The lift force, or simply lift, is a mechanical force, generated by a solid object as it moves through a fluid, directed perpendicular to the flow direction.^[1] Lift is commonly associated with the wing of an aircraft, although lift is also generated by 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 that lift opposes gravity, the lift force is related to flow direction and doesn't necessarily oppose gravity. For other uses, see Force (disambiguation). ... A fluid is defined as a substance that continually deforms (flows) under an applied shear stress regardless of the magnitude of the applied stress. ... For other uses, see Wing (disambiguation). ... Airplane and Aeroplane redirect here. ... A rotor is the rotating part of a helicopter which generates lift, either vertically in the case of a main rotor, or horizontally in the case of a tail rotor. ... For other uses, see Helicopter (disambiguation). ... A gaff-rigged cutter flying a mainsail, staysail and genoa jib For other uses, see Sail (disambiguation). ... For other uses, see Keel (disambiguation). ... Diagram of Sailboat, in this case a typical monohull sloop with a bermuda or marconi rig. ... This article is about marine engineering. ... Juuso Pykälistö driving a Peugeot 206 World Rally Car at the 2003 Swedish rally Racing cars redirects here. ... This article is about the machine for converting the kinetic energy in the wind into mechanical energy. ...

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] The Wright brothers, Orville (19 August 1871 – 30 January 1948) and Wilbur (16 April 1867 – 30 May 1912), were two Americans who are generally credited[1][2][3] with inventing and building the worlds first successful airplane and making the first controlled, powered and sustained heavier-than-air human...

Physical description on an airfoil

The basic definition of lift is simple. However, the mechanisms by which lift is generated is governed are the conservation of mass and the balance of momentum (where the latter is the fluid dynamics version of Newton's second law).^[4] Unfortunately, these principles do not lend themselves easily to simplification^[5] and, as a result, there is no universally-accepted explanation of how lift is generated, even among experienced aerodynamicists.^[6] All the examples of continuity equations below express the same idea; they are all really examples of the same concept. ... The Navier-Stokes equations, named after Claude-Louis Navier and George Gabriel Stokes, are a set of equations which describe the motion of fluid substances such as liquids and gases. ... Fluid dynamics is the sub-discipline of fluid mechanics dealing with fluids (liquids and gases) in motion. ... Newtons laws of motion are the three scientific laws which Isaac Newton discovered concerning the behaviour of moving bodies. ... For the Daft Punk song, see Aerodynamic (song). ...

To attempt a physical explanation of lift as it applies to an airplane, consider the flow around a 2-D, symmetric airfoil at positive angle of attack in a uniform free stream. Instead of considering the case where an airfoil moves through a flow as seen by a stationary observer, it is equivalent and simpler to consider the picture when the observer follows the airfoil and the flow moves past it. For the kite, see foil kite. ... In this diagram, the black arrow represents the direction of the wind. ...

Lift in an established flow

Streamlines around a NACA 0012 airfoil at moderate angle of attack.

If one assumes that the flow naturally follows the shape of an airfoil, as is the usual observation, then the explanation of lift is rather simple and can be explained primarily in terms of pressures using Bernoulli's principle (which is derived from Newton's second law) and conservation of mass, following the development by John D. Anderson in Introduction to Flight. ^[4] Bernoullis Principle states that for an ideal fluid (low speed air is a good approximation), with no work being performed on the fluid, an increase in velocity occurs simultaneously with decrease in pressure or a change in the fluids gravitational potential energy. ... Newtons laws of motion are the three scientific laws which Isaac Newton discovered concerning the behaviour of moving bodies. ... John D. Anderson, Jr. ...

