UNIT 1.pptx

ppt

1. TACHEOMETRIC SURVEYING Tacheometry or tachemetry or telemetry is a branch of angular surveying in which the horizontal and Vertical distances of points are obtained by optical means as opposed to the ordinary slower process of measurements by tape or chain. The method is very rapid and convenient . It is best adapted in obstacles such as steep and broken ground, deep revines, stretches of water or swamp and so on, which make chaining difficult or impossible, The primary object of tacheometry is the preparation of contoured maps or plans requiring both the horizontal as well as Vertical control. Also, on surveys of higher accuracy, it provides a check on distances measured with the tape. Tacheometry (from Greek, quick measure), is a system of rapid surveying, by which the positions, both horizontal and vertical, of points on the earth surface relatively to one another are determined without using a chain or tape or a separate leveling instrument.

2. Uses of Tacheometry The tacheometric methods of surveying are used with advantage over the direct methods of measurement of horizontal distances and differences in elevations. Some of the uses are: Preparation of topographic maps which require both elevations and horizontal distances. Su r v e y w o r k i n di f f i cul t te r rai n w h er e d i re c t inconvenient Detail filling Reconnaissance surveys for highways, railways, etc. Checking of already measured distances Hydrographic surveys and Establishing secondary control. m e th o ds a r e

3. INS T R U MEN T S - An ordinary transit theodolite fitted with a stadia diaphragm is generally used for tacheometric survey. - The stadia diaphragm essentially consists of one stadia hair above and the other an equal distance below the horizontal cross-hair, the stadia hairs being mounted in the ring and on the same vertical plane as the horizontal and vertical cross-hairs. Stadia is a tacheometric form of distance measurement that relies on fixed angle intercept. Different forms of stadia diaphragm commonly used

4. The telescope used in stadia surveying are of three kinds: The simple external-focusing telescope the external-focusing anallactic telescope (Possor`s telescope) the internal-focusing telescope. A tacheometer must essentially incorporate the following features: The multiplying constant should have a nominal value of 100 and the error contained in this value should not exceed 1 in 1000. The axial horizontal line should be exactly midway between the other two lines. The telescope should be truly anallactic. ( i v ) The tel e s c o p e sho u l d b e p o w e r f ul h a v i n g a m a g n i fic a ti o n of 2 to 30 diameters. The aperture of the objective should be 35 to 45 mm in diameter to have a sufficiently bright image. For small distances (say upto 100 meters), ordinary levelling staff may be used. For greater distances a stadia rod may be used. A stadia rod is usually of one piece, having 3 – 5 meters length. A stadia rod graduated in 5 mm (i.e. 0.005 m) for smaller distances and while for longer distances, the rod may be graduated in 1 cm (i.e. 0.01 m).

5. 10' 7"

6. Different systems of Tacheometric Measurement: The v a r i o us s y stem s of ta c heom e tric su r v e y ma y be cl a s s if i e d as follows: The stadia System Fixed Hair method of Stadia method Movable hair method, or Subtense method The tangential system Measurements by means of special instruments The principle common to all the systems is to calculate the horizontal distance between two points A and B and their distances in elevation, by observing The angle at the instrument at A subtended by a known short distance along a staff kept at B, and the vertical angle to B from A.

7. (a) Fixed hair method In this method, the angle at the instrument at A subtended by a known short distance along a staff kept at B is made with the help of a stadia diaphragm having stadia wires at fixed or constant distance apart. The readings are on the staff corresponding to all the three wires taken. The staff intercept, i.e., the difference of the readings corresponding to top and bottom stadia wires will therefore depend on the distance of the staff from the instrument. When the staff intercept is more than the length of the staff, only half intercept is read. For inclined sight, readings may be taken by keeping the staff either vertical or normal to the line of sight. This is the most common method is tacheometry and the same ‘stadia method’ generally bears reference to this method.

8. Subtense Method This method is similar to the fixed hair method except that the stadia interval is variable. Suitable arrangement is made to vary the distance between the stadia hair as to set them against the two targets on the staff kept at the point under observation. Thus, in this case, the staff intercept, i.e., the distance between the two targets is kept fixed while the stadia interval, i.e., the distance between the stadia hair is variable. As in the case of fixed hair method, inclined sights may also be taken. Tangential Method In t his me t h od, t he s t a d i a hai r s a r e not us e d, t h e r e a dings be ing t ake n against the horizontal cross-hair. T o m e a s ure the st a ff in te r c e pt, t w o pointings o f the i nstrum e nts are, therefore, necessary. This necessitates measurement of vertical angles twice for one single observation.

