Transcript Surveying Intro - Angelo Filomeno

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
Site station 1
National
Reference
point
Site station 2
The Coordinates of the site stations
are determined from the angular
and distance measurements
Site station 1
National
Reference
point
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
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
Northings
North Partial = L x Sin (Θ)
L
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
WCB
Northings
East Partial = L x Sin( WCB)
L
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.