Here's a quote from the user's manual provided with the automotive accident reconstruction program CRASHEX (Computerized Reconstruction of Approach Speeds on the Highway, EXtended), of which (both manual and program) I am the author. It explains the "upside-down" axis system used in the aircraft and (therefore) automotive industries. That is, upside-down when compared with the X=right, Y=up "scientific" axis system.Albert G. Fonda, King of Prussia, PA (see www.crashex.com). Permission granted to quote.
The axis system naturally adopted for the automobile was formalized in SAE J670, Vehicle Dynamics Terminology, still in print and still applicable. The J670 automotive axis system is exactly the industry-standard aircraft system, as automobiles are simply airplanes with a different shape--preferably not airborne. But a further and less evident fact is that the aircraft system in turn is exactly the ancient maritime and map-making system, expanded from two to three dimensions.
Maritime navigators and map-makers long ago standardized on the compass rose. But the compass echoes the clock face, which in turn mimics the direction of sweep of the sun across the sky when facing South in the Northern hemisphere, and the consequent sweep across the ground of any shadow as observed in the dominant culture of that hemisphere. Accordingly, navigational angles increase toward the right when facing out from any location, with zero usually at the top. Rotation (yaw) is thus positive "clockwise." This is a convention which is not to be contradicted.
But rotation, like translation, is a vector. Using the right-hand screw rule for angular vectors (same as the right-hand screw rule for wood screws), rotation is a downwardly positive vector. If we accept the right-hand screw rule, and yaw as positive clockwise, then we are not free to make height positive upward!
In the resulting system, submarines dive positively from the surface; airplanes and buildings rise negatively. Of course, we can use "altitude" or "height" as a name for the absolute value of the vertical coordinate, which merely ignores the sign. Still, in the navigational axis system, "up" is necessarily and unavoidably negative. This is a lesser evil than counterclockwise positive yaw would have been. [For the "mathematical" system of X to the right (thumb) and Y forward (first finger), Z (second finger) would be acceptably positive Up, but Yaw would be unacceptably positive counterclockwise.]
For two-dimensional navigation, the conventional maritime axis system has one axis positive to the North, and one axis positive to the East. Locations are measured by the distances from such axes (Cartesian coordinates). While two other possible XYZ options exist, we further decide that X (the thumb, using the right-hand analogy) should be North, Y (the first finger) should be East, with Z (the second finger) Down. The respective rotations then are called roll, pitch, and yaw.
Thus the general vehicular axis system has been meticulously developed and widely agreed upon for use on land and sea, and in the air. As arbitrary as it may first appear, it does in fact trace back to the medieval map-makers, the first clock-makers, and our right-handedness. It is a widely accepted, logical, and appropriate system.