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Tutorials Dynamic Analysis of Lightly Iced Conductor Galloping in Two Degrees of Freedom A.S. Richardson, Jr., B.Sc., M.Sc., Sen. Mem. I.E.E.E. This particular paper was selected for the first Tutorial is because it illustrates the "Root Locus Method," as it is applied to the control of Galloping Conductors. This method has been applied in automatic control theory and in the field of Aeroelasticty for well over thirty years. It is a powerful tool to use in explaining the variation of system parameters, such as wind speed, on the dynamic response of the system. Here, the system is assumed to behave linearly; i.e., a particular input parameter, when varied, produces a proportional response in the variables of the system. Usually, the theory is limited to "small changes of the variables about some initial condition". If the root locus identifies certain ranges of the parameters that become unstable, then that regime of amplitude build-up must be treated by other methods to be introduced in subsequent Tutorials. Such responses are termed "non-linear." Link to text entitled: Dynamic Analysis of Lightly Iced Conductor Galloping in Two Degrees of Freedom Predicting Galloping Amplitudes by A. S. Richardson, Jr., P.E. These companion papers are based on the Describing Function Method used by control system designers to predict behavior of dynamic systems. The method is based on the assumption that the system is lightly damped and when it vibrates it takes on the response of one mode at a time, which simplifies the analysis. In the case of galloping conductor motion the assumption may be applied to the first mode or second mode. In part I of the paper the analysis assumes zero mechanical damping. The predicted amplitude of gallop is a limit reached by energy balance between wind input and aerodynamic drag. The amplitude of gallop in this case is found from the dynamic angle of attack, which in this case is constant, and depends upon the ice shape. The gallop amplitude increases with wind speed and is inversely proportional to the gallop natural frequency. In part II of the paper the role of mechanical damping is introduced. The dynamic angle of attack is found to build up from zero to the same angle of attack found in Part I for the given ice shape. Again, the gallop amplitude may be calculated as in Part I along this build-up curve. The mechanical damping is what establishes a

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