# Lift (force)

Lift consists of the negative product of all the aerodynamic forces normal to the direction of the external airflow. 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.

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Forces on an aircraft
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## Reaction due to accelerated air

Lift is created as an airstream passes by an airfoil and is deflected downward. The force created by this deflection of the air creates an equal and opposite force upward on an airfoil (see Newton's third law.) The deflection of airflow downward during the creation of lift is known as downwash. (Note: Confusingly, the term "downwash" has two somewhat different meanings with regard to aircraft. See downwash for a more complete explanation.)

It is important to note that the acceleration of the air does not simply occur as the air molecules "bounce off" the bottom of the airfoil. Rather, both the top and bottom surfaces of the airfoil play important roles in deflecting the airflow downward. In fact, the acceleration of the air during the creation of lift can also be described as a "turning" of the airflow.

Nearly any shape will produce lift if tilted with respect to the air flow direction (inclined) or cambered (curved). However, 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 drag.

Invariably, the creation of lift creates drag - this is called lift-induced drag, or just induced drag.

The airflow normally follows the curvature of the wing surface as it changes direction - this is known as the Coanda Effect.

It is possible to measure lift using the reaction model. The force acting on the airfoil 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 thence the lift derived.

## Bernoulli's principle

The force on the wing can also be examined in terms of the pressure differences above and below the wing. (This method of explanation is mathematically equivalent to the Newton's 3rd law explanation as developed above.) The relationship between the velocities and pressures above and below the wing are nearly predicted by Bernoulli's equation.

More generally, the resulting force (Lift + Drag) is, according to Bernoulli's equation, the integral of pressure on the contour of the wing.

[itex]\mathbf{L}+\mathbf{D} = \oint_{\partial\Omega}p\mathbf{n} \; d\partial\Omega [itex]

The differences between the Bernoulli-predicted pressure values and the true values are small and related to viscosity, which is neglected in the Bernoulli equation.

## Circulation

A third way of calculating lift is a mathematical construction called circulation. Again, it is mathematically equivalent to the two explanations above. It is often used by practicing aerodynamicists as a convenient quantity, but is not often useful for a layperson's understanding. 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:

[itex]l = \rho \times V \times \Gamma [itex]

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

The Helmholtz theorem states that circulation is conserved. When an aircraft is at rest, there is no circulation. As the 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 gets dissipated by a number of effects, as do the wing-tip vortices far behind the aircraft.

## Coefficient of lift

Aerodynamicists are one of 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:

[itex]L = C_L \times \rho \times {V^2\over 2} \times A[itex]

where:

• [itex] C_L [itex] is the coefficient of lift,
• [itex] \rho [itex] 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.

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