The science of determining the position in three dimensions of natural and man-made features on or beneath the surface of the earth [W.Schofield 1972]
There are indications of surveying about 6000 years ago used by Egyptians for the reconstruction of the Nile boundaries after its overflowing. Also the Romans were traced to being one of the forefathers of surveying which simply means act of horizontal and vertical measurement on the earth surface in nowadays civil engineering and construction studies.
LEVELLING
An huge term in surveying with wide scope of meanings. Prior to my understanding and after reliable researches .Levelling could be simply defined as a process carried out so as to derive elevation of points in reference to a particular datum or the differences between them.
Nowadays surveying is regarded as one of the most important aspect of construction due to the fact that everywhere is either halfway or fully occupied with construction works therefore the concentration has now moved to places with very poor topography that was been avoided by older builders or surveyors. So with the aid of levelling it has made it easy to make any part of the earth surface with extremely poor topography suitable for building. The following are some of the various types of levelling practiced by surveyors. They include;
-reciprocal levelling
-digital levelling
-trigonometrical levelling
-sectional levelling
-precise levelling e.t.c.
1.2.1 RECIPROCAL LEVELLING: The use of equal, continuous points of pegging to measure a wide or long distance so as to avoid errors which could set in terms of collimation, earth curvature and even refraction.
1.2.2 DIGITAL LEVELLING: Involves the use of electronic image processor, Bar-coded leveling staff and wild N A 2000 level. This type of levelling has helped in total elimination of some types of errors that can be committed by both the surveyor or observing or even the machineries been made use of.
1.2.3 TRIGONOMETRICAL LEVELLING: This comes to play when there are huge obstructions such as contours and trees. The total station is used to carry out this type of levelling .But the value given by this piece of machinery is most likely to have errors due to actions of refraction and curvature.
This is mostly used in road constructions especially in places with very poor topography.
1.2.4 SECTIONAL LEVELLING: This type of levelling is used to produce ground profile for the design of roads, railways, dams and buildings. This type of levelling is mostly used in the construction of anything that has to do with the earth surface. Mostly auto levels and normal staffs like the Philadelphia rods are used.
Other types of leveling include precise levelling which was used in the construction of peninsular Malaysia in the 1980`s. Also we have the stadia tracheometry which also involves the use of a total station.
SETTING-OUT
Setting out is one of the most important aspect of good construction. It is like an outline to the final state of how the building would look like. When constructing it all starts with a plan. A plan is drawn on a large piece of paper in those days but due to technological advancements the use of AutoCAD and other relative software’s have taken charge of drawing on a paper. Thus, the plan of buildings, roads, bridges and railways have gone digital.

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The second stage is the setting out. It is like the interpretation of plan. It involves the use of pegs, levels and tapes to transfer the real dimensions of the plans to the earth surface. At times it is regarded as the opposite of levelling in the sense that levelling entails transferring of ground values into paper work, while setting-out is the transfer of paper work onto the earth surface. Mostly it has to do with only the horizontal distances and also in reference to the temporary bench marks.
ERROR HANDLING
According to www.thefreedictionary.com error can be defined as an act, assertion or belief that unintentionally deviates from what is correct, right or true or the condition of having incorrect or false knowledge of results in a certain work.
In surveying, surveyors would rightly define error as something unavoidable which happens when carrying out different aspects of surveying such as levelling and setting out thereby forcing incorrect values or pegging as the case maybe.
Errors have been classified and categorized depending on the way it comes and the extent at which it makes the final outcome deviates from the true value. Different categories of error include;
-Natural error
-Instrumental error
-Personal error.
NATURAL ERRORS:- They come as a result of natural occurrences such as weather condition, gravity e.t.c. These are absolutely unavoidable because humans have no control over such. E.g. while measuring if the weather is too hot the tape extends by some few mm therefore giving wrong values and when it goes vice versa the tape would shrink and give also a wrong lower value.
