Appendix A 

 PROPAGATION OF MEASUREMENT ERRORS 



The random error, Oy , in relative elevation, y(, is computed from the equation: 



< = Z 



a?i "'■' 



where ^j = Rj 

 tj = H 



U = h 



From Equations 1 through 5 presented in the main text: 



v;— = - I sin 6 + — cos 6 I 



9R2 B \ V / 



r?h) sine +(^-?-^)cose 

 ) sine + (^-^-^^cose 





3yt 1 



Example calculation: 



Let Rj = 83 feet; Oj^ = 0.5 foot 



R, 



121 feet; 



0.5 foot 



H = 42 feet; CTjj = 0.5 foot 

 h = 20 feet; a^^ = 0.5 foot 



Therefore, 9yj/9Rj = 3.76 

 ay(/aR2 = -3.58 

 9yj/3H = 3.58 

 ayj/ah = -1.18 



Oy^ = 'V<*'-5)^|(3-76)2 + (3.58)2 +(3.58)^ + (1.18)^ [ ^ 3.2 feet 



(A-1) 



14 



