OPM3B CISM Module 5 Tutorial 1 Traverse Calculation PDF

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National Diploma: Civil engineering Technology B.Eng: Civil Engineerin ng Science gineering Surveying OPM3B CISB Civil Eng Module 5 Tutorial 1 Tra averse calculation INSTRUCTIONS: • Complete all the exercisess • The use MS Excel to com mplete the exercises is OPTIONAL!

The purpose of this tutorial is s to provide the student with the background d to make the correct observations, red duce these observations and use the reduceed observations to calculate and d adjust observations made to obtain the co o-ordinates and elevation of a point using a traverse calculation with the use of basic surveying equipment. ou to find the position (co-ordinates and elev vation) of an 1. The Traverse enables yo unknown point by measu uring its position relative to the position of a MINIMUM OF TWO known points. T The accuracy of observations will determine e the precision and accuracy oof your calculations.

2. You need to understand the following terms:

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Station – a known po oint at which the surveyor will set up his instrument to make observations to o a second known point (BACKSIGHT) foor orientation p purposes. Observatio ons are made from the STATION to a new point (FORESIGHT) to dettermine the co-ordinates and elevation of su uch a point

•

ervation taken to a point of known co-ordinaates and Backsight – an obse elevation, taken to orrientate the instrument and determine the an ngle between the referenc ce object and new point.

OPM3B CISB Civil Engineering Surveying Tutorial •

Foresight - an observation taken to a point of unknown co-ordinates and elevation, taken to orientate the instrument and determine the angle between the reference object and new point.

•

Arc of observation – a set of observations made to the backsight and foresight. The arc will include two sets of observations to each point, called a Face Left and Face Right observation.

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Face Left (F/L) or “Direct” implies that the horizontal screw of the instrument is located on the right-hand side of the instrument (when using a Leica Total station)

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Face Right (F/R) or “Transit” implies that the instrument telescope is rotated in the vertical plane through 180 degrees and the instrument rotated on the horizontal axis through 180 degrees.

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Traverse calculation implies the calculation of co-ordinates and elevation of a new point from the horizontal and vertical angles observed as well as the measured distances between the station and foresight

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Backcheck implies the back calculation of the co-ordinates and elevation of the KNOWN BACKSIGHT in order to ensure that the observations made and the bearings and distances calculated “CHECKS” with the original information.

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Closed traverse implies a traverse that starts from a known base and is “closed” on the same base or another point of KNOWN co-ordinates.

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Open traverse implies a traverse that starts from a known base but does not stop on a known point. This is by far the most common form of traversing. It means that the accuracy of the traverse cannot be independently verified by “closing” on a known point.

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Base or Baseline refers to the direction and distance between TWO KNOWN points. This will be the starting point for a traverse. If the direction is not given, it can be calculated from the co-ordinates using a JOIN or University of Johannesburg Mine Survey Department

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OPM3B CISB Civil Engineering Surveying Tutorial POLAR calculation. It is essential for accurate surveying to ensure that this information is available before starting the traverse. •

Balancing of a Traverse. In the case of a CLOSED traverse it is expected that the co-ordinates determined by the traverse of the final known point, agree exactly or within the prescribed limits of error (for the sake of the survey camp 20mm will be allowed). Should the closure exceed these limits, it will be necessary to repeat the survey until these limits are met. In the case that the survey falls within the limits of error, the traversed points can be adjusted using the BOWDITCH rule.

•

Target or “Bob” refers to the target placed over or under the fixed point, used to observe the angles and distances to the BACKSIGHT or FORESIGHT. In the mining industry the target may be in the form of a target suspended from thin aluminium poles or a weighted plumb bob suspended from a string, from the roof of the excavation It is a common mistake to omit taking this measurement! If this measurement is not taken it means that your observations will be of no use and you will have to repeat the observations again!

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Target or bob Height refers to the vertical distance measured from the survey station to the optical centre of the prism or in the case of a plumb bob to the knot or button signifying the sighting point on the bob string. The value of this height may be positive if the reference point is in the ground or negative if the reference point is in the roof of a tunnel. It is a common

mistake to omit taking this measurement! If this measurement is not taken it means that your observations will be of no use and you will have to repeat the observations again!