9. PRINCIPLE OF STADIA METHOD O The stadia method is based on the principle that the ratio of the perpendicular to the base is constant in similar isosceles triangles. A A 1 A 2 B 2 B 1 C 2 C 1 C ) β B In figure, let two rays OA and OB be equally inclined to central ray OC. Let A 2 B 2 , A 1 B 1 and AB be the staff intercepts. Evidently, OC 2 A 2 B 2 A 1 B 1 = OC 1 AB = OC = constant k = ½ cot β 2 This constant k entirely depends upon the magnitude of the angle β.

10. In actual practice, observations may be made with either horizontal line of sight or with inclined line of sight. In the later case the staff may be kept either vertically or normal to the line of sight. First the distance-elevation formulae for the horizontal sights should be derived. Horizontal Sights: i . f 2 f 1 s O d M b C B A c a D Consider the figure, in which O is the optical centre of the objective of an external focusing telescope . Let A, C, and B = the points cut by the three lines of sight corresponding to three wires. b, c, and a = top, axial and bottom hairs of the diaphragm. ab = i = interval b/w the stadia hairs (stadia interval) AB = s = staff intercept; f = focal length of the objective

11. f 1 = horizontal distance of the staff from the optical centre of the objective f 2 = horizontal distance of the cross-wires from O. d = distance of the vertical axis of the instrument from O. D = horizontal distance of the staff from the vertical axis of the instruments. M = centre of the instrument, corresponding to the vertical axis. Since the rays BOb and AOa pass through the optical centre, they are straight so that AOB and aOb are similar. Hence, f 1 = s f 2 i Again, since f 1 and f 2 are conjugate focal distances, we have from lens formula, 1 = 1 + 1 f f 2 f 1 Multiplying throughout by ff 1 , we get f 1 = f + f f 1 f 2 Substituting the values of f 1 i = s in the above, we get f 2 s i f 1 = f + f D = s + (f + d) = k . s + C Horizontal distance between the axis and the staff is D = f 1 + d f i

12. Above equation is known as the distance equation . In order to get the horizontal distance, therefore, the staff intercept s is to be found by subtracting the staff readings corresponding to the top and bottom stadia hairs. The constant k = f/i is known as the multiplying constant or stadia interval factor and the constant (f + d) = C is known as the additive constant of the instrument .

13. Example: T h e stadia readin g s wi t h h o ri z o n tal sid e s o n a ver t ical st a f f held in 50m fro m the tacheometer were 1.285m (lower stadia) and 1.780m (upper stadia). The focus length of the object of lens was 25cm. The distance between object lens and vertical axis of the tacheometer (d) was 15cm. Calculate the stadia interval (i)? v i a c b A B F f = 25cm O A’ B ’ d=15cm C C s u D = 50m Ui= 1.780m Li = 1.285m

14. Data’s : f = 25cm, d = 15cm, D = 50m, Ui = 1.780m and Li = 1.285m From the tacheometric equation, Horizontal distance D = K(S) + C 𝐟 D = ( 𝐢 ) S + (f + d) 50m = ( 𝟎 .𝟐𝟓𝐦 𝐢 ) (1.780m – 1.285m) + (0.25m + 0.15m) i = 2.495mm Answer :

15. 2.Distance and Heighting for Inclined sights from the Tacheometer

16. 2.Distance and Heighting for Inclined sights from the Tacheometer … 2.1 Horizontal distance from the staff station … Staff is held vertical at E. AB is not perpendicular to LoS OC. M a k e A ’ B ’ per p endicu l ar t o AB @ C . Tacheometric Computations cont… I n  OC F ; OC F  90   BCB '    ACA ' A ' O C   2 A A ' C  90   2 O h A ’ B B ’ C A V L D F E     is th e V – Angle with Main-axis