INSTRUMENTAL ERRORS:- This type of error could be avoided to some certain extent because they are caused by improper construction or erection of surveying instruments, so while surveying a surveyor might take note of this and take care of it immediately but as a human being one can’t be fully observant so there are times surveyors fall victims of such error. Thus, efficiency and reliability of surveying equipments is very important.
PERSONAL ERRORS:- This error are the ones committed by the individual observing. I.e. errors made by the surveyor from either poor sight, poor sense of touch and even communication with fellow fieldsmen. During field work surveyors are required to be extremely sharp in taking readings and during evaluation.
Errors in tape measurements are mostly caused by the following factors which could be easily evaluated to get right values, they are
-temperature
-tension
-sag
-pull
-incorrect tape graduation
Temperature affects in the sense of increase or decrease in length in respect to the degree of hotness or coldness. If hot, the tape increases and if cold it shrinks therefore forcing wrong values. It could be evaluated using the formula below.
Ct=α(t-t0)L
Tension is the amount of force i.e. the extent of pull thereby subjecting the measurements to being error bounded. While others like sag comes to play in terms of how long the tape is being stretched then if its too long the tape would definitely have to sag. Another is the incorrect tape graduation, this ussually happen due to the manufacturer’s error and all this errors could be evaluated.
LITERATURE REVIEW
LEVELLING
During construction levelling is the most common aspect of surveying. Practically every aspect of construction requires some application of levelling.
The concept of leveling is simple measurement of vertical distance in relation to an horizontal line of sight. Also this is used in obtaining the elevation of ground point relative to a reference datum.
2.1.1 PRINCIPLES AND CONCEPT OF LEVELLING
The instrument is set up in a leveled manner such that the bubble fits into the right position and the line of sight through the telescope of the level is horizontally inclined to human point of view. Also the staff is kept vertically erect; the values taken from the staff are recorded to the nearest millimeter.
Another concept regarding this aspect of surveying (levelling) is the taking of the foresight and the back sight and also the intermediate sight.
There are different methods of booking levelling:
-Rise and fall method
-The height of point collimation. Simply known as the H.P.C method
The rise and fall method simply means subtracting either the intermediate sight from the fore sight or the back sight from the intermediate sight; whichever comes first, thereby getting values that are positive and negative. The positive values would be placed in the rise column because technically it means the contour is going higher while the negative values would be placed in the fall column because the terrain appears to be going deep down.
On the other hand the H.P.C. method involves the subtraction of staff readings from the reduced level. These two methods involve the use of the temporary bench mark.
Though in levelling error occurs both with the instrument and the surveyor and even in calculating. Error being one of our focus, it’s necessary to discuss the test in checking errors in levelling so we would talk about the two peg test below:
As described earlier, the accuracy of levelling operations is dependent on the quality of the instrument used and its adjustment. There are many factors that can affect the accuracy of readings, some of which are not controllable by the construction worker. Conditions such as the curvature of the earth and atmospheric conditions affecting the light have minimal effect on most levelling operations on a building site.
Another factor that is controllable, and can be reduced by testing and adjustment of the instrument is called collimation error. This occurs when the desired horizontal axis viewed through the instrument is not a true horizontal level line
The diagram below illustrates this point.
Collimation error
The two peg test is used to check the amount of collimation error, and by following the manufacturer’s handbook procedures, can be adjusted by a simple calibration of the instrument.
 
The two peg test can be carried out by following these steps:
Install levelling marks (A) and (B) approximately 30 – 40 meters apart. These marks should be identified by hammering pegs into the ground and then using the levelling staff held by others. Set up the instrument as normal as close to the middle as possible. See diagram below.
Two peg test step 1
Take a back sight reading to staff A (reading a1) and record; take a foresight reading to staff B (reading b1) and record.
Move and set up the instrument to a position approximately 3 meters away from staff (A).  Take a back sight reading to staff A (reading a2) and record; take a foresight reading to staff B (reading b2) and record. See diagram below.
Two peg test step 3
Apply the following formula: b1 – a1 = b2 – a2.
That is, find the difference between the first set of readings and the second set of readings.
If there is no or little difference recorded then no adjustment should be necessary.
