Tacheometry for Geomatics Enginering.pptx

Lecture notes on tacheometry

1. MMJ14203 GEOMATICS ENGINEERING MRS SITI KAMARIAH MD SA’AT FKTM, UniMAP

2. TACHEOMETRY

3. What is tacheometry? Tacheometry is defined as an optical distance measurement method. “fast measurement”: rapid and efficient way of indirectly measuring distances and elevation differences. Also known as tachymetry or telemetry. Primary objectives: Preparation of contoured plan, details on topography maps, preliminary location survey (railway, roadways, canals, resevoir). Also provide checks on distance measurement using taping/chaining.

4. Measurement Electronic Tacheometry : Uses a total station which contains an EDM, able to read distance by reflecting off a prism. Subtense Bar system: An accurate theodolite, reading to 1" of arc, is directed at a staff, two pointings being made and the small subtended angle measured

5. Equipment Measurement can be taken with theodolites , and levels and stadia rods/staves While in the past, distances were measured by the “surveyor’s chain” or tape This can be done easier and faster using a telescope equipped with stadia hairlines in combination with a stadia rod (auto level and staff)

6. Stadia Method The term stadia is a greek word for unit length. The theodolite is directed at the level staff the distance is measured by reading the top and bottom stadia hairs on the telescope view.

7. Stadia Method

8. Fixed Hair Method The horizontal and vertical distance (elevation) of a point determined by the fixed hair (fixed stadia interval). A theodolite is kept at one point and the staff is placed on the point and the staff is placed on the points whose elevations and distances from the instrument point, are to determined.

9. Fixed Hair Method

10. Stadia Readings Middle Hair Upper Hair Lower Hair

11. Stadia Principles D= Distance between vertical axis to the staff K= multiplying constant C = Additive constants

12. Constant determination In practice, the multiplicative constant generally equals 100 and the additive constant equals zero. This is certainly the case with modern instruments by may not always be so with older theodolites . The values are usually given by the makers but this is not always the case. It is sometimes necessary to measure them in an old or unfamiliar instrument. The simplest way, both for external and internal focusing instruments, is to regard the basic formula as being a linear one of the form: D = K.S + C

13. Stadia Equations Horizontal sights Inclined sights K= multiplying constant C = Additive constants S = staff intercept

14. Inclined sight

15. L = K (A’B’) + C = KS cos θ + C So D = L cos θ = KS cos 2 θ + C cos θ Similarly FC = V = L sin θ = KS cos θ sin θ + C sin θ = ½ KS sin 2 θ + C sin θ S = staff intercept h = mid-hair reading Elevation of staff station for angle in elevation: H.I + V –h Elevation of staff station for angle in depression: H.I - V –h

16. Work Sheet

17. Tacheometry Field Procedure Set up the instrument (Theodolite) at a reference point Read upper, middle, and lower hairs. Release the rodperson for movement to the next point. Read and record the horizontal angle (azimuth). Read and record the vertical angle (zenith).

18. Error Sources There are 3 main sources of error: Instrument: incorrect staff graduation, index error Personal: improper positioning of staff, incorrect staff reading, careless during measurement of vertical angles Natural: wind and temperature Mistake sources Recording wrong staff intercept Using wrong stadia interval Confusing in vertical angles is angle of depression/elevation

19. Example 1 A levelling staff is held vertical at distance of 100m and 300m form the axis of tacheometer and the staff intercept for horizontal sight are 0.99 m and 3.00 m, respectively. Find the constant of instrument. Solution D= Ks + C D1=100 m, s1= 0.99 m, D2= 300m, s2=3.00m 100 = 0.99 K+C (1) 300=3K+C (2) Solve (1) and (2), 200 = 2.01K, K = 99.5 Substitute K into equation, C = 300-3(99.5) = 1.5 , D= 99.5s + 1.5

20. Example ( cont ) The instrument is setup at station A and the staff is held vertically at point B. With the telescope inclined at angle of depression of 10 o to the horizontal, the staff reading are 2.670, 1.835 and 1.000 m. Calculate RL of B and its horizontal distance from A. The HI is 1.42 m and RL is 450.5 m. Solution s= 2.670-1.00 = 1.670 m, θ = 10 o Horizontal distance D = 99.5 (1.670) cos 2 10 + 1.5 cos 10 = 162.63 m Vertical distance V= 99.5 (1.670)/2 sin 2(10) + 1.5 sin 10 = 28.67 m RL of B = RL of A + HI –V – h = 450.5 + 1.42 – 28.67 – 1.835 = 421.415 m

21. Example 2 The reading in Table Q6 were taken by tacheometer from station B on station A, C and D in clockwise direction. The line AB has a bearing of 58 o 46’ and instrument constants, K and C are 100 and 0, respectively. Calculate the slope of line CD and its azimuth.

