Surveying made easy
Contents
1. Surveying made easy Karl Zeiske Geosystems Introduction This booklet will tell you about the basic principles of surveying The most important instruments for surveying are levels and total stations they are intended for routine survey tasks Anyone wishing to know how and where they are used will find the answers here What are the main features of these instruments What needs to be taken into account when measuring with a level or with a total station What are the effects of instrument errors How can such errors be recognized determined and eliminated How can simple surveying jobs be performed The use of levels and total stations is illustrated by a series of practical examples In addition applications programs are described these are incorporated into the modern total stations manufactured by Leica Geosystems and they solve survey tasks even more easily and elegantly Equipped with the knowledge in this booklet and with the help of the appropriate user manual anyone can carry out simple survey tasks confidently and efficiently This booklet does not describe the range of instruments available today from Leica Geosystems neither does it touch on their individual performance features These aspects are covered by the com prehensive brochures by the technical consultants in the Leica Geosystems agencies and by the home pages in the Internet www leica geosystems co2. a large number of points at different heights need to be staked out or monitored it often makes sense to use a rotation laser In this type of instrument a rotating laser beam sweeps out a horizontal plane which serves as the reference plane for staking out or monitoring heights such as four foot marks A detector is slid down a levelling staff until it encounters the laser beam the height can then be read directly from the staff There is no need for an observer at the instrument station Extrapolating a straight line 1 Position the instrument at point B 4 Transit the telescope again and mark the point C2 Point C the mid point between C4 and Co corresponds exactly to the extrapolation of the line AB 2 Target point A transit the telescope i e reverse it and mark point C4 3 Turn the instrument 200 gon 180 and target point A again A line of sight error is re sponsible for the discre pancy between C4 and Cp Where the line of sight is in order the influence of the errors is a combination of target error tilting axis error and vertical axis error 16 Polar setting out of a point The setting out elements angle and distance here relate to a known point A and to a known starting direction from A to B 1 Set up the instrument at point A and target the point B 2 Set the horizontal circle to zero refer to the user manual 3 R
3. staking them out always Hz 0 The coordinates of the tie remember to take the points can be entered height of the instrument manually or they can be and that of the reflector stored in the instrument into account beforehand Free stationing has the great advantage that for large projects involving surveying or staking out you can choose the most favourable station for the instrument You are no longer forced to use a known point that is in an unsatisfactory location E y 33 The applications programs available Recording points Orientation and height transfer Resection Tie distance Staking out Remote heights Free station surveys Reference line Hidden points Area computation Sets of angles Traversing Local resection COGO computations Automatic storage Scanning surfaces Digital terrain models Offset 34 Surveying with GPS GPS surveys use the signals transmitted by satellites having trajectories such that any point on the Earth s surface can be determined around the clock and independently of weather conditions The positioning accuracy depends on the type of GPS receiver and on the observation and post processing techniques used Compared with the use of a total station GPS surveying offers the advantage that the points to be measured do not have to be mutually visible Today provided that the sky is relatively unobstructed by trees buildings etc and there fore tha
4. A at the defined distance d from the upper boundary it will be the first location for the total station 3 Using a boning rod mark the point B at the end of the baseline 4 Set up the total station on point A target point B and set out the points Aj Ag and A3 in this align ment in accordance with the planned length of the side of the building 5 With point B sighted set the horizontal circle to zero turn the total station by 100 gon 90 and set out the second line AC with the points A4 As and Ag 6 The points on the profile boards are then set out in a similar manner starting from the points Aj to Ag respectively If the foundations have not yet been excavated you can set out the sides H H9 and H4Hg3 of the building directly and use them as the starting line for marking the points on the profile boards For smaller buildings it is easier to set out the profile boards using an optical square right angle prism and a measuring tape A building alignment software program incorporated into many Leica total stations enables profile boards to be set out directly starting with any instrument station Measuring with the total station 21 Inspecting the line of sight two peg test In new levels the com pensator has been adjusted at room temperature so that the line of sight is hori zontal even if the instru ment is tilted slightly This situation changes if the temperature fluctuat
