42 



TRANSPORTATION ON LAND BY VEH1CLES:-THE ROADS 



16' 



of (d) perpendiculars (e) the length of which is equal to . Join the end of (e) with the ends 



b 

 of (d). Erect in the middle of each line of junction a perpendicular, the length of which is 



The ends of the perpendiculars and of the lines of junction are points of the curve. 



3. The chord method :- Divide each side of the angle into an equal number of sections. Join the 

 section points 1, 2, 3, 4, ii of one side with the section points N-IV, ill, 11, 1, of the opposite side. 

 The intersections of corresponding lines are the curve points. 



4. The plane -table method :-Sm\ey and sketch the tangents to be joined by a curve and the 

 distance between them; draw into the sketch thus obtained, with the help of dividers, the curve 

 in such manner as suits the topography and of such n 



radius as is indicated. Stake out with the help of the 

 plane table as many of the curve points thus obtained 

 as may be necessary. In the absence of a plane table, 

 a camera tripod or even a soap box can be used to 

 good advantage. 



PROBLEM :- Connect AD and B D by a curve, using the 

 plane table, starting at A, and ending at any point on line B D. 



1. Set up the plane table at A, and enter direction A D and A B. 

 (B assumed point.) 



2. Measure and enter distance A B. 



3. Move table from A to B ; adjust it by backsighting to A; get 

 and enter direction B D. 



4. Cut off and enter A D on B D, reaching E. 



5. Draw perpendiculars in A and E, finding the center of the 

 curve in the point of intersection. 



6. Draw the curve, on the paper, with the help of a string, or of 

 dividers. Sketch a series of chords, of convenient length, 

 (e. g. 1 chain long), from A on round the curve to E. 



7. Set-up the table at A, transfer the chords, one after the other, from the table to the field, marking the end -points 

 consecutively by stakes. 



5. The method of equal offsets in equal chords (hamtnering method). The usual offset or "hammer" 

 is (tg ci ;■ P) feet, the chord subtended over angle a being P feet long. For small angles, tg a 

 can be substituted for sin a. The way of proceeding is as follows :- Prolong the straight line 

 (tangent) over the beginning point (E) of the curve by P feet. Erect a perpendicular offset, the 



Join B to beginning 



point E; prolong this line by P feet and erect at the end A of the prolongation a perpendicular 

 offset, the length of which is P tg ?, ending in C. Then join C to B, and prolong the line of 

 junction by P feet, erecting a perpendicular P x tg 'j. at the end of the prolongation, &c., &c. 

 The ratio between 'j, P, and the radius of the curve R is:- 



P 



length of which is P < tg , at the end of the P feet which brings you to B. 



sm y- = 



PROBLEM: -Connect E E, and 

 F F, , two parallel lines, by the best pos- 

 sible curve with the help of the ham- 

 mering method. The length of the tape 

 (or of a pole cut in the woods) is P. 



1. Measure E F (vertical distance 

 of the parallels) using it for 

 diameter of the curve to be 

 designed. If the diameter 

 equals 160 feet, the radius R 

 equals 80 feet. 



2. Obtain by calculation the length 

 of the ham merh, in triangle ABC. 



2R 



