# Chain Surveying

Chain survey is suitable in the following cases:

- Area to be surveyed is comparatively small.
- Ground is fairly level.
- Area is open and details to be filled up are simple and less.

In chain surveying only linear measurements are made i.e. no angular measurements are made. Since triangle is the only figure that can be plotted with measurement of sides only, in chain surveying the area to be surveyed should be covered with a network of triangles.

Figure 1 shows a typical scheme of covering an area with a network of triangles. No angle of the network triangles should be less than 30^{o} to precisely get plotted position of a station with respect to already plotted positions of other station. As far as possible, angles should be close to 60º.

However, the arrangements of triangles to be adopted depend on the shape, topography, natural and artificial obstacles in the field.

## Technical Terms

Various technical terms used in connection with the network of the triangles in surveying are explained below:

**Station**: Station is a point of importance at the beginning or at the end of a survey line. Main station: These are the stations at the beginning or at the end of lines forming main skeleton. They are denoted as A, B, C etc.

**Subsidiary or tie stations**: These are the stations selected on main lines to run auxiliary/secondary lines for the purpose of locating interior details. These stations are denoted as a, b, c, …., etc., or as 1, 2, 3, … etc.

**Base line**: It is the most important line and is the longest. Usually it is the line plotted first and then frame work of triangles is built on it.

**Detail lines**: If the important objects are far away from the main lines, the offsets are too long, resulting into inaccuracies and taking more time for the measurements. In such cases the secondary lines are run by selecting secondary stations on main lines. Such lines are called detail lines.

**Check lines**: These are the lines connecting main station and a substation on opposite side or the lines connecting to substations on the sides of main lines. The purpose of measuring such lines is to check the accuracy with which main stations are located.

## Selection of Stations

The following points should be considered in selecting station points:

- It should be visible from at least two or more stations.
- As far as possible main lines should run on level ground.
- All triangles should be well conditioned (No angle less than 30
^{o}). - Main network should have as few lines as possible.
- Each main triangle should have at least one check line.
- Obstacles to ranging and chaining should be avoided.
- Sides of the larger triangles should pass as close to boundary lines as possible.
- Trespassing and frequent crossing of the roads should be avoided.

## Offsets

Lateral measurements to chain lines for locating ground features are known as offsets. For this purpose perpendicular or oblique offsets may be taken (Ref. Fig. 2). If the object to be located (say road) is curved more number of offsets should be taken. For measuring offsets tapes are commonly used.

For setting perpendicular offsets any one of the following methods are used:

(i) Swinging (ii) Using cross staffs (iii) Using optical or prism square.

(i) **Perpendicular Offset by Swinging**: Chain is stretched along the survey line. An assistant holds the end of tape on the object. Surveyor swings the tape on chain line and selects the point on chain where offset distance is the least (Fig. 3) and notes chain reading as well as offset reading in a field book on a neat sketch of the object.

(ii) **Perpendicular Offsets Using Cross Staffs**: Figure 12.14 shows three different types of cross staffs used for setting perpendicular offsets. All cross staffs are having two perpendicular lines of sights. The cross staffs are mounted on stand.

First line of sight is set along the chain line and without disturbing setting right angle line of sight is checked to locate the object.

With open cross staff (Fig. 4 (a)) it is possible to set perpendicular only, while with french cross staff (Fig. 12.14 (b)), even 45^{o }angle can be set.

Adjustable cross staff can be used to set any angle also, since there are graduations and upper drum can be rotated over lower drum.

(iii) **Perpendicular Offsets Using Optical Square and Prism Square**: These instruments are based on the optical principle that if two mirrors are at angle ‘θ’ to each other, they reflect a ray at angle ‘2θ’. Figure 5 shows a typical optical square.

Optical square consists of a metal box about 50 mm in diameter and 125 mm deep. In the rim of the box there are three openings:

- A pin hole at E,
- a small rectangular slot at G, and
- a large rectangular slot at F.

A and B are the two mirrors placed at 45^{o} to each other. Hence the image of an object at F which falls on A gets reflected and emerge at E which is at right angles to the line FA.

The mirror A which is opposite to the opening at F is fully silvered. It is fitted to a frame which is attached to the bottom plate. If necessary this mirror can be adjusted by inserting a key on the top of the cover.

The mirror B which is in the line with EG is silvered in the top half and plain in the bottom half. It is firmly attached to the bottom plate of the box. The ranging rod at Q is directly sighted by eye at E in the bottom half of the B which is a plain glass. At the same time in the top half of B, the reflected ray of the object at P is sighted.

When the image of P is in the same vertical line as the object at Q, then the lines PA is at right angles to the line EB. This instrument can be used for finding foot of the perpendicular or to set a right angle.