The image to the right shows the flow over a NACA 0012 airfoil. The flow approaching an airfoil airfoil can be divided into two streamtubes, which are defined based on the area between streamlines. By definition, fluid never crosses a streamline; hence mass is conserved within each streamtube. One streamtube travels over the upper surface, while the other travels over the lower surface; dividing these two tubes is a dividing line that intersects the airfoil on the lower surface, typically near to the leading edge. The NACA airfoils are airfoil shapes for aircraft wings developed by the National Advisory Committee for Aeronautics (NACA). ... In fluid dynamics, a streamline is the path that an imaginary massless particle would make if it followed the flow of a fluid in which it was embedded. ...

The upper stream tube is squashed as it flows up and around the airfoil, the so-called upwash. From the conservation of mass, the flow speed must increase as the area of the stream tube decreases. Relatively speaking, the bottom of the airfoil presents less of an obstruction to the free stream, and often expands as the flow travels around the airfoil, slowing the flow below the airfoil. (Contrary to the equal transit-time explanation of lift, there is no requirement that particles that split as they travel over the airfoil meet at the trailing edge. It is typically the case that the particle traveling over the upper surface will reach the trailing edge long before the one traveling over the bottom.)

From Bernoulli's principle, the pressure on the upper surface where the flow is moving faster is lower than the pressure on the lower surface. The pressure difference thus creates a net aerodynamic force, pointing upward and downstream to the flow direction. The component of the force normal to the free stream is considered to be lift; the component parallel to the free stream is drag. In conjunction with this force by the air on the airfoil, by Newton's third law, the airfoil imparts an equal-and-opposite force on the surrounding air that creates the downwash. Measuring the momentum transferred to the downwash is another way to determine the amount of lift on the airfoil. An object moving through a gas or liquid experiences a force in direction opposite to its motion. ... Newtons laws of motion are the three scientific laws which Isaac Newton discovered concerning the behaviour of moving bodies. ... The term downwash has two nearly unrelated meanings within the field of aerodynamics. ...

Stages of lift production

In attempting to explain why the flow follows the upper surface of the airfoil, the situation gets considerably more complex. To offer a more complete physical picture of lift, consider the case of an airfoil accelerating from rest in a viscous flow. Lift depends entirely on the nature of viscous flow past certain bodies^[7]: in inviscid flow (i.e. assuming that viscous forces are negligible in comparison to inertial forces), there is no lift without imposing a net circulation. Viscosity is a measure of the resistance of a fluid to deformation under shear stress. ... A fluid flow where viscous (friction) forces are small in comparison to inertial forces is said to be inviscid. ... In fluid dynamics, circulation is the path integral around a closed curve of the fluid velocity. ...

When there is no flow, there is no lift and the forces acting on the airfoil are zero. At the instant when the flow is “turned on”, the flow is undeflected downstream of the airfoil and there are two stagnation points on the airfoil (where the flow velocity is zero): one near the leading edge on the bottom surface another on the upper surface near the trailing edge. The dividing line between the upper and lower streamtubes mentioned above intersects the body at the stagnation points. Since the flow speed is zero at these points, by Bernoulli's principle the static pressure at these points is at a maximum. As long as the second point is at its initial location on the upper surface of the wing, the net pressure difference between the upper and lower surfaces is zero and there is no lift. The flow field at this instant is time in fact the same as it is in the inviscid case without circulation. The term downstream has several possible meanings: In geography, downstream means literally away from the source of a stream or river, along the normal direction of water flow. ... A point in a flow where the velocity is zero, where any streamline touches a solid surface at an angle. ... Static pressure is a term used in ventilation engineering, airspeed indication, fluid statics, hydraulics and flow measurement. ...

