# Camber (aerodynamics)

Camber (aerodynamics)

Camber, in aerospace engineering, is the asymmetry between the top and the bottom curves of an airfoil in cross-section.

Overview

Camber is often added to an airfoil to increase lift and/or reduce the critical angle of attack (the angle at which the airfoil begins to stall). The camber of a wing may vary from wing root to wing tip. Camber is not necessary for the generation of lift, and some airfoils have no camber. Airfoils with no camber (symmetric airfoils) do not generate lift at 0 angle of attack, however. Traditionally the upper camber of an airfoil has been greater than the lower, but some recent designs use negative camber. One such design is called the supercritical airfoil. It is used for near sonic flight, and produces a more efficient lift to drag ratio at near supersonic flight than traditional airfoils. The idea is that they will speed up the air underneath the airfoil so that it forms a shockwave on the bottom of the wing, which then serves as a high pressure region underneath the wing.

Adding camber doesn't necessarily increase "lift"; it depends on the airfoil shape. If too much camber is added, the flow over the airfoil may not stay attached to the wing even at an angle of attack of zero. When this occurs, we say the flow has separation over the airfoil, if the entire top of the wing has separation, the wing is stalled. Wings with camber don't as a result have the ability to produce more lift in general. As an example, the C-5 is a heavy lift aircraft used by the US military; in order to produce the lift needed, one might think it uses a cambered wing, but its wing is symmetrical. Cambered wings will produce lift at zero angle of attack, but as mentioned, too much camber can also be a bad thing.

An additional note is that a designer may reduce the camber on the outboard section of the wings to increase the critical angle of attack (stall angle) at the wing tips. When the wing approaches the stall angle this will ensure that the wing root stalls before the tip - giving the aircraft resistance to falling into a spin.

Definition

The camber of an airfoil can be defined by a camber line, which is the curve that is halfway between the upper and lower surfaces of the airfoil. Call this function "Z(x)". To fully define an airfoil we also need a thickness function "T(x)", which describes the thickness of the airfoil at any given point. Then, the upper and lower surfaces can be defined as follows:

$Z_\left\{upper\right\}\left(x\right)=Z\left(x\right)+frac\left\{1\right\}\left\{2\right\}T\left(x\right)$

$Z_\left\{lower\right\}\left(x\right)=Z\left(x\right)-frac\left\{1\right\}\left\{2\right\}T\left(x\right)$

Example - An airfoil with reflexed camber line

An airfoil where the camber line curves back up near the trailing edge is called a reflexed camber airfoil. Such an airfoil is useful in certain situations, such as with tailless aircraft, because the moment about the aerodynamic center of the airfoil can be 0. A camber line for such an airfoil can be defined as follows ("note that the lines over the variables indicates that they have been nondimensionalized by dividing through by the chord"):

$overline\left\{Z\right\}\left(x\right) = aleft \left[left\left(b-1 ight\right)overline\left\{x\right\}^3-boverline\left\{x\right\}^2+overline\left\{x\right\} ight\right]$

An airfoil with a reflexed camber line is shown at right. The thickness distribution for a NACA 4-series airfoil was used, with a 12% thickness ratio. The equation for this thickness distribution is:

$overline\left\{T\right\}\left(x\right) = frac\left\{t\right\}\left\{0.2\right\}left\left(0.296375sqrt\left\{overline\left\{x-0.12635overline\left\{x\right\}-0.35195overline\left\{x\right\}^2+0.283775overline\left\{x\right\}^3-0.10185overline\left\{x\right\}^4 ight\right)$

Where "t" is the thickness ratio.

References

* Desktop Aerodynamics Digital Textbook. Retrieved 9/7/08. [http://www.desktopaero.com/appliedaero/airfoils1/airfoilgeometry.html]

* Chord
* NACA airfoil

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