• Home
  • Download PDF
  • Order CD-ROM
  • Order in Print
Figure 7-8.Latitude and departure. - 14070_129
Figure  7-14.Form  for  adjusting  latitudes  and  departures. - 14070_131

Engineering Aid 1 - Advanced Structural engineering guide book
Page Navigation
  109    110    111    112    113  114  115    116    117    118    119  
Figure 7-11.—Graphic solution of a closed traverse by latitude and  departure. Figure 7-11 is a graphic demonstration of the fact that, in a closed traverse, the algebraic sum of the plus and minus latitudes is zero; and the algebraic sum of the plus and minus departures is zero. The plus latitude of CA is equal in length to the sum of the two minus latitudes of AB and BC; the minus departure of BC is equal in length to the sum of the two plus departures of CA and AB. LINEAR ERROR OF CLOSURE.— In  practice, as you will learn, the sum of the north latitudes usually differs  from  the  sum  of  the  south  latitudes.  The difference  is  called  the  error  of  closure  in  latitude. Similarly, the sum of the east departures usually differs from the sum of the west departures. The difference is called  error  of  closure  in  departure. From the error of closure in latitude and the error of closure in departure, you can determine the linear error of closure. This is the horizontal linear distance between the location of the end of the last traverse line (as computed  from  the  measured  angles  and  distances)  and the actual point of beginning of the closed traverse. For example, you come up with an error of closure in  latitude  of  5.23  feet  and  an  error  of  closure  in departure of 3.18 feet. These two linear intervals form the sides of a right triangle. The length of the hypotenuse of this triangle constitutes the linear error of closure in the traverse. By the Pythagorean theorem, the length of the  hypotenuse  equals  approximately  6.12  feet.  Suppose the total length of the traverse was 12,000.00 feet. Then your  ratio  of  linear  error  of  closure  would  be 6.12:12,000.00,  which  approximately  equates  to 1:2,000. CLOSING A TRAVERSE.— You close or balance a traverse by distributing the linear error of closure (one within the allowable maximum, of course) over the traverse. There are several methods of doing this, but the one most generally applied is based on the so-called compass rule. By this rule you adjust the latitude and departure  of  each  traverse  line  as  follows: 1. Correction in latitude equals the linear error of closure in latitude times the length of the traverse line divided by the total length of traverse. 2. Correction in departure equals the linear error of closure in departure times the length of the traverse line divided by the total length of traverse. Figure 7-12 shows a closed traverse with bearings and distances notes. Figure 7-13 shows the computation of the latitudes and departures for this traverse entered on the type of form that is commonly used for this purpose. As you can see, the error in latitude is +0.33 foot, and the error in departure is +2.24 feet. The linear error of closure, then, is The total length of the traverse is 2614.85 feet; therefore, the ratio of error of closure is 2.26:2614.85, or about 1:1157. We will assume that this ratio is within the allowable maximum. Proceed now to adjust the latitudes and departures  by  the  compass  rule.  Set  down  the  latitudes and departures on a form like the one shown in figure 7-14 with the error of closure in latitude at the foot of the latitudes column and the error of closure in departure at the foot of the departures column. Figure 7-12.—Closed traverse by bearings and distances. 7-10







Western Governors University

Privacy Statement
Press Release
Contact

© Copyright Integrated Publishing, Inc.. All Rights Reserved. Design by Strategico.