3741 HYDROGRAPHIC MANUAL PaGE 290 



This completes the' work on the layout sheet. The same procedure is followed for 

 every pair of stations to be used on the survey sheet. 



6. Computations 



Before the arcs can be constructed on the large-scale sheet the following computa 

 tions must be made: 



(1) Compute the distance and azimuth, by an inverse computation if necessary, between each 

 pair of stations to be used. 



(2) Compute the geographic position of midpoint D between adjacent stations. 



Where distances between stations do not exceed 25,000 meters and the latitudes are not higher than 15°, the position may be 

 obtained by taking the means of the latitudes and longitudes of the adjacent stations. This gives the position as accurately as it can 

 be plotted. 



(3) By means of equation (4) compute the d distances along the perpendicular bisector (Line of 

 Centers) from the midpoint D to the centers of the curves for the entire range of curves to be drawn 

 ■»n the sheet. Compute also the radii of the curves (c distances) by means of equation (5). 



Curves should be drawn to the limits of the sheet, as a fix is often desired beyond the limits of the hydrography. Arcs drawn for 

 every degree above 20° and tor every half degree between 10° and 20° usually give sufficient accuracy. For plotting between the arcs 

 small spacing dividers will be found helpful for interpolation. 



(4) Compute the geographic positions of the centers for the four arcs selected on the layout 

 sheet (see 3741a(2)). 



(5) Compute the geographic positions of the three points {A, B, and C) selected on each of the 

 four arcs on the layout sheet. This is readily done by using the computed radii (see (3) above) and 

 the assumed azimuths as scaled from the layout sheet (see 374 la (4)). 



c. Constructio7i of arcs 



When the graduated perpendicular method is used, the physical construction of 

 the arcs on the large-scale sheet can be accompHshed in one of the following three 

 ways; 



1. With beam compass. 



2. By computation. 



3. With three-arm protractor. 



1. With beam compass. — In this method, a special beam compass about 8 feet long is required. 

 This will permit drawing curves with a 30-mile radius on a 1:20,000 scale sheet and will probably 

 meet most requirements. The beam should be of sturdy construction to eliminate sag. A beam 

 made of well-seasoned wood in the form of a 2 -inch T in cross section has been found to have the 

 required amount of rigidity. Two beams spliced together have been found unsatisfactory. A drafting 

 table large enough to accommodate the survey sheet and the Line of Centers is necessary. 



A projection is first constructed on the survey sheet. It is then placed on the drafting table in 

 such a position that none of the centers is beyond the limits of the table top. This can be easily 

 ■done from an inspection of the layout sheet and by determining the direction of the Line of Centers 

 and its approximate distance from one of the edges of the survey sheet. The latter is then thumb- 

 tacked in position. A piece of boat-sheet paper is then tacked on the drafting table where the Line 

 ■of Centers is expected to fall. The width of the boat-sheet paper will allow for the approximation 

 in position. 



A narrow strip of boat-sheet paper slightly longer than the radius of the longest arc to be swung 

 is secured to the table for use in measuring long distances. Intervals of 10,000 meters (the length 

 of the 1:10,000 scale meter bar) are laid off along a straight line on the strip of paper and marked 0, 

 10,000, 20,000, 30,000, etc. A small piece of celluloid is fastened over the zero point to prevent 

 •excessive wear from the repeated measurements necessary from this point (see 7631). In laying off 

 the lengths of the radii, the increments from the 10,000-meter intervals should first be plotted and 

 then the total distances set on the beam compass. 



The three points, A, B, and C(fig. 63), on each of the four arcs on the layout sheet are plotted on 

 the survey sheet by their geographic positions (see 37415(5)). With these points as centers and with 

 the c values as radii (see 37416(3)) arcs are swung on the strip of paper on which the Line of Centers 



