Therefore 2.75” needs to be deducted from our survey to allow for the error during the survey. Because we need to avoid decimal of seconds, what is preferable is that I minus 3” from the three bigger external angle readings and the minus 2” from the lowest external angle reading. This will result in a total of 11” correction to the traverse survey and lead to the correct sum angle of 1080° 00’ 00”.
Calculation of the Whole Circle Bearings and Reduced Bearings of the Lines of the Traverse.
The whole circle bearing (WCB) of a line is the angle measured from north in a clockwise direction to the line and has a value of 0º - 360º.
The reduced bearing (RB) of a line is the angle measured from the north south line in an easterly or westerly direction and has a value of 0º - 90º. The reduced bearing are always prefixed N or S and suffixed E or W.
Rule for finding the WCB of a line when the WCB of the preceding line is known
WCB of line = WCB of preceding line + 180º + external angle between the line
Line AB
Whole Circle Bearing of line AB = 48º 40’ 25”
Reduced Bearing of line AB = N 48º 40’ 25” E
Line BC
Whole Circle Bearing of line BC = 48º 40’ 25” + 180º + 241º 27’ 29”
= 470º 07’ 54” (deduct 360º)
=110º 07’ 54”
Reduced Bearing of line BC = S 69º 52’ 06” E
Line CD
Whole Circle Bearing of line CD = 110º 07’ 54” + 180º + 255º 45’ 27”
= 545º 53’ 21” (deduct 360º)
= 185º 53’ 21”
Reduced Bearing of line CD = S 5º 53’ 21” W
Line DA
Whole Circle Bearing of line DA = 185º 53’ 21” + 180º + 282º 12’ 07”
= 648º 05’ 28” (deduct 360º)
= 288º 05’ 28”
Reduced Bearing of line DA = N 71º 54’ 32” W
Check Line AB
Whole Circle Bearing of line AB = 288º 05’ 28” + 180º + 300º 34’ 57”
= 768º 40’ 25” (deduct 360º)
= 408º 40’ 25” (deduct 360º)
= 48º 40’ 25” (check is correct).
Calculation of Partial Co-ordinates
The Partial Co-ordinates of a station fix its position relative to another station, generally the preceding station.
The difference in the easting ▲ E of a station is its distance east (positive) or its distance west (negative) of the preceding station.
The difference in the northing ▲ N of a station is its distance north (positive) or its distance south (negative) of the preceding station.
▲ E is the same as a departure
▲ N is the same as latitude
All the lengths of the traverse survey are then calculated as eastings and northings (departures and latitudes). This has been implemented in the table which follows.
Actual closing error = √ (0.071² + 0.019²)
Actual closing error = 0.0735m
Accuracy = Closing error / total length of traverse
Accuracy = 0.0735 / 53.775
Accuracy = 1/731.6
N.B. an error of between 1/5,000 and 1/20,000 (and smaller) is generally acceptable in surveying for construction / engineering works.
In our case the error is to large if we where to undertake constucton or engineering works.
Correction of the Closing Error of the Sum of the Partial Co-ordinates ▲ E’s (- 0.071m) and ▲ N’s (+ 0.019m)
The sum of the partial co-ordinates ▲ E and ▲ N should both be zero, as the traverse starts and finishes at the same point (station A). Hence a correction of +0.071 m must be made to the ▲ E’s and a correction of –0.019 m must be made to the ▲ N’s. The errors are due to the inaccuracy in measuring lengths, in measuring angles and in the calculations.
The errors are distributed proportionately (according to the lengths of the traverse lines) between the partial co-ordinates ▲ E’s and ▲N’s.
Line AB
Line BC
Line CD
Line DA
Calculation of the Total Co-ordinates of the Station of the Traverse
The total co-ordinates of the stations fix their positions relative to the first station or some other origin. Hence the total co-ordinates of any station is the (algebraic) sum of the corrected partial co-ordinates ▲ E and ▲ N of all the traverse lines preceding the station to the origin. The first station of the traverse can be given arbitrary co-ordinates i.e. 0.000 E and 0.000 N or 100.000 E and 100.000 N or if they are known, the Ordnance Survey National Grid reference co-ordinates.
Traverse Survey has been plotted on graph paper attached.
Calculation of traversed area.
Our closed traverse encloses a plot of land and is bound by the point and these points have co-ordinates (which are all illustrated in the diagram above).
So therefore we can use the double longitudes method of tabulated calculation to work out the area, which follows: -
Negative values