Theory of Design and Calibration of Vibrating Reed Indicators for Radio Range Beacons

This paper gives a general treatment of the theory of design of vibrating reed indicators, which was developed in connection with measurement and design work on the tuned-reed course indicator for the aircraft radio range beacon. The equations and conclusions may be readily adapted to apply to any similar vibrating system. By assuming that a reed may be replaced by an equivalent particle, vibrating in the plane of the driving poles, the differential equation of motion is simplified greatly and becomes readily solvable for small vibrations. Equations are given for determining the constants of the equivalent particle from the dimensions and constants of the reed. The expression for the frequency of a loaded uniform reed, computed by a method equivalent to one given by Rayleigh, checks very closely with that obtained by Drysdale and Jolley for a similar reed. This theory for small vibrations is applicable when the amplitude is small enough so that its square may be neglected in comparison with the square of the air gap. From an analysis of large vibrations of tuning forks by Mallett, the behavior of the reed at relatively large amplitudes of vibration is inferred, although an exact quantitative verification of the theory is difficult. Design equations are given for uniform reeds and for the type used in the reed indicator.