Lift (force)

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Lift consists of the sum of all the fluid dynamic forces on a body perpendicular to the direction of the external flow approaching that body.

The most straightforward and frequently-mentioned application of lift is the wing of an aircraft. However there are many other common, if less obvious, uses such as propellers on both aircraft and boats, rotors on helicopters, fan blades, sails on sailboats and even some kinds of wind turbines.

There are a number of ways of explaining the production of lift, all of which are equivalent. That is, they are different expressions of the same underlying physical principles.

Contents

1 Reaction due to accelerated air
2 Bernoulli's principle
3 Circulation
4 Coefficient of lift
5 Common misconceptions

5.1 Equal transit-time
5.2 Coanda effect
5.3 Venturi nozzle

6 Further reading
7 External links

Reaction due to accelerated air

In air (or comparably in any fluid), lift is created as flow interacts with an airfoil or other body and is deflected downward. The force created by this deflection of the air creates an equal and opposite upward force according to Newton's third law of motion. The deflection of airflow downward during the creation of lift is known as downwash.

It is important to note that the acceleration of the air does not just involve the air molecules "bouncing off" the lower surface of the wing. Rather, air molecules closely follow both the top and bottom surfaces, and so the airflow is deflected downward. The acceleration of the air during the creation of lift has 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. However, lift generation by most shapes will be very inefficient and create a great deal of drag. One of the primary goals of wing 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.

The total force (Lift + Drag) is the integral of pressure over the contour of the wing. [\mathbf+\mathbf = \oint_p\mathbf \; d\partial\Omega ]

where:

L is the Lift,
D is the Drag,
[\partial\Omega] 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/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 the upper parcel of air should speed up to synchronize with the lower parcel. 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 a mathematical construction called circulation or "lifting-line theory". Again, it is mathematically equivalent to the two explanations above. It is often used by practising aerodynamicists as a convenient quantity, but is not often useful for a layperson's understanding. (That said, 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!)

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:

[l = \rho V \times \Gamma ]

where [ \rho ] is the air density, [ V ] is the free-stream airspeed, and [ \Gamma ] is the circulation.

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.

Coefficient of lift

Aerodynamicists are among the most frequent users of dimensionless numbers. The coefficient of lift is one such term. When the coefficient of lift is known, for instance from tables of airfoil data, lift can be calculated using the Lift Equation:

[L = C_L \times \rho \times \times A]

where:

[ C_L ] is the coefficient of lift
[ \rho ] is the density of air (1.225 kg/m³ at sea level)*
V is the freestream velocity, that is the airspeed far from the lifting surface
A is the 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.

* Note that at altitudes other than sea level, the density can be found using the barometric formula

Compare with: Drag equation.

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 lift produced at all. Only if the air above has a lower transit time, lift is produced (as well as a downward deflection of the air and a vortex). There are wind tunnel smoke streamline pictures available. [link][link]

Such an explanation would predict that an aircraft could not fly inverted, which is demonstrably not the case. When an aircraft is flying inverted, the air moving over the bottom (in the aircraft reference frame) surface of the airfoil is moving faster. The explanation also fails to account for airfoils which are fully symmetrical yet still develop significant lift.

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 will also generate lift[link].

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.

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.

Coanda effect

Jef Raskin and a few others have claimed that the Coandă effect is needed to explain lift from an airfoil. They state that flow attachment and the "turning of the airflow" above the airfoil is caused at the microscopic level by the Coandă Effect, and, without this phenomenon, a perpetual stall would exist. However, the conventional explanation of lift makes verifiable predictions of lift using the lift equation, without invoking the Coandă Effect. Proponents of the Coandă Effect correctly claim that the effect is not fully understood, but currently their predictions are at variance with experiment. The practical applications of Coandă effect, such as blown flaps and other lift augmentation devices, create conditions different from the normal airflow over a wing.

This construction will lift the plane up into the air long before a wing not incorporating blown flaps will, as mentioned earlier. Using Newton's laws, most likely forms the theory behind the work of Henri Coandǎ. Newton stated that for every forceful action there will be an equal and opposite reaction; in this case, the use of the engines to thrust the aircraft down the runway and the use of Coandǎ's thesis behind the use of blown flaps diverts the air towards the ground and the reaction force is the lift of the aircraft (as mentioned earlier in this article).

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. The top of a wing is only one surface, and the air is not confined above the wing. A wing is therefore not a Venturi nozzle, and thus it is incorrect to analyze it as such.

External links

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