MEASUREMENTS IN SURVEYING

Transcription

1 1 MEASUREMENTS IN SURVEYING Lecture 2

2 MEASUREMENTS IN SURVEYING There are five major types of measurements in surveying: Horizontal distances Horizontal angles Vertical distances Vertical angles Slope distances The magnitudes measured must always be reported in terms of specific units 2

3 MEASUREMENTS IN SURVEYING When reporting the measurements, it is very important to maintain the following: Integrity Legibility Arrangement Clarity 3

4 SIGNIFICANT FIGURES The accuracy of the measurement could be indicated by the number of significant figures (SF) recorded. SF of any observed value is the number of certain digits plus one digit that is estimated or rounded off. If a measuring tape smallest division is m and the reported measurement is then it has 4 SF (3 certain and 1 estimated). 4

5 SIGNIFICANT FIGURES Decimal Places may be used to maintain the correct number of SF. Two SF: 32, 3.2, 0.32, 0.032, Three SF: , , Four SF: 3245, 32.45, , , ?????? 5

6 SIGNIFICANT FIGURES Zeroes at the end of an integer may be expressed in terms of power of 10 to eliminate any uncertainty about SF x SF x SF 3.20 x SF Or SF SF SF 6

7 SIGNIFICANT FIGURES In mathematical operations it is important that the number of SF reported is consistent with the data used (+, -) rightmost significant digit (x, /) least number of SF =?? / 5.0 =?? 7

8 ROUNDING OFF NUMBERS Rounding off numbers is usually performed to have only the SF in a number Less than 5 Greater than 5 Equals five (nearest even number) 8

9 PRECISION AND ACCURACY Precision is an indication of the consistency of a group of readings Accuracy indicates the absolute nearness of the readings to their true value 9

10 PRECISION AND ACCURACY 10

11 PRECISION AND ACCURACY If two teams measured a horizontal 90 o angle five times in the field and the following results were obtained: 11

12 PRECISION AND ACCURACY Max difference in readings: Team 1: Team 2: (more precise) Deviation from the true value: Team 1: (more accurate) Team 2: 12

13 ERRORS IN SURVEYING All types of measurements entail some degree of error (± ε) When dealing with errors, surveyors must understand: The different kinds of errors The sources of errors Estimate the magnitudes of the error Error propagation 13

14 ERRORS IN SURVEYING There are three general sources of error: Natural errors caused by variation in or adverse weather conditions, refraction. Instrumental errors caused by imperfect construction and adjustment of the surveying instruments used Personal errors caused by the inability of the individual to make exact observations 14

15 ERRORS IN SURVEYING Classes of errors: Blunders Systematic errors (constant or variable) Random errors Constant errors 15

16 ERRORS IN SURVEYING Weights: The are expressed numerically and an indication of the relative precision of quantities within a set The greater the weight, the greater the precision of the observation to which it relates 16

17 Frequently measured as a spatial distance in three-dimensional space, however, it is usually the horizontal component which is required There are three basic methods of measuring distances: Direct (tape) Indirect (stadia or tacheometry) Electronic 17

18 Methods of measurement: Pacing: a rapid means of estimating a distance distance = individual pace distance x number of paces Odometer: Distance = number of revolutions of the wheel x circumference of the wheel 18

19 Stadia (or Tacheometry) 19

20 Stadia (or Tacheometry) 20

21 Chains 21

22 EDM 22

23 Tapes: Four kinds of tapes are used: Synthetic/Fibre-Glass Reinforced tape Synthetic/ Steel - Plastic tapes Steel tapes Invar tapes 23

24 Synthetic/Fibre-Glass Reinforced tape hard-wearing, durable and water proof materials can easily be stretched used for measurements that do not need to be highly precise 24

25 Steel/Plastic Composite Tape more precise than the fiber-glass tape temperature and tension variations can be corrected 25

26 Steel Tapes more precise and more stable nominal length: temperature = 20 C and applied tension between 50 N to 80 N 26

27 Invar tapes most precise tape made from an alloy of 36% nickel and 64% iron low coefficient of expansion (only 1/13 that of steel tape) Disadvantages: soft and weak price is more expensive than steel tape 27

28 Tape ancillary tools: Chaining pins Ranging poles Thermometer Plump bob Tripod Tension gauge Bubble 28

29 Sloping distances 29

30 Errors in taping Instrumental error Human error Natural error To express the precision, the numerator should be set to 1 while the denominator should be as large as possible. Precision = 30

31 Tape calibration 31

32 Correction for measurement: Correction = L * α * (tm - ts) where L = measured length α = coefficient of expansion, ( per C for steel) tm = temperature at measurement ts = temperature at standardization 32

33 Correction for slope 33

34 Correction for sag: correction = Where, w = unit weight of tape p = tension applied to the tape L = length measured 34

35 Examples 35

36 Ranging 36