Using Rotations to Build Aerospace Coordinate Systems - Defence ...

DSTO–TN–0640ZNorthEastωDownαYXFigure 2: A plane tangent to Earth’s hypothetical spheroidal surface containsthe local East and North directions, which set those axes for the North–East–Down frame. The Down axis is normal to this plane. The latitude α ofthe point at the origin of the NED frame is set by the angle at which theDown axis intercepts Earth’s equatorial plane. Because Earth is modelledas an oblate spheroid, the Down axis only points toward its centre when theNED origin is on the equator or at the poles. An alternative set of axes isEast–North–Upfirst estimate (2.4) and not even iterating at all. Finally, after an acceptable estimate of αhas been obtained, the height is calculated:h =√X 2 + Y 2cos α−a 2√a 2 cos 2 α + b 2 sin 2 α . (2.6)2.2 The Local Geographic FrameAt any point on Earth’s surface, the local geographic frame is defined by the almost flatground and the vertical direction, and is relevant because it is the basic reference theaircraft flies against, defining straight and level flight and of course the direction of down.This is an intuitive frame for any scenario whose total extent is no more than some tensof kilometres.Two coordinate systems are used: both cartesian with their origins at the point inquestion. In the North–East–Down or NED frame, shown in Figure 2, the local directionsof north, east, and down define a right-handed set of three axes. An alternative choiceof cartesian axes is the local East–North–Up set (ENU). In both axes sets, the north andeast directions define a plane tangent to Earth’s surface. At any point, north points alongthe local meridian, while east points along the local small circle of constant latitude.The up/down or vertical direction is perpendicular to this plane. In general, the verticaldirection does not intersect Earth’s centre. Rather, it makes an angle of the latitude withthe equatorial plane, shown as the angle α in Figure 2.4