Empirical Formula of the Attenuation Constant of Microwave band in Head Race Tunnels

Abstract

This paper derives an empirical formula of an attenuation constant inside small cross-section tunnels (2m²-13m²) which are used as headraces in hydroelectric power stations. E lectric feild strength/distance inside the tunnel was measured (1.9GHz-18GHz), and the obtained data was submitted to statistical analysis.
The attenuation constant obtained from linear regression analysis was larger than that reported by researchers.
With the attenuation constant as a criterion variable, multiple regression analysis was conducted. Examining the correlation and regression coefficients gave two parameters with highly partial F values. One is the fundamental attenuation constant term of (λ²/r³), the same as the previously reported parameter, and the other is the additional loss term of (λ^0.28/e^0.66r) We proposed.
The parameters yielded an empirical formula which estimates the attenuation constant in the waveband (0.006m≤λ≤1.5m) broader than before. [4175•(λ²/r³)+64.4•(.λ^0.28/e^0.66r)] The attenuation constant using the empirical formula agreed with that obtained from experiments, confirming the effectiveness of our proposed empirical formula.
It was concluded that the attenuation constant in the Giga-hertz range includes additional loss, resulting in the analysis value larger than the previous value.