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- 1. SCHOOL OF ARCHITECTURE, BUILDING AND DESIGN BACHELOR OF QUANTITY SURVEYING (HONOURS) QSB60103103946-M Site Surveying Fieldwork Report 2 TRAVERSE GROUP MEMBERS STUDENT ID Liew Li Wen 0324297 Lim Kar Yan 0325602 Tan Hwee Min 0326057 Esther Chuah Ning Sie 0321422
- 2. 1 TABLE OF CONTENT Content Pages Cover Page 1 Table of Content 2 Introduction 3 - 8 Objectives 9 Data and Results 10 - 22 Discussion 23 - 25
- 3. 2 1.0 Introduction to traversing Traversing is that type of survey in which a number of connected survey lines form the framework and the directions and lengths of the survey lines are measured with the help of an angle measuring instrument and a tape or chain respectively. 1.1 Types of Traverse ➔ Closed traverse: When the lines form a circuit which ends at the starting point, it is known as closed traverse. ➔ Open traverse : When the lines form a circuit ends elsewhere except starting point, it is said to be an open traverse. 1.11 Open Traverse An open traverse is one which does not close on the point of the beginning. It begins at a point of known position and ends at a station whose point is unknown. This traverse type is not recommended because there is no geometric verification possible with respect to the actual positioning of the traverse stations.It is commonly used for the line center survey for highway,railroad and etc. OPEN TRAVERSE Image source:www.artillerysurveyors131.com.au
- 4. 3 1.12 Closed Traverse A closed traverse is one enclosing a defined area and having a common point for its beginning and end point or at a point whose relative position is known. It is commonly used for locating the boundaries of lakes,property and etc. There are two types of closed traverse:- 1. Loop Traverse - The starting point and the ending point of the loop are located at the same point, a closed geometric figure called a polygon will be formed. The ending point will be the same with the beginning point if you were to move along the sides of the closed traverse. Loop traverse are best surveyed in a counterclockwise direction,with interior angles ‘turned’ to the right. Image source:files.carlsonsw.com 2. Connecting Traverse - It looks like an open traverse ,except that it begins and ends at points (or lines) of known position (and direction) at each end of the traverse. Deflection angles must be identified as being turned either clockwise,that is,to the right (R) ,or counterclockwise to the (L). Image source:jerrymahun.com
- 5. 4 1.2 Azimuths The azimuth of a line defined as the clockwise horizontal angle from reference line. The reference direction normally is from north .The range of the angle should be from 0º to 360º. The example of the azimuth is 120º or 140º. 1.3 Bearing A bearing of a line defined as the acute angle(<90º) from the north (N) or the south (S) end of meridian. It has the addition designation of east (E) or west (W), whichever applies . The angle of the bearing should never greater than 90º. The example of bearing is S60ºE or N70ºW. Image source:www.e-education.psu.edu 1.4 Selection of Traverse Stations ● The chosen control traverse stations need to be as close as possible to the features or objects ● The chosen control traverse stations need to form a suitable shape. ● Cost and time of the survey will increase if too many points are established ● Sufficient control may not be provided for the survey if too few points are established. ● The ground of the survey area should be accessible where the traverse legs are tapped. ● The length of the traverse legs are needed to be almost the same.
- 6. 5 1.5 Acceptable Misclosure In common, for land surveying an accuracy of about 1:3000 is typical. The acceptable misclosure can be calculated by using the formulae below:- Accuracy= 1 : (P/Ec) P= Perimeter E= Error of closure (computed from the error in departure and error in latitude ,using the Pythagorean theorem) Classification First Order Second Order (Class I) Second Order (Class II) Third Order (Class I) Third Order (Class II) Recommended spacing of principal stations Network stations 10- 15km ; other surveys seldom less than 3km Principal stations seldom less than 4km, except in metropolitan area surveys ,where the limitation is 0.3 km Principal stations seldom less than 2km, except in metropolitan area surveys ,where the limitation is 0.2 km Seldom less than 0.1 km in tertiary surveys in metropolitan area surveys ; as required for other surveys Seldom less than 0.1 km in tertiary surveys in metropolitan area surveys ; as required for other surveys Position closure after azimuth adjustment 0.04m √K or 1:100,000 0.08m √K or 1:50,000 0.2m √K or 1:20,000 0.4m √K or 1:10,000 0.8m √K or 1:5000 Table: Traverse Specifications - United States Source: From Federal Control Committee,United States,1974.
