The theory of design optimization based on stability maximization of a passive gyroscopic damper(PGD)is discussed and applied to the stabilization of a ropeway carrier. The design formulae maximize the degree of stability of the linearized model, which is defined as the negative of the maximum value of the real part of the characteristic roots. The new design is analyzed using the linearized model of the PGD and the nonlinear model in order to investigate the practical characteristics of the formulae. It is found that the transient responses are almost the same as those obtained from numerical optimization designs. The new design formulae are very simple, but the responses are improved compared to those obtained using previous linear designs. The formulae have been successfully used to design a V-gimbaled PGD for a full-scale ropeway carrier. The step responses of this test are presented.