and an engineer’s scale, just to have a general idea ofwhere to start. Make sure that the figure will fitproportionately on the paper of the desired size. Startingat point A, you draw the meridian line lightly. Then youlay off AO, 10 inches (or any convenient round-figurelength) along the referenced meridian. Now, from O youdraw a line OP perpendicular to AO. Draw a light lineOP as shown. In a trigonometric table, look for thenatural tangent of the bearing angle 26°90', whichequals to 0.49098. Find the distance OP as follows:OP = AO tan 26°09' = 4.9098, or 4.91 inches.You know that OP is equal to 4.91 inches. Draw APextended; then you lay off the distance AB to scale alongAP. Remember that unless you are plotting a closedtraverse, it is always advantageous to start your offsetsfrom the referenced meridian. The reason is that, afteryou have plotted three or more lines, you can always usethis referenced meridian line for checking the bearingof the last line plotted to find any discrepancy. Thebearing angle, used as a check should also be found bythe same method (tangent-offset method).Now to plot the directions of lines from deflectionangles larger than 45°, you have to use the com-plementary angle (90° minus the deflection angle). Toplot the direction of line BC in figure 7-37, draw a lightperpendicular line towards the right from point B.Measure off again a convenient round-figured length,say 10 inches, representing BOJ. The complement of thedeflection angle of BC is 90° – 78°25' = 11°35'.The natural tangent value of 11°35’ is equal to0.20497. From O1 draw OIP1 perpendicular to BOI.Solving for OIPl, you will haveO]PX= BO]tan 11°35' = 2.0497, or 2.05 inches.Now lay off the distance OIPA Draw a line from Bthrough PI extended; lay off the distance BC to scalealong this line. The remaining sides, CD and DA, areplotted the same way. Make sure that the angles used foryour computations are the correct ones. A rough sketchof your next line will always help to avoid majormistakes.When the deflection angle is less than 45°, theprocedure of plotting by tangent is as shown in figure7-38. Here you measure off a convenient round-figurelength (say 500.00 feet) on the extension of the initialtraverse line to locate point O, and from O, draw OPperpendicular to AO. The angle between BO and BC is,Figure7-38.—Plotting by tangent-offset method from deflectionangle smaller than 45°.Figure 7-39.—Plotting by coordnates.in this case, the deflection angle. Assume that23°21'. The formula for the length of OP isthis isOP = BO tan 23°21' = 500 x 0.43170= 215.85 feet.PLOTTING BY COORDINATES.— A commonand accurate method of plotting by coordinates is shownin figure 7-39. Here you simply locate each station byits coordinates and have no angular measurements tobother about. To plot station B, for instance, you wouldlayoff from O on the Y axis a distance equal to theY coordinate of B (847.60 feet). Draw a light line fromthis point perpendicular to the Y axis, and measure offon this line a distance equal to the X coordinate of B(125.66 feet). The remaining points are plotted in thesame way.7-26

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