- 1. SHREE SA’D VIDYA MANDAL INSTITUTE OF TECHNOLOGY DEPARTMENT OF CIVIL ENGINEERING
- 3. Presented by:- Name Arvindsai Nair Dhaval Chavda Nirmal Patel Rupesh Patel Saptak Raval Enrollment no. 130454106002 130454106001 140453106009 140453106010 140453106015
- 4. Contents Topics Slides 1. Tacheometric survey(intro)……….....05 2. Fixed hair method…………………..…06 3. Stadia constant…………………....……30 4. Movable hair method…………….........34 5. Tangential method……………………..39 6. Anallatic lens……………………….…...50 7. Subtense bar…………………………....53 8. Field work in tacheometric survey…57
- 5. Tacheometric survey Tachometry is a method of measuring both horizontal distance and vertical elevation of a point in the distance, without the use of sophisticated technology, such as electronic distance measurement (EDM) or satellite transmissions.
- 7. Fixed hair method • This is a method of finding the distance and elevation of staff from the theodolite (Tachometer). •Different formulas are used in finding distance for different cases. •Some cases are discussed as follows:-
- 8. Case 1 : When line of sight is horizontal and staff is held vertically.
- 9. Where, A,B =Point on staff cut but upper and lower hair a,b=upper and lower cross hair ab=i=Stadia interval AB=S= staff intercept D=distance from axis of tachometer to staff D=distance between optical center and axis of tachometer.
- 10. Proof: From Similar triangle ABf and a’b’f we get, ( f0=f ; AB=S; a’b’=i) Now total distance(D)=fC+f+d +f+d
- 11. Now as i ,f and d are constants we can write that the total horizontal distance i.e. D= K.S + C where , K= =Multiplying constant C=f+d= Additive constant Here, vertical distance is zero.
- 12. Case 2: When line of sight is inclined but staff is held vertically.
- 13. C A O’ D O A` B C` P P’ h V Ө α (a) Angle of elevation {+} α S Line of axis
- 14. Horizontal distance (D)= Formula for horizontal distance cos.L cos)cos.( CsKD coscos. 2 CsKD
- 15. Vertical distance (V)= Formula for vertical distance sin 2 2Sin . CsKV sin)cos.( CsKV sin.L
- 16. Reduced level of Q = Reduced level of H.I. + V -h Formula for elevation of staff station
- 17. D Line of Axis A B C’ C V h P’ P O θ O’ (b) Angle of Depression {-}
- 18. Horizontal distance (D)= L. Formula for horizontal distance coscos2 CKSD cos)cos( CKSD
- 19. sin 2 2Sin SK. CV Vertical distance (V)= L. Formula for vertical distance sincossinSK. CV
- 20. Reduced level of P = Reduced level of H.I. -V -h Formula for elevation of staff station
- 21. Case 3: When line of sight is inclined but staff is held normal to the line of sight.
- 22. (a) Angle of elevation {+} C A O’ D O A` B C` P P’ h V Ө α α S Line of axis hcosθ h sin θ L cos θ
- 23. Horizontal distance (D) Formula for horizontal distance sincos. hL sincos).( hCsK sincoscos. hCsK
- 24. Vertical distance (V) Formula for vertical distance sinL sin).( CsK sinsin. CsK
- 25. Reduced level of Q = Reduced level of H.I. + V -h Formula for elevation of staff station cos
- 26. (b) Angle of Depression {-} Line of Axis A B C V h cosθ P P1 O θ O’ D L cos θ L h sinθ
- 27. Horizontal distance (D) Formula for horizontal distance sincos. hL sincos).( hCsK sincoscos. hCsK
- 28. Vertical distance (V) Formula for vertical distance sinL sin).( CsK sinsin. CsK
- 29. Reduced level of Q = Reduced level of H.I. -V -h Formula for elevation of staff station cos
- 30. STADIA CONSTANTS
- 31. STADIA CONSTANTS Stadia or tacheometric constants are:- 1. Multiplying constant where, f =focal length of the lens i =stadia intercept The value of multiplying constant is generally 100. i f A
- 32. 2. Additive constant B=(f+d) where, f=focal length of the lens d= horizontal distance between instrument axis to optical centre of a lens The value of additive constant. varies from 0.15 m to 0.60 m.