5. To eliminate systematic errors related to atmospheric conditions or to residual line of sight error the instrument should be about equidistant from the two points 2 521 di Reading The height difference is calculated from the difference between the two staff readings for the points A and B respectively R backsight V foresight rate AH R V 2 521 1 345 1 176 10 Reading 1 345 Measuring distances optically with the level The reticle carries two stadia lines arranged symmetrically to the crosshair Their spacing is such that the distance can be derived by multiplying the corresponding staff section by 100 This diagram is a schematic representation Accuracy of the distance measurement 10 30 cm Example Reading on upper stadia line B 1 829 Reading on lower stadia line A 1 603 Staff section I B A 0 226 Distance 100 22 6 m Measuring with the level 11 Line levelling lf the points A and B are widely separated the height difference between them is determined by line levelling with target distances generally between 30 and 50 metres Pace out the distances between the instrument and the two staffs they need to be about the same 1 Set up the instrument at S4 2 Set up the staff precisely vertically at point B read off and record the height backsight R 3 Set up the staff at the turning point 1 ground plate o
6. eica Geosystems levels are also equipped with a horizontal circle that is very useful for setting out right angles e g during the recording of transverse profiles In addition these levels can be used to determine distances optically with an accuracy to 0 1 0 3 metres A total station consists of a theodolite with a built in distance meter distancer and so it can measure angles and distances at the same time Today s electronic total stations all have an opto electronic distance meter EDM and electronic angle scanning The coded scales of the horizontal and vertical circles are scanned electronically and then the angles and distances are displayed digitally The horizontal distance the height difference and the coordinates are calculated automatically and all measurements and additional information can be recorded Leica total stations are supplied with a software package that enables most survey tasks to be carried out easily quickly and elegantly The most important of these pro grams are presented in the section Applications programs Total stations are used wherever the positions and heights of points or merely their positions need to be determined The level The total station Coordinates In order to describe the position of a point two coordinates are required Polar coordinates need a line and an angle Cartesian coordinates need two lines within an orthogonal system T
7. es by more than ten or fifteen degrees after a long jour ney or if the instrument is subjected to strong vibra tion It is then advisable to inspect the line of sight particularly if more than one target distance is being used 1 In flat terrain set up two staffs not more than 30 metres apart 2 Set up the instrument so that it is equidistant from the two staffs it is enough to pace out the distance 22 3 Read off from both staffs and calculate the height difference illustration above Staff reading A 1 549 Staff reading B 1 404 AH A B 0 145 4 Set up the instrument about one metre in front of staff A and take the staff reading illustration below Staff reading A 1 496 5 Calculate the required reading B Staff reading A 1 496 AH 0 145 Required reading B 1 351 6 Take the staff reading B If it differs from the required reading by more than 3mm adjust the line of sight refer to instruction manual 1 549 Actual 1 496 Required 1 351 AH Inspecting the EDM of the total station Permanently mark four runs within the range typical for the user e g between 20 m and 200 m Using a new distancer or one that has been cali brated on a standard baseline measure these distances three times The mean values corrected for atmospheric influences refer to the user manual can be regarded as being the required values Using these four runs mea sure wi
8. he total station measures polar coordinates these are recalculated as Cartesian coordinates within the given orthogonal system either within the instrument itself or subsequently in the office Direction of reference Polar coordinates Recalculation given D a required x y y Dsina x Dcosa P Abscissa x y P Ordinate y Cartesian coordinates X Y P given x y required D a D vVy2 x2 sina y D or X cos a x D Measuring angles An angle represents the difference between two directions The horizontal angle a between the two directions leading to the points P4 and P is independent of the height difference between those points provided that the telescope always moves in a strictly vertical plane when tilted whatever its horizontal orientation This stipulation is met only under ideal conditions The vertical angle also termed the zenith angle is the difference between a prescribed direction namely the direction of the zenith and the direction to the point under consideration The vertical angle is therefore correct only if the zero reading of the vertical circle lies exactly in the zenith direction and also this stipulation is met only under ideal conditions Deviations from the ideal case are caused by axial errors in the instrument and by inadequate levelling up refer to section Instrument errors Z4 zenith angle to P4 Z zenith angle to P2 a H
