Random Errors

Distance measured depends on observations and on the determination of quantities such as temperature t, tension or pull p, slope angle q or elevation difference h. Each of these quantities is subject to random errors which when propagated through the corresponding relations result in random errors in the distance. Thus the random errors cause random variation in the distance corrected for systematic errors. The random errors are of much lower magnitude than the systematic errors. The different sources of random errors in taping, designated by their standard error and these are: sv (standard error due to the plumbing of the tape ends), sm (standard error due to the marking the supported tape ends), sp r(standard error due to uncertainty in the value of the applied pull or tension), sh (standard error in determining either the slope angle q or elevation difference h), st (standard error in determining the temperature). A summary of the random errors in taping is given in Table 9.2

Table 9.2 Random errors in Taping

 

Designation

 

Source of random variation

Governing conditions, causes, and manner of cumulation

sv

Plumbing and uncertainty in making tape ends

Rugged terrain breaking tape frequently ;

cumulates randomly

sm

Uncertainty in marking tape ends with tape fully supported

Tape graduated to mm; cumulates randomly

sp

Uncertainty in applying tension

Change in sag correction due to variations in tension of 0.9 kg form standard tension;

cumulated

sh

Uncertainty in determining elevation difference or slope angle

In h ± 0.09 m

In q = ± 0o 10' ;

Cumulates

st

Uncertainty in reading temperature

Observe t to ± 1o C

Cumulates an

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