Collimation error is often very difficult to eliminate and it is generally accepted that a difference of up to say two millimeters will not have an impact on most readings, provided the instrument is set up in a reasonably central position, amongst all the readings to be taken.
If an error is considered too large, simple adjustment of the reticule lines according to the instructions in the manufacturer’s handbook will reduce the impact of collimation error.
2.1.2 TERMINOLOGY
1- T.B.M (temporary bench mark):- A point or height in which past surveyors have measured and know the value and would be used as a reference in future calculations in levelling.
2- R.L (reduced level):- A point that its height is either above or below a reference datum and it’s been measured in relative to that datum.
3- DATUM: – A surface to which elevation of points are referred to e.g. sea level or ordance datum
4- LEVELLING STAFF: – Staffs are made of wood, metal or steel. Well graduated in meters. It’s quite thick and it’s mostly as tall as 10 meter. The calibration is clear and bold because it’s been viewed through the telescope of different levels to read the height of floors.
5-TRIPOD: – A three legged stand on which different machineries such as the auto levels are mounted during levelling.
6- MEASURING TAPE: – Graduated in either meters or ft`s used to measure distances.
7-AUTO LEVEL: – Used to measure horizontally indirectly because it views reading from the levelling staff from any but known distance. It has a kind of telescopic mode of view.
8- THEODOLITE:- Similar as auto level but it is more advanced because it also measures angles both horizontally and vertically and its digital in its orientation.
9-H.I (height of instrument):- Distance between the floor and eyepiece of a level.
10- B.S (back sight):- measurement with a level back to a point inclined to a known point known as front sight or T.B.M.
11- F.S (front sight):- measurement with a level to determine the height of a point on a straight line i.e. on an angle of zero degree before turning the level to either an intermediate sight or back sight.
12- I.S (intermediate sight): – A point whose value is known after a shot at the front sight i.e. it is not a changing point, but only used when the distance between the front sight and the back sight is long so it’s kind of a middle sighting.
13- CHANGING POINT: – point that has both back sight and front sight both on the same reduced level.
2.1.3 IMPORTANCE, USES AND PURPOSE OF LEVELLING
For the constructions of railways, roads e.t.c.
For the construction of dams, sewers, canals and water supply system.
To design a good drainage system.
To know the topography of an area.
For the construction of buildings.
Used in determination of slopes.
Used in construction of bridges.
2.2 SETTING-OUT.
Setting-out simply entails transfer of paper work to the earth surface with the use of pegs and markers.
While pegging or marking there are three basic principles or laws that an engineer has to abide by:
First is the primary setting out points which incurs that marking should be permanent throughout the life of the construction because they are for setting points on the control transverse or control triangulation system which could be referenced to the national grid for orientation.
Secondary setting out:- these are points referenced from primary stations i.e. from the control triangulation system. Thus, they are referenced in measurement and they could be points on a grid. Another function of this principle is that they provide control to the construction.
Temporary bench mark (T.B.M):- As earlier discussed under leveling as a point in which earlier surveyors have found the reduced level, in setting out this point are used as vertical control and also provide a bench mark (starting point) adjacent to the work and helps in avoiding substantial runs of flying. It is also a permanent set out.
2.2.1 CONTROL DURING SETTING-OUT
An action taken by engineers to ensure that the transferred measurements marked out does not get exceeded by the available space so this method is adopted to make sure construction works are aligned properly both horizontally and vertically. They are explained further as follows:
2.2.1.1 HORIZONTAL CONTROL
Accuracy is the greatest aim of any engineer in whatever he/she does. And so it is in horizontal control, the first thing is to get all the parts and directions of the building. The next thing in horizontal control is by not restricting it to any part it should pass through the four corner of a building i.e. the use of primary site control e.g. transverse and secondary, site control e.g. baselines. This control has to do with the floor dimensions i.e. it deals with the baselenght of buildings so in terms of machinery ordinary auto level could be used to make sure pegging are accurate. Different methods of applying this include
Grids
Offset pegs
GRIDS:- According to the joint collaboration of J.F. Uren and W.F. Prince which resulted in surveying for engineers defined surveying grid as I quote “surveying grids are lines running from both north to south and west to east drawn on the surveying plan from the original transverse or network, they are referenced to as an arbitrary origin”.
