# Principal Axis Inclination Instability

Lateral-directional dynamic instability due to nose-down inclination of the princi­pal axis is not strictly a high Mach number or compressibility phenomenon. However, this type of instability is linked to high-speed flight, and so it is included in this chapter.

The symmetric principal axis is defined as that airplane body axis in the plane of sym­metry for which the product of inertia Ixz vanishes. Mathematically, Ixz = f xz dm, where x and z are the X – and Z-axis coordinates of each elementary mass particle dm. Weights high on the vertical tail, such as a T-tail, cause the principal axis to be inclined nose-downward with respect to normal body axes.

A nose-down inclination of the principal axis with respect to the flight path desta­bilizes the lateral-directional or Dutch roll oscillation (Sternfield, 1947). Actual lateral – directional dynamic instability due to a nose-down inclination was encountered dramati­cally in May 1951 by the NACA test pilot Bill Bridgeman. This was in a series of flight tests of the Douglas D-558-2 Skyrocket research airplane. In tests reaching a Mach number of 1.79 serious rolling instability occurred during pushovers after rocket-powered steep climbs. The principal axis inclination to the flight path becomes quite nose-down during pushovers.

The test team evidently failed to connect the rolling instability with the principal axis effect and concluded that even higher speeds could be reached safely. Bridgeman was asked to nose over from the climb to a very low factor of 0.25, in an effort to reach a Mach number of 2.0. According to Richard Hallion (1981):

the Skyrocket rolled violently, dipping its wings as much as 75 degrees. He cut power, but the motions, if anything, became even more severe. Finally he hauled back on the control column, for the Skyrocket was in a steep dive and getting farther and farther away from the lakebed. The plane abruptly nosed up and regained its smooth flying characteristics, and he brought it back to Muroc.

However, concerns about Dutch roll instability due to principal axis nose-down inclina­tion have been eliminated by the almost universal use of yaw damping stability augmentation on high-speed airplanes.