•

Instrument Height refers to the vertical distance measured from the survey station to the optical centre of the instrument. The value of this height may be positive if the reference point is in the ground or negative if the reference point is in the roof of a tunnel. It is a common mistake to omit

taking this measurement! If this measurement is not taken it University of Johannesburg Mine Survey Department

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OPM3B CISB Civil Engineering Surveying Tutorial means that your observations will be of no use and you will have to repeat the observations again!

3. You will be required to complete the observations for a CLOSED traverse which will be explained in detail in the Practical Project Tutorial. 3.1. Adhere to all safety regulations! ZERO HARM! 3.1.1. Take extra precautions between the vehicles! 3.2. Work in a team. PLAY NICE! 3.3. Give the other groups a chance, you will be sharing observation points

4. Observation Methodology: Please refer to the detailed slideshow indicating the sequence of observation and booking of observations. 5. PLEASE remember to make use of good observation practice: 5.1.1. Early morning or late afternoon 5.1.2. Cool overcast conditions are best 5.1.3. Stop a little ahead of the point and then slowly bring the cross hairs onto the point 5.2. Always observe a minimum of two arcs, one in the “face left” and one in the “face right” position. For this exercise you will need to observe FOUR arcs!

6. Project Requirements 6.1. A co-ordinate list will be supplied. Should your assigned/chosen base NOT have co-ordinates and Elevation, please select an alternative base as your starting point. If this is not possible, assume the elevation of your starting point to be 1000.000m above mean Sea Level.(if the elevations are not available) •

UJ DFC survey stations are a red pin on a yellow washer over a gray disk that will have the station number written on it (DFC)

•

UJ APK survey stations will be a brass disk with a silver Hilti pin University of Johannesburg Mine Survey Department

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OPM3B CISB Civil Engineering Surveying Tutorial

6.2. Take observations to determine the position of unknown points in your allocated project area. 6.3. EVERY TIME before taking the theodolite and tripod down, check that all the entries have been made in the field book and that the differences and additions are correct. Having satisfied yourself that all the entries in the field book have been made, are in order and are correct, remove the theodolite from the tripod and replace it carefully in this carrying case or box. 6.4. CLOSE your traverse on your starting point or a point with KNOWN Coordinates and Elevation i) Reduce the observed directions from your fieldwork ii) Calculate the final co-ordinates of the points using the required traverse LAYOUT and CALCULATION method. iii) Show the following in your project portfolio: (1) Original field notes. A Fieldbook page is NOT the same thing as a calculation! (2) All reductions done to observations (3) All the completed traverse calculations including the check (4) The Bowditch calculation (if required, if not STATE your results and comment why the balance was not required) ii) A plan of the project area indicating the baseline and the traverse points to a suitable scale.

6.5.

AT NO STAGE WILL ANY EQUIPMENT BE LEFT

UNATTENDED FOR ANY REASON WHATSOEVER! 6.6. Hand in equipment back in a better /cleaner condition than

you received it in.

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OPM3B CISB Civil Engineering Surveying Tutorial

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7. Specific Outcomes

Outcome 7.1. Use the approved layout for

Demonstrated Skill Divide the page into 4 equal portions

the manual calculation of Traverse

Demonstrate the correct layout in calculations

7.2. Check the accuracy of Horizontal observations

Calculate the sum of angles to ensure that it adds up to 360 degrees, within a 2minute limit of tolerance

7.3. Check the accuracy of Vertical observations

Calculate the sum of angles to ensure that it adds up to 360 degrees, within a 2minute limit of tolerance

7.4. Calculate the average

Calculate the average Horizontal

Horizontal Clockwise and Anti-

Clockwise and Anti-Clockwise

Clockwise observations

observations

7.5. Calculate the average Vertical

Calculate the average vertical angle from the vertical circle

Angle

graduation

7.6. Calculate the correct forward

Calculate the correct forward and

and backward bearings from

backward bearings from the station

the station to the foresight

to the foresight. Check that the difference is 180 degrees

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OPM3B CISB Civil Engineering Surveying Tutorial

7.7. Calculate the correct

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Calculate the:

Horizontal- and Vertical

VD=Sin  * SD

distances

HD=Cos  * SD

7.8. Calculate the elevation of the FORESIGHT

Demonstrate the correct calculation method to determine the sign of the instrument height, target height and vertical distance. In order to calculate the correct elevation of the FORESIGHT

7.9. Calculate the co-ordinates of the Foresight

Demonstrate the correct calculation of the forward bearing () and calculate :

y = Sin  * HD x = Cos  * HD 7.10.

