Catenary line of absolutely flexible inextensible thread

Abstract

The paper deals with the comparison of experimental and theoretical catenary lines. It is assumed that the thread is in a uniform field of gravity. Theoretical catenary lines are obtained taking into account the assumption that the thread is absolutely flexible and inextensible. The calculation used the exact catenary equation and the approximate equation. It is shown that the exact catenary equation agrees well with experimental data in a wide range of thread sag values. The approximate catenary equation satisfactorily correlates with the experimental data for small sag. With an increase in the sag of the thread, the calculation error increases significantly. A catenary constructed using an approximate equation deviates considerably from the experimental curve. Based on the good agreement between the exact theoretical chain lines and the experimental curves, the results of calculating the sag and the maximum thread tension are compared using exact and approximate theoretical formulas, and the relative error of the calculation results obtained using the approximate formulas is determined. The limiting value of the ratio of the length of the thread to the length of the span is also determined, at which it is possible to use approximate formulas for a given calculation error.