- 7. 6 1.6 Traverse Computations Traverse computations is the process of taking field measurement through a series of mathematical calculations to determine final traverse size and configuration. These calculations include error compensation as well as reformation to determine quantities not directly measured. Traditional traverse computation steps are: 1. Balance (adjust) angles 2. Determine line directions 3. Compute latitudes and departures 4. Adjust the traverse misclosure 5. Determine adjusted line lengths and directions 6. Compute coordinates 7. Compute area The order of some steps can be changed. For example, steps 1 and 2 would be reversed for closed link traverses with directions at both ends. Balancing angles would normally not be done If a least squares adjustment is used at step 4. The complete series of computations can only be performed on closed traverses. That's because some of the steps require adjustment of errors and, as discussed before, errors can't be identified in an open traverse.
- 8. 7 1.7 Outline Apparatus Theodolites are used mainly for surveying applications. It is a precision instrument for measuring angles in the horizontal and vertical angles, distance, depth and etc. It is used to identify the ground level and the ways to construct ‘super- structure or sub-structure. A modern theodolite consists of a movable telescope and it is able to rotate 360 degree on a tripod stand by the leveling system. When the telescope is pointed at a target object, the angle of each of these axes can be measured with great precision. The calculation of the angles is based on the used in triangulation network and geo-location work. Tripod stand consists of a portable three-legged frame. It is used to provide stability by supporting the weight and maintaining the balance of the instrument on top of it. The three legs are moved away from the vertical centre and the leg lengths are adjusted to bring the tripod head to a convenient height and make it roughly level. After that screw the instrument on it and make sure both of them are precisely positioned. Plumb bob is an instrument to make sure the object is placed perpendicularly. It is a weight with a pointed bottom that is suspended from a string to determine a vertical line. It’s usually used to mark a point directly under the theodolite.
- 9. 8 Spirit level is designed to indicate whether the surface is horizontal or vertical. A slightly curved glass tube which incompletely filled with either alcohol or spirit, leaving a bubble in the tube. On a flat surface, the bubble naturally rest in the center, the highest point. Optical ‘plumnet is a detachable base for theodolites to indicate the center of it over a ground station. It is used in place of plumb bob to center theodolites and transits over a given point due to its steadiness in strong winds during surveying process. It can speed up the set-up procedure and protect the theodolite from any accident because there’s a lock below it to screw itself towards the device using during the fieldwork. Ranging poles are used to mark areas and to set out straight lines on the field. They are also used to mark points that must be seen from a distance, in which case a flag may be attached to improve the visibility. Ranging poles are straight round stalks, 3 to 4 cm
