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Section 1 Introduction

Section 2 Using Theodolites

Section 3 Survey Data Calculations

Section 4 Converting Slope to True Distance

Section 5 Total Stations

Section 6 Building Surveys


Description:  This unit has been designed to guide learners when traversing using a digital theodolite or total station and recording data for use in design/construction work.

Author:  Gates MacBain Associates

Section 1  Introduction

This Module is designed to complement your lectures and the practical work within your course.  It does not replace the lectures or experience that you will need to get by carrying out the practical tasks. You may find it useful to reinforce or clarify the tuition you receive on your course.   

In this unit we explore in greater detail the processes used to collect and record both horizontal and vertical angles. We contrast the use of a digital theodolite with that of a total station to carry out similar tasks.  

We also link with the other units by showing how co-ordinates may be determined from survey data and then in setting out buildings or points. 

Towards the end of this unit we explore how a range of equipment might be used to collect data for a measured survey of a building which can then be used to produce drawings. 

The site we have used throughout these units is shown below and we will carryout a survey using a theodolite.

Section 2  Using Theodolites

Aims and Objectives

At the end of this section you should be able to:
  • Competently set up a theodolite and record data in an acceptable format.

A theodolite is essentially a device which measures vertical and horizontal bearings with the difference between two bearings being the angle subtending those points in either a horizontal or vertical plane. 

If we were to carry out a survey of this area using a digital theodolite we would begin with a closed traverse (a traverse which returns to the starting point) with a sufficient number of points to enable collection of site data. From the data collected we could accurately determine the location of the survey stations and then calculate co-ordinates for all main features on the site.   


Figure 1 : Closed traverse   

Points A, B, C, & D are survey stations on a closed traverse. These stations are traversed in the order shown in the table below and target stations B & D must be visible when the instrument is at station A and so on for the other instrument positions. We position the theodolite over each of these points and in turn and sight on to two others to build accurate data on their relative positions. The order in which the data is collected is indicated in Table 1. At each instrument position we record bearings and distances as shown.   

 Instrument  Target Horizontal Bearings Vertical Bearings Distance (Slope)
 C B    
 D C   

 Table 1    

We begin the traverse at Station A which has a height above Ordnance Datum of 62.500m and for the purpose of this exercise assumed co-ordinates of 100.000 East and 100.000 North. The actual co-ordinates related to the National Grid could be used for Station A (if known).It is usual to locate true north at the first station and set the horizontal reading to zero with the theodolite in the face left position.   

The instrument in the photograph above is in the face left (FL) position because the vertical angle scale is to the left of the telescope whilst reading a bearing. To move to face right (FR) position we rotate the base 180º and flip over the telescope and read the bearing on the same point as from face left. Two readings are taken on the same point to increase the accuracy of the survey. Most standard theodolites measure to an accuracy of 20 seconds. This procedure will bring that accuracy to within 10 seconds.  

The instrument must be set accurately over each station which usually take the form of a square wooden peg with a round headed nail tapped into the wood.

The tripod is set with a plumb bob hung from it to locate the centre of tripod directly over the peg. With the instrument fixed to the tripod and levelled it is possible to finely adjust the instrument position by viewing the peg and nail. Carefully loosen the theodolite and slide it so that the black circle in the viewer sits exactly over the nail. It is necessary to check that the instrument is still level and several minor adjustments may be required before it is both level and exactly over the station. 

Bearing are usually taken on a ranging rod which is marked with the height of the instrument. This mark is changed each time the instrument is moved. The ranging rod is held on the nail for horizontal readings and on the ground next to the peg for vertical reading.   


Figure 2 : Reading Positions on Ranging Rods   

The survey data shown in Table 2 records the following data from each survey station 
  • Horizontal bearings in both FL and FR on both target points (4 bearings)
  • Vertical bearings in both FL and FR on both target points (4 bearings)
  • Distances from instrument to each target station (2 measurements)

Figure 3:  Maths Basics  

The format used in Table 2 is used to record data from an instrument position before moving to the next position. All bearings are shown in degrees, minutes and seconds.         


  • Irvine, W, (1995) Surveying for Construction, McGraw-Hill: Berkshire (Chapter 7)

Self-Assessment Task

  • Set up a Theodolite and carry out a traverse of at least FOUR survey points.
  • Record horizontal and vertical bearings along with slope lengths.

