Solution to problems in sags and spans

Solutions for sag and span problems occurring in overhead line construction have been developed from time to time by many authors. Frequently during the process of development one author has taken up the work where his predecessor left off and has endeavored to make the formula more complete. Such solutions heretofore developed are approximate, and apply to the case where the sag is very small compared to the span. All solutions up to the present time are based upon the assumption that a span of wire forms the arc of a parabola. The formulæ are approximately derived and are mathematically inconsistent. For instance, the formula for length of arc in a span, instead of being derived from the parabola is derived in an approximate manner from the circle. Again the stress value is taken at the center of span and assumed to be constant at every point along the wire, when in reality it varies at every point, reaching maximum values at the supports. Further certain small errors occur in formulæ dealing with the effect of changes in temperature and stress. Again, in the case where one support is higher than the other, a certain discrepancy occurs which will be explained later under that particular heading. However, when the sag is very small compared to the span, the error introduced by the formulæ is of no practical consequence, although when the sag increases sufficiently there may be considerable error introduced. The data produced by the solutions are adaptable to a limited number of span values and usually are adaptable to only one material. Complete recalculation is necessary for a second material.