The site grid aids proper setting-out by showing some unknown portions of the plans and makes it easily transferrable. Bearing in mind that setting-out is all about transferring of drawings, all dimensions in a plan should be dealt with sectionally i.e. every section of the plan in a particular grid box is gently transferred to the floor regardless of other parts at the moment of the setting-out.
OFFSET PEGS:- After setting out the next stage is foundation which involves excavation. The land must have been pegged during setting so to avoid re-setting out, another peg into the ground some distance to the original peg on a straight line so to serve as a kind of reference pegs. Refer to the illustration below as a diagrammatic example: IMG_0003.jpg
2.2.1.2 VERTICAL CONTROL
First step is the establishment of series of temporary bench marks, Next is the use of sight rails to transfer the information to the workforce. These sight rails are horizontal timbers or planks established by the engineer so that they define the plane of the finished works below the sight rail plane. At times engineers do make use of better roles which its traveler can also do with slopes.
VERTICAL ALIGNMENT
This is a very vital aspect of setting out in building; it has to do with the proper erection of the building especially in multi storey buildings. To be able to carry out this setting out exceptionally well , you can do so with the following instrument provided all method of combating errors are taken into consideration. They include;
Plumb bob or spirit level
Theodolite
Optical plumbing device
Laser plumbing device.
2.3 ERROR HANDLING.
In surveying, No matter how care full things are executed we would always come by error. Errors are unavoidable so we can never eliminate them but only work towards that by taking all precautions to handle them well, so that they would have extremely minimum effects on our projects.
2.3.1 CLASSIFICATION OF ERRORS
GROSS ERROR:- Also known as MISTAKES in English language. This mostly happen due care freeness, inexperience, reluctances, fatigue and even unprofessional hypothesis. All this class of error needs to get combated is carefulness by surveyors during surveying.
SYSTEMATIC ERROR:- This is a known error so it can be kept constant throughout surveying works so that they can be calculated and corrected. They are mostly under the influence of natural condition such as shrinking of the tape due to abnormal temperature. So this can be calculated at all times.
Researchers are still doubtful whether systematic errors truly can be fully eliminated because at times you may seem to know the error value whereas due to everyday wear and tear of machineries and instruments, the values may keep increasing, whatever the case maybe, Careful calibration of all equipment is an essential part of controlling systematic errors.
2.3.2 SOME TERMS IN ERROR HANDLING
1-ACCURACY:- These is how close a measured value is to the true or known value or the ability of a measurement to match the actual value of the quantity been measured. Or how close they all are to getting to a desired point
http://upload.wikimedia.org/wikipedia/commons/thumb/1/10/High_accuracy_Low_precision.svg/100px-High_accuracy_Low_precision.svg.png
2-PRECISION:- This involves repetition of which it is the degree by which repeated measurements show the same or very much similar results provided they are all taken under the same condition. Also could be defined as a place though not the right position where all the repeated measurements are falling into.
http://upload.wikimedia.org/wikipedia/commons/thumb/3/3a/High_precision_Low_accuracy.svg/100px-High_precision_Low_accuracy.svg.png
3- ACCURACY AND PRECISION:- In error handling both of this must be taken into consideration because the more accurate and precise values are, means the farther the results are to errors i.e. helps in avoiding errors.
http://www.mathsisfun.com/images/hi-accuracy-hi-precision.gif
4-MOST PROBABLE VALUE (M.P.V.):- Mostly this simply means mean or average of a set of given data. Most approximable value to the true value. i.e. Nearest to the actual value after careful approximation.
5- RELATIVE ERROR:- This is commonly used in expressing the accuracy of linear measurement. It is the measure of error in relation to the size of the measurement.
