276 



DEEP BOREHOLE SURVEYS AND PROBLEMS 



^Off Vertical 

 Angle 



NOMOGRAPHIC AND ALIGNMENT METHODS 



These simple and easily understood charts are becoming 

 more and more popular because they can, as a rule, be 

 manipulated by the boring personnel and others who wish 

 to save time. 



Figure 185^ shows the well-known versed-sine relation 

 which can be applied to a hole the deviation of which is 

 either regular or can be approximately meaned throughout 

 its course, giving a straight deflection; that is to say, a 

 constant off -vertical angle. The alignment chart itself 

 (Fig. 186) is constructed by putting on the left 

 the logarithmic scale A with the scale of versed 

 sines Bi or Ci on its right and the vertical 

 correction scales corresponding at B2 and Co- 

 To get a correction, place a straightedge 

 at the desired depth of hole on A scale, say 

 100 ft., and at the proper off-vertical angle on 

 Bi scale; continue and read off the correction 

 on B2 or C'z scale. If the straightedge falls 

 off scale B2, then use scales Ci and C2. If the 

 measured depth is greater than scale A divide 

 it by 10 and multiply the corresponding results 

 on B2 or C2 by 10. Thus if the depth is 2,500 

 ft. and the off-vertical angle 10 deg. use 

 250 ft. and multiply the resultant vertical correction of 

 3.75 ft. by 10, giving 37.5 ft. Use a transparent cellu- 

 loid straightedge with a fine black parallel line near one 

 edge. 



Based on Fig. 185 Mr. BrindeP discusses a simple employ- 

 ment of mathematical tables and formula, noting that 



1. By the Cosine Method. 

 The corrected measurement = (actual measurement) X 



(cosine of off- vertical angle), 

 i.e., in Fig. 185 AB = AD 

 cos BAD. 



1 Brindel, H. F., Oil Gas Jour., p. 41, Apr. 11, 1929. 



2 Ibid., p. 41. 



Fig. 185. 



