is caused by the decreased pressure on the curved surface where it curves away from the flow.
Jef Raskin and a few others have observed that the Coandă effect accounts for part of the lift generated by an airfoil. The decrease in pressure above the airfoil is caused by the interaction of the flow, at the microscopic level, with the curved surface. The effect is caused by a decrease of the pressure on the top of the wing as air particles are blown away from the surface (fewer particles, less pressure due to thermal molecular motion). This contributes to the pressure field under the integral sign in the lift equation.
For large angles of attack and/or high flow rates the Coandă effect results in vortices which may impinge normally on the surface thus increasing the pressure there. Under these circumstances the wing will lose lift and ultimately stall. This aspect of the Coandă effect has been used successfully in the design of the wings in Formula One race cars to pressurize the back of the car and partially offset drag.
For supersonic airplanes to be able to maintain lift at the low speeds necessary for safe landings on aircraft carriers, the stall-producing vortices must be dissipated. This is effected by blowing the boundary layer and other lift augmentation devices.
Some airliners exploit the Coandă effect by deploying slats at the leading edge of the wing. On takeoff when maximum lift is needed at low air speed, the slat moves away from the leading edge leaving a slot which allows some of the high pressure air from the bottom of the wing to blow up over the top of the wing, thus creating a lifting Coandă effect by disrupting vortices that would form there on takeoff. Another use of the Coandă effect to produce lift is the use of Fowler flaps, the aerodynamic surfaces that are deployed from the wing's trailing edge on takeoff and landing. These flaps in effect extend the curved surface of the wing. This extension utilizes the Coandă effect to decrease the pressure on the top of the wing and also "dams" the air as it passes under the wing thus increasing the pressure there. The latter is done at the expense of an increased drag but at the low speeds of takeoff and landing, the increased lift is much more beneficial than the increased drag is detrimental.
The Coandă effect provides one aspect of the lift generated on subsonic airfoils.
Many web sites claim that an airfoil can be analyzed as a Venturi nozzle. The mass flow rate through a Venturi nozzle is constant, so the air must flow faster over the top of the wing. Therefore, there is a lower pressure over the top of the wing, producing lift. However, a Venturi nozzle requires that air is squeezed between surfaces. While this situation does exist with "infinite wing" experiments in wind tunnels, in an aircraft the top of a wing is only one surface. The air is not confined above the wing, therefore a wing is not a Venturi nozzle and it is incorrect to analyze it as such.
The lift coefficient is a dimensionless number. When the lift coefficient is known, for instance from tables of airfoil data, lift can be calculated using the ''Lift Equation'':
:
where:
★ is the ''lift coefficient''
★ is the density of air (1.225 kg/m³ at sea level)
★
★ ''V'' is the freestream velocity, that is the speed of the lifting surface relative to the atmosphere far enough away to be unaffected by the surface
★ ''A'' is the projected (planform) surface area of the lifting surface
★ ''L'' is the lift force produced
This equation can be used in any consistent system. For instance, if the density is measured in kilograms per cubic metre, the velocity is measured in metres per second, and the area is measured in square metres, the lift will be calculated in newtons. Or, if the density is in slugs per cubic foot, the velocity is in feet per second, and the area is in square feet, the resulting lift will be in pounds force.
★
Compare with: Drag equation.
★ Drag force
★ Lift-induced drag
★ Lift-to-drag ratio
1. What is Lift?
2. The Bishop's Boys : A Life of Wilbur and Orville Wright, , Tom D., Crouch, W. W. Norton, 1989,
3. How do airplanes fly, really? : A Staff Report by the Straight Dope Science Advisory Board aerodave
4. http://user.uni-frankfurt.de/~weltner/Flight/PHYSIC4.htm
5. http://www.av8n.com/how/htm/airfoils.html
6. http://www.av8n.com/how/htm/airfoils.html#sec-thin-wings
7.
What Does Keep Them Up There? Kenneth Chang
8. The Student Pilot's Flight Manual, , William K., Kershner, , 1979,
★ ''Quest for an improved explanation of lift'' Jaako Hoffren (Helsinki Univ. of Technology, Espoo, Finland) AIAA-2001-872 Aerospace Sciences Meeting and Exhibit, 39th, Reno, NV, Jan. 8-11, 2001 This paper focuses on a physics-based explanation of lift. Calculation of lift based on circulation with artificially imposed Kutta condition is interpreted as a mathematical model, having limited "real-world" physics, resulting from the assumption of potential flow. Also the role of viscosity is discussed. Author's claim is that viscosity is not important for lift generation.
