14 



TUNNELINC 



FIG. 6. Diagram Showing Method 

 of Determining Tangent Offsets 

 for Arcs of over 90. 



Substituting these values in equations (1) and (2) we 



have, y = r Vr* d*. 



When the arc AB is greater than a quadrant, as in Fig. 6, 



the projection AF of the arc becomes equal to its radius, and 



for any value of d between this pro- 

 jection and that of the chord AK 

 there are thus two values of y, viz., 

 y and y 2 , both deduced from the 

 formula, y = r Vr 2 cP. 



Assuming the value of d = AG, 

 to locate the point If, GH = y^ = r 

 Vr 2 d?, and to locate the point 

 I,GI= y 2 = r + Vr 2 - d?. 

 By giving to d the values between and AF, the various 



values for the tangent offsets are obtained. 



In staking out the center line of a curvilinear tunnel the 



greatest accuracy is required, since a very small error will throw 



the work out and cause 



serious trouble. At the 



beginning the excava- 

 tion is conducted as 



closely as may be to the 



line of the curve, and 



as soon as it has pro- 

 gressed far enough the 



tangent AT, Fig. 7, is 



ranged out. At B a 



point is located over 



which to set the instru- 

 ment, and the distance 



AB is measured for the 



purpose of finding the ordinate of the right angle triangle OA B. 



Now OA = r, AB d, and < = angle ABO. Then: Tang. 

 r 



*-y 





FIG. 7. Method of Laying Out the Center Line of 

 Curvilinear Tunnels. 



