Information about Lift (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.
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.
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 positive 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.
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, or holding your hand out of the car window. Without any assistance from you, the sheet of paper or your hand will rise in the air. 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
The total Lift force is the integral of vertical pressure forces over the entire wetted surface area of the wing:
where:
parallel to the freestream in lieu of 
in the integral, we obtain an expression for the Pressure Drag 
(which includes Induced Drag in a 3D wing). If we use the spanwise vector 
, we obtain the Sideforce 
.
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.
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.
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. [4]
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 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/span
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 acting on the boundary layer, causing it to separate at different points between top and bottom. The assymetric separation then produces a circulation in the outer inviscid flow.
The Helmholtz theorem states that circulation is conserved; put simply this is conservation of the air's angular momentum per unit mass. 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.)
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.[5][6]
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.[7][8]
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.[9]
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.[10]
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.
where:
* Note that at altitudes other than sea level, the density can be found using the barometric formula
Compare with: Drag equation.
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 positive 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, or holding your hand out of the car window. Without any assistance from you, the sheet of paper or your hand will rise in the air. 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
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 Lift force is the integral of vertical pressure forces over the entire wetted surface area of the wing:
where:
is the Lift,
is the wing surface area
is the value of the pressure,
is the normal unit vector pointing into the wing
- is the vertical unit vector, normal to the freestream direction
parallel to the freestream in lieu of in the integral, we obtain an expression for the Pressure Drag (which includes Induced Drag in a 3D wing). If we use the spanwise vector , we obtain the Sideforce .
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
.
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.
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. [4]
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.
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 practicing aerodynamicists as a convenient quantity in calculations, see thin-airfoil theory for example.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/span
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 acting on the boundary layer, causing it to separate at different points between top and bottom. The assymetric separation then produces a circulation in the outer inviscid flow.
The Helmholtz theorem states that circulation is conserved; put simply this is conservation of the air's angular momentum per unit mass. 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.[5][6]
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.[7][8]
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.[9]
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.[10]
- Further information: List of works with the equal transit-time fallacy
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
* Note that at altitudes other than sea level, the density can be found using the barometric formula
Compare with: Drag equation.
See also
References
1. ^ Benson, Tom (2006-02-14). What is Lift?. Retrieved on 2007-02-18.
2. ^ Crouch, Tom D. (1989). The Bishop's Boys : A Life of Wilbur and Orville Wright. W. W. Norton, pp. 220-226. ISBN 0-393-02660-4.
3. ^ aerodave (2005-07-12). How do airplanes fly, really? : A Staff Report by the Straight Dope Science Advisory Board. Chicago Reader, Inc.. Retrieved on 2007-02-18.
4. ^ [1]]
5. ^ http://user.uni-frankfurt.de/~weltner/Flight/PHYSIC4.htm
6. ^ http://www.av8n.com/how/htm/airfoils.html
7. ^ http://www.av8n.com/how/htm/airfoils.html#sec-thin-wings
8. ^ Chang, Kenneth. "What Does Keep Them Up There?", The New York Times, 2003-12-09.
9. ^ Kershner, William K. (1979). The Student Pilot's Flight Manual, 5th ed.. ISBN 0-8138-1610-6.
10. ^ Grosz, Peter (February 1988). "Herr Dr Prof Albert Who? Einstein the Aerodynamicist, That's Who!". WWI Aero 118: 42.
2. ^ Crouch, Tom D. (1989). The Bishop's Boys : A Life of Wilbur and Orville Wright. W. W. Norton, pp. 220-226. ISBN 0-393-02660-4.
3. ^ aerodave (2005-07-12). How do airplanes fly, really? : A Staff Report by the Straight Dope Science Advisory Board. Chicago Reader, Inc.. Retrieved on 2007-02-18.
4. ^ [1]]
5. ^ http://user.uni-frankfurt.de/~weltner/Flight/PHYSIC4.htm
6. ^ http://www.av8n.com/how/htm/airfoils.html
7. ^ http://www.av8n.com/how/htm/airfoils.html#sec-thin-wings
8. ^ Chang, Kenneth. "What Does Keep Them Up There?", The New York Times, 2003-12-09.
