Introduction to Surveying: Direct Distance Measurement Dr. Dheeraj Kumar,

Associate Professor, Department of Mining Engineering, ISM Dhanbad Distance Definition: The horizontal distance between two points Different Methods

Direct Measurement Chain, tape are generally used Measurement by optical means Observations are taken through a telescope and calculations are done for distances eg. Tacheometry, triangulation Electromagnetic methods: Distances are measured with instruments that rely on propagation, reflection and reception of radio/light/infrared waves

Measurement Techniques:

• pacing • odometer • stadia (Tacheometry) • Chaining/ taping • EDM (electronic distance measurement) • GPS (global positioning system)

Procedure:

- Clear line - lay out tape on ground making sure there are no kinks - apply tension (10-12 kg) - use plumb bob or vertical angles on uneven ground - read the tape

Instruments for chaining

• Chain or tape • Arrows : 370mm • Pegs : 9cm • Ranging rods : 1.8 – 2.0 m (alternate blocks of red/black and white 25cm each)

CHAIN 100 / 150 pieces of tempered steel wire, 8 or 10 SWG of 4 mm dia called links. Each ends are bent into a loop and connected together by means of three oval rings

The joints of the links are usually open. End of the chain are provided with brass handles for dragging the chain on the ground .The metric chains are made in lengths of the 20 and 30 meters. Tallies are used for marking the distances in a metric chain. Types of tallies:

1. Single tooth : these are attached with 2m, 12m, and 22m with the chain 2. Double teeth : These indicate 4m, 14m, and 24 m with the chain 3. Triple teeth tally : These are attached at 6m, 16m, and 26m with the chain 4. Four teeth tally : 8m, 18m, and 28 m

Single circular tally: at a distance with 10m Double circular tally: this indicates 20m distance in the chain Least Count: 20 cm METALLIC TAPE Linen tapes reinforced with brass or copper wires to make in durable. L. C: 1cm. They are available in lengths: 15m, 20m, and 30m. It is mould in a better case with a brass handle at the end. Commonly used in all survey works STEEL TAPES They are made of steel ribbon of width varying from 6 – 10 mm and commonly available in length 10m, 15m, 20m, 30m and 50m. Mainly used for standardizing chains and for measurements in constructional works, L.C: 1 mm CORRECTION APPLIED TO CHAINS i. correction to measured length l = l’ (L’/L) l = actual length l’ = measured length L’ = incorrect length of the chain/tape L = designated length of tape / chain ii. Correction to area

A = A’(L’/L) 2 OR A = (1+ 2e)A’

iii Correction to volume V = V’ (L’/L) 3 OR V = (1+e) 3 V’ ERRORS IN CHAINING i. Incorrect length of chain or tape : cum + or - ii. Bad ranging : cum + iii. Careless holding and marking : comp + or - iv. Bad straightening : cum + v. Non- horizontality : cum + vi. Sag in chain : Cum + vii. Variation in temp : cum + or – viii. Variation in pull : comp/cum +,- ix. Personal mistakes COMMON TAPING ERRORS

1. Incorrect length of tape 2. Temperature variation 3. Non-standard tension 4. Sag 5. Poor alignment 6. Slope

TAPE STANDARDIZATION It is done by comparison with standard tape or known baseline. Standardization usually defined in terms of: - Tension (e.g. 10 kg) - Temperature (e.g. 68°F) 1. Correction for incorrect length ca = (L’.c / l) L = L’ + ca Where: Ca = correction for absolute length l = designated length of tape L’ = measured distance L = corrected distance

2. Temperature correction (Additive when temp at measurement is more than standardized temp/ subtractive when temp at measurement is less then standard temp) Due to rise in temp, the length of tape increases and hence distance measured is less so error becomes negative. Therefore the correction to be applied will be +ve Ct = α (Tm - To) L’ L = L’ + Ct Where: Ct = temperature correction α = coefficient of expansion/contraction of steel = 0.000 0065 per unit length per °F = 0.000 0116 per unit length per °C Tm = mean tape temp. at time of measurement To = temperature during the standardization of tape L’ = measured distance L = corrected distance 3. Tension (pull) correction (Additive when pull applied is more than standard pull/ subtractive when pull applied is less then std pull) If the pull applied at the time of measurement is more than the standardization pull, the length of tape is increased and hence distance measured is less and error becomes negative. Therefore correction to be applied will be +ve CP = (P - Po) * L’/ AE L = L’ + C p Where: Po = standard tension for tape (N) P = tension applied to tape (N) L’ = measured distance (m) L = corrected distance (m) A = cross-sectional area of tape (cm2) E = modulus of elasticity of steel (N/cm2) The pull applied in the field should be less than 20 times the weight of the tap

4. Sag or catenary correction (subtractive) Cs = - (W2 l) / (24 n2 P 2) = nl1(wl1)

2/24P2= nl1W2/24 P2

L = L’ + C s Where: W = total weight of tape w = weight per unit length of tape

l = total length of the tape P = pull/tension (actual) n =number of equal spans L = corrected distance L’ = measured distance Due to sag, the measured distance will be always too much and therefore the error will be positive and thus the correction applied will always be negative 5. Misalignment of tape (should be avoided)

Due to misalignment of the tape, the measured distance will be always too much and therefore the error will be positive and thus the correction applied will always be negative

d l

Ch = d2/2L

L1 L2

l Ch = d2/2L1 + d2/2L2

L

d

6. Correction for slope (subtractive)

Due to sloping ground, the measured distance will be always too much and therefore the error will be positive and thus the correction applied will always be negative

L

H

Cv = L(1 - cos α)))) = = = = α = vertical angle = h2/2L

α h

A

B

7. Reduction to MSL

L = measured horizontal distance D = equivalent length at MSL h = mean equivalent of the base line above MSL R = Radius of the earth θ = angle subtended at the centre of the earth

θ

MSL

L

D h

R

Cmsl = Lh/R (subtractive)