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**Errors and Horizontal distance measurement**

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**Concept and Types of errors**

Gross errors (blunders or mistakes) Systematic errors Random and accidental errors Gross errors are results of mistakes due to carelessness of observer. Examples pointing on wrong survey target, incorrect reading on the scale, recording wrong reading.

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**Careful checking all the points on survey targets.**

Taking multiple reading on scale and checking for consistency Taking repeated measurement independently and checking for consistency Using simple geometric and algebraic checks, such as sum of all the angles taken at a station is 360 ⁰, sum of three angles in a plane triangle is 180⁰ Systematic errors: These are the errors which occur from well-understood causes and can be reduced by adopting suitable method. These errors follow same pattern. Example sag of tape supported at the end can be calculated and subtracted from each measurement. However the tape can be supported through out its length at short intervals and the sag errors may be reduced to a negligible quantity.

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Systematic error A systematic error follows a definite mathematical or physical law and therefore, a correction can always be determined and applied. Also known as cumulative error. Random error/ accidental error: after all mistakes are detected and removed and the measurements are corrected for all known errors, there will still remain some errors due to combination of various causes and are beyond the control of surveyor. It can be plus or minus. These are probabilistic errors and can not be calculated using standard functional relationship. Human eye has limitation of distinguishing between two close readings.

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**Horizontal distance measurements**

Method of horizontal distance measurements Direct: using chain (chaining) or tape (taping) Low precision work: chaining High precision work: taping or bars Engineer’s chain: 100 ft long, 100 links each 1 ft, at every 10 links brass tags are fastened. Notches on the tag indicates the number of 10 link segment between th tag and the end of the chain. Gunter’s chain: 66 ft long, 100 links, each ft. distances are recorded in chains and links. Indirect: the distances are not measured directly on the field but are computed indirectly using observed quantities. EDM: electromagnetic distance measuring instrument.

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Metric chain

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EDM

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**Procedure for distance measurements**

Ranging and chaining Taping on flat ground: length of the line is less than length of the tape easily measure the line with tape. If length of the line is greater than length of the tape subdivide the line to lengths less than tape length. Taping on sloping or uneven ground Direct method Indirect method Errors in tapping and tape correction Gross errors Systematic errors

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**Examples: Ranging Ranging if the points are intervisible**

Ranging when points are not visible S B A P Q R

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**Examples taping or chaining**

Horizontal distance measurement by on moderately flat ground Horizontal distance measurement on slopping ground

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**Corrections for Systematic Errors in Taping-1**

1. Correction for absolute length: Before using a tape, the actual length is ascertained by comparing it with a standard tape of known length. If the actual tape length is not equal to the standard value, a correction will have to be applied to the measured length of the line. Ca = correction for absolute length C = correction per tape length l = the designated or nominal length of the tape L= measured length of the line

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**Corrections for Systematic Errors in Taping-2**

2. Correction for temperature Ct = temperature correction α = the coefficient of linear expansion of tape material tm = mean temperature during the measurement to= standard temperature 3.Correction for pull: if the pull applied to the tape during the measurement is more than the standard pull at which the tape was standardized, its length increases. Hence the distance measured will become less than the actual. Correction is +ve if applied pull is greater than standard pull and its is –Ve if applied pull is less than standard pull

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**Corrections for systematic error in taping-3**

Cp = the pull correction P = pull applied in the field during measurement, Po = the standard pull A= Cross sectional are of the tape E = the modulus of elasticity 2.1 X 105 N/mm2 for steel 1.54 X 105 N/mm2 for invar 4. Correction for the sag When the measurements is made by stretching the tape above the ground, supports are needed at the end of the tape. Consequently the tape sags under its own weight, with the maximum dip occurring at the middle of the tape, and the tape takes the shape of a catenary. This necessitate the correction known as sag correction.

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**Corrections for systematic error in taping-4**

Cg= sag correction W= weight of the tape per span length P=pull applied during the measurement If both the ends of line are not at the same level, a further correction to Cg is required as α= angle of slope between the end support

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**Corrections for systematic error in taping-5**

5. Corrections for the slope: If the two ends of the tape are at different elevations, the measured length needs a correction known as correction for slope α h D L

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**Derivation of Slope Correction if Angle is not Known**

h D L

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**Corrections for systematic error in taping-6**

Correction for alignment If the intermidiate points are not in correct alignment with the ends of the line, or they are not on the line to be measured, a correction known for alignment has to be applied to the measured length. d= distance by which the other end of the tape is out of alignment Cm is always negative

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**Corrections for systematic error in taping-6**

Reduction to mean sea level The length of the line measured at an altitude of h meteres above mean sea level is always more compared to length measured on mean sea level surface. The necessity of reducing distances to a common datum arises when the survey are to be connected to national grid. CR=h*L/R R= radius of the earth

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Normal tension The pull which, when applied to a tape suspended in the air, equalizes the correction due to pull and sag is known as normal tension The value of P may be calculated by trial and error

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Problem-1 A steel tape of nominal length 30 m was suspended between supports to measure the length of a line. The measured length of the line on a slope of angle 3⁰ 50’ is m. The mean temperature during the measurement was 12 ⁰C and the pull was 100 N. If standard length of the tape is m at 20 ⁰C, and the standard pull is 45.0 N, calculate the corrected horizontal length. Take the weight of the tape 0.15 N/m, its cross-sectional area = 2.5 mm2, α=1.15 X10-5 per ⁰C, and E= 2.0 X 105 N/mm2.

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Problems-2 The measured distance between two points is 615 m. If the angle of slope between the points is 7⁰, what is the horizontal distance between the points. The distance between two points A and B, is measured along the slope as 435 m. The difference in elevation of these points is 49 m. Determine the horizontal distance between A and B. If the slope of the ground is 1 in 5, and the measured distance between two points is 503 m, what is the horizontal equivalent of the measures distance. What slope distance must be laid out along a line that rises 5 m/100 m in order to establish a horizontal distance of 830 m.

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Problems-3 5. A measurement is made along a line that is inclined by a vertical angle of the measured slope distance is m. to what accuracy must the slope angle be measured if the relative accuracy of the horizontal distance is to be 1/25000? Also compute the horizontal distance. 6. To what accuracy must the slope angle of example 3.5, be measured if the horizontal distance is to be accurate to m. 7. What is the correct length of a line which is measured as 350 m with 20 m tape, 10 cm too long.

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Problems-4 8. At the end of a survey of a parcel land, a tape of length was found to be 10 cm short. The area of the plan drawn with the measurements taken with this tape is found to be 135 cm2. if the scale of the plan is 1/1000, what is the true area of the field assuming that the chain was exact 30 m at commencement of survey? 9. A line was measured with a steel tape which was exactly 30 m at 25 C at a pull of 10 kg, the measured length being m. the temperature during measurement was 34 C and the pull applied was 18 kg. compute the length of the line if the cross sectional area of the tape is cm2. take α = 3.5 X 10-6 per 1 C and E= 2.1 X 106 kg/cm2 for the material of the tape.

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**Assignment-1 Collect from scoops today afternoon**

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