pecified case. The equation is As it is difficult to determine A directly with sufficient curacy, it is usually advisable to determine the product E, which is equal to (P2- P1)L/AL, where L is the nomal length of the tape supported throughout, and AL is the ange in length when the tension is changed from P1 P. Nomogram for Tension of Accuracy. The solution of the bie equation to determine the tension of accuracy of a pe supported in a catenary can be carried out rapidly graphical means, using a nomographic chart, the nation being in Soreau's canonical form IV。. Figure 6 is such a chart, the value of a being 0.00000645 r deg F, and t。 is 68° F. To use this chart to find the sion of accuracy, P1, for a tape, place a straightedge the point representing the constant AEa, axis A, and the point representing the observed temperature t1, lined scale B. The intersection of the straightedge th the dummy axis C is noted. The straightedge is en placed on this point and on the point representing the lue Po, axis D. The point where the straightedge ersects axis E is determined. Place the straightedge Sureau, Nomographie, pages 172, 174, 184, and 192 (Chiron, Paris, 1921). (AEw2d2)/24, axis G. The point where the straightedge intersects curve F determines the tension to apply to the tape under the given method of support and at the observed temperature t1. It should be noted that the constants AEa, Po, and (AEw2d2)/24 are constants of the tape, independent of the conditions of its use and can be permanently marked on the chart for each tape, in the office, in preparation for use of the chart in the field. It should be noted that for short lengths of tapes the value of the constant K=(AEw2d2)/24 will be small. The point of intersection of the straightedge with axis F will then often be somewhat indefinite on the chart, although the calculated value of the intersection is of course definite. This, however, is not serious as the length of a short interval of a tape changes very little for a 1 or 2 lb change in tension. For example, a 25-ft length of tape weighing 0.010 lb/ft will change in length only approximately 0.002 in, when the tension is changed from 10 to 12 lb when supported at the 0 and 25-ft intervals. For 100-ft tapes, using the 100-ft interval, the change in length is very apparent for a 0.5-lb change in tension. In this case the chart and formula have been found to be in agreement with the observed values determined by actual test for various tapes tested at the Bureau. Although fewer tests have been made for tapes longer than 100 ft, it is believed that the chart and formula will apply equally as well. Other nomograms may be drawn whose constants do not come within the scales on the nomogram shown in figure 6, of if conditions are such that a greater accuracy can be used than can be obtained on this chart, a new one can be drawn on suitable paper, with axes E and G further apart. Attention is also called to the fact that the value Po determined for the total length or for one specified interval of a tape does not necessarily apply to all intervals on the tape. This may be due to one or more of the following conditions: A slight nonuniformity of graduation, a lack of homogeneity, or a lack of uniformity in cross section of the tape. For example, for one tape weighing 0.010 lb/ft, the value Po was found to vary from 0.5 to 1 lb for the intervals 0 to 25 ft 0 to 50 ft, 0 to 75 ft, and 0 to 100 ft. WASHINGTON, May 31, 1955. U. S. GOVERNMENT PRINTING OFFICE: 1956 |