9. ^ Kershner, William K. (1979). The Student Pilot's Flight Manual, 5th ed.. ISBN 0-8138-1610-6.
10. ^ Grosz, Peter (February 1988). "Herr Dr Prof Albert Who? Einstein the Aerodynamicist, That's Who!". WWI Aero 118: 42.
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.
- Explanation of Lift with animation of flow around an airfoil.
In physics, force is an action or agency that causes a body of mass m to accelerate. It may be experienced as a lift, a push, or a pull. The acceleration of the body is proportional to the vector sum of all forces acting on it (known as net force or resultant force).
..... Click the link for more information.
..... Click the link for more information.
FLUID (Fast Light User Interface Designer) is a graphical editor that is used to produce FLTK source code. FLUID edits and saves its state in text .fl files, which can be edited in a text editor for finer control over display and behavior.
..... Click the link for more information.
..... Click the link for more information.
airfoil (in American English, or aerofoil in British English) is the shape of a wing or blade (of a propeller, rotor or turbine) or sail as seen in cross-section.
An airfoil shaped body moved through a fluid produces a force perpendicular to the motion called lift.
..... Click the link for more information.
An airfoil shaped body moved through a fluid produces a force perpendicular to the motion called lift.
..... Click the link for more information.
Fluid dynamics is the sub-discipline of fluid mechanics dealing with fluids (liquids and gases) in motion. It has several subdisciplines itself, including aerodynamics (the study of gases in motion) and hydrodynamics (the study of liquids in motion).
..... Click the link for more information.
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perpendicular (or orthogonal) to each other if they form congruent adjacent angles. The term may be used as a noun or adjective. Thus, referring to Figure 1, the line AB is the perpendicular to CD through the point B.
..... Click the link for more information.
..... Click the link for more information.
<noinclude></noinclude>
The Wright brothers, Orville (August 19, 1871 – January 30, 1948) and Wilbur (April 16, 1867 – May 30 1912), were two Americans who are generally credited with building the world's first successful airplane and
..... Click the link for more information.
The Wright brothers, Orville (August 19, 1871 – January 30, 1948) and Wilbur (April 16, 1867 – May 30 1912), were two Americans who are generally credited with building the world's first successful airplane and
..... Click the link for more information.
An aerodyne is a heavier-than-air aircraft which derives lift from motion, as opposed to an aerostat which uses buoyancy (such as a balloon) to fly.
..... Click the link for more information.
Types of aerodynes
There are many types of aerodynes, shown below divided into the following categories:..... Click the link for more information.
Static lift can refer to:
For an aerostat:
..... Click the link for more information.
For an aerostat:
- Buoyancy the lifting force of the gas
- For an aerodyne:
- Lift (force) the lifting force generated by the wings
- Lift (soaring) rising air used by soaring birds and gliders
See also
- Dynamic soaring
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In physics, buoyancy is the upward force on an object produced by the surrounding fluid (i.e., a liquid or a gas) in which it is fully, or partially immersed, due to the pressure difference of the fluid between the top and bottom of the object.
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..... Click the link for more information.
An aerostat is a lighter than air craft including free balloons, airships, and moored balloons. Such a vehicle is lifted by buoyancy, containing a gas less dense than air within an envelope.
..... Click the link for more information.