- 10. 9 thick and about 2m long. They are usually painted with alternate red-white or black-white bands. 2.0 Objectives ● To learn the principles of running a closed field traverse. ● To enhance the student knowledge in the traversing procedure ● To be familiar with the setting up of the theodolite ● To determine the error of misclosure in order to compute the accuracy of the work ● To determine the adjusted independent coordinates of the traverse station so that they can be plotted on the drawing sheet
- 11. 10 3.0 Field Data Station A 82º 44’ 30’’ B 94º 39’ 50’’ C 87º 46’ 30’’ D 94º 46’ 50’’ Sum 359º 57’ 40’’
- 12. 11 3.1 Compute the angular error and adjust the angles. The sum of the interior angles in any loop must be equal (n - 2) (180º) for geometric consistency; Sum of interior angle= (n - 2) (180º) = (4 - 2) (180º) = 360º Total angular error = 360º 00’ 00’’ - 359º 57’ 40’’ = 0º 02’ 20’’ Error per angle = 0º 02’ 20’’ / 4 = 0º 0’ 35’’ per angle Station Angles Correction Adjusted Angles A 82º 44’ 30’’ + 0º 0’ 35” 82º 45’ 05’’ B 94º 39’ 50’’ + 0º 0’ 35” 94º 40’ 25’’ C 87º 46’ 30’’ + 0º 0’ 35” 87º 47’ 05” D 94º 46’ 50’’ + 0º 0’ 35” 94º 47’ 25” Sum 359º 57’ 40’’ 360º 00’ 00”
- 13. 12 3.2 Calculate the Horizontal and Vertical Distance Between the Survey Points and the Theodolite Survey Points and the Theodolite The horizontal and vertical distances between the survey points and the theodolite can be calculated using the equations as follows: Equation ; D = k x S x cos2 (θ) + C x cos Where, D = Horizontal distance between survey point and instrument S = Difference between top stadia and bottom stadia θ = Vertical angle of telescope from the horizontal line when capturing the stadia readings K = Multiplying constant given by the manufacturer of the theodolite, (normally = 0 ) C = Addictive factor given b y the manufacturer of the theodolite (normally = 0 )
- 14. 13 Distance A-B Top Stadia: 1.730 Medium Stadia: 1.465 Bottom Stadia: 1.250 Top Stadia: 1.670 Medium Stadia: 1.475 Bottom Stadia: 1.280 Distance A-B = [ (K x s x Cos2 θ) + ( C x Cos θ ) = [ 100 x ( 1.730 - 1.250 ) Cos2 θ ] + ( 0 x Cos θ ) = 53.7742 m Distance A-B = [ (K x s x Cos2 θ) + ( C x Cos θ ) = [ 100 x ( 1.670 - 1.280 ) Cos2 θ ] + ( 0 x Cos θ ) = 45.5760 m Average distance = ( 53.7742 m + 45.5760 m ) / 2 = 49.6751 m Distance B-C Top Stadia: 1.520 Medium Stadia: 1.453 Bottom Stadia: 1.263 Top Stadia: 1.326 Medium Stadia: 1.260 Bottom Stadia: 1.080 Distance B-C = [ (K x s x Cos2 θ) + ( C x Cos θ ) = [ 100 x ( 1.520 - 1.263 ) Cos2 θ ] + ( 0 x Cos θ ) = 33.7420 m Distance B-C = [ (K x s x Cos2 θ) + ( C x Cos θ ) = [ 100 x ( 1.326 - 1.080 ) Cos2 θ ] + ( 0 x Cos θ ) = 24.7060 m Average distance = ( 33.7420 m + 24.7060 m ) / 2 = 29.2240 m
- 15. 14 Distance C-D Top Stadia: 1.490 Medium Stadia: 1.272 Bottom Stadia: 1.030 Top Stadia: 1.620 Medium Stadia: 1.550 Bottom Stadia: 1.130 Distance C-D = [ (K x s x Cos2 θ) + ( C x Cos θ ) = [ 100 x ( 1.490 - 1.030 ) Cos2 θ ] + ( 0 x Cos θ ) = 49.7726 m Distance C-D = [ (K x s x Cos2 θ) + ( C x Cos θ ) = [ 100 x ( 1.620 - 1.130 ) Cos2 θ ] + ( 0 x Cos θ ) = 46.4762 m Average distance = ( 49.7726 m + 46.4762 m ) / 2 = 48.1244 m Distance D-A Top Stadia: 1.463 Medium Stadia: 1.350 Bottom Stadia: 1.189 Top Stadia: 1.826 Medium Stadia: 1.680 Bottom Stadia: 1.530 Distance D-A = [ (K x s x Cos2 θ) + ( C x Cos θ ) = [ 100 x ( 1.463 - 1.189 ) Cos2 θ ] + ( 0 x Cos θ ) = 30.9954 m Distance C-D = [ (K x s x Cos2 θ) + ( C x Cos θ ) = [ 100 x ( 1.826 - 1.530 ) Cos2 θ ] + ( 0 x Cos θ ) = 31.9806 m Average distance = ( 30.9954 m + 31.9806 m ) / 2 = 31.4880 m
