Elementary Surveying (14th Edition)
Elementary Surveying (14th Edition)
14th Edition
ISBN: 9780133758887
Author: Charles D. Ghilani, Paul R. Wolf
Publisher: PEARSON
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Chapter 16, Problem 16.35P
To determine

Parameters of anerror ellipse

   The parameters of the error ellipse are:t=71˚5536Sx=±0.033ftSy=±0.021ft

Given that

(ATWA)-1 = qxxqxyqxyqyy = 0.00048940.00008900.00008900.0002457

Standard deviation of unit weight is given as S0= 1.45

Determine the rotational angle t using the equation:

tan(2t)=2(0.0000890)0.00

We know that

   qxy= 0.0000890qxx= 0.0004894qyy= 0.0002457

tan(2t)=2(0.0000890)0.00024570.0004894=0.730406

   t=12tan1(0.73046)+180=7155'36"

Determine the values of semi major axis Sm=S0qxxsin2t+2qxycosθsinθ+qyycos2θ

We know that,

   qxx= 0.0004894 qyy= 0.0002457 qxy= 0.0000890                       S0=1.45

Sx=S0 0.0004894sin2(7155'36")+2((0.0000890)cos(7155'36")sin(7155'36"))+(0.0002457cos27155'36")

= ±0.033ft

Determine the values of semi minor axis Sm=S0 qxxsin2t2qxycosθsinθ+qyycos2θ

We know that,

   qxx= 0.0004894 qyy= 0.0002457 qxy= 0.0000890 S0=1.45

Sy=S0 0.0004894sin2(7155'36")2((0.0000890)cos(7155'36")sin(7155'36"))+(0.0002457cos27155'36")

= ±0.021ft

Conclusion:

   The parameters of the error ellipse are:t=71˚5536Sx=±0.033ftSy=±0.021ft

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