9. levelling staff is then moved upwards or down wards until the required j 4 i value can be read off with SE 1B the level R 1 305 V 2 520 AH 1 00 m 13 Longitudinal and transverse profiles Longitudinal and transverse profiles form the basis for the detailed planning and stakeout of communications routes e g roads and also for the calculation of fill and for the best possible accom modation of the routes to the topography First of all the longitudinal axis road line is staked out and stationed this means that points are established and marked at regular intervals A longitudinal profile is then created along the roadline the heights of the station points being deter mined by line levelling At the station points and at prominent topographic fea tures transverse profiles at right angles to the roadline are then recorded The ground heights for the points in the transverse profile are determined with the aid of the known 14 instrument height First po sition the staff at a known station point the instru ment height comprises the sum of the staff reading and the station point height Now subtract the staff readings at the points on the transverse profile from the instrument height this gives the heights of the points involved The distances from the station point to the various points in the transverse profiles are determined either with the survey
10. m The level The total station Coordinates Measuring angles Preparing to measure Setting up the instrument anywhere Levelling up the instrument Setting up the total station over a ground point Measuring with the level Height difference between two points Measuring distances optically with the level Line levelling Staking out point heights Longitudinal and transverse profiles The digital level The rotation laser Measuring with the total station Extrapolating a straight line Polar setting out of a point Plumbing down from a height point Surveys polar method AJ 0 61 o 00 00 10 10 11 12 13 14 15 15 16 16 16 17 18 Contents Measuring distances without a reflector Automatic target recognition Setting out profile boards Instrument errors Inspecting the line of sight Inspecting the EDM of the total station Instrument errors in the total station Simple surveying tasks Aligning from the mid point Measuring slopes Measuring right angles Applications programs Calculating areas Staking out Remote heights Tie distances Free station surveys The applications programs available Surveying with GPS 19 19 20 22 22 23 24 26 26 27 28 29 29 30 31 32 33 34 35 A level essentially comprises a telescope rotatable about a vertical axis it is used to create a horizontal line of sight so that height differences can be determined and stakeouts can be performed The L
11. ntation after this has been targeted the horizontal circle is set to zero refer to the user manual If a coordinate system already exists set up the instrument on a known point within it and line up the horizontal circle with a second known point refer to the user manual 18 Measuring distances without a reflector Each of the TCR total stations from Leica Geosystems includes not only a conventional infra red distancer that measu res to prisms but also an integrated laser distancer that requires no reflector You can switch between these two distancers This arrangement brings many advantages where points are accessible only with difficulty or not at all for example during the recording of frontages in positioning pipes and for measurements across gorges or fences The visible red laser dot is also suitable for marking targets in connection with the recording of tunnel profiles or with indoor work The DISTO hand held laser meter from Leica Geosystems is another simple instrument that uses a visible laser beam and needs no reflector it is particularly suitable for indoor measurements to ascertain spacings areas and volumes Measuring with the total station Automatic target recognition The TCA total stations from Leica Geosystems are equipped with an automatic target recognition system ATR This makes tar geting faster and easier It is enough to point the tele scope app
12. o target the centre of the prism Simple surveying tasks Measuring right angles The most accurate way to set out a right angle is to use a theodolite or a total station Position the instrument on the point along the survey line from which the right angle is to be set out target the end point of the survey line set the horizontal circle to zero see user manual and turn the total station until the horizontal circle reading is 100 gon 90 For setting out a right angle where the accuracy requirements are less demanding e g for small buildings or when determining longitudinal and transverse profiles the horizontal circle of a level can be used Set up the level over the appropriate point of the survey line with the help of a plumb bob suspended from the 28 central fixing screw of the tripod Then turn the horizontal circle by hand to zero in the direction of the survey line or of the longitudinal profile Finally turn the level until the index of the circle is set to 100 gon 90 An optical square is the best solution for the orthogonal surveying of a point on a survey line or vice versa and for the setting out at right angles of a point in the near distance The beam of light from the object point is turned through 90 by a pentagonal prism so that it reaches the observer The optical square consists of two superimposed pentagonal prisms with their fields of view facing right and left