- 33. In tachometric surveying, instrument used is known as a tachometer. With the help of a tachometer observations (stadia readings and vertical angles) are taken and horizontal and vertical distances are determined by using formulae. Before doing calculations we should known the values of two constants for a tachometer to be used for survey work. Generally their values are mentioned in the catalogue supplied by the manufacturer. Also the constants may be determined by: 1. Laboratory measurement 2. Field measurement
- 35. MOVABLE HAIR METHOD In this method the staff intercept is kept constant, but the distance between the stadia hairs is variable. This of theodolite is known type as substense theodolite. The diaphragm consists of a central wire fixed with the axis of the telescope. The upper and lower stadia wires can be moved by micrometer screws in a vertical plane. The distance by which the stadia wires are moved is measured according to the number of turns of the micrometer screws.
- 36. Fig. A special type diaphragm of a moving hair theodolite
- 37. The full turns are read on the graduated scale seen in the filed of view and the fractional part of a turn is of the read on the graduated drum micrometer screw placed one above and one below the eye piece. The total distance through which stadia is the sum wires move, equal to of the micrometer readings. If the distance between the instrument station and staff position is within 200 m, an ordinary leveling staff may be used and a full meter reading used for the purpose of observing a constant intercept.
- 38. In such cases two vanes or targets fixed at a known distance apart on a staff, are observed. A third target is fixed at the mid-point of the two targets. For taking the observation, the middle target is first bisected by the central wire. Then the micrometer screws are simultaneously turned to move the stadia wires until the upper and lower targets are bisected. The readings are then noted.
- 40. Tangential Method No stadia hairs Levelling staff with vanes or targets at known distance Horizontal and vertical distances are measured by measuring the angles of elevation or depression. Some cases are discussed as follows:-
- 41. Case 1 : Both Angles of target are Angles of elevation.
- 42. O’ O S h V B A D C1 C2 θ2θ1 O’ -Instrument axis O – Instrument station C1 – Staff station V – vertical distance between lower vane and axis of instrument S – distance between the targets θ1 - vertical angle by upper targets θ2 - vertical angle lower targets h – height of lower vane above the staff station
- 43. From figure we can say that, Formula 21 2 21 21 2 1 tantan tan tantan )tan(tan tan tan S V S D DS DV DSV RL of station C1 = RL of instrument axis + V - h
- 44. Case 2 : Both angles of target are Angles of Depression
- 45. V S h θ1 θ2 C2 A B C1 O’ O D O’ -Instrument axis O – Instrument station C1 – Staff station V – vertical distance between lower vane and axis of instrument S – distance between the targets θ1 - vertical angle by upper targets θ2 - vertical angle lower targets h – height of lower vane above the staff station
- 46. From figure we can say that, Formula 12 2 12 12 1 2 tantan tan tantan )tan(tan tan tan S V S D DS DSV DV RL of station A = RL of instrument axis - V - h
- 47. Case 3 : One angle is angle of elevation and the other is angle of depression.
- 48. O’ -Instrument axis O – Instrument station C1 – Staff station V – vertical distance between lower vane and axis of instrument S – distance between the targets θ1 - vertical angle by upper targets θ2 - vertical angle lower targets h – height of lower vane above the staff station S V h θ1 θ2 C2 C1 O’ O D
- 49. From figure we can say that, Formula 21 2 21 1 2 tantan tan tantan tan tan S V S D DVS DV RL of station A = RL of instrument axis - V - h
- 50. Anallatic lens
- 51. Anallatic lens • It is an additional lens generally provided in the external focusing tachometer between object glass & eyepiece • Advantages of anallatic lens:- 1) For calculation of horizontal & vertical distances constant (f+c)=0, if tacheometer is provided with anallatic lens. 2) Calculation becomes simple.
- 52. Disadvantages of anallatic lens :- 1. The anallatic lens absorbs some of the incident light which consequently results in reduction of the brightness of the image. 2. It also adds to the initial cost of the instrument because of one extra lens
- 53. SUBTENSE BAR
- 54. 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.
- 55. SUBTENSE BAR
- 56. 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.
- 57. FIELD WORK IN TACHEDMETRY 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).
- 58. 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 fie. alignments of highways,railways, canals, etc)
- 59. Procedure:- 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 bubble and 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 trunnion axis).
- 60. 2. 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. 3. The instrument is oriented with reference to any pre-determined station by taking its magnetic bearing and consider it as first ray at 0.
- 61. 4. To cover the area (details) from the station, rays at 15 or 30 intervals are extended from the station The overlap of the rays from nearby stations should be 10 to 15.Also the 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 (1e, A to E) 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. Take fare sight the traverse a station and observe the vertical angle and the staff readings the three wires. 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.
- 62. 5. 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 ray.First ray must be extended to its fun length from B to A Sight all the representative points on the rays observe vertical angles and staff readings, and complete the station. Take a for 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. 6. 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.
- 63. 7. From the metric book, the distances of the points from the instrument stations and their respective RLs are calculated by using tachometric table. 8. 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. 9. 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