NAVWEPS 00-8OT-80  STABILITY AND CONTROL  depending on the nature of the dihedral effect  of the airplane.  pitch frequency and yaw frequency. Gen-  erally, the greater the static longitudinal and  directional stability, the higher will  be the  coupled pitch-yaw frequency. When the air-  plane is subject to roiling motion, the inertia  couple disturbs the airplane in pitch and yaw  with each roll revolution and provides a dis-  turbing forcing function.’  If the airplane is  rolled at a rate equal to the coupled pitch-yaw  frequency, the oscillatory motion will either  diverge or stabilize at some maximum ampli-  tude depending on the airplane characteristics.  It should be noted that initial inclination of  the inertia axis above the aerodynamic axis  will cause  the inertia couple to provide adverse  yaw with rolling motion.  If the inertia axis  were initially inclined below the aerodynamic  axis (as may happen at high 4 or negative load  factors), the roll induced inertia couple would  provide proverse yaw.  Thus, roll coupling  may present a problem at both positive and  negative inclination of the inertia axis depend-  ing on the exact aerodynamic and inertia  characteristics of the configuration.  The longitudinal stability of the typical high  speed configuration is much greater than the  directional stability and results in a pitch fre-  quency higher than the yaw frequency. In-  creasing the directional stability by increasing  the vertical tail area, addition of ventral hns,  or use of stabilization systems  will increase  the  coupled pitch-yaw frequency and raise the roll  rate at which a possible divergent condition  could exist. Increasing directional stability  by the addition of ventral fins rather than by  addition to the vertical tail has an advantage  of not contributing to the positive dihedral  effect at low or negative angles of attack.  High dihedral effect makes higher roll rates  more easily attainable in roll motion where  proverse yaw occurs.  As a result of the aerodynamic and inertia  coupling, rolling motion can induce a great  variety of longitudinal, directional, and lateral  forces and moments. The actual motion of  the airplane is a result of a complex combina-  tion of the aerodynamic and inertia coupling.  Actually, all airplanes exhibit aerodynamic  and inertia coupling but of varying degrees.  The roll coupling causes  no problem when the  moments resulting from the inertia couple are  easily counteracted by the aerodynamic re-  storing moments. The very short span, high  speed modern aircraft has the capability for  the high roll rates which cause large magni-  tudes of the inertia couple. The low aspect  ratio planform and flight at high Mach number  allow large inclination of the inertia axis with  respect to the aerodynamic axis and also add  to the magnitude of the inertia couple. In  addition, the aerodynamic restoring moments  deteriorate as a result of high Mach number  and angle of attack and can create the most  serious roll coupling conditions.  Since the uncoupled yawing frequency is  lower than the pitching frequency, a divergent  condition would lirst reach critical proportions  in yaw, closely followed by pitch.  Of course,  whether the airplane motion becomes  divergent  directionally or longitudinally is of academic  interest only.  There is one additional type of coupling  problem that is referred to as “autorotative  rolling.”  A rolling airplane which has a high  positive dihedral effect may reach a large pro-  verse  sideslip as a result of the inertia couple and  the rolling moment due to sideslip may exceed  that available from lateral control.  In such  a case it would not be possible to stop the air-  plane from rolling although lateral control  was held full against the roll direction.  The  Since the roll coupling induces pitching and  yawing motion,  the longitudinal  and direc-  tional stability is important in determining the  overall characteristics of the coupled motion.  A stable airplane, when disturbed in pitch and  yaw, will return to equilibrium after a series  of oscillations.  For each flight condition, the  airplane will  have a coupled pitch-yaw fte-  quency between the uncoupled and separate  317 