13. or s tape or optically using the level When representing a longitudinal profile graphi cally the heights of the station points are expressed at a much bigger scale e g 10x greater than that of the stationing of the longi tudinal direction which is related to a round reference height illustration above Longitudinal profile planned height a a 9 424 00 Roadline planned 25m 423 50 420 m Reference height 00L azl OSL G L 002 Transverse profile 175 Reference height 420 m The digital level The digital levels from Leica Geosystems are the first ones in the world to be equipped with digital elec tronic image processing for the determination of heights and distances the bar code on a staff is read by electro nic means completely auto matically see illustration The staff reading and the distance are displayed digitally and can be recor ded the heights of FF am Ey amn FN the staff stations are calcu lated continuously and so there can be no errors re lated to reading recording and calculating Leica Geo systems can offer software packages for post pro cessing the recorded data A digital level is recom mended for use where a lot E of levelling needs to be carried out under these circumstances the saving in time can amount to 50 Measuring with the level The rotation laser If on a large construction site for example
14. orizontal angle between the two directions leading to the points P and P9 i e the angle between two vertical planes formed by dropping perpendiculars from P4 and P respectively Py The level The total station Zenith j da Setting up the instrument anywhere Extend the legs of the tripod as far as is required and tighten the screws firmly 2 Set up the tripod so that the tripod plate is as horizontal as possible and the legs of the tripod are firm in the ground 3 Now and only now place the instrument on the tripod and secure it with the central fixing screw Levelling up the instrument After setting up the instrument level it up approximately with the bull s eye bubble Turn two of the footscrews together in opposite directions The index finger of your right hand indicates the direction in which the bubble should move illustration top right Now use the third footscrew to centre the bubble illustration bottom right To check rotate the instru ment 180 Afterwards the bubble should remain within the setting circle If it does not then readjustment is required refer to the user manual For a level the compen sator automatically takes care of the final levelling up The compensator consists basically of a thread suspended mirror that directs the horizontal light beam to the centre of the crosshair even if there is residual tilt in the tele scope ill
15. ossible to take mea surements practically free of error even using just one telescope face The deter mination of these errors and their storage are described in detail in the appropriate user manual Vertical axis tilt does not rate as being an instrument error it arises because the instrument has not been adequately levelled up and measuring in both telescope faces cannot eliminate it Its influence on the measurement of the horizontal and vertical angles is automatically corrected by means of a two axis compensator d Height index error i the angle between the zenith direction and the zero reading of the vertical circle i e the vertical circle reading when using a horizontal line of sight is not 100 gon 90 but 100 gon i By measuring in both faces and then averaging the index error is eliminated it can also be determined and stored Note The instrument errors change with temperature as a result of vibration and after long periods of transport If you want to measure in just one face then immediately before the measurements you must determine the instrument errors and store them Instrument errors Vertical axis tilt Height index error i V index Line of sight error c Hz collimation Tilting axis error a 25 Aligning from the mid point If intermediate points are to be aligned within a line of measurement and each of the two end points cannot be seen from
16. otate the instrument until a appears in the display 4 Guide the reflector carrier person into and along the line of sight of the telescope continually measuring the horizontal distance until point P is reached Plumbing down from a height point Plumbing down from a height point plumbing up from a ground point and inspecting a vertical line on a structure can be carried out exactly in just one tele scope face but only if the telescope describes a pre cisely vertical plane when it is tilted To ascertain that this is so proceed as follows 1 Target a high point A then tilt the telescope downwards and mark the ground point B 2 Transit the telescope and repeat the procedure in the second face Mark the point C The mid point between the points B and C is the exact plumbing point The reason why these two points do not coincide can be a tilting axis error and or an inclined vertical axis Measuring with a total station For work of this type make sure that the total station has been levelled up pre cisely so that the influence of vertical axis tilt on steep sights is minimized Surveys polar method To create e g a location plan the position and height of a point on the object are determined by measuring angles and distances To do this the instrument is set up on any prominent point in a local coordinate system A second prominent point is selected for the purposes of orie