★ ''Introduction to Flight'', John D. Anderson, Jr., McGraw-Hill, ISBN 0-07-299071-6. The author is the Curator of Aerodynamics at the National Air & Space Museum Smithsonian Institute and Professor Emeritus at the University of Maryland.
★ ''Understanding Flight'', by David Anderson and Scott Eberhardt, McGraw-Hill, ISBN 0-07-136377-7. The authors are a physicist and an aeronautical engineer. They explain flight in non-technical terms and specifically address the equal-transit-time myth. Turning of the flow around the wing is attributed to the Coanda effect, which is quite controversial.
★ ''Fundamentals of Flight'', Richard S. Shevell, Prentice-Hall International Editions, ISBN 0-13-332917-8. This book is primarily intended as a text for a one semester undergraduate course in mechanical or aeronautical engineering, although its sections on theory of flight are understandable with a passing knowledge of calculus and physics.
★ Discussion of the apparent "conflict" between the various explanations of lift
★ NASA tutorial, with animation, describing lift
★ Explanation of Lift with animation of fluid flow around an airfoil
★ An treatment of why and how wings generate lift that focuses on pressure.
★ Physics of Flight - reviewed. Online paper by Prof. Dr. Klaus Weltner.
While many types of objects can generate lift, the most common and familiar object in this category is the airfoil, a relatively flat object of which the common airplane wing is an example. For the sake of simplicity, this article will discuss lift primarily in the context of airfoils and wings.
Overview
Technically, lift is the sum of all the fluid dynamic forces on a body perpendicular to the direction of the external flow approaching that body. The mathematical equations describing lift have been well established since the Wright Brothers experimentally determined a reasonably precise value for the "Smeaton coefficient" more than 100 years ago,[2] but the practical explanation of what those equations mean is still controversial, with persistent misinformation and pervasive misunderstanding.[3]
Sometimes the term 'dynamic lift' or 'dynamic lifting force' is used for the perpendicular force resulting from motion of the body in the fluid, as in an aerodyne, in contrast to the static lifting force resulting from buoyancy, as in an aerostat. Lift is commonly associated with the wing of an aircraft. However there are many other examples of lift such as propellers on both aircraft and boats, rotors on helicopters, sails and keels on sailboats, hydrofoils, wings on auto racing cars, and wind turbines. While the common meaning of the term "lift" suggests an upward action, the lift force is not necessarily directed up with respect to gravity.
Physical explanation
Lift is generated when an object turns a fluid away from its direction of flow. When the object and fluid move relative to each other, the object turns the fluid flow in a direction perpendicular to that flow, and the force required to do this creates an equal and opposite force that is lift. The object may be moving through a stationary fluid, or the fluid may be flowing past a stationary object—the effect is the same in both cases.
In the case of an aircraft wing, the wing turns the passing flow of air downward towards the ground as it passes. The force required to do this engenders an equal and opposite force that is lift, and this latter force supports the aircraft in the air.
The lift generated by an airfoil depends on such factors as the speed of the airflow, the density of the air, the total area of the airfoil, and the ''angle of attack.'' The angle of attack is the angle at which the airfoil meets the oncoming airflow (or vice versa). A symmetric airfoil must have a positive angle of attack to generate positive lift. At a zero angle of attack, no lift is generated. At a negative angle of attack, negative lift is generated. A cambered airfoil may produce positve lift at zero, or even small negative angles of attack.
The basic concept of lift is simple. However, the details of how the relative movement of air and airfoil interact to produce the turning action that generates lift are complex. Below are several explanations of lift, all of which are different but equivalent descriptions of the same phenomenon from different viewpoints.
Reaction due to deflection
Lift is created as the fluid flow is deflected by an airfoil or other body. The force created by this acceleration of the fluid creates an equal and opposite force according to Newton's third law of motion. Air deflected downward by an aircraft wing, or helicopter rotor, generating lift is known as downwash.
