Surveying JE Coaching 1

Chain and Tape Corrections

1 Errors in Chaining

It is important to understand the basic difference between cumulative and compensating errors,and between positive and negative errors. A cumulative error is that which occurs in the samedirection and tends to accumulate while a compensating error may occur in either directionand hence tends to compensate. Errors are regarded as positive or negative according as theymake the result too great or too small, respectively.

The various sources of error are:

1. Erroneous length of chain or tape: (Cumulative + or –) Error due to wrong lengthof chain is always cumulative. It is the most serious source of error.

• If length of chain is too long, the measured distance will be less and hence the errorwill be negative.

• If the chain is too short, the measured distance will be more and hence he error willbe positive.

2. Sag in Chain (Cumulative + ) When chain is stretched above the ground due to undula-tions or irregular ground, the chain sags and takes the form of a catenary. The measureddistance is therefore too great and the error is cumulative and positive.

3. Variations in Pull: (Compensating ±, Cumulative + or –) If the pull applied instraightening the chain or tape is not equal to that of the standard pull at which thechain or tape was calibrated, its length changes. If the pull applied is not measured butis irregular (sometimes more, sometimes less), the error tends to compensate. However, achainman may apply too great or too small pull every time and in such a case, the errorbecomes cumulative.

4. Variations in Temperature: (Cumulative + or –) When a chain or tape is used attemperature different from that at which it was calibrated, its length changes.

• If temperature increases, the length of chain increases. The measured distance isthus less and the error becomes negative.

• If temperature decreases, the length of chain decreases. The measured distance isthus more and the error becomes positive.

5. Bad ranging: (Cumulative + ) If the chain is stretched out of the line, the measureddistance will always be more and hence the error will be positive. For each stretch of thechain, the error due to bad ranging will be cumulative.

6. Bad straightening: (Cumulative + ) If the chain is not straight but is lying in anirregular horizontal curve, the measured distance will always be too great. The error istherefore cumulative and positive.

7. Non–Horizontality: (Cumulative + ) If the chain is not horizontal (especially in caseof sloping or irregular ground), the measured distance will always be too great. The erroris therefore, cumulative and positive.

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2 Chain and Tape Corrections

2.1 Tape Corrections

1. Temperature correction, Ct: The correction is necessary because the length of thetape or chain may be increased or decreased due to rise or fall in temperature duringmeasurement. The correction is given as:

Ct = α (Tm − T0) L (1)

where,

Ct = correction for temperature, in metresα = coefficient of thermal expansion, in ◦C−1

Tm = temperature during measurement, in ◦CT0 = temperature at which the tape was calibrated, in ◦CL = length of tape, in m

The sign of Ct may be positive or negative according as Tm > T0 or Tm < T0.

2. Pull correction, Cp: During measurement, the applied pull may be either more or lessthan the pull at which the chain or tape was calibrated. The correction is given by thefollowing expression:

Cp =(Pm − P0) L

A E(2)

where,

Cp = correction for pull, in metresPm = pull applied during measurement, in kgP0 = pull at which the tape was calibrated, in kgL = length of tape, in mA = cross-sectional area of tape, in cm2

E = modulus of elasticity of tape, in kg/cm2

The sign of Cp will be positive or negative according as Pm > P0 or Pm < P0.

3. Slope correction, Ch: Slope correction is calculated as follows:

Ch = l(1− cos θ) . . . exact (3a)

Ch = l −√l2 − h2 . . . exact (3b)

Ch =h2

2l. . . approx (3c)

This correction is always negative.

4. Sag correction, Cs: This correction is necessary when the measurement is taken withtape in suspension (i.e. in the form of a catenary). It is given by the expression:

Cs =L(ωL)2

24n2P 2m

(4a)

Cs =L(W )2

24n2P 2m

(4b)

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where,

Cs = sag correction, in mL = length of the tape or chain, in mω = weight of tape per unit length, in kg/mW = total weight of tape, in kgn = number of spansPm = pull applied during measurement, in kg

2.2 Chain Corrections

1. Correction applied to incorrect length: It is given by the expression:

True Length =L′

L×Measured Length (5)

where, L = standard or true length of the chain, L′ = true length ± error. Use positivesign when the chain is too long, and negative sign when the chain is too short.

2. Correction applied to incorrect area: The correction to be applied in this case isgiven as:

True Area =

(L′

L

)2

×Measured Area (6)

3. Hypotenusal Allowance: Hypotenusal allowance (HA) per tape length is given as:

HA = L(sec θ − 1) (7)

where, L is length of chain and θ is slope of the ground. This allowance is always addedto the chain length.

Figure 1: HypotenusalAllowance

Concept of Hypotenusal Allowance

Method of hypotenusal allowance is an indirect method of chain-ing on sloping ground. In this method, the slope of the ground isfirst determined using a clinometer or Abney level. Hypotenusalallowance is then made for each tape or chain length.Let θ be the angle of slope measured by clinometer. From theFigure:

BC = A′B = 1 chain = 100 linksAB = BC sec θ = 100 sec θ linksAA′ = AB – A′B = 100 sec θ – 100 = 100 (sec θ – 1) links

Hypotenusal Allowance = 100(sec θ − 1) (8)

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