Editing Lift (force) (section)

==Quantifying lift==

===Pressure integration===
When the pressure distribution on the airfoil surface is known, determining the total lift requires adding up the contributions to the pressure force from local elements of the surface, each with its own local value of pressure. The total lift is thus the [[integral]] of the pressure, in the direction perpendicular to the farfield flow, over the airfoil surface.<ref>Anderson (2008), Section 5.7</ref>

: <math>L = \oint p\mathbf{n} \cdot\mathbf{k} \; \mathrm{d}S, </math>

where:
* '''S''' is the projected (planform) area of the airfoil, measured normal to the mean airflow;
* '''n''' is the normal unit vector pointing into the wing;
* '''k''' is the vertical unit vector, normal to the [[freestream]] direction.

The above '''lift equation''' neglects the [[skin friction]] forces, which are small 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<sub>p</sub>'' (which includes the pressure portion of the profile drag and, if the wing is three-dimensional, the induced drag). If we use the spanwise vector '''j''', we obtain the side force ''Y''.

:<math>\begin{align}
  D_p &= \oint p\mathbf{n} \cdot\mathbf{i} \; \mathrm{d}S, \\
    Y &= \oint p\mathbf{n} \cdot\mathbf{j} \; \mathrm{d}S.
\end{align}</math>

The validity of this integration generally requires the airfoil shape to be a closed curve that is [[piecewise smooth]].

===Lift coefficient===
{{Main|Lift coefficient}}

Lift depends on the size of the wing, being approximately proportional to the wing area. It is often convenient to quantify the lift of a given airfoil by its ''lift coefficient'' <math>C_L</math>, which defines its overall lift in terms of a unit area of the wing.

If the value of <math>C_L</math> for a wing at a specified angle of attack is given, then the lift produced for specific flow conditions can be determined:<ref>{{citation|last=Anderson|first=John D.|year=2004|title=Introduction to Flight|edition=5th|publisher=McGraw-Hill|isbn=978-0-07-282569-5|page=257}}</ref>

:<math>
L = \tfrac12\rho v^2 S C_L
</math>

where 
* <math>L</math> is the lift force
* <math>\rho</math> is the [[air density]]
* <math>v</math> is the velocity or [[true airspeed]]
* <math>S</math> is the planform (projected) wing area
* <math>C_L</math> is the lift coefficient at the desired angle of attack, [[Mach number]], and [[Reynolds number]]<ref>{{citation|last=Yoon|first=Joe|title=Mach Number & Similarity Parameters|publisher=Aerospaceweb.org|url=http://www.aerospaceweb.org/question/aerodynamics/q0156.shtml|date=28 December 2003|access-date=11 February 2009|archive-date=February 24, 2021|archive-url=https://web.archive.org/web/20210224153817/http://www.aerospaceweb.org/question/aerodynamics/q0156.shtml|url-status=live}}</ref>