Section 3  Survey Data Calculations

Aims and Objectives

At the end of this section you should be able to:
  • Process the data collected during a traverse and apply checks and adjustments.

This section deals with the techniques used when processing survey data into a form which can be used to formulate setting out and co-ordinate data. 

  • Calculations Horizontal Angles (starting at instrument position A) 
  • Calculate the difference between FL for targets B&D (69  20  20)
  • Repeat process for FR for targets B&D (69  20  20)
  • Determine the mean horizontal angle(69  20  20)
  • Repeat this process for instrument positions B, C and D
  • You will note that at Stations B & C the FL & FR angles are different and it is necessary to calculate the mean.
  • Note also that the difference in the FR bearing at station B is 273  21  20. This is clearly incorrect because it is actually the external angle. The correct angle begins at 316 20 20 and moves clockwise to 42  59  00. The internal angle is therefore 360 minus 273  21  20 which is  86  38  40.
  • Check – When all the internal angles are calculated they must conform to :-
             Sum of Angles  = (2n – 4) 90 for internal angles or                                           
(2n + 4) 90 for external angles                                           
Where n = the number of stations 

An acceptable error is 30 √n  (seconds)In this survey they add up to 360  00  10 Sum of Angles therefore should be (8 – 4) 90 = 360 degreesAn acceptable error would be 30 x √ 4 = 60 seconds 
  • 10 seconds is an acceptable error and the internal angles are adjusted equally to compensate.
  • The 10 seconds in this case is divided by n and deducted from each internal angle. So the corrected adjusted angles are now:-
          69   20   20   minus 2.5 secs   = 69  20  17.5  (Angle A)
86   38   30   minus 2.5 secs   = 86  38  27.5  (Angle B)
94   35   00   minus 2.5 secs   = 94  34  57.5   (Angle C)
109  26   20  minus 2.5 secs   = 109 26  17.5  (Angle D) 


Figure 4: Revised Angles (NTS) 

Vertical Angles 


Table 4  

Table 4 shows the vertical bearings and calculated mean vertical angles.  

To understand this calculation we must first remember that normally the vertical bearings on the theodolite are set as shown in Figure 5 with the zenith angle going upwards. The vertical bearings for AB are shown in red whilst the AD bearings are shown in blue.     


Figure 5 : Vertical Bearings   

AB is therefore showing the ground going upwards (FL between 0 and 90 and FR between 270 and 360) whilst AD is downwards (FL between 90 and 180 and FR between 180 and 270)  

Mean Vertical angle between A & B is the mean value of:-        
90 minus  89  54  20  =  0  05  40          
270 minus 270  05  40  =  0  05  40   

And at A & D         
94  30  00  minus 90   =  4  30  00           
270 minus 265  30  00  =  4  30  00        


  • Irvine, W, (1995) Surveying for Construction, McGraw-Hill: Berkshire

Self-Assessment Task

  • Use the data collected on your four point traverse.
  • Calculate all the mean horizontal and vertical angles as shown in this section.
  • Apply the accuracy rules and necessary adjustments.

Section 4  Converting Slope to True Distance

Aims and Objectives

At the end of this section you should be able to:
  • Take slope distances and vertical angles and convert these into true distances for use on accurate plans and sections.
  • Use this data with whole circle bearings to produce co-ordinates for a given point.

To enable distance data to be used on plans it is necessary to ensure that all measurements on a variety of slopes are converted into true horizontal distance. This data can then be used to calculate levels and co-ordinates at given points.

Table 5 shows the slope distances recorded during the survey


Table 5

True Distance =  Cosine of Mean Vertical Angle x Slope Distance

Example @ AD/DA : Cos 4 degrees 30 mins  x  39.522  =  39.400


If we assume that Station A has a height above Ordnance Datum of 100.000m then the levels at each of the other stations can be determined using the following data:-

Station A to Station B : True distance  =  59.600

Mean Vertical Angle =  Up 0 05 40

Station B to Station C : True distance  =36.001

Mean Vertical Angle =  Down 4 36 20

Station C to Station D : True distance  =  43.601

Mean Vertical Angle =  Down 0 23 35

Station D to Station A : True distance  =  39.400

Mean Vertical Angle =  Up 4 30 00

Note the check slope measurement AC was 67.858m

It is now possible to calculate the difference in level between each of these points using :-