- 16. 15 3.3 Compute course bearing and azimuth Azimuth Bearing A-B 00° 00’ 00” N 00° 00’ 00” B-C 180° 00’ 00” + 94° 40’ 25” _____________ 274° 40’ 25” _____________ N 85° 19’ 35” W
- 17. 16 C-D 87° 47’05” + 94° 40’ 25” ____________ 182° 27’ 30” ____________ 182° 27’ 30” - 180° 00’ 00” ____________ 2° 27’ 30” ____________ S 2° 27’ 30” W D-A 94° 47’ 25” + 2° 27’ 30” ____________ 97° 14’ 55” ____________ 180° 00’ 00” - 97° 14’ 55” ____________ 82° 45’ 05” ____________ S 82° 45’ 05” E
- 18. 17 3.4 Compute Latitude and Departure Image source:www.cfr.washington.edu Cos β Sin β L cos β L sin β Station Bearing, β Length, L Cosine Sine Latitude Departure A N 00° 00’ 00” 49.6751 1.0000 0.0000 + 49.6751 0.0000 B N 85° 19’ 35” W 29.2240 0.0818 0.9967 + 2.3905 - 29.1276 C S 2° 27’ 30” W 48.1244 0.9991 0.0429 - 48.0811 - 2.0645 D S 82° 45’ 05” E 31.4880 0.1262 0.9920 - 3.9738 + 31.2361 A Total Perimeter (P) = 158.5115 Sum of Latitude: ΣΔy = 0.0107 Sum of Departure: ΣΔx = 0.0440
- 19. 18 3.5 Determine The Error of Closure Accuracy = 1 : (P/Ec) For average land surveying an accuracy of about 1 : 3000 is typical Ec = [ (sum of latitude)2 + (sum of departure)2 ]1/2 = [ ( 0.0107 )2 + ( 0.0440 )2 ]1/2 = 0.0453 m P = 158.5115 m Accuracy = 1 : ( 158.5115 / 0.0453 ) = 1 : 3499 Therefore, the traversing is acceptable.
- 20. 19 3.6 Adjust Course Latitude and Departure The Compass Rule Correction = - [ ΣΔy ] / P x L or - [ ΣΔx ] P / L Where, ΣΔy and ΣΔx = The error in latitude and departure P = Total length of perimeter of the traverse L = Length of a particular course Station Unadjusted Corrections Adjusted Latitude Departure Latitude Departure Latitude Departure A + 49.6751 0.0000 - 0.0034 - 0.0138 + 49.6717 - 0.0138 B + 2.3905 - 29.1276 - 0.0020 - 0.0081 + 2.3885 - 29.1357 C - 48.0811 - 2.0645 - 0.0032 - 0.0134 - 48.0843 - 2.0779 D - 3.9738 + 31.2361 - 0.0021 - 0.0087 - 3.9759 + 31.2274 A Σ= + 0.0107 + 0.0440 - 0.0107 - 0.0440 0.00 0.00 Check Check
- 21. 20 Latitude correction ● The correction to the latitude of course A-B is [ - 0.0107 / 158.5115 ] x 49.6751 = - 0.0034 ● The correction to the latitude of course B-C is [ - 0.0107 / 158.5115 ] x 29.2240 = - 0.0020 ● The correction to the latitude of course C-D is [ - 0.0107 / 158.5115 ] x 48.1244 = - 0.0032 ● The correction to the latitude of course D-A is [ - 0.0107 / 158.5115 ] x 31.4880 = - 0.0021 Departure correction ● The correction to the departure of course A-B is [ -0.0440 / 158.5115 ] x 49.6751 = - 0.0138 ● The correction to the departure of course B-C is [ -0.0440 / 158.5115 ] x 29.2240 = - 0.0081 ● The correction to the departure of course C-D is [ -0.0440 / 158.5115 ] x 48.1244 = - 0.0134 ● The correction to the departure of course D-A is [ -0.0440 / 158.5115 ] x 31.4880 = - 0.0087 3.7 Compute station coordinates
- 22. 21 N2 = N1 + Lat1-2 E2 = E1 + Dep1-2 Where, N2 and E2 = The Y and X coordinates of station 2 N1 and E1 = The Y and X coordinates of station 1 Lat1-2 = The latitude of course 1-2 Dep1-2 = The departure of course 1-2 Station N Coordinate* Latitude E Coordinate* Departure A 100.0000 ( Assumed ) + 49.6717 129.1495 -0.0138 Start/ return here for lat. check Start/ return here for dep. Check (Course lat. and dep.) B 149.6717 +2.3885 129.1357 -29.1357 C 152.0602 -48.0843 100.0000 -2.0779 D 103.9759 -3.9759 97.9221 +31.2274 A 100.0000 129.1495 * Compass - Adjusted Coordinates Table 0f Computation of Station Coordinate
- 23. 22 3.8 Loop Traverse Plotted Using Coordinate ( Graph) The adjusted loop traverse plotted by coordinates.