In prism square, instead of two mirrors at 45^{o} to each other a prism which has two faces at 45^{o} to each other is used [Fig. 6.]. Its advantage is it will not go out of adjustment even after long usage.

## Field Book

All observations and measurements taken during chain surveying are to be recorded in a standard field book. It is a oblong book of size 200 mm × 120 mm, which can be carried in the pocket. There are two forms of the book

(i) single line and (ii) double line.

The pages of a single book are having a red line along the length of the paper in the middle of the width. It indicates the chain line. All chainages are written across it.

The space on either side of the line is used for sketching the object and for noting offset distances. In double line book there are two blue lines with a space of 15 to 20 mm is the middle of each book.

The space between the two lines is utilised for noting the chainages. Figure 7 shows typical pages of a field books.

## Field Work

As soon as the survey party arrives in the field the following details are entered in the field book:

- Title of the survey work
- The date of survey
- The names of the members of the party.

The field work may be divided into the following:

- Reconnaissance survey.
- Marking stations, drawing reference sketches.
- Line by line surveying.

(1) **Reconnaissance survey** consists in going round the field and identifying suitable stations for the network of triangles. Neat sketch of network is drawn and designated. The typical key plan drawn is similar to one shown in Fig. 1.

All main stations should be marked on the ground. Some of the methods used for marking are:

- Fixing ranging poles
- Driving pegs
- Marking a cross if ground is hard
- Digging and fixing a stone.

Then reference sketches are drawn in the field book so as to identify stations when the development works are taken up. For this measurements with respect to three permanent points are noted. The permanent points may be

- Corner of a building
- Posts of gates
- Corners of compound walls
- Electric poles
- A tree.

After that, line by line surveying is conducted to locate various objects with respect to chain lines.

## Office Work

It consists in preparing the plan of the area to a suitable scale making use of measurements and sketches noted in the field book.

## Ranging

When a survey line is longer than a chain length, it is necessary to align intermediate points on chain line so that the measurements are along the line.

The process of locating intermediate points on survey line is known as ranging. There are two methods of ranging viz., direct ranging and reciprocal ranging.

(1) **Direct Ranging**: If the first and last points are intervisible this method is possible.

Figure 8 shows the inter-visible stations A and B in which an intermediate point C is to be located.

Point C is selected at a distance slightly less than a chain length. At points A and B ranging rods are fixed.

The assistant holds another ranging rod near C. Surveyor positions himself approximately 2 m behind station A and looking along line AB directs the assistant to move at right angles to the line AB till he aligns the ranging rod along AB.

Then surveyor instructs the assistant to mark that point and stretch the chain along AC.

(2) **Indirect or Reciprocal Levelling**: Due to intervening ground, if the ranging rod at B is not visible from station A, reciprocal ranging may be resorted.

Figure 9 shows this scheme of ranging. It needs two assistants one at point M and another at point N, where from those points both station A and station B are visible.

It needs one surveyor at A and another at B. To start with M and N are approximately selected, say M_{1} and N_{1}. Then surveyor near end A ranges person near M to position M_{2} such that AM_{2}N_{1} are in a line.

Then surveyor at B directs person at N, to move to N_{2} such that BN_{2}M_{2} are in a line. The process is repeated till AMNB are in a line.

## Obstacles in Chaining

Though it is desirable to select stations so as to avoid obstacles, occasionally the obstacles are unavoidable.

Various obstacles to chaining may be grouped into:

- Obstacles to ranging (chaining free-vision obstructed)
- Obstacles to chaining (chaining obstructed-vision free)
- Obstacles to both ranging and chaining.

Various methods of overcoming these obstacles are explained is this article.

(i) **Obstacles to Ranging**: These obstacles can be further classified into the following categories:

- Both ends of the line are visible from some intermediate points. Intervening ground is an example of such obstacle. By resorting to reciprocal ranging this difficulty can be overcome.
- Both ends of the line may not be visible from intermediate points on the line, but may be visible from a point slightly away from the line. Intervening trees and bushes are the examples of such obstacles. This obstacle to chaining may be overcome by measuring along a random line as shown in Fig. 10. In this case required length

(ii) **Obstacles to Chaining**: In this type the ends of lines are visible but chaining is obstructed. Examples of such obstructions are ponds, lakes, marshy land etc.

Various geometric properties may be used to find obstructed length CB as shown in Fig. 11.

From eqn. (a), cos θ can be found and substituting it in eqn. (b), the obstructed length CB can be found.

(iii) **Obstacles to Both Chaining and Ranging**: Building is a typical example of this obstacle.

Referring to Fig. 12, line AB is to be continued beyond the obstacle, say as GH. Four possible methods are presented below:

(a) Set perpendiculars AC, BD such that AC = BD [Fig. 12 (a)]. Extend line CD to F. Drop perpendiculars EG and FH to line CF such that EG = FH = AC. GH is the continuation of line AB and DE = BG.

