SP-367 Introduction to the Aerodynamics of Flight

- Appendix C -

[193] COORDINATE SYSTEMS

A point in space may be located by referencing it to a known point. The known point is considered to be the origin of three mutually perpendicular lines which constitute what is known as a rectangular Cartesian coordinate system. The unknown point is then located by specifying the number of units along each of the three axes as measured from the origin. This system is shown in figure 163(a). Additionally, a vector oriented at random in space whose tail is set at the origin may be resolved into its three components along the X, Y, and Z axes. (See fig. 163(b).) Three coordinate systems, employing right-handed rectangular Cartesian axes, are generally used. They are the Earth-axis system, the body-axis system, and the wind-axis system.

 (a) Location of a point in a right-hand rectangular coordinate system. Right-hand system-X, Y, Z axes point along thumb, first and second fingers of right hand, respectively. (b) Location of a vector in a right-hand rectangular Cartesian coordinate system. Resolution into components. Figure 163.- Rectangular Cartesian coordinate system.

Earth-Axis System

In the Earth-axis system the Earth is considered to be flat and nonrotating. The X and Y axes lie in the geometric plane of the Earth, X pointing north and Y pointing east. The Z-axis points down toward the center of the Earth as shown in figure 164.

[
194]

Figure 164.- Earth-axis system.

Body-Axis System

In the body-axis system the rectangular Cartesian axis system is oriented such that the X-axis points out of the nose of the aircraft and is coincident with the longitudinal axis of the aircraft. The Y- axis is directed out of the right wing of the aircraft and the Z-axis is perpendicular to both the X and Y axes and is directed downward. The origin of the entire system is taken to be the center of gravity of the aircraft. At this point it is useful to define the important angular displacement terms roll, pitch, and yaw.

 Roll: the airplane rotates about its longitudinal axis (that is, X-axis). A positive roll is defined as the Y-axis turning toward the Z-axis, that is, the right wing drops. Pitch: the airplane rotates about the Y-axis. A positive pitch is defined as the Z-axis turning toward the X-axis, that is, the nose of the airplane rises. Yaw: the airplane rotates about the Z-axis. A positive yaw is defined as the X-axis turning towards the Y-axis, that is, the nose moves to the right "Clockwise when viewed from above).

[195] The body-axis system and the concepts of roll, pitch, and yaw are illustrated in figure 165.

Figure 165.- Body-axis system.

Wind-Axis System

In the general wind-axis system, the origin of the rectangular Cartesian system is at the center of gravity of the aircraft. The X-axis points into the direction of the oncoming free-stream velocity vector. The Z-axis lies in the plane of symmetry of the airplane and is perpendicular to the X-axis and is directed generally downward. The Y-axis is perpendicular to both the X and Z axes (fig. 166(a)). In many problems of interest airplane motion is in the geometric plane of symmetry (no yawing motion) so that the X-axis also lies in the plane of symmetry. This means that the Y-axis points out of the right wing. The Z-axis again is in the plane of symmetry. The system then is termed the simplified wind-axis system and is illustrated in figure 166(b)).

[
196]

(a) General wind-axis system. Z-axis in plane of symmetry.
(b) Simplified wind-axis system. X and Z axes in plane of symmetry
Figure 166.- Wind-axis system.