A century of phugoid approximations

Abstract

It is stated in most flight dynamics texts that the phugoid approximations provide poor estimates while the short period approximations are accurate. The survey in this paper reveals that there are at least five approximations to the phugoid. The extent of departure of each of these from the exact value is determined for a fairly extensive database representing various aircraft in different flight conditions. It is found that most of them are inadequate in predicting the phugoid characteristics accurately. Nonetheless, two approximations to the phugoid frequency that seem to have remained unnoticed are seen to be exemplary. On the other hand, no worthy approximation exists for the phugoid damping. With this background, a fresh approximation for the phugoid mode is put forth herein. It is derived by equating the coefficients of the product of the short period equation (which has been shown to be very accurate) and the phugoid equation (as yet unknown) to the coefficients of the fourth-order characteristic polynomial. The new approximation is shown to be accurate.