Tan (Mean Vertical Angle)  x  True Distance

Therefore differences are:-

A to B  Tan 0 05 40 x 59.600  =  Plus 0.098m

B to C  Tan 4 36 20 x 36.001  =  Minus 2.900m

C to D  Tan 0 23 35 x 43.601  =  Minus 0.299m

D to A  Tan 4 30 00 x 39.400  =  Plus 3.101m

The levels at each Station can now be calculated:-

Station A  (100.000)    Station B  100.000 + 0.098 = 100.098

Back to Station A  = 96.899 + 3.101= 100.000


Pegs have been placed at Stations A to D. For these to be used for setting out, the co-ordinates of each must be determined. We are assuming that Station A has the co-ordinates of 100.000 East and 100.000 North. (see Figure 6)

The remaining coordinates are calculated using the following procedure:
  • Calculate the whole circle bearing (WCB) from Station A
  • The start point for WCBs is the true north bearing
  • Using calculation we determine clockwise angle from north
  • We also calculate the true distance from Station A to each of the other points
  • From this data it is then possible to determine eastings and northings for each main station

Figure 6

Whole Circle Bearings (WCB)



Table 6

Calculations (using Fig 6 and Table 6)

Data known

Line AB is 86 30 00 clockwise from north

True Distance AB = 59.600

True Distance BC = 36.001

True Distance AC = 67.800

Angle ABC = 86 38 27.5

Refer to Figure 7

Calculate Angle BAC using sine rule (a/ Sin A = b/ Sin B c/ Sin C)

Therefore Sin Angle BAC = (Sin 86 38 27.5 x 36.001) / 67.800  =  0.530075953

Using Shift Sin on your calculator - Angle BAC = 32 ( to nearest second)


Figure 7


WCB to Station C is 86 30 00 + 32 00 38 = 118 30 38

WCB to Station D is 86 30 00 + 69 20 17.5 = 155 50 17.5

We now have all the data to calculate the co-ordinates

Co-ordinates at A is 100.000 East and 100.000 North

To navigate to Station B we calculate distances east and north from A to B (see Figure 8)


Figure 8

Distance East from A = Sin 86 30 00 x 59.600 = 59 489m

added East and North co-ordinates at Station A to give Station B co-ordinates (159.489 East , 103.638 North)


Figure 9

118 30 38   Distance AC = 67.800

WCB minus 90 gives the angle shown above (28 30 38)

Distance East from A = Cos 28 30 38 x 67.800 = 59.578

Distance South from A = Sin 28 30 38 x 67.800 = 32.362

Co-ordinates at Station C are 159.578 East (100 + 59.578), 67.638 North (100 – 32.362). Remember that values are deducted when moving South or West.


  • Irvine, W, (1995) Surveying for Construction, McGraw-Hill: Berkshire

Self-Assessment Task

  • Use this procedure to complete the Station D co-ordinates in Table 6.

Section 5  Total Stations

Aims and Objectives

  • At the end of this section you should have a general knowledge of how total stations are used. (Specific details will vary with the software format used on the equipment at your Institution).

A Total Station (TS) is a theodolite with an on board processor and software which is capable of accurate direct distance measurement. All the data can be collected and processed as soon as it is collected.  

Total stations take the hard work and inaccuracy out of surveying by having an on board processor and software. The software will vary and it is advisable to be trained before using a particular total station. 

All the possibilities cannot be covered by these notes but some general guidance will be useful at this stage. The images used are from the Topcon TS software. 

The TS must be set up over a station in the same manner as a digital theodolite but the differences begin when recording data directly on to the hard drive or a memory card. 

The main stages when using a TS are as follows: 
  • Switch on and select the Survey Software using a small plastic stylus which is tapped on the required icon in the menu
  • To begin a new survey the New Job tab is tapped and this allows you to enter details about the survey. The buttons are usually alpha-numeric so it will be necessary to press the alpha key before entering words. You may also open a previous job which has been given a file name.(See Figure 10)

Figure 10 

Once the job details are saved by selecting create tab the next stage is to enter data about the Occupation point (the peg over which the TS is set) and to identify north using the Backsight.    


