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Nomogram for Tension of Accuracy. The solution of the bic equation to determine the tension of accuracy of a ape supported in a catenary can be carried out rapidly y graphical means, using a nomographic chart, the quation being in Soreau's canonical form IV。.
Figure 6 is such a chart, the value of a being 0.00000645 er deg F, and to is 68° F. To use this chart to find the ension 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, melined scale B. The intersection of the straightedge ith the dummy axis C is noted. The straightedge is hen placed on this point and on the point representing the alue Po, axis D. The point where the straightedge tersects axis E is determined. Place the straightedge
Soreau, Nomographie, pages 172, 174, 184, and 192 (Chiron, Paris, 1921).
on this point and the point representing the constant (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
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