It is important to note that the acceleration of air flowing over an aircraft wing does not just involve the air molecules "bouncing off" the lower surface. Rather, air molecules closely follow both the top and bottom surfaces, and the airflow is deflected downward when the wing is producing lift. The acceleration of the air during the creation of lift can also been described as a "turning" of the airflow.
Many shapes, such as a flat plate set at an angle to the flow, will produce lift. This can be demonstrated simply by holding a sheet of paper at an angle in front of you as you move forward. However, lift generation by most shapes will be very inefficient and create a great deal of drag. One of the primary goals of airfoil design is to devise a shape that produces the most lift while producing the least Form drag.
It is possible to measure lift using the reaction model. The force acting on the wing is the negative of the time-rate-of-change of the momentum of the air. In a wind tunnel, the speed and direction of the air can be measured (using, for example, a Pitot tube or Laser Doppler velocimetry) and the lift calculated. Alternately, the force on the wind tunnel itself can be measured as the equal and opposite forces to those acting on the test body.
Bernoulli's principle
The force on the wing can also be examined in terms of the pressure differences above and below the wing, which can be related to velocity changes by
Bernoulli's principle.
The total force (Lift + Drag) is the integral of pressure over the contour of the wing:
where:
★ 'L' is the Lift,
★ 'D' is the Drag,
★ is the frontier of the domain,
★ ''p'' is the value of the pressure,
★ 'n' is the normal to the profile.
Since it is a two-dimensional vector equation, and since lift is perpendicular to drag, this equation suffices to predict both lift and drag. The drag component is Lift-induced drag rather than Form drag.
This equation is always exactly true, by the definition of force and pressure.
One method for calculating the pressure is Bernoulli's equation, which is the mathematical expression of Bernoulli's principle. This method ignores the effects of viscosity, which can be important in the boundary layer and to predict drag, though it has only a small effect on lift calculations.
Bernoulli's principle states that in fluid flow, an increase in velocity occurs simultaneously with decrease in pressure. It is named for the Dutch-Swiss mathematician and scientist Daniel Bernoulli, though it was previously understood by Leonhard Euler and others. In a fluid flow with no viscosity, and therefore one in which a pressure difference is the only accelerating force, it is equivalent to Newton's laws of motion.
Bernoulli's principle also describes the Venturi effect that is used in carburetors and elsewhere. In a carburetor, air is passed through a Venturi tube in order to decrease its pressure. This happens because the air velocity has to increase as it flows through the constriction.
In order to solve for the velocity of inviscid flow around a wing, the Kutta condition must be applied to simulate the effects of inertia and viscosity. The Kutta condition allows for the correct choice among an infinite number of flow solutions that otherwise obey the laws of conservation of mass and conservation of momentum.
Some lay versions of this explanation use false information due to lack of understanding the Kutta condition, such as the incorrect assumption that the two parcels of air which separate at the leading edge of a wing must meet again at the trailing edge. There is no reason that a parcel of air on one side of the wing must rejoin a neighboring parcel with which it was originally synchronized on the other side. In fact, the requirement for circulation (see below) in order to generate non-zero lift specifies that parcels must never meet.
Circulation
A third way to calculate lift is to determine the mathematical quantity called circulation; (this concept is sometimes applied approximately to wings of large aspect ratio as "lifting-line theory"). Again, it is mathematically equivalent to the two explanations above. It is often used by practising aerodynamicists as a convenient quantity in calculations, see say thin-airfoil theory.
The circulation is the line integral of the velocity of the air, in a closed loop around the boundary of an airfoil. It can be understood as the total amount of "spinning" (or vorticity) of air around the airfoil. When the circulation is known, the section lift can be calculated using the following equation:
:
where is the air density, is the free-stream airspeed, and is the circulation. This is sometimes known as the 'Kutta-Joukowski Theorem.'
A similar equation applies to the sideways force generated around a spinning object, the Magnus effect, though here the necessary circulation is induced by the mechanical rotation, rather than aerofoil action.
