# 7.1.1: Reference frames

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Consider the following reference frames:1

##### Definition 7.1 (Earth Reference Frame)

An Earth reference frame $$F_e(O_e, x_e, y_e, z_e)$$ is a rotating topocentric (measured from the surface of the Earth) system. The origin Oe is any point on the surface of Earth defined by its latitude θe and longitude λe. Axis ze points to the center of Earth; xe lays in the horizontal plane and points to a fixed direction (typically north); ye forms a right-handed thrihedral (typically east).

Such system it is sometimes referred to as navigational system since it is very useful to represent the trajectory of an aircraft from the departure airport.

##### Definition 7.2 (Wind Axes Frame)

A wind axes frame $$F_w (O_w, x_w, y_w, z_w)$$ is linked to the instantaneous aerodynamic velocity of the aircraft. It is a system of axes centered in any point of the symeetry plane (assuming there is one) of the aircraft, typically the center of gravity. Axis $$x_w$$ points at each instant to the plane of symmetry, perpendicular to $$x_w$$ and pointing down according to regular aircraft performance. Axis $$y_w$$ forms a right-handed thrihedral.

Orientation angles

There exist several angles used in flight mechanics to orientate the aircraft with respect to a determined reference. The most important ones are:

• Sideslip angle, $$\beta$$, and angle of attack, $$\alpha$$: The angles of the aerodynamic velocity, $$\vec{V}$$, (wind axes reference frame) with respect the body axes reference frame.

• Roll, $$\mu$$, pitch, $$\gamma$$, and yaw, $$\chi$$, velocity angles: The angles of the wind axes reference frame with respect of the Earth reference frame. This angles are also referred to as bank angle, flight path angle, and heading angle.

1. Please, refer to Section 2.4 and/or Appendix A for a more detailed definition of the different reference frames.

7.1.1: Reference frames is shared under a CC BY-SA 3.0 license and was authored, remixed, and/or curated by Manuel Soler Arnedo via source content that was edited to conform to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.