17. r prominent ground point read off and record the height foresight V 12 4 Set up the instrument at Sp the staff remains at the turning point 1 5 Carefully rotate the staff at the turning point 1 so that it faces the instrument 6 Read off the backsight and continue The height difference between A and B is equal to the sum of the backsight and the foresight R u L RE Sen T Station Point Backsight R Foresight V Height Remarks no A 420 300 S1 A 2 806 T 1 328 421 778 height A R V S2 1 0 919 2 3 376 419 321 S3 2 3 415 B 1 623 421 113 Sum 7 140 6 327 6 327 0 813 height B height A AH 0 813 height difference AB Measuring with the level Staking out point heights In an excavation a point B is to be set out at a height AH 1 00 metre below street level Point A 1 Set up the level so that the sighting distances to A and B are about the same 2 Set up the staff at A and read off the backsight R 1 305 3 Set up the staff at B and read off the foresight V 2 520 The difference h from the required height at B is calculated as h V R AH 2 520 1 305 1 00 0 215m 4 Drive in a post at B and mark the required height 0 215m above ground level In another frequently used method the required staff reading is calculated in advance V R AH 1 305 1 000 2 305 The
18. respectively Between the two prisms is an unrestricted view of the object point You as the observer can position yourself in the survey line defined by two vertically positioned alignment rods in that you move perpen dicularly to the line until you see the images of the two rods exactly super imposed Then you move yourself along the survey line until the object point and the two images of the alignment rods all coincide Applications programs Calculating areas 1 Set up the total station in the terrain so that it is within view of the entire area to be surveyed It is not necessary to position the horizontal circle 2 Determine the boundary points of the area sequentially in the clockwise direction You must always measure a distance 3 Afterwards the area is calculated automatically at the touch of a button and is displayed 29 Staking out 1 Set up the instrument at a known point and position the horizontal circle refer to the sec tion Setting the station in the user manual 2 Enter manually the coor dinates of the point to be staked out The program automatically calculates direction and distance the two parameters needed for staking out 3 Turn the total station until the horizontal circle reads zero 4 Position the reflector at this point point P 5 Measure the distance the difference in the distance AD to the point P will be displayed automa
19. roximately at the reflector a touch on a button then automatically triggers the fine pointing and the angle and distance measurements and records all of the values This technology also makes it possible to carry out fully automatic measurements with the help of a computer The ATR can also be switched to a mode in which moving targets can be followed and measured after establishing the initial contact with the target the instrument locks on to it and tracks it The practical applications of this option include the precise guidance of construction machinery Advantages of ATR High speed of measurement combined with a constant measuring accuracy that is independent of the observer A V 19 Setting out profile boards During building alignment it is useful to extrapolate the sides of the building to beyond the limits of the ex cavation and there to erect profile boards on which the extensions are marked exactly by hammering in nails These can be connec ted to strings or wires at any time during the con struction sequence indi cating the required positions of the walls In the following example profile boards are to be erected parallel to the pro posed walls of a large building and at distances of a and b respectively from the boundaries illustration left 1 Establish a baseline AB parallel to the left hand boundary and at a freely selectable distance c 20 2 Mark the point
20. t adequate satellite signals can be received GPS equipment can be applied to many survey tasks that until recently were carried out using electronic total stations The new GPS System 500 from Leica Geosystems enables the most diverse range of survey tasks to be carried out with centimetre accuracy on the tripod on the plumbing pole on ships vehicles and construction plant and using both static and kinematic applications Surveying with GPS 35 Illustrations descriptions and technical data are not binding and may be changed Printed in Switzerland Copyright Leica Geosystems AG Heerbrugg Switzerland 2000 722510en VII 00 RVA eca Geosystems Leica Geosystems AG CH 9435 Heerbrugg Switzerland Phone 41 71 727 31 31 Fax 41 71 727 46 73 www leica geosystems com
