Improved closed-form approximation for Dutch roll

An improved Dutch-roll approximation that includes the effects of roll as w ell as those of sideslip and yaw is presented. This new approximation is ba sed on a Taylor series expansion in one over the roll damping derivative. T he eigenvalues obtained from this solution are identical to those obtained from the traditional Dutch-roll approximation when the roll-damping derivat ive approaches infinity. From the new closed-form approximation, the Dutch- roll frequency is shown to be a function of a dimensionless parameter, whic h the author has called the Dutch-roll stability ratio. In addition, this n ew solution shows that there are three distinct components to the Dutch-rol l damping. The first is the conventional yaw damping term, but the present solution points out two other contributions to the Dutch-roll damping, Thes e are called the Dutch-roll coupling and phase damping In most cases, the y aw damping is the largest of these three components. However, both the coup ling and the phase damping can degrade the total Dutch-roll damping and, un der certain conditions, could cause the Dutch-roll motion to become diverge nt.