- 24. 23 4.0 Discussion In this field work, we are required to investigate the survey method which is the closed loop traverse. A traverse is a series of consecutive lines whose ends have been marked on the field, and whose lengths and directions (angle, bearing, or azimuth) have been determined from measurements. There are two types of traverse which is the closed traverse and open traverse. We found that the close traverse gives a higher accuracy because open traverse offers no means of checking for errors or mistakes. First, we are exposed to the method of using the apparatus which is the electronic distance measurement (EDM). A detailed explanation has been given by our lecturer before the work is conducted. Four points are roughly set and was noted as station A, B, C and D. These four points are set to form a quadrilateral shape as we are conducting the simplest closed loop traverse. Then, we used the theodolite to measure the angle of the station A, B, C and D and the data is recorded for further calculations. We first start with the angle measurement at station A. The apparatus is set up at station A, the data is collected by reading through the theodolite on station B and D. This step is repeated by setting the apparatus on the following stations to obtain the angle on that particular station. Both vertical and horizontal angles which are showed on the digital panel of the theodolite have been recorded. The stadias (top, middle and bottom) readings are recorded for calculation of the horizontal
- 25. 24 and vertical distances between the stations. This is known as the stadia method. The calculation is given by the equation: D = k x S x cos2 (θ) + C x cos When calculating the error, we have obtained 359º 57’ 40’’ for our total interior angle, which is 2’ 20’’ less than the optimum total interior angle of a quadrilateral (360º). The optimum total interior angle is calculated by 𝛴 = (𝒏− 𝟐) ∗ 𝟏𝟖𝟎º The error at each angle has been calculated and each angle is adjusted by adding 0º 0’ 35”. Latitude and departure error is calculated then, which are 0.0107 and 0.0440 respectively. The total error is 0.0453 which is given by equation Ec = [ (sum of latitude)2 + (sum of departure)2 ]1/2 And so, the accuracy is calculated with equation Accuracy = 1 : (P/Ec) The value obtained is 1:3499 which meets the optimum accuracy for average land surveying 1:3000 and hence, our traverse survey is acceptable. Latitude and departure are then being adjusted by using the compass rule: Correction = - [ ΣΔy ] / P x L or - [ ΣΔx ] P / L Lastly, a graph is plotted with the coordinates achieved for all the four stations. There are few precautions have to be taken in consideration when using the apparatus when measurement is conducting.
- 26. 25 1. Special care should be taken to avoid any situation that might result in the theodolite being dropped or otherwise subjected to a severe jar. 2. Inspect the theodolite for loose parts and screws. Remove dust from the objective lens and eyepiece with a lens brush and lens tissue using procedures consistent with delicate optics. Keep the lens covered with the theodolite is not in use. Use a sunshade to protect the lens from the direct rays of the sun. 3. The graduated circles and venires are coated with a lacquer to retard oxidation. Avoid touching these parts. A thin film of oil applied with a lintless cloth will aid in keeping the surfaces clean. 4. Store the theodolite in its case or other dry dust free location when not in use. 5. If the theodolite is to be taken from a cool environment to a warm one (especially in humid conditions) allow the theodolite to warm up inside its case where it will not be subject to condensation. As any surveyor should understand, all measurements are in error. We may only try to minimize error and calculate reasonable tolerances, but not eliminating the errors. In conclusion, we have gained some useful knowledge on how a survey is done as it’s a hand-on work that we have to conduct ourselves to obtain the data needed. It links up all the theories we learned in class, giving us a deeper understanding as we worked practically on field. It can be useful in the future as we know how a distance is measured in order to construct a level building, or how a boundary of certain area is determined by this surveying method. It is pleased to have team members which are able to work together as a team in completing the task given. The objectives set primarily are achieved easily since everyone in the team gives fully support and cooperation throughout the survey work and report writing. Each team members is willing to share their thoughts and ideas when discussion is conducted and it’s a good attitude as we are able to learn from each other and broaden our mindset. Credits are to be given to our lecturer as well for teaching and guiding us on how the survey work is done and how the apparatus is used. It will be our pleasure if we are able to work together in the next work soon.