A technique for the solution of the catenary problem in surveying

A technique for solving efficiently the catenary problem encountered in surveying with tapes is presented. The theory of the catenary solution is outlined, and our technique is shown to solve correctly the catenary for all conditions. Analysis of error that compared the catenary correction to the more commonly used parabolic correction indicated that for slopes over 10 degrees and taped distances greater than 200 feet, systematic error inherent in the parabola may preclude the accuracy required for second- or even third-order surveys. An analysis of tension-gauge bias on taping errors is similar, but here the error is found to depend almost entirely upon taping distance.