Relative efficiencies of square and triangular grids in the search for elliptically shaped resource target

The relative efficiencies of equivalent-density, square and equilateral triangular (hexagonal) grids used in the search for elliptical targets are determined for ellipses having relative semi-major axes ranging from 0.50 to 1.00 of the square grid spacing and having shapes (minor axes/major axes) ranging from 0.2 to 1.0. Using the probability of one or more hits, the grid types are equally efficient for targets having semi-major axes less than or equal to one-half of the grid spacing. The triangular grid is as much as 6 percent more efficient for targets having relative sizes greater than 0.50. The square grid is less than 1 percent more efficient in a small region centered on a relative size of 0.80 and a shape of 0.45. Both grids are equally efficient for targets that are hit with certainty and tend toward equal efficiency as the ellipses become more needlelike in shape. A random search is more efficient than both grid types when the relative size is less than 0.50 and the probability of two or more hits is used to define relative efficiency. For two or more hits and targets having relative sizes larger than 0.50, the triangular grid is as much as 91 percent less efficient than the square grid; however, the probabilities are small. In a region centered on a relative size of 0.80, the triangular grid is slightly more efficient if the criterion is two or more hits. The probability of two or more hits is inversely related to the probability of one or more hits for many target sizes and shapes.