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City of license Dayton, Ohio
Broadcast area Dayton
Branding "ESPN 1410"
Slogan Same as branding
First air date 1921
Frequency 1410 KHZ
Format Sports Talk
ERP 5,000 watts-D/N
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City of license Dayton, Ohio
Broadcast area Dayton
Branding "ESPN 1410"
Slogan Same as branding
First air date 1921
Frequency 1410 KHZ
Format Sports Talk
ERP 5,000 watts-D/N
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fixed-wing aircraft is a heavier-than-air craft where movement of the wings in relation to the aircraft is not used to generate lift. The term is used to distinguish from rotary-wing aircraft, or ornithopters, where the movement of the wing surfaces relative to the aircraft
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propeller is essentially a type of fan which transmits power by converting rotational motion into thrust for propulsion of a vehicle such as an aircraft, ship, or submarine through a fluid such as water or air, by rotating two or more twisted blades about a central shaft, in a
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aircraft is a vehicle which is able to fly through the air (or through any other atmosphere). All the human activity which surrounds aircraft is called aviation. (Most rocket vehicles are not aircraft because they are not supported by the surrounding air).
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A boat is a watercraft designed to float or plane on, and provide transport over, water. Usually this water will be inland (lakes) or in protected coastal areas. However, boats such as the whaleboat were historically designed to be operated from a ship in an offshore environment.
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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.
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History and development
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helicopter is an aircraft which is lifted and propelled by one or more horizontal rotors, each rotor consisting of two or more rotor blades. Helicopters are classified as rotorcraft or rotary-wing aircraft to distinguish them from fixed-wing aircraft because the helicopter derives
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sail is any type of surface intended to generate thrust by being placed in a wind — in essence a vertically-oriented wing. Sails are used in sailing.
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Use of sails
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KEEL 710AM is a general talk radio station in Shreveport, Louisiana. It is owned by Gap Broadcasting.
The station's lineup includes Rush Limbaugh, Sean Hannity, Michael Savage, and a local sports talk show hosted by the team of "J.J. and Bonzai Ben.
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The station's lineup includes Rush Limbaugh, Sean Hannity, Michael Savage, and a local sports talk show hosted by the team of "J.J. and Bonzai Ben.
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sailboat or sailing-boat is a boat propelled partly or entirely by sails. The term covers a variety of boats, larger than small vessels such as sailboards and smaller than sailing ships, but distinctions in size are not strictly defined and what constitutes a sailing ship,
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hydrofoil is a boat with wing-like foils mounted on struts below the hull. As the craft increases its speed the hydrofoils develop enough lift for the boat to become foilborne - i.e. to raise the hull up and out of the water.
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Automobile racing (also known as auto racing, motor racing, or car racing) is a sport involving racing automobiles. Auto racing began in 1895,[1] and is now one of the world's most popular sports.
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wind turbine is a machine that converts the kinetic energy in wind into mechanical energy. If the mechanical energy is used directly by machinery, such as a pump or grinding stones, the machine is usually called a windmill.
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Lift may mean:
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- Lift (force), a mechanical force generated by a solid object moving through a fluid
- Lift (soaring), rising air used by soaring birds and glider, hang glider and paraglider pilots for soaring flight
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Gravitation is a natural phenomenon by which all objects with mass attract each other. In everyday life, gravitation is most familiar as the agency that endows objects with weight.
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Angle of attack (AOA, , Greek letter alpha) is a term used in aerodynamics to describe the angle between the airfoil's chord line and the relative airflow, wind, effectively the direction in which the aircraft is currently moving.
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airfoil (in American English, or aerofoil in British English) is the shape of a wing or blade (of a propeller, rotor or turbine) or sail as seen in cross-section.
An airfoil shaped body moved through a fluid produces a force perpendicular to the motion called lift.
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An airfoil shaped body moved through a fluid produces a force perpendicular to the motion called lift.
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Newton's laws of motion are three physical laws which provide relationships between the forces acting on a body and the motion of the body, first compiled by Sir Isaac Newton.
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downwash has two meanings within the field of aerodynamics.
1. One meaning, used most often by non-engineers (in particular pilots), refers to the forcing of air downward during the creation of lift.
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1. One meaning, used most often by non-engineers (in particular pilots), refers to the forcing of air downward during the creation of lift.
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drag (sometimes called resistance) is the force that resists the movement of a solid object through a fluid (a liquid or gas). Drag is made up of friction forces, which act in a direction parallel to the object's surface (primarily along its sides, as friction forces at the
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Herod_Archelaus