The Helmholtz theorem states that circulation is conserved; put simply this is conservation of the air's angular momentum. When an aircraft is at rest, there is no circulation. As the flow speed increases (that is, the aircraft accelerates in the air-body-fixed frame), a vortex, called the starting vortex, forms at the trailing edge of the airfoil, due to viscous effects in the boundary layer. Eventually the vortex detaches from the airfoil and gets swept away from it rearward. The circulation in the starting vortex is equal in magnitude and opposite in direction to the circulation around the airfoil. Theoretically, the starting vortex remains connected to the vortex bound in the airfoil, through the wing-tip vortices, forming a closed circuit. In reality, the starting vortex is dissipated by a number of effects, as are the wing-tip vortices far behind the aircraft. However, the net circulation in "the world" is still zero as the circulation from the vortices is transferred to the surroundings as they dissipate. (Note that despite being an idealisation of the real world, the 'vortex system' set up round a wing is both real and observable, and is one of the reasons that a light aircraft cannot take off immediately after a jumbo jet.)
Common misconceptions
Equal transit-time
One misconception encountered in a number of explanations of lift is the "equal transit time" fallacy. This fallacy states that the parcels of air which are divided by an airfoil must rejoin again; because of the greater curvature (and hence longer path) of the upper surface of an airfoil, the air going over the top must go faster in order to "catch up" with the air flowing around the bottom.
Although it is true that the air moving over the top of the wing is moving faster (when the effective angle of attack is positive) there is no requirement for equal transit time. In fact if the air above and below an airfoil has equal transit time, there is no circulation, and therefore no lift. Only if the air flowing above has a ''shorter'' transit time than the air flowing below, is upward lift produced, along with downward deflection of the air behind the wing and a vortex at each wing tip. Wind tunnel smoke streamline pictures reveal these flow features.[4][5]
A further flaw in this explanation is that it requires an airfoil to have a curvature in order to create lift. In fact, a thin, flat plate inclined to a flow of fluid also generates lift.[6][7]
It is unclear why this explanation has gained such currency, except by repetition by authors of populist (rather than rigorously scientific) books and perhaps the fact that the explanation is easiest to grasp intuitively without mathematics. At least one common flight training book depicts the equal transit fallacy, adding to the confusion.[8]
Albert Einstein, in attempting to design a practical aircraft based on this principle, came up with an airfoil section that featured a large hump on its upper surface, on the basis that an even longer path must aid lift if the principle is true. Its performance was terrible. Herr Dr Prof Albert Who? Einstein the Aerodynamicist, That's Who!, , Peter, Grosz, WWI Aero,
Coanda effect
There are two techniques for increasing the lift on an airfoil. One is to decrease the pressure on the side of the airfoil normal to the direction of the desired lift and the other is to increase the pressure on the other side. (The latter is the primary cause of the lift of a paper airplane.) In order to generate lift one must create a pressure differential between the top and bottom of the airfoil.
The Coandă effect is the name given to the tendency of an airflow, under some conditions, to deflect toward a surface that curves away from the flow direction. This effect is caused by the decreased pressure on the curved surface where it curves away from the flow.
Jef Raskin and a few others have observed that the Coandă effect accounts for part of the lift generated by an airfoil. The decrease in pressure above the airfoil is caused by the interaction of the flow, at the microscopic level, with the curved surface. The effect is caused by a decrease of the pressure on the top of the wing as air particles are blown away from the surface (fewer particles, less pressure due to thermal molecular motion). This contributes to the pressure field under the integral sign in the lift equation.
For large angles of attack and/or high flow rates the Coandă effect results in vortices which may impinge normally on the surface thus increasing the pressure there. Under these circumstances the wing will lose lift and ultimately stall. This aspect of the Coandă effect has been used successfully in the design of the wings in Formula One race cars to pressurize the back of the car and partially offset drag.
For supersonic airplanes to be able to maintain lift at the low speeds necessary for safe landings on aircraft carriers, the stall-producing vortices must be dissipated. This is effected by blowing the boundary layer and other lift augmentation devices.
Some airliners exploit the Coandă effect by deploying slats at the leading edge of the wing. On takeoff when maximum lift is needed at low air speed, the slat moves away from the leading edge leaving a slot which allows some of the high pressure air from the bottom of the wing to blow up over the top of the wing, thus creating a lifting Coandă effect by disrupting vortices that would form there on takeoff. Another use of the Coandă effect to produce lift is the use of Fowler flaps, the aerodynamic surfaces that are deployed from the wing's trailing edge on takeoff and landing. These flaps in effect extend the curved surface of the wing. This extension utilizes the Coandă effect to decrease the pressure on the top of the wing and also "dams" the air as it passes under the wing thus increasing the pressure there. The latter is done at the expense of an increased drag but at the low speeds of takeoff and landing, the increased lift is much more beneficial than the increased drag is detrimental.
