Surveying Tony Price & Nikki Meads

Surveying The main object of surveying is the preparation of maps or plans which are the basis in the planning and design of engineering projects such as route location, e.g. roads, railway lines, pipelines, tunnels, etc.

Classification of Surveys Surveying is divided into two main categories- i) Plane survey ii) Geodetic Survey

Geodetic Survey Where a survey extends over a large area greater than 200 sq. km. and the required degree of accuracy is also great. The curvature of earth is taken into account. Used to provide control points to which small surveys can be connected. Not common in Civil works.

Plane Survey For small projects covering an area less than 200 sq.km. Earth’s curvature is not accounted for in distances. Earth surface is considered as a plane. (Angular error of 1” in 200 sq. km. area by assuming plane). www.tektonics.org/af/flatearth.jpg

Basic Principles in Surveying Ruling principles of surveying are : i) “ to work from whole to part”. For surveying you should establish control points of high precision by use of triangulation and precise levelling. This area is further divided into smaller triangles which are surveyed with less accuracy. ii) to fix the position of new stations by at least two independent processes – e.g. linear and angular

Setting-out Whereas surveying maps the existing world, setting-out establishes points for the control of construction processes, e.g. Positioning foundations Placing the line of a road or service Controlling levels and gradients on earthworks

Health & Safety http://www.kempengineeringsurvey.co.uk/land-surveys/road-surveys.html

Health & Safety Police said the surveyor was pinned beneath a 12-wheel truck Friday morning for more than an hour. The truck was backing up when it struck the worker. A 60-year-old man was taken to hospital with critical injuries. He was pronounced dead Friday afternoon. http://uk.news.yahoo.com/que-surveyor-killed-road-construction-accident-010548047.html

Health & Safety Surveyor electrocuted - Employer fined 20 year old Surveyor Russell Donald died after he was electrocuted passing under a high-voltage power line with a metal pole in Echt, Aberdeenshire. His employer, W A Fairhurst and Partner, has been fined £25,200. The Glasgow based engineering firm were charged with failing to instruct Mr Donald that it was inappropriate to use a long surveying pole in the vicinity of electric lines. http://www.dprhd.co.uk/news/2010/jan/surveyor-electrocuted-employer-fined

Principles of Measurements

Principles of Measurements

Principles of Measurements

Source of Errors Personal Errors - no surveyor has perfect senses of sight and touch Instrument Errors - devices cannot be manufactured perfectly, wear and tear and compatibility with other components Natural Errors - temperature, wind, moisture, magnetic variation, etc.

Systematic and Accidental Errors Systematic or Cumulative Errors -typically stays constant in sign and magnitude Accidental, Compensating, or Random Errors - the magnitude and direction of the error is beyond the control of the surveyor Gross Errors – operator stupidity?

Normal Distribution Curve This is the target value

Precision

Accuracy & Precision

Accuracy and Precision Better precision does not necessarily mean better accuracy In measuring distance, precision is defined as:

Standard Deviation is an individual measurement is the arithmetic mean (most probable value) is a residual such that

Standard Error is an individual measurement is the arithmetic mean (most probable value) is a residual such that (n-1) is known as the number of degrees of freedom or redundancy

Standard Error of Arithmetic Mean Example: 30 m tape with a standard error of 6 mm. If we require a standard error of 3 mm on the distance measured, how many measurements are required? Giving n = 4

Probabilities Associated with the Normal Distribution Probability % Confidence interval 68.3  1 90.0 1.65 95.0  1.96 95.4  2 99.0  2.58 99.7  3 99.9  3.29 -1 s x _ +1 s x _ Assumes normal distribution without gross or systematic errors -2 s x _ +2 s x _ +3 s x _ -3 s x _

Example: Most Probable Value and Standard Error Calculate the most probable value and its standard error.

Solution The most probable value is given by the arithmetic mean as:

Solution cont. Based upon the most probable value, the residuals and squares of these are calculated:

Solution cont. Therefore the most probable value of the angle is:

Example : Distance Calculate the most probable value for this distance, its standard error and confidence interval for a 95% probability.

Solution

For 95% probability level the confidence interval for the true value is: REJECT

Recalculate with remaining measurements:

Propagation of Standard Error Special law of propagation of standard error for a quantity U D=a+b or a-b A=xy

Example

Converts “ to radians

Propagation of Errors Activity Standard Error Levelling Angular measurement Trigonometrical heighting Traversing Ss = standard error of reading staff; D = distance; l = sight length (foresight, backsight) Sm = std. error in angle reading; Sb = std. error bisecting target; n = number of measurements; SHA = std. error height of station A; Shi = std.error of height of total station above A; Shr = std.error of height of reflector above B; SL = std.error of slope length; Sa = std.error of angle;

Example If total station has a precision of 6” and targets and observers are such that Sb = 7.5” how many readings must be taken to achieve a precision of 5” in ? Sm =  6, hence 4 readings are required.