The effects of viscosity are contained within a thin layer of fluid close to the body called the boundary layer. Inside the boundary layer, the flow accelerates from rest at the surface of the airfoil (due to the no-slip condition) to the free-stream velocity some distance away from the surface. Almost immediately after the flow starts, the flow is unable to maintain the turn from around the sharp trailing edge from the lower surface to the upper, and the boundary layer separates at the trailing edge. The flow accelerates over the upper surface, pushing the stagnation point there downstream, moving it closer to the trailing edge. As this happens, the starting vortex is shed into the wake, and is a necessary condition to produce lift on an airfoil. If the flow were stopped, there would be a corresponding "stopping vortex".^[8] Despite being an idealization of the real world, the “vortex system” set up around a wing is both real and observable; the trailing vortex sheet most noticeably rolls up into wing-tip vortices. In physics and fluid mechanics, a boundary layer is that layer of fluid in the immediate vicinity of a bounding surface. ... The starting vortex is a concentration of vorticity which forms at the trailing edge of an airfoil as it is accelerated from rest in a fluid. ...

The upper stagnation point continues moving downstream until it is coincident with the sharp trailing edge (a feature of the flow known as the Kutta condition). The flow downstream of the airfoil is deflected downward from the free-stream direction and, from the reasoning above in the basic explanation, there is now a net pressure difference between the upper and lower surfaces and an aerodynamic force is generated. The Kutta condition is a principle in fluid dynamics, especially aerodynamics, applied at sharp corners such as trailing edges of airfoils in steady flow. ...

Methods of determining lift

Pressure integration

The force on the wing can be examined in terms of the pressure differences above and below the wing, which can be related to velocity changes by Bernoulli's principle. This article is about pressure in the physical sciences. ... Bernoullis Principle states that for an ideal fluid (low speed air is a good approximation), with no work being performed on the fluid, an increase in velocity occurs simultaneously with decrease in pressure or a change in the fluids gravitational potential energy. ...

The total lift force is the integral of vertical pressure forces over the entire wetted surface area of the wing: This article is about the concept of integrals in calculus. ...

where:

• L is the lift,
• A is the wing surface area
• p is the value of the pressure,
• n is the normal unit vector pointing into the wing, and
• k is the vertical unit vector, normal to the freestream direction.

The above lift equation neglects the skin friction forces, which typically have a negligible contribution to the lift compared to the pressure forces. By using the streamwise vector i parallel to the freestream in place of k in the integral, we obtain an expression for the pressure drag D_p (which includes induced drag in a 3D wing). If we use the spanwise vector j, we obtain the side force Y. In Aerodynamics, skin friction is the component of parasitic drag arising from the friction of the fluid against the skin of the object that is moving through it. ... Parasitic drag (also called parasite drag) is drag caused by moving a solid object through a fluid. ... In aerodynamics, lift-induced drag, induced 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. ...

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 friction drag, which is the other component of the total drag in addition to D_p. In fluid dynamics, Bernoullis equation, derived by Daniel Bernoulli, describes the behavior of a fluid moving along a streamline. ... For other uses, see Viscosity (disambiguation). ... In physics and fluid mechanics, a boundary layer is that layer of fluid in the immediate vicinity of a bounding surface. ... Parasitic drag (also called parasite drag) is drag caused by moving a solid object through a fluid. ... An object moving through a gas or liquid experiences a force in direction opposite to its motion. ...

The Bernoulli principle states that the sum total of energy within a parcel of fluid remains constant as long as no energy is added or removed. It is a statement of the principle of the conservation of energy applied to flowing fluids.

A substantial simplification of this proposes that as other forms of energy changes are inconsequential during the flow of air around a wing and that energy transfer in/out of the air is not significant, then the sum of pressure energy and speed energy for any particular parcel of air must be constant. Consequently, an increase in speed must be accompanied by a decrease in pressure and vice-versa. It should be noted that this is not a causational relationship. Rather, it is a coincidental relationship, whatever causes one must also cause the other as energy can neither be created nor destroyed. It is named for the Dutch-Swiss mathematician and scientist Daniel Bernoulli, though it was previously understood by Leonhard Euler and others. Leonhard Euler, considered one of the greatest mathematicians of all time A mathematician is a person whose primary area of study and research is the field of mathematics. ... A scientist, in the broadest sense, refers to any person that engages in a systematic activity to acquire knowledge or an individual that engages in such practices and traditions that are linked to schools of thought or philosophy. ... Daniel Bernoulli Daniel Bernoulli (February 8, 1700 – March 17, 1782) was a Dutch-born mathematician who spent much of his life in Basel, Switzerland where he died. ... Euler redirects here. ...