Figure 11      
  • For the Occupation Point the following data must be entered
a)   Point number (eg 1)
b)   Instrument height (IH)
c)   Reflector (target) height (RH)
d)   Eastings and Northings ( eg 100,100) using drop down data tab
e)   Elevation or ground level at the occupation point 
  • The direction of north can be set by turning the instrument northwards and selecting Set. This must have point number (eg2), eastings, northings and elevation identified. You may just set the eastings as 100 and northings as 105.
 In this case then point 2 is the backsight 5m north of the occupation point. 
  • We can now begin to collect data as the TS has an identified location and is orientated to north by using a backsight. Select the sideshot –direct tab in the menu.(Figure 12)
  • Each point recorded is identified (Point 101) and given a code depending upon its nature and point can be joined using the string option. The TS is pointed towards the reflector(a prism on a stick which reflects a pulse back to the TS) which is on the point to be recorded. An electromagnetic pulse is sent out and when the measure tab is selected the TS measures both horizontal (HA) and vertical angles (VA) along with the slope distance (SD) 

Figure 12 

  • This can then be converted directly into eastings (E), northings (N) and elevation (Z). This is then recorded on the file and appears in a data file and is displayed on a map. These options are available by selecting the tabs.
  • This process continues until all the data is collected. If the TS needs to be moved it would be necessary to establish another control point by knocking a peg into the ground. A foresight to that point would establish co-ordinates and elevation.
  • Setting up over that point and sighting back to point 1 would continue the survey as the data for the new occupation point is known.
  • Several control points set around a site in this way with sideshots from each will both collect data and give points from which setting out may be carried out. The data collected can then be downloaded into AutoCad or CivilCad and accurate drawings produced.
  • Setting out co-ordinates for buildings etc can be found by:
a)   positioning the TS over a control point, 
b)   backsighting to another control point 
c)   accessing a setting out file with the co-ordinates already entered 
d)   identifying a point to be set out and selecting the set out option
e)   the TS will point the direction and indicate the distance and elevation
f)    the reflector is used to find the exact position of the point to be set out. 

Unit 4 will explore more fully the techniques and methods used in setting out.


  • Total Station Articles  – Good introduction to all aspects of Total stations
  • Setting up a Total Station 

Self-Assessment Task

  • Using the Total Station, open a new job file; enter details of the occupation point and perform a backsight, collect data and store this on the hard drive or memory card.

Section 6  Building Surveys

Aims and Objectives

At the end of this section you should be able to: 
  • Explain the procedure to be adopted in carrying out a building survey.

Apart from measuring land you may also be called upon to measure existing buildings. This will entail the completion of a Measured Building Survey, which is the accurate measurement of a building in order to produce: 
  • plans
  • sections
  • elevations
 These surveys are carried out to facilitate: 
  • planning applications
  • construction and refurbishment operations
 An accurate survey can be carried out using simple equipment or alternatively complex equipment such as a reflectorless total station. The most basic form of measured survey would use the following equipment: 
  • Digital Camera
  • Digital measure (Figure 13)
  • Tape measure
  • 30m Tape
  • Spirit Level
  • Adjustable Set Square
  • Paper & pencil 


Figure 13 

The procedures used in collecting measured survey data on external elevations are: 
  • Take digital photographs of all the elevations
  • Take each elevation in turn and produce a neat sketch
  • Measure those features which are accessible and note on the sketch
  • Measure the average distance between bricks both horizontally and vertically
  • Count the numbers of bricks and courses to windows and doors etc within the elevation
  • Convert the bricks and course into actual measurements and note these on the elevation
  • Progress around the elevations until all are sketched and dimensions noted.
  • The pitch of the roof should be measured using an adjustable set square and large spirit level
  • The pitch can be confirmed from within the loft if accessible
The procedures used in collecting measured survey data on internal areas are: 
  • Produce a sketch plan of each floor showing the position of rooms, doors and windows.
  • Using the digital measure and record all the dimensions on the sketch plan
  • Continue the measurement and recording procedure until all rooms are completed
  • Vertical heights within rooms are noted in order to verify external dimensions. 

The photographs, sketches and notes are taken back to the office and used to produce accurate drawings. 

Alternatively the use of electronic data loggers and reflectorless total stations can be used to automatically record both internal and external data which is downloaded directly into AutoCad.


  • Irvine, W, (1995) Surveying for Construction, McGraw-Hill: Berkshire (Chapter 16)

Self-Assessment Task

  • Explain the procedure to be adopted in carrying out a building survey.

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