2.3.3 ERRORS IN LEVELLING AND SETTING OUT
Since error is prone to all aspect of surveying, It is also a major factor to watch out for during levelling and setting out. They all arise from the normal sources of error. They include the following
1-INSTRUMENTAL ERROR
Error due to incorrect or sluggish bubble movement.
Error due to defective joint.
Error due to imperfect adjustments, tilting and positioning.
2-PERSONAL ERROR
Mistake in recording.
Mistake in reading the rod.
Mistake in rod handling.
3- NATURAL ERRORS
Variation in temperature.
Atmospheric refraction.
Settlement of tripod or turning point.
Earth curvature e.t.c.
REFERENCE: W.Scofield, 1988
D.H. Fryer, 1966
A.R. Benton, 1991
Stanley Raymond & Raymond baker & Authur Bannister 1977
Barry .F. Kavanagh 2003
J. Uren & W.F. Prince 2006
www.hsc.csu.edu.au
METHODOLOGY
This are the steps and procedures followed during the fieldwork in setting out the perimeter and getting the angle the upper frame of the surrounding building is inclined to.
Measurement of the floor to get a 20m by 10m perimeter. A meter tape is used. It is done in a four side manner to form a rectangle with two opposite sides been same values
The next is mounting of the auto level on a tripod with a plum bob, open up the lens of the auto level and getting the staff out of its pouch.
Mounting the auto level in one of the right angled corner of our perimeter, made sure the plum bob is directly facing the point of the pegging. Then we made sure the bubble of the auto level is exactly at the position it’s meant to be.
The rod person took the rod to the directly opposite corner to where the auto level was mounted. He was given a bubble to make sure the rod is standing vertically erect so the man with the auto level looked through the telescope and made sure he found the rod person. The point at which he found the staff was re-pegged.
The auto level is then positioned at zero degree at that point of the previous view. So after then the telescope of the auto level was turned to ninety degree so that we would be able to view the other pegging that’s on the side to our auto level i.e. was beside the level while we were looking at an angle of zero degree.
The rods person was directed there, then the auto level was used again in viewing, the point at which he got the staff was also remarked.
The auto level was taken to the other corner of the perimeter, made sure all the bubbles fell into their right positions. Then the rods man went to the opposite angle. It was viewed and re-pegged
Same was done when the auto level got to the third angle and all same precautions were taken.
The new positions that have been pegged were re-measured and they happened to be correct but if it wasn’t correct we were meant to start again right from the measurement.
After we were able to get a perfect rectangle as our perimeter the next step is it’s levelling. This is going to be round the perimeter i.e. through the four sides of the perimeter.
The first step is getting the temporary bench mark, this is a point that past surveyors have known the value, so not far from there and facing one side of our perimeter was were the auto level was mounted.
Its tripod and bubble were made to be in perfect position as usual the T.B.M. was first viewed as a B.S. the H.I. Was measured too. Then we made sure we were taking the readings at a zero degree angle. Staff’s readings were recorded at this time.
The F.S. which was the first tip of the side of the perimeter that was facing the T.B.M. at this time the angle was recorded and also the staff readings. This front sight is also the back sight of that side of the perimeter so the angle was made to be zero degree again though with the same staff value then the intermediate sight was taken.
The I.S. is the half point of the distance of each side i.e. on the 10mm side the I.S. is on the 5mm mark. So the rods person goes there and held the rod and its bubble, and made sure it was vertically erect as usual so the angle and staff value was recorded.
Then the rods person moves to the extreme end of that side of the perimeter so that the front sight would be taken. After recording its staff value and angle.
The auto level is then shifted to another side of the perimeter to get that sides F.S., B.S., and I.S. so after mounting it its height was taken again because it has left is normal position.
The B.S. was taken first as usual then the I.S. at 10 m mark because it was on a 20m line.
These steps and precautions were well followed until we got to the last side of the perimeter, all angles and staff readings were measured and recorded and error was avoided as much as possible.
After finishing this, the next stage was to get the value of the upper frame of the windows of the building behind our perimeter. This could only be done with the use of a theodolite.
The theodolite was well mounted, switched on because its digital. Then it has to be inside the perimeter which was taken to proper consideration.
