## Correction in Chaining/Taping and Ranging in Surveying

## ranging

Ranging can be carried out through any of the following methods:

### a) Direct ranging:

- On the intermediate points along the chain line, the ranging rods are placed by direct observation from either of the end stations.

### B) Indirect ranging:

In the indirect ranging, the end stations are not visible due to the long distances between them or due to the raised ground level. It can be carried out as follows:

- In this case, two chainmen's stand at some arbitrary point C
_{1}, D_{1}in between two end stations A, B such that chainmen at C_{1}can see both D_{1}and B and chainmen at the D_{1}can see both C_{1}and A. - Now these both chainmen direct to each other towards the survey line AB up to an extent they reach the intermediate point C, D on the survey line AB.

### C) Random line ranging:

- This method is used when the survey stations to be ranged are obstructed by inaccessible area eg- forest.

- In this case, a random line in the estimated direction of the line to be ranged is established such that from the end point of this random line, the end survey station is visible and is at right angles.

- Then ranging of intermediate points is done using similarity.

AB = ✓AB'^{2} + BB'^{2}

(AB'/BB') = (AP'/P'P)(AB'/BB') = (AQ'/Q'Q)

### example 1

**Which of the following statement(s) is/are true?**

a) The total number of links provided in Gunter's chain is 66.

b) Every 20 m chain should be accurate to within 15mm.

c) Check lines are drawn to collect the details of an object in an area.

d) A well condition triangle does not have any angles less than 30°.

Sol: The total number of links provided in Gunter's chain is 100 and the length of the Gunter's chain is 66 ft.

To collect the details of the object in an area, tie line is used.

So, the correct answer is **b)** and **d)**.

### example 2

**The correct order of the tapes based on their accuracy is:**

a) Metallic tape > Invar tape > Steel tape >Linen tape

b) Linen tape > Metallic tape > Invar tape > Steel tape

с) Invar tape > Steel tape > Metallic tape >Linen tape

d) Metallic tape >Linen tape > Steel tape > Invar tape

Sol: The correct order of the tapes based on their accuracy is:

Invar tape > Steel tape > Metallic tape > Linen tape

So, the correct answer is **c)**.

### example 3

**The chain which is found to be too short on testing can be adjusted by**:

a) Replacing one or more small circular rings by bigger ones

b) Straightening the links

c)Flattening the circular rings

d) All the above

- Sol: If a chain is found to be short, it can be adjusted by:
- i) Replacing one or more small circular rings by bigger ones.
- ii) Straightening the links
- iii)Flattening the circular rings.
- iv)Inserting additional circular rings.
- v) Adjusting the links at the end.

So, the correct answer is**d)**.

## chaining

The methods used to carry out chaining are as follows:

### a) On smooth level ground:

- It is necessary to establish the intermediate points by ranging for a distance longer than 1 chain length.
- To carry out the process a leader & a follower is required. The duty of the leader is to move forward along the survey line & insert arrows at the end of a chain, whereas the duty of the follower is to collect the arrows. Thus, the number of chain lengths measured is represented by the number of arrows collected by the follower at the end of the survey.

## what is chaining?

Linear measurement with means of chain is termed as chaining

### b) On sloping ground:

- The distance measured should be horizontal in the plane surveying.
- In some cases, the chain cannot be kept horizontal because the change in elevation is larger between one end of the chain to another end.
- In such case chaining can be carried out by any of the following methods:

Chaining on slopping ground

### chaining on slopping ground

### stepping method

- Used when the slope is variable
- The follower holds the end of the chain at A while the leader selects any suitable length of the chain and moves forward.

The follower directs the leader for ranging. The leader pulls the tape tight makes it horizontal and point 1 is then transferred to the ground by a plumb bob. The procedure is repeated to find the length.

### measuring along slope

- Used when the slope is almost constant.
- In the case of a regular or even slope, the sloping distance can be measured, and the horizontal distance can be calculated. In addition to the sloping distance, the angle of the slope or the difference in elevation between the points is also measured.

### important question

**Q. What is the disadvantage of stepping method ?**

Sol: It is difficult to measure the length along the uphill as compared to the downhill. Because it is a difficult job to hold a tape / chain by the follower at a particular height and while holding the chain, follower have to direct the leader.

## errors and correction in chaining / taping

### errors

- The difference between the measured length and true length is termed as error.

Error = Measured length - True length

True length = Measured length - Error

Correction = True length - Measured length

True length = Measured length + Correction

- Error in chaining can be of the following types:

**a) Mistakes:****b) Cumulative / systematic error:** This error is directly proportional to the length of line and may be positive or negative.**c) Compensating / random error:** This error is directly proportional to square root of length of line to be measured.