Bernoulli's principle provides an explanation of pressure difference in the absence of air density and temperature variation (a common approximation for low-speed aircraft). If the air density and temperature are the same above and below a wing, a naive application of the ideal gas law requires that the pressure also be the same. Bernoulli's principle, by including air velocity, explains this pressure difference. The principle does not, however, specify the air velocity. This must come from another source, e.g., experimental data. Erroneous assumptions concerning velocity, e.g., that two parcels of air separated at the front of the wing must meet up again at the back of the wing, are commonly found.^[9] Isotherms of an ideal gas The ideal gas law is the equation of state of a hypothetical ideal gas, first stated by Benoît Paul Émile Clapeyron in 1834. ...

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. The Kutta condition is a principle in fluid dynamics, especially aerodynamics, applied at sharp corners such as trailing edges of airfoils in steady flow. ... The law of conservation of mass/matter, also known as law of mass/matter conservation (or the Lomonosov-Lavoisier law), states that the mass of a closed system of substances will remain constant, regardless of the processes acting inside the system. ... In physics, a conservation law states that a particular measurable property of an isolated physical system does not change as the system evolves. ...

Mathematical approximations

Kutta-Joukowski Theorem

Main article: Kutta-Joukowski Theorem

Lift can be calculated using potential flow theory by imposing a circulation. It is often used by practicing aerodynamicists as a convenient quantity in calculations, for example thin-airfoil theory and lifting-line theory. The lift force, lifting force or simply lift is a mechanical force generated by a solid object moving through a fluid. ... A potential flow is characterized by an irrotational velocity field. ... In fluid dynamics, circulation is the path integral around a closed curve of the fluid velocity. ... This article or section does not cite any references or sources. ... The horseshoe vortex model is a simplified representation of the vortex system of a wing. ...

The circulation Γ 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. The section lift/span L' can be calculated using the Kutta-Joukowski Theorem: This article is about path integrals in the general mathematical sense, and not the path integral formulation of physics which was studied by Richard Feynman. ... Vorticity is a mathematical concept used in fluid dynamics. ...

L' = − ρVΓ

where ρ is the air density, V is the free-stream airspeed. 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. It has been suggested that this article or section be merged with :Fundamental theorem of vector analysis. ...

The challenge when using the Kutta-Joukowski Theorem to determine lift is to determine the appropriate circulation for a particular airfoil. In practice, this is done by applying the Kutta condition, which uniquely prescribes the circulation for a given geometry and free-stream velocity.

A physical understanding of the theorem can be observed in the Magnus effect, which is a lift force generated by a spinning cylinder in a free stream. Here the necessary circulation is induced by the mechanical rotation acting on the boundary layer, causing it to separate at different points between top and bottom. The asymmetric separation then produces a circulation in the outer inviscid flow. The Magnus effect, demonstrated on a ball. ...

Common misconceptions

Equal transit-time

An illustration of the equal transit-time fallacy.

One misconception encountered in a number of popular explanations of lift is the "equal transit time" fallacy. This fallacy assumes that the parcels of air that are divided above and below an airfoil must rejoin behind it. The fallacy states that because of the 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.^[10] Although it is true that the air moving over the top of a wing generating lift does move faster, there is no requirement for equal transit time. In fact the air moving over the top of an airfoil generating lift is always moving much faster than the equal transit theory would imply. ^[11]

A further flaw in this explanation is that it requires an airfoil to have thickness and curvature in order to create lift. In fact, thin flat plate wings and sails create lift under a range of angles of attack. If lift were solely a result of shape, then aircraft would not be able to fly inverted.

