Energy-Efficient Regular Strip Covering with Fixed-Size Identical Sectors

We consider the problem of covering a strip with identical sectors of given size in order to minimize the coverage density. Early in the literature, researchers considered the problems of constructing strip covers with circles, ellipses, and sectors of minimum density by proposing various covering models and determining the optimal values of the parameters of the covering figures for each model. In this paper, we consider identical sectors as covering figures and specify their parameters instead of optimizing them. We propose several new covering models and found a formula for calculating density for each model. Unfortunately, these formulas are quite cumbersome, which did not allow us to compare the densities of all covers analytically. Therefore, we defined some properties programmatically. As a result, a minimum density coverage model was determined for different values of the sector’s parameters.