17. 2.Distance and Heighting for Inclined sights from the Tacheometer … 2.1 Horizontal distance from the staff station cont… S i m il a rl y f r o m  OC B '; B B ' C  90   2 i s ver y s ma l l , b y i gno ri n g i t ang le s A A ' C & B B ' C ca n a ss u m e 90 2 S i n c e  F r o m  ' s A A ' C & B B ' C ; A ' B '  A B cos   S cos  S lo p e l e n g t h O C  ( f  A ' B ' )  ( f  d )  ( f  S c o s  )  ( f  d ) i i Horizontal length D  L cos  D  f S c o s 2   ( f  d ) co s  i D  K . S . c o s 2   C . c o s 

18. 2.Distance and Heighting for Inclined sights from the Tacheometer … 2.2 Elevation of the staff station … 2 i F r o m  OC F ; C F  V  L si n    ( f  S c o s  )  ( f  d )  si n       ( f . S c o s  . si n  )  ( f  d ).s i n  i  K . S . c o s  . s i n   C .si n  sin 2   K . S . C sin  O h A ’ B B ’ C A V L D F E     is th e V angle

19. Reduced level Calculation for angle of elevation RL of Q RL of P Datum Line or MSL or Zero Level CQ

20. Reduced level Calculation for angle of depression RL of P C Q V h RL of Q Datum Line or MSL or Zero Level

21. Anallatic lens

22. Anallatic lens It is an additional lens generally provided in the external focusing tachometer between object glass & eyepiece Advantages of anallatic lens :- For calculation of horizontal & vertical distances constant ( f+ i )= 0, if tacheometer is provided with anallatic lens. Calculation becomes simple.

23. Disadvantages of anallatic lens :- 1. Th e an a ll a tic l e ns absorbs so m e o f the incident light which consequently results in reduction of the brightness of the image. 2. I t a l so adds to the i n itial cost o f the instru m ent because of one extra lens

24. SUBTENSE BAR

25. SUBTENSE BAR The subtense bar is an instrument used for measuring the horizontal distance between the instrument station and a station where the subtense bar is to be set up. Substense method is an indirect method of distance determination. This method essentially consists of measuring the angle subtended by two ends of a horizontal rod of fixed length, called a subtense bar. In this method a staff or target rod is not necessary, and the theodolite required is also of the ordinary transit type.

26. SUBTENSE BAR

27. The subtense bar is a metal bar of length varying from 3 to 4 m. There are two discs of diameter about 20 cm at both ends of the bar. The discs are painted black or red in front and white on the other side. The alidade is made perpendicular to the axis of the bar. A spirit level is included for levelling. The bar is mounted on a tripod stand which contains a ball and socket arrangement for levelling.

28. Tacheometric Surveying - Field Procedure… Two steps: Running the Traverse, Locating Details and Spot Heights for the Contours Set the instrument over the 1 st station, center & level it. Measure the instrument height with a tape. Sight the back sight (orient) Assume or determine the RL of the starting station by holding the staff over a nearby BM. Pick the details and Spot heights. (H angle, V angle to the middle hair, stadia readings). Take the foresight on the next traverse station. (H,V angles, stadia readings). Transfer the instrument and repeat the same process .

29. FIELD WORK IN T ACH E DME T R Y 1. Suitability :- A tacheometric survey is conducted mainly for preparing a contour map of a reservoir site, alignment of highways or railways, canals etc. It is also suitable for carrying out traverses and filling in detail in rough and rugged terrain where direct chaining is very difficult. By means of a tacheometer the relative distances and RLs of different points can be computed from the instrument station by taking observations (vertical angles and staff readings).

30. 2. Reconnaissance:- Before starting the survey work the area to be surveyed is thoroughly inspected examined ) and the instrument stations are selected according to the nature of the area. If the survey is conducted along a narrow belt . the stations are selected along the centre line of the belt ( alignments of highways,railways, canals, etc)

31. Procedur e : - The tacheometric survey should be conducted in the following steps:- 1. The tacheometer is set at station. It is centred up the starting and levelled with respect to the plat e bubble or altitude bubble.The height of the instrument (HI) is measured by leveling staff or stadia rod or tape. (i.e. height from ground to centre of the telescope axis).

32. Set-up horizontal and vertical vernier to zero. Sight the staff held on the nearby bench mark and observe the vertical angle (for inclined sight, and the readings of the three hairs on staff held vertically bench mark. If there is no bench mark nearby, fly levelling may be done from any nearby BM. To establish another one near the site area to know the RL of the starting station. The instrument is oriented with reference to any pre-determined station by taking its magnetic bearing and consider it as first ray at 0.