Calculate the co-

Demonstrate the correct calculation

ordinates of the BACKSIGHT

of the old back bearing () and

as a CHECK

calculate :

y = Sin  * HD x = Cos  * HD

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OPM3B CISB Civil Engineering Surveying Tutorial

8. Calculation 8.1. In the case where you have a complete direction sheet with a number of set-ups it will be necessary to calculate corrected observations to the unknown point 8.2. Reduce the angular observations. Ensure that your observations add up to

180 or 360 degrees depending on the type of observation! 8.3. These calculated angles will be used in calculation. 8.4. Please refer to the slideshow tutorial and notes. 8.5. It is REQUIRED that you adhere in the strictest detail to the

calculation layout. 9. Example of Field observations:

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OPM3B CISB Civil Engineering Surveying Tutorial

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9.1. You should have the co-ordinates and elevation of the Station [P] and Backsight [A]. Point

P A

Y Co-ordinate

-846.435 -858.618

Y Co-ordinate

Elevation

999.065 955.052

477.298 476.522

10. If the bearing and distance is not available, you will have to calculate a Join to determine the correct bearing and Horizontal distance. If a bearing is not available please calculate the Join between the station and backsight now.

10.1.

You are required to calculate the co-ordinates and elevation of

foresight [B] and to show the correct layout and all the required checks for the calculation.

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OPM3B CISB Civil Engineerinng Surveying Tutorial 10.2.

Step 1. Use the approved layout for the manual calculation of

Traverse. Divide your answer sheet into four equal parts. •

Use the first two columns for the calculation and the second two columns for the check c calculations

10.3.

s Step 2. Calcula ate the Horizontal observations. It is good surveying

practice to calculate these observations in the field at the survey station BEFORE you move to t the next point! (it will save you a lot of effort later)

10.3.1.

Subtract the observed angles in the following order:

10.3.1.1. Clockwise Angle = Subtract TOP from BOTTOM

75:22:10 Clockwise Ang gle or (Set1) = 310:28:10 – 235:06:00 = 7 ockwise Angle = Subtract BOTTOM from TOP 10.3.1.2. Anti-Clo

20 = Anti-Clockwise Anngle (Set 2) = 360 + 180:17:30 – 255:39:2 284:38:10

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OPM3B CISB Civil Engineering Surveying Tutorial Remember that if the Observation is smaller than the observation that must be deducted from it you will need to ADD 360 degrees 10.3.2.

Repeat this for the observations made in Set 3 and Set 4

Notice that the answers are not EXACTLY the same, but is well within the 2 minute tolerance that you are allowed in your observations 10.3.3.

The average Clockwise angle will be:

= (75:22:10 +75:21:40) / 2 = 75:21:55 10.3.4.

and the average Anti-clockwise Angle will be:

= (284:38:10+ 284:37:50) / 2 = 284:38:00 10.4.

Step 3. Balance the Clockwise and Anti-clockwise angles to add

to 360°, if you are outside the 2 minute tolerance. It WILL NOT HELP

TO BALANCE OUT THE ERROR. It will mean that you have to repeat the field observations. Refer to the comment made about good observation practice in Step 1.

REMEMBER: The corrected angles MUST add up to 360:00:00! 10.4.1.

The average Clockwise angle PLUS the average Anti-

clockwise Angle should be equal to 360:00:00, but this will almost never be the case. 75:21:55 + 284:38:00 = 359:59:55 10.4.2.

In this case it means that there is a 5 second error that needs

to be distributed between the two angles. Because the sum of the Raw observations are LESS THAN 360:00:00, the difference is added in order to obtain 360:00:00 University of Johannesburg Mine Survey Department

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OPM3B CISB Civil Engineerinng Surveying Tutorial 10.4.3.