21. th each distancer at least four times per year Provided that there are no systematic errors in excess of the expected measuring uncertainty the distancer is in order Instrument errors 23 Instrument errors in the total station Ideally the total station should meet the following requirements a Line of sight ZZ perpen dicular to tilting axis KK b Tilting axis KK perpen dicular to vertical axis VV c Vertical axis VV strictly vertical d Vertical circle reading precisely zero at the zenith If these conditions are not met the following terms are used to describe the particular errors a Line of sight error or colli mation error c deviation from the right angle bet ween the line of sight and the tilting axis b Tilting axis error a devia tion from the right angle between the tilting axis and the vertical axis c Vertical axis tilt angle 24 between plumb line and vertical axis The effects of these three errors on the measurement of horizontal angles increase with the height difference between the target points Taking measurements in both telescope faces eliminates line of sight errors and tilting axis errors The line of sight error and for highly precise total stations also the tilting axis error which is generally very small can also be determined and stored These errors are then taken into consideration automatically whenever an angle is measured and then it is p
22. the other proceed as follows 1 Select two points 1 and 2 both approximately in the alignment from which both end points A and E are visible Use sight poles to mark the points 2 From point 1 align point 2 in the straight line 1 A 3 From point 2 align point 3 in the straight line 2 E 26 4 From point 3 align point 4 in the straight line 3 A and continue in the same manner until no further lateral deviations are visible at the two inter mediate points A Measuring slopes If slopes are to be deter mined in or to be staked out e g for gutters pipelines or foundations two different methods are available 1 With a level Measure the height difference and the distance either optically with the stadia hairs or with the tape The slope is calculated as follows 100 AH D slope in 2 With a theodolite or total station Place the instrument on a point along the straight line the slope of which is to be deter mined and position a staff at a second point along that line Using the telescope determine the instrument height i at the staff The vertical circle reading giving the zenith angle in gon or degrees can be reset to refer to user manual so that the slope can be read off directly in The distance is irrelevant A reflector pole fitted with a prism can be used instead of the staff Extend the reflector pole to the instrument height i and use the telescope t
23. tically 30 Alternatively the coordi nates of the points to be staked out can be trans ferred beforehand back in the office from the computer to the total station Under these circumstances in order to stake out only the point number then needs to be entered Remote heights Set up a reflector verti cally beneath that point the height of which is to be determined The total station itself can be situated anywhere N Measure the distance to the reflector wo Target the high point A The height difference H between the ground point and the high point is now calculated at the touch of a button and is displayed Applications programs 31 Tie distances The program determines the distance and height difference between two points 1 Set up the total station at any location 2 Measure the distance to each of the two points A and B 3 The distance D and the height difference H are displayed at the touch of a button 32 Applications programs Free station surveys This program calculates The options for measuring the position and height of and the measuring the instrument station procedure are described in along with the orientation detail in the user manuals of the horizontal circle from measurements to at Note least two points the When performing survey coordinates of which are tasks that involve known determining heights or
24. ustration bottom If now you lightly tap a leg of the tripod then pro vided the bull s eye bubble is centred you will see how the line of sight swings about the staff reading and always steadies at the same point This is the way to test whether or not the compensator can swing freely Setting up the total station over a ground point 1 Place the tripod approxi mately over the ground point 2 Inspect the tripod from various sides and correct its position so that the tripod plate is roughly horizontal and above the ground point illustration top left 3 Push the tripod legs firmly into the ground and use the central fixing screw to secure the instrument on the tripod 4 Switch on the laser plummet or for older instruments look through the optical plummet and turn the footscrews so that the laser dot or the optical plummet is centred on the ground point illustration top right 5 Centre the bull s eye bubble by adjusting the lengths of the tripod legs illustration below 6 After accurately levelling up the instrument re lease the central fixing screw so that you can displace it on the tripod plate until the laser dot is centred precisely over the ground point 7 Tighten the central fixing screw again Preparing to measure Height difference between two points The basic principle of levelling involves determining the height difference between two points
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