33. Vernier Theodolite (brainkart.com)

34. 4. To cover the area (details) from the station, rays are extended from the station s. th e extension of rays depends on the topography of the area of the station. Staff positions on these rays depend on the slope of the ground. Sight all the representive points from the starting station and first must be extended up to the whole length of the ray traverse leg to know the length of the line. Observe the vertical angle and the staff readings at the three hairs at each staff position. This way take observations all rays and complete the station . Also measure the horizontal angle between the two traverse legs . Close the work the BM. before shining the instrument on second station get the check.

35. Shifting the instrument and set up at the second station. it is centered and leveled. Measure the height of instrument. Take the first reading from the BM and then orient the telescope the first . Sight all the representative points on the rays observe vertical angles and staff readings, and complete the station. Take a for e sight on the third station and observe vertical angle and staff readings. Also measure horizontal angle between the two traverse legs. Same way close the the work on the BM. to get the check. All readings are recorded in the tachometric book. Proceed similarly at each of the successive stations and all the traverse stations are connected and the necessary observations for all the points are taken from each station and recorded clearly in the book.

36. From the metric book, the distances of the points from the instrument stations and their respective RLs are calculated by using tachometric table. Since each station is sighted twice, the two values for the length and elevation are obtained. If they are within the limits of accuracy, the average of the two values may be taken and if not work should be repeated. The traverse is plotted to any suitable scale. Rays are drawn from each station. The points are marked on these rays considering their horizontal distances from the station and RLs of the respective written. Then lines may points are the contour be drawn by the method of interpolation or by approximate method. North-line is plotted considering the magnetic bearing of the first traverse line. This way field work is carried out and contour map is prepared.

37. Errors in Tacheometric Surveying … Instrumental Due to manipulation and sighting Natural errors 1. Instrumental Errors : Mainly include the followings # Imperfect Adjustments # Irregular graduation of the staves. # Incorrect values of the Tacheometric constants . (It is advi s ab l e to determ i n e the constan t s b ef o r e the ob s erva t ions)

38. Errors in Tacheometric Surveying cont… Human Errors : # Inaccurate Centering & Levelling of the instrument. # Non-verticality of the staves. (use a sprit bubble) # Inaccurate estimation of the stadia intercept. Natural Errors : # Refraction. (bending of LoS) # Expansion of the staves.

39. Ex a mple: A levelling staff is held vertically at distances of 100m and 300m from the axis of a tacheometer and the staff intercept for horizontal sights are 0.99m and 3.00m respectively. Find the constants of the instrument (K & C). After that the above instrument is setup at station A and the staff is held vertical at a point B . With the telescope inclined at an angle of elevation of 10º00’ to the horizontal , the readings on the staff are 2.670, 1.835, 1.000m . Calculate the R.L of B and its horizontal distance from A. The height of Instrument (H.I) is 1.42m and R.L of A is 350.5m

40. Answer (Part – 01) Data’s : Horizontal distances – 100m and 300m Staff intercept : 0.99m and 3.00m D = K(S) + C At 100m, 100 = K(0.99) + C At 300m, 300 = K(3.00) + C 0.99m 100 m 300 m 3. 00m 1 2 Equation 2 – 1, K = 99.5 C = 1.5

41. Answer (Part – 02) Data’s : U = 2.670m, L = 1.000m, M = 1.835m, hi = 1.42m,   10º00’ & RL of A= 350.5m S i n( 10 ) = 28 . 6 7 m ν  K . S si n 2   C sin  2  [ 99 . 5 × 1 . 67 × S i n ( 20 ) ] / 2 + 1 . 5 O h L = 1.000m M= 1.835m U = 2.670m V D F B   = 1 0º ’  S = 2 . 67 – 1 . 00  1 . 67 m D  K . S . c o s 2   C . c o s    ×1.67× cos 2 10 + 1.5 × cos 10 = i 162.63m RL of B = RL of A + hi + V – h RL of B = 350.5 + 1.62 + 28.67 – 1.835 = 321.415m

42. CHAPTER 2: GEODETIC SURVEYING