Mathematical justification of the minimum required number of strain gauges for accurate ice load monitoring in an automated overhead contact wire monitoring system

Subject, purpose of work: This article analyzes the mechanical response of block compensator systems in overhead contact wires to mass increments from ice accretion. The work formally describes force interactions in two-block and three-block configurations and determines the sensitivity of reaction forces at attachment points to localized weight increases. Method or methodology: Using static equilibrium equations and geometric relationships, the study derives expressions for calculating compensator support forces while varying conductor mass and parameters. The analysis provides detailed formulas for reaction forces, deflection angles, and horizontal tension components. Through linearization, we establish sensitivity estimates for system response to small mass increments modeling initial ice formation stages. Work results: We demonstrate that increasing the number of blocks fundamentally alters force equilibrium structure and produces distinctly different sensitivity values. The study derives mathematical expressions enabling calculation of compensator support forces under varying conditions. Scope of results: The results enable practical applications in force sensor placement, weight measurement algorithms, engineering calculations for tension sections, and contact suspension behavior modeling under variable loading conditions. Conclusions: Our findings substantiate the effectiveness of mathematical block compensator models for quantitative diagnostics of overhead contact wire systems during winter operations and establish the methodological foundation for further research investigations.