As the error e must be equally divided between the tw wo angles

ie. 5 seconds div v ided by 2 , I am adding 3 seconds to the clo ockwise

onds to the anti-clockwise angle. angle and 2 seco

10.4.4.

My angles now add up to 360:00:00, so the calcula ation is

CHECKED! 10.5.

e vertical Step 4. A similar process must be followed to calculate the

angels to the BACKS SIGHT and FORESIGHT. 10.5.1.

Add the two vertical angles observed to the BACKS SIGHT

together, it must add up to 360°, if not balance the angles un ntil it does.

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OPM3B CISB Civil Engineering Surveying Tutorial 10.5.1.1. In the case of observations made to BACKSIGHT [A] the following observations were booked: :

So we need to ADD (4/2)=2 seconds to each angle to add up to 360°,Therefore:

10.5.1.2. In the case of observations made to FORESIGHT [B] the following observations were booked:

So we need to ADD(20/2)= 10 seconds to each angle to add up to 360°, therefore:

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OPM3B CISB Civil Engineering Surveying Tutorial 10.6.

Step 5. Calculate the True Vertical Angle from the circle graduation

Bevery careful! The angles are still in a raw format and needs to be converted into a TRUE vertical Angle referenced from the horizontal planed. Most Survey instruments are graduated in the same manner, with the vertical angle reading 0:00:00 if pointed up exactly vertical and

180:00:00 when pointed down exactly vertical. That implies that if the instrument is properly levelled, that the instrument line of sight will be exactly horizontal if the angle reading is 90:00:00 or 270:00:00. 10.6.1.

If the observed Angle () is:

 < 90º then 90º- Angle = + Vertical Angle (positive)  > 90º then 90º- Angle = - Vertical Angle (negative) 10.6.2.

Similarly if the observed Angle () is:

 < 270º then 270º- Angle = + Vertical Angle (positive)  > 270º then 270º- Angle = - Vertical Angle (negative)

Please refer to the sketch:

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OPM3B CISB Civil Engineering Surveying Tutorial

10.6.2.1. Angle A1 is 91:12:34 > 90º therefore the Vertical Angle will be Negative , thus: 91:12:34 - 90:00:00 = - 01:12:34 10.6.2.2. Angle A2 is 268:47:22 < 270º therefore the Vertical Angle will be Negative , thus: 270:00:00 - 268:47:22 = - 01:12:38, and ; 10.6.2.3. Average Angle A = (01:12:34 01:12:38) / 2 = - 01:12:36

10.6.2.4.

YOU WILL NOTE THAT in this example the

angles are only averaged out AFTER the calculation. It is your choice if you want to do it in STEP4 or STEP 5. 10.6.3.

Repeat the process for angle B

10.6.3.1. Angle B1 is 66:46:30 < 90º therefore the Vertical Angle will be Positive , thus: 90:00:00 – 66:46:30 = + 23:13:30, and 10.6.3.2. Angle B2 is 293:13:10 > 270º therefore the Vertical Angle will be Positive, thus: 293:13:10 – 270:00:00 = + 23:13:10 10.6.3.3. Average Angle B = (23:13:30 + 23:13:10) / 2 = +

23:13:20. 10.6.3.4. Your calculation should look like this by now:

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OPM3B CISB Civil Engineering Surveying Tutorial 10.7.

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Step 6. Calculate the Vertical Distance and Horizontal Distance to

the FORESIGHT. 10.7.1.

Vertical Distance (VD) = Sin  * Slope distance

This is why you must only book the SLOPE DISTANCE in your Fieldbook! 10.7.2.

Horizontal Distance (HD) = Cos  * Slope distance

An independent check can be done to check if the calculation is correct 2

2

2

using Pythagoras SD = VD + HD

10.8.

Step 7. Calculate the Vertical Distance and Horizontal Distance to

the BACKSIGHT. 10.8.1.

Vertical Distance (VD) = Sin  * Slope distance

10.8.2.

Horizontal Distance (HD) = Cos  * Slope distance

An independent check can...