(b) Referring to Fig. 12 (b), set BC ⊥ to AB. Select D on extended line of AC. Set perpendicular DH such that AD = DH. Select point E on DH such that DE = DC. Then arcs of length EG = BC and arc of length HG = AB are drawn from E and H respectively and G is located. GH is continuation of AB and BG = CE.

(c) Referring to Fig. 12 (c), C is located such that AC = BC = AB. Extend AC to D and construct equilateral triangle DEF. Extend DF to H such that DH = DA. Locate convenient point I on HD and construct equilateral triangle to locate G. Then GH is the continuation of line AB and length BG is given by BG = AH – AB – GH = AD – AB – GH

(d) In the method shown in Fig. 12 (d), points C and D are selected such that CBD is in a line. Extend AC to E and I such that AE = n × AC and AI = m × AC.

Similarly Extend AD to F and J such that, AF = n × AD and AJ = m × AD. Locate G and H on lines EF and IJ such that, EG = n × BC and IH = m × BC. Then GH is the continuation of line AB.

Now, AG = n × AB

∴ BG = n × AB – AB = (n – 1) AB

## Errors in Chaining

Errors in chaining may be classified as: (i) Personal errors (ii) Compensating errors, and (iii) Cumulating errors.

(i) **Personal Errors**: Wrong reading, wrong recording, reading from wrong end of chain etc., are personal errors. These errors are serious errors and cannot be detected easily. Care should be taken to avoid such errors.

(ii) **Compensating Errors**: These errors may be sometimes positive and sometimes negative. Hence they are likely to get compensated when large numbers of readings are taken. The magnitude of such errors can be estimated by theory of probability. The following are the examples of such errors:

- Incorrect marking of the end of a chain.
- Fractional part of chain may not be correct though total length is corrected.
- Graduations in tape may not be exactly same throughout.
- In the method of stepping while measuring sloping ground, plumbing may be crude.

(iii) **Cumulative Errors**: The errors that occur always in the same direction are called cumulative errors. In each reading the error may be small, but when large numbers of measurements are made they may be considerable, since the error is always on one side. Examples of such errors are:

- Bad ranging
- Bad straightening
- Erroneous length of chain
- Temperature variation
- Variation in applied pull
- Non-horizontality
- Sag in the chain, if suspended for measuring horizontal distance on a sloping ground.

Errors (1), (2), (6) and (7) are always +ve since they make measured length more than actual. Errors (3), (4) and (5) may be +ve or –ve.

## Tape Corrections

The following five corrections may be found for the measured lengths of tape:

- Corrections for absolute length
- Corrections for pull
- Corrections for temperature
- Corrections for slope and
- Corrections for sag.

(i) **Corrections for Absolute Length:**

Let, l = designated length of tape,

l_{a} = actual length of tape.

Then correction for chain length c = l_{a} – l

Hence, if the total length measured is L, the total correction

(ii) **Corrections for Pull:** If pull applied while standardising the length of tape and pull applied in the field are different, this correction is required.

Let, P_{0 }= Standard pull

P = Pull applied in the field

A = Cross-sectional area of the tape

L = Measured length of line.

E = Young’s modulus of the material of tape,

then C_{p} = (P – P_{o} )L ÷ AE

The above expression takes care of sign of the correction also.

(iii) **Correction for Temperature**

Let T_{0} = Temperature at which tape is standardised

T_{m} = Mean temperature during measurement

α = Coefficient of thermal expansion of the material of the tape and

L = Measured length,

Then the temperature correction C_{t} is given by,

C_{t }= Lα(T_{m} – T_{0})

The above expression takes care of sign of the correction also.

(iv) **Correction for Slope**: If the length measured is ‘L’ and the difference in the levels of first and the last point is ‘h’, then slope correction

If measured length is L and slope is ‘θ’,

then C_{sl} = L – L cos θ = L (1 – cos θ)

This correction is always –ve.

(v) **Correction for Sag**: While measuring on unevenly sloping ground, tapes are suspended at shorter length and horizontal distances are measured. This technique eliminates errors due to measurement along slopes, but necessitates correction for sag [Fig. 13].

Hence, measured length is more than actual length. Thus the correction is –ve. The correction, which is difference between the length of catenary and true length is given by

Where, W = the weight of the tape of span length

P = the pull applied and

L = measured length

It may be noted that if pull is more than standard pull, the correction for pull is +ve, while correction for sag is always –ve.

The pull for which these two corrections neutralise each other is called ‘normal tension’. Hence normal tension P_{n }may be found as,

C_{p }= C_{s}

The value of P_{n} is to be determined by trial and error method.