A NEW METHOD FOR LAYING OUT CIRCULAR CURVES 

 BY DEFLECTIONS FROM THE P. I. 



By T. F. HiCKERSON 



With Three Text Figures 



The writer hopes that the tables based upon formulas given be- 

 low will fill the long-felt need of a simple and time-saving method 

 for laying out circular curves by deflections from the point of inter- 

 section of the tangents (the P. I.), thus avoiding the trouble of 

 moving the instrument and resetting the vernier. 



Referring to Fig. 1, P is any point on the circular arc CB and A 

 is the point of intersection of the tangents. Also C is the point of 

 curve (P. C), and B is the point of tangent (P. T.). Lines from 

 points A and to point P makes angles of and o. with the line AO, 

 these angles being plus when measured above AO and minus when 

 below it. PN is drawn perpendicular to AO. The deflection angle is 

 called A. 



PN R siu a R sin a 

 Ton e = — = 



AN E + E — R t-os a R (sec V^ A — 1) -|- R — R cos a 



sin a 



Hence, tan 6 = (1). 



see y-2 A — cos a 



Formula (1) shows that for a given value of A^ the angle is 

 independent of the radius of the curve or the length of curve. 



Imagine the curve divided into ten equal parts, then formula (1) 

 gives the deflections to these points of division as follows : 



sin ti A 

 a = tio A, tan 91 = — 



a = •)i() A . tan 9^ :=: 



a = ri A , tan 9 ;, = 



a =z '',](i A , tan 9 < = 



sec y. A — cos lioA 



a = (). 9 , =: O , 



a = — iioA, 9 „ = — e,, 



^ = — -;ioA, 9 , = — 9:., 



a = — %oA, 9 , = — 9„ 



a = — Mo A, 9 ,, = — 9,, 



a =3 — s^ioA, 9,„ = — i/,(18() — A). 



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