### important question

**Q Error due to bad ranging, is a type of cumulative error or compensating error?**

Sol: The error due to the bad ranging is classified as a cumulative positive error. If the chain is stretched out of the line, the measured distance will always be more and hence, the error will be positive. For each and every stretch of the chain, the error is due to the bad ranging will be cumulative.

### Correction in chaining and taping:

#### I) Correction for standardisation (C_{s}):

- Due to the incorrect length of the chain/tape, this correction needs to be provided which can be positive or negative according to the actual distance.
- It is applicable to both chain or tape.

Correct length (L) = True length (l) of chain/tape **X** number of times the chain/ tape was used for measurement of length line.

L = l' * (L'/l)

Where

L = Correct length of line measured

L' = Incorrect length of measured line

l = True length of chain/tape

l' = Wrong length of chain/tape

**Note: The same concept can be used for area & volume:**

a) True area = (l'/l)^{2 } * measured area

b) True volume = (l'/l)^{3 } * measured volume

**Correction for standardisation :**

C_{s }= true length - measured length

C_{s} = L-L'

C_{s} = {(l'/l)L} - L'

C_{s} = L'{(l'/l)-1}

C_{s} = {(l'-l)/l} - L'

### important questions

**Q1 - A plan of an old survey was plotted to a scale of 1 cm = 10 m, which has shrunk such that the original line of 10 cm length is now 9.77 cm. It was mentioned on the plan that the chain (20 m) used for the measurement was 0.8 link (16 cm) too short. If the area of a plot on the available plan was found to 58.2cm, then the correct area (in hectare) of plot will be:**

**Q2 - A 20m chain was used to measure a distance of 2500 m and found that the chain was 10 cm too long. By the end of the day a total distance of 5000 m was measured, and the chain was found to be 18 cm too long. What is the true distance if the chain was correct before the commencement of work?**

#### Ii) Correction for slope (C_{g}):

It is applicable to both chain & tape.

C_{g} = D-L

a) When **slope angle** (θ) is known

C_{g} = Lcosθ - L

C_{g} = -L(1 - cos θ)

**NOTE**: Slope correction is always negative

b) When elevation difference (h) is Known:

C_{g} = D-L

C_{g} = ✓(L^{2} - h^{2}) - L

C_{g} = -h^{2} / 2L

**NOTE:** Correction is increased by h^{4} / 8L^{3} when higher terms of h are considered.

**NOTE:** Now all the further correction are applicable for TAPE only.

#### Iii) Correction for pull (C_{p}):

Correcction due to pull is given by:

C_{p} = {(P-P_{s} )L}/AE

Where

P_{s}= Standard pull

P = Applied pull

A = Cross section area of tape

E = Modulus of elasticity of tape

L = Measured length.

**Case 1:** When the applied pull is greater than the standard pull (P > Ps), the length of the tape increases and the measured distance is found to be lesser than the actual distance, then the applied correction (C_{p}) becomes positive (+).

**Case 2:** When the applied pull is lesser than the standard pull (P < Ps), the length of the tape decreases, and measured distance is found to be greater than the actual distance, then the applied correction (C_{p}) becomes negative (-).

#### Iv) Correction for sag (C_{sag}):

- For higher accuracy in taping, tape must be hanged in catenary and correction for the sag in the tape needs to be applied.
- For sag correction the profile is considered to be parabolic.

C_{sag} = (w^{2} l^{3} ) / 24p^{2}

Where w = Weight per unit length of tape

I = Length of tape suspended between supports.

р = Applied pull

**Case a):** If the tape has been standardised on flat and used in catenary, then applied sag correction (C_{sag}) would be negative (-).

**Case b):** If the tape has been standardised on catenary and is used on flat, then applied sag correction (C_{sag}) would be positive (+).

#### v) Correction for temperature(C_{t}):

Due the temperature variation the length of tape varies, and correction is given by:

C_{t} = **α** (T_{m} - T_{o}) L

Where

T_{m} = Mean temperature during measurement

T_{o} = Temperature during standardisation**α** = Coefficient of thermal expansion

L = Measured length

**Case 1:** When the temperature during measurement is greater than the standard temperature, the applied correction (C_{t}) becomes positive (+).

**Case 2:** When the temperature during measurement is lesser than the standard temperature, the applied correction (C_{t}) becomes negative (-).

#### v) Correction for misalignment(C_{m}):

- When the survey line is not accurately ranged out, error takes place due to the misalignment.
- In such cases, the measured distance would be greater than the correct distance, and positive error would take place which results in negative correction.

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