Surveying for non-surveyors National Reference points whose Coordinates are known are used to determine coordinate value of points ( or stations) on site

National Reference points connected to site stations by angular and distance measurement

The Coordinates of the site stations are determined from the angular and distance measurements Eastings Northings National Reference point Site station 1 Site station 2

The survey measurement can never be without errors So we do calculations to distribute the errors evenly around all our measurements In the hope that this will mean smaller errors on any particular set of coordinates.

Angles and distances are measured with an instrument called a Total Station This may be thought of as a particularly expensive protractor! The angles can be measured to the 5th decimal place of accuracy. The angles in this country are measured in Degrees, Minutes and seconds. Distances are measured electromagnetically (i.e. by light reflection)

Consider the angular measurement 360 degrees = 1 complete circle 1 Degree = 60 Minutes 1Minute = 60 Seconds Also remember that angles can also be measured by the arc length to radius ratio………i.e. Radians ( л radians = 180 degree)

To reduce errors angles are measured twice at each station These are known as Face 1 and Face 2 readings---- the average value is used ( = the mean included angle) The readings are simply the values pointed to on the protractor and we need to subtract one reading from another to determine the angle.

Example Angle turned through = 165 ° – 35 ° = 130 ° First reading = 35° Second reading =165° Angle turned through = 165 ° – 35 ° = 130 °

Do not be fooled by these readings! First reading = 335° Second reading =85° Angle turned through = 85 ° – 335 ° = 110 ° Note: when the readings pass through 360° the subtraction becomes thus: 335° to 360 ° = 25 ° PLUS 0 ° to 85 ° = 85 ° Total angle turned through = 25 ° + 85 ° = 110 °

The survey usually closes on itself for greater accuracy Hence we can check that the sum of the internal angles are correct And distribute around the survey any errors present.

Correcting Angular Errors ΣInternal angles of polygon = (2N-4)90° Dist. Coeff. = closing error / N Corrected angle = Measured angle – Dist. Coeff. Where closing error = Theorectical sum – actual sum of internal angles N = Number of sides or angles in polygon

Distance are often also measured several times Again the average value is used to help determine the coordinates of the site stations.

Trigonometry A recap of your knowledge of trigonometry may be useful here. Refer to Trig. File This knowledge will be used to determine the North and East vectors for the distance between stations These are known are North and East Partials.

Partials East Partial = L x Cos( Θ) Θ North Partial = L x Sin (Θ) L Northings Eastings

Whole Circle Bearings The angle used in the Partial calculations is the angle between the line from station to station and the North or East axis. A more general solutions is to use the Whole Circle Bearing (WCB) of the line. A WCB is the angle a line makes with the North Measured in clockwise direction. Only the WCB of the first line is determined on site. The rest are calculated from the known relationship between adjacent lines.

Partials from WCB value East Partial = L x Sin( WCB) L Northings North Partial = L x Cos (WCB) Eastings NB sin & cos different to previous

Coordinates The coordinates of stations are then calculated from adjacent stations, starting with the first known reference point. Pe N1 Pn N2 = N1 - Pn E1 E2 = E1 + Pe

Site Measurement errors Of course the coordinates we end up with have errors and if we do a closed survey ( returning to the starting point) we will notice that the coordinates for the end point ( which is in fact the starting point) do not match the starting point values – the closing error. We do a correction called the Bowditch correction to compensate for this.

Closing errors N1 en N1’ Closing error ee E1’ E1

Bowditch Correction This suggests that the greater the length of a measured line the greater the error in measurement is present. The amount of correction to a line therefore depends on it’s length. The longer the line the more correction is needed.

Formula in Bowditch Correction The closing error in the North and East directions are found first by summing all the partials. Correction to Partials: = (Line length / Σ line lengths) x closing error in east or north direction i.e. a fraction x closing error the partials are corrected in accordance with this premise. The corrected coordinates are then computed.