The Coandă effect provides one aspect of the lift generated on subsonic airfoils.
Venturi nozzle
Many web sites claim that an airfoil can be analyzed as a Venturi nozzle. The mass flow rate through a Venturi nozzle is constant, so the air must flow faster over the top of the wing. Therefore, there is a lower pressure over the top of the wing, producing lift. However, a Venturi nozzle requires that air is squeezed between surfaces. While this situation does exist with "infinite wing" experiments in wind tunnels, in an aircraft the top of a wing is only one surface. The air is not confined above the wing, therefore a wing is not a Venturi nozzle and it is incorrect to analyze it as such.
Lift coefficient
The lift coefficient is a dimensionless number. When the lift coefficient is known, for instance from tables of airfoil data, lift can be calculated using the ''Lift Equation'':
:
where:
★ is the ''lift coefficient''
★ is the density of air (1.225 kg/m³ at sea level)
★
★ ''V'' is the freestream velocity, that is the speed of the lifting surface relative to the atmosphere far enough away to be unaffected by the surface
★ ''A'' is the projected (planform) surface area of the lifting surface
★ ''L'' is the lift force produced
This equation can be used in any consistent system. For instance, if the density is measured in kilograms per cubic metre, the velocity is measured in metres per second, and the area is measured in square metres, the lift will be calculated in newtons. Or, if the density is in slugs per cubic foot, the velocity is in feet per second, and the area is in square feet, the resulting lift will be in pounds force.
★
Compare with: Drag equation.
See also
★ Drag force
★ Lift-induced drag
★ Lift-to-drag ratio
References
1. What is Lift?
2. The Bishop's Boys : A Life of Wilbur and Orville Wright, , Tom D., Crouch, W. W. Norton, 1989,
3. How do airplanes fly, really? : A Staff Report by the Straight Dope Science Advisory Board aerodave
4. http://user.uni-frankfurt.de/~weltner/Flight/PHYSIC4.htm
5. http://www.av8n.com/how/htm/airfoils.html
6. http://www.av8n.com/how/htm/airfoils.html#sec-thin-wings
7.
What Does Keep Them Up There? Kenneth Chang
8. The Student Pilot's Flight Manual, , William K., Kershner, , 1979,
Further reading
★ ''Quest for an improved explanation of lift'' Jaako Hoffren (Helsinki Univ. of Technology, Espoo, Finland) AIAA-2001-872 Aerospace Sciences Meeting and Exhibit, 39th, Reno, NV, Jan. 8-11, 2001 This paper focuses on a physics-based explanation of lift. Calculation of lift based on circulation with artificially imposed Kutta condition is interpreted as a mathematical model, having limited "real-world" physics, resulting from the assumption of potential flow. Also the role of viscosity is discussed. Author's claim is that viscosity is not important for lift generation.
★ ''Introduction to Flight'', John D. Anderson, Jr., McGraw-Hill, ISBN 0-07-299071-6. The author is the Curator of Aerodynamics at the National Air & Space Museum Smithsonian Institute and Professor Emeritus at the University of Maryland.
★ ''Understanding Flight'', by David Anderson and Scott Eberhardt, McGraw-Hill, ISBN 0-07-136377-7. The authors are a physicist and an aeronautical engineer. They explain flight in non-technical terms and specifically address the equal-transit-time myth. Turning of the flow around the wing is attributed to the Coanda effect, which is quite controversial.
★ ''Fundamentals of Flight'', Richard S. Shevell, Prentice-Hall International Editions, ISBN 0-13-332917-8. This book is primarily intended as a text for a one semester undergraduate course in mechanical or aeronautical engineering, although its sections on theory of flight are understandable with a passing knowledge of calculus and physics.
External links
★ Discussion of the apparent "conflict" between the various explanations of lift
★ NASA tutorial, with animation, describing lift
★ Explanation of Lift with animation of fluid flow around an airfoil
★ An treatment of why and how wings generate lift that focuses on pressure.
★ Physics of Flight - reviewed. Online paper by Prof. Dr. Klaus Weltner.
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