This explanation has gained currency by repetition in populist (rather than technical) books. At least one common pilot training book depicts the equal transit fallacy, adding to the confusion.^[12]

Further information: List of works with the equal transit-time fallacy

An illustration of the equal transit-time fallacy (from NASA). ...

Coandă Effect

Main article: Coandă effect

The Coandă effect refers to the tendency of a fluid jet to stay attached to an adjacent curved surface. The origins of the effect are in a patent for an annular lifting device by Henri Coandă. There are several physical aspects of flow sometimes ascribed to the Coandă effect beyond its proper context, that of a fluid jet impacting a surface (e.g. as occurs in high-lift device such as a blown flap). Coanda effect as demonstrated with a spoon and a water stream. ... Henri Marie Coandă (June 7, 1886 – November 25, 1972) (IPA: /ɐʁi maʁi kwandÉ™/) was a Romanian inventor, aerodynamics pioneer and the builder of worlds first jet powered aircraft, the Coanda-1910. ... In aircraft design, high-lift devices are a variety of mechanisms intended to add lift during certain portions of flight. ... Blown flaps are a powered aerodynamic high-lift device on the wings of certain aircraft to improve the low-speed lift during takeoff and landing. ...

The most common misconception related to lift is the bulk flow of air over the surface of a wing, where the tendency of the flow to follow the curvature is described as a consequence of the effect.^[13] However, for the general wing in a free stream, there is no jet involved and the Coanda effect cannot explain the starting vortex in the wake of a wing, which is necessary for lift generation. The tendency for the boundary layer to remain attached, meanwhile, can be explained more completely by the viscous Navier-Stokes equations that arise from the balance of linear momentum.

Other effects frequently attributed to the Coandă effect are low scale and do not significantly contribute to the production of lift. They include Van der Waals forces which, for example, causes a drip of water flowing down the back of the spoon to follow the surface of the spoon rather than drop off at the widest part. In chemistry, the term van der Waals force originally referred to all forms of intermolecular forces; however, in modern usage it tends to refer to intermolecular forces that deal with forces due to the polarization of molecules. ...

References

Year 2006 (MMVI) was a common year starting on Sunday of the Gregorian calendar. ... is the 45th day of the year in the Gregorian calendar. ... Year 2007 (MMVII) was a common year starting on Monday of the Gregorian calendar in the 21st century. ... is the 49th day of the year in the Gregorian calendar. ... Year 2005 (MMV) was a common year starting on Saturday (link displays full calendar) of the Gregorian calendar. ... is the 193rd day of the year (194th in leap years) in the Gregorian calendar. ... Year 2007 (MMVII) was a common year starting on Monday of the Gregorian calendar in the 21st century. ... is the 49th day of the year in the Gregorian calendar. ... Year 2006 (MMVI) was a common year starting on Sunday of the Gregorian calendar. ... is the 74th day of the year (75th in leap years) in the Gregorian calendar. ... 2008 (MMVIII) is the current year, a leap year that started on Tuesday of the Anno Domini (or common era), in accordance to the Gregorian calendar. ... is the 86th day of the year (87th in leap years) in the Gregorian calendar. ...

See also

• Drag force
• Lift-induced drag
• Lift-to-drag ratio
• Circulation control wing
• Kutta condition

An object moving through a gas or liquid experiences a force in direction opposite to its motion. ... In aerodynamics, lift-induced drag, induced 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 aerodynamics, the lift-to-drag ratio, or L/D ratio (ell-over-dee in the US, ell-dee in the UK), is the amount of lift generated by a wing or vehicle, compared to the drag it creates by moving through the air. ... The Kutta condition is a principle in fluid dynamics, especially aerodynamics, applied at sharp corners such as trailing edges of airfoils in steady flow. ...

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
• A treatment of why and how wings generate lift that focuses on pressure.
• Physics of Flight - reviewed. Online paper by Prof. Dr. Klaus Weltner.
• Explanation of Lift with animation of flow around an airfoil.