The lens was made to be at ninety degree angle i.e. going straight then the height of instrument was measured.
The upper frame was viewed and its angle was recorded.
Then the theodolite was inclined to an angle making it to view the baselenght of the building, this was also recorded.
The distance from the theodolite to the base of the building was measured and recorded using the measuring tape.
This procedure continued until the third window then we were obstructed by a tree so we had to shift the theodolite to a new position.
New height of instrument was measured and recorded then normal procedures continued till the last window.
DATA
IMG_0001.jpg
This are the data’s gotten from the field work both with the use of an auto level, a theodolite and a levelling staff.
B.S.
I.S.
F.S.
H.I.
1.37
1.44
1.44
1.61
1.49
1.52
1.52
1.51
1.51
1.49
1.53
1.57
1.43
1.48
1.68
1.63
The previous table is the results obtained with the auto level to get the back sight, front sight and the intermediate sights on the edge of the perimeter.IMG.jpg
This diagram above illustrates how to get all the angles needed from each window and also how to get the distances. The window measurement, the v1 and v2 were gotten following the right angled triangle principle. i.e. SOHCAHTOA. And for the change of elevation the formula below was used
É…elevation = (v1 + HI) – ( v1 + v2)
Where H I is the height of instrument.
Window 1
Window 2
Window 3
Window 4
window 5
Window 6
Angle 1
28â-¦ 34`18“
16â-¦ 42`40“
19â-¦ 39`6“
19â-¦ 27`53“
19â-¦ 39`24“
16â-¦ 1`55“
Angle 2
2â-¦ 52`54“
2â-¦ 58`09“
2â-¦ 31`22“
2â-¦ 34`50“
0â-¦ 33`10“
1â-¦ 58`32“
V1
13.89
15.04
13.30
17.37
8.97
13.10
V2
1.77
0.41
1.59
1.60
1.55
1.62
Distance (m)
39.30
42.10
46.30
31.90
29.90
36.90
The above values are those gotten with the theodolite to read the angle at which the windows are inclined and they belong to my own group 4. After values have been exchanged with every group the resulting table is as follows:
Window 1:
Group1
Group2
Group3
Group4
Group5
Group6
V1
13.24
13.12
11.89
17.37
14.50
14.64
V2
1.56
1.59
1.71
1.60
1.30
1.59
Window 2:
Group 1
Group 2
Group 3
Group 4
Group 5
Group 6
V1
13.26
13.18
13.33
8.97
13.30
13.28
V2
1.57
1.42
1.73
1.55
1.40
1.60
Window 3:
Group1
Group2
Group3
Group4
Group5
Group6
V1
13.18
12.87
12.56
13.10
13.32
12.95
V2
1.56
1.51
1.71
1.62
1.28
1.64
Window 4:
Group 1
Group 2
Group 3
Group 4
Group 5
Group 6
V1
13.17
13.52
15.63
13.89
9.20
12.73
V2
1.61
1.67
1.26
1.77
1.50
1.62
Window 5:
Group 1
Group 2
Group 3
Group 4
Group 5
Group 6
V1
13.30
13.25
13.12
15.04
13.32
13.23
V2
1.56
1.36
1.69
0.41
1.57
1.80
Window 6:
Group 1
Group 2
Group 3
Group 4
Group 5
Group 6
V1
13.35
13.54
12.97
13.30
13.80
8.91
V2
1.59
1.55
1.66
1.59
1.55
1.50
ANALYSIS AND DISCUSSION
TASK 4:
group length of tape= 7.0m
Total length of perimeter= 60m
Total tape error= 0.02m
Therefore 60÷7=8.57 the perimeter would be measured 8 times with more than half of 7.0 remaining so to get the total error. ; 8.57Ã-0.02 =0.17, the total measurement error of the tape has now been evaluated to be 0.17m.
TASK 5:
There are two methods of evaluating the sighted values they are both the H.P.C. and the rise and fall method.
H.P.C. method as discussed earlier consists of finding the elevation of the point of collimation for every position of the inst