Levelling

Profile Boards Define level Define slope, e.g. on bank http://cgsr.ie/store/images/cross%20bone%20complete%20batter%20rail.jpg

www.ruralworks.com/reports/profileboard/ProfileBoard.html

(after CIRIA Manual of Setting-out Procedures)

Closed Traverse N

What is a traverse? A polygon of 2D (or 3D) vectors Sides are expressed as either polar coordinates (,d) or as rectangular coordinate differences (E,N) A traverse must either close on itself Or be measured between points with known rectangular coordinates A closed traverse A traverse between known points

Rectangular coordinates Point A Point B North East EB NB (EB,NB) N=NB-NA EA NA (EA,NA) E=EB-EA

Polar coordinates North Point B d  Point A  ~ whole-circle bearing East Point A Point B d   ~ whole-circle bearing d ~ distance

Whole circle bearings North 0o Bearing are measured clockwise from NORTH and must lie in the range 0o   < 360o 4th quadrant 1st quadrant West 270o East 90o 3rd quadrant 2nd quadrant South 180o

Coordinate conversions Rectangular to polar Polar to rectangular E N d  d  E N

Applications of traversing Establishing coordinates for new points (E,N)known (,d) (,d) (,d) (E,N)new (E,N)new

These new points can then be used as a framework for mapping existing features (E,N)new (E,N)known (E,N)new (E,N)new (E,N)new (,d) (,d)

They can also be used as a basis for setting out new work (E,N)new (E,N)known

Equipment Traversing requires : An instrument to measure angles (theodolite) or bearings (magnetic compass) An instrument to measure distances (EDM or tape)

Measurement sequence You start with a known point and bearing AB At each station measure the internal horizontal angle Measure the vertical angle between each station Measure the distance between each station

Whole circle bearing A to B: WCBAB= 038° 17’ 34” Point A has coordinates: 322.600E, 742.800N Sum of internal angles = (2n – 4)x90° = 720° because n = 6 090° 33’ 04” 083° 58’ 44” 114° 04’ 38” 237° 11’ 31” 105° 59’ 45” 088° 13’ 30”

Computation sequence Calculate angular misclosure Adjust angular misclosure Calculate adjusted bearings Reduce distances for slope etc… Compute (E, N) for each traverse line Calculate linear misclosure Adjust linear misclosure

Correction to angles Station Accepted Angle Correction Corrected Angle ° ´ ´´ A 114 04 38 -12 26 B 090 33 32 52 C 083 58 44 D 237 11 31 19 E 088 13 30 18 F 105 59 45  720 01 12 00 Correction = -72”/6 = -12” to each angle

Proportional Error between Tape Lengths Stations Proportional Error between Horizontal distance From To Out & back lengths (m) A B 1:6100 90.202 C 1:7020 86.756 D 1:5010 48.928 E 1:8230 69.187 F 1:5930 57.345 1:4930 108.784

Bowditch adjustment The adjustment to the easting component of any traverse side is given by : Eadj = Emisc * side length/total perimeter The adjustment to the northing component of any traverse side is given by : Nadj = Nmisc * side length/total perimeter

Bowditch Adjustment Knowns Checks Line Stn Back B’g Corr’d Angle Forward B’g Horiz dist Unadjusted Correction Adjusted Coords ° ‘ “ E N E N E N AB 038 17 34 A 114 04 26 322.600 742.800 AF 152 22 00 108.784 50.455 -96.375 0.021 -0.033 50.476 -96.408 FA 332 F 105 59 33 373.076 646.392 FE 078 21 57.345 56.166 11.571 0.011 -0.017 56.176 11.554 EF 258 088 13 18 429.252 657.946 ED 346 51 69.187 -16.056 67.298 0.013 -0.021 -16.043 67.277 DE 166 D 237 11 19 413.209 725.223 DC 043 46 10 48.928 33.846 35.332 0.009 -0.015 33.856 35.318 CD 223 C 083 58 32 447.065 760.541 CB 307 44 42 86.756 -68.602 53.108 0.016 -0.026 -68.585 53.082 BC 127 B 090 52 378.479 813.622 BA 90.202 -55.896 -70.795 0.017 -0.027 -55.879 -70.822  461.202 -0.087 0.138 0.000 Knowns Checks

Linear misclosure & accuracy Convert the rectangular misclosure components to polar coordinates Accuracy is given by Beware of quadrant when calculating  using tan-1

Quadrants and tan function E +  negative add 360o + positive okay  positive add 180o  + negative add 180o

For the example… Misclosure (E, N) Convert to polar (,d) Accuracy (-0.087, 0.138) Convert to polar (,d)  = -032.23o (4th quadrant) = 327.77o d = 0.163 m Accuracy 1:(461.202 / 0.163) = 1:2827

Curve Ranging

Location Methods (a) right angle offset tie. B B B P P P C A A A (a) right angle offset tie. (b) the angle distance tie (polar tie). (c) angle at A and B of distance BP of AP (intersection technique).

Means of fixing a curve r a

Means of fixing a curve Establish line through ROr on line of radius. – How? ROr Locate position of pegs measuring angles at T from line to Q in combination with cord lengths T-1, 1-2, 2-3 and 3-4. You cannot tape between 4 and 5 so how will you establish 5, 6 and 7?

Means of fixing a curve How far should R1 be from T? Locate lines through the position of pegs 5, 6 and 7 by measuring angles at R1. Which direction should angles be read from and why? ROr Method 1: R1 How far should R1 be from T?

Means of fixing a curve ROr Method 2: R1 R2

First line of sight marked by pegs and string Second line of sight marked by pegs and string Point marked by peg and nail at intersection of strings Pegs must be firmly anchored in the ground