22. answer

23. Answer ( cont )

24. CONTOUR MAP PRODUCTION Topographic Map

25. Topographic Map A topographic map, also known as a contour map, is a map that shows the shape of the land using contour line. It is a map that shows and elevation field, meaning how high and low the ground is in relation to sea level.

26. Contour definition Imaginary line passing through points of equal elevation or reduced level. A contour is a line connecting points of equal elevation. Contour lines are lines that connect points that are of the same elevation. They show the exact elevation, the shape of the land, and the steepness of the land’s slope A contour line is a line on the map representing a contour.

27. contour lines – represent elevation, relief and slope and connect points of equal elevation contour intervals – change in elevation from one contour line to another

28. Uses of contours Proper and precise location of engineering works such as roads, canal, etc. can be decided The location of water supply, water distribution and to solve problem in stream pollution Planning and designing of dams, reservoir, transmission lines, etc. To estimate the quantity of cutting, filling and the capacity of reservoir

29. Contour interval The vertical distance between two successive contours is known as ‘Contour interval’. It remains constant for a given map. The difference in R.L.’s of two contour gives contour interval. Usually taken 1 to 15 m. The smaller the interval, the more precise the terrain relief

30. Common contour interval For large scale maps of flat country, for building sites, for detailed design work and for calculation of quantities of earth work; 0.2 to 0.5 m. For reservoirs and town planning schemes; 0.5 to 2m. For location surveys. 2 to 3m. For small scale maps of broken country and general topographic work; 3m,5m,10m,or 25m.

31. Characteristic of contour All points in a contour line have the same elevation. Flat ground is indicated where the contours are widely separated and steep- slope where they run close together. A uniform slope is indicated when the contour lines are uniformly spaced A plane surface when they are straight, parallel and equally spaced.

32. Slopes

33. High-lying form A series of closed contour lines on the map represent a hill , if the higher values are inside

34. Low-lying forms A series of closed contour lines on the map indicate a depression if the higher values are outside

35. Contour lines never run into one another except in the case of a vertical cliff. In this case, several contours coincide and the horizontal equivalent becomes zero. Depressions between summits is called a saddle . It is represented by four sets of contours as shown. It represents a dip in a ridge or the junction of two ridges.

36. Method of contouring There are mainly two methods of locating contours:- Direct Method Auto-level and staff Indirect Method: Square method Cross sections Tacheometric method: Theodolite and staff

37. Interpolation Drawing contour lines to produce a topographic map requires the ability to interpolated between points. Interpolation is required because contour lines are lines of constant elevation and the station elevations that are measured in the field seldom fall on the desired contour elevation. Interpolating is finding the proportional distance from the grid points to the contour line elevation.

38. Interpolation Interpolating can be done by estimation for low precision maps. It should be done by calculation and measurement for higher precision maps. A combination of methods can also be used, depending on the use of the map.

39. Contour Interpolation There are three main methods of interpolation: By Estimation: - The position of the contour points between ground - points are estimated roughly and the contours are then drawn through these points. This is a rough method and is suitable for small scale maps. By arithmetical calculation: - This is very tedious but accurate method and is used for small areas where accurate results are necessary. By graphical method: most rapid and convenient.

40. Consider to draw a contour map on a plot; Draw a grid Measure distance between the point Determine the spot height using selected method Draw the contour line using contour interpolation techniques

41. Example: Consider the ADMP is surveyed plot, then whole area is divided into no. of squares and RL are plotted at every spot. Then if the required contour is 89.000m, then consider small square ABGH

42. Elevation from Contours Elevations of points between contours can be determined by interpolation.

43. Drawing section from contouring

44. Drawing section from contouring

45. From sectioning from contour lines; Proposed the platform level Estimate the volume of cut and fill

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