Compass Surveying: Measuring Directions and Angles with a Prismatic Compass, Lecture notes of Survey Sampling Techniques

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IV Semester (Civil Engineering) CE: 14102 – SURVEYING Unit-II: Measurement of Direction and Angle, Traversing (Part-I: Measurement of Direction) By Prof. RD Gupta, MNNIT Allahabad (India) 1 Unit-II: Measurement of Direction and Angle, Traversing Syllabus ➢ Designation of Bearings and inter-conversion, ➢ Included angles from bearings and vice versa, ➢ Magnetic declination, local attraction, ➢ Temporary adjustments and parts of prismatic compass; ➢ Vernier Theodolite, measurement of horizontal angles: repetition method & reiteration method, traversing by compass and theodolite, computations of traverse coordinates, traverse adjustment; Total Station By Prof. RD Gupta, MNNIT Allahabad (India) 2 Compass Surveying By Prof. RD Gupta, MNNIT Allahabad (India) 5 Location of a Point by Distance and Direction The direction of a line is defined by a horizontal angle with respect to a reference line. ✓ This reference line is known as Meridian. ✓ The horizontal angle measured with respect to reference line (i.e. meridian) is termed as Bearing. In relative direction, the reference line does not remain fixed over a period of time. Meridians & Bearings By Prof. RD Gupta, MNNIT Allahabad (India) 6 Meridians and Bearings 1. Magnetic Meridians : Magnetic Bearing 2. True Meridian : True Bearing 3. Arbitrary Meridian : Arbitrary Bearing By Prof. RD Gupta, MNNIT Allahabad (India) 7 Bearings By Prof. RD Gupta, MNNIT Allahabad (India) 10 Bearing of a line is its direction measured with reference to a given meridian. Three types of Bearings: 1. True Bearing 2. Magnetic Bearing 3. Arbitrary Bearing ✓ True Bearing or Azimuth of a line is its horizontal angle from the true meridian, i.e. Geographical North. ✓ Arbitrary Bearing of a line is the horizontal angle which it makes with any arbitrary meridian ✓ The horizontal angle which a line makes with the magnetic meridian is called Magnetic Bearing. Designation of Bearings & Inter-conversion By Prof. RD Gupta, MNNIT Allahabad (India) 11 Designation of Bearings WCB : Whole Circle Bearing System RB / QB : Reduced Bearing or Quadrantal Bearing System By Prof. RD Gupta, MNNIT Allahabad (India) 12 Inter-conversion: WCB to RB By Prof. RD Gupta, MNNIT Allahabad (India) 15 Inter-conversion: RB to WCB By Prof. RD Gupta, MNNIT Allahabad (India) 16 Fore Bearing & Back Bearing By Prof. RD Gupta, MNNIT Allahabad (India) 17 By Prof. RD Gupta, MNNIT Allahabad (India) 20 Thanks to all of You Any Questions ! Magnetic Declination & Magnetic Dip By Prof. RD Gupta, MNNIT Allahabad (India) 21 Magnetic Declination ✓ Horizontal angle between true meridian and magnetic meridian. By Prof. RD Gupta, MNNIT Allahabad (India) 22 True Bearing = Magnetic Bearing ± Declination Use + sign when declination is towards East Use ─ sign when declination is towards West A B TN MN δE Declination (East) TNMN δW Declination (West) Magnetic Dip or Magnetic Inclination or Dip Angle ✓ Magnetic dip or dip angle or magnetic inclination is the angle made by the Earth's magnetic field lines with the horizontal. ▪ The magnet or magnetic needle when freely suspended will align itself along the line of magnetic field of the Earth passing through that point. ✓ Thus, dip can also be defined as the angle which a magnetic needle makes with the horizontal at a place when freely suspended. By Prof. RD Gupta, MNNIT Allahabad (India) 25 Magnetic Dip or Magnetic Inclination or Dip Angle ✓ Magnetic dip is 0° at the Equator an d 90° at the magnetic Poles. ✓ This angle varies at different points on the Earth's surface. ✓ Thus, in Northern hemi-sphere, the North end of the magnetic needle dips downwards. ✓ Hence, to make the magnetic needle horizontal, there is need of putting a counter weight (a clip/ ring of non-magnetic metal) near the South end of the needle to act as counter weight. By Prof. RD Gupta, MNNIT Allahabad (India) 26 Included Angles from Bearings By Prof. RD Gupta, MNNIT Allahabad (India) 27 Calculations of Included Angles from Bearings ✓ At any survey station, we generally measure FB of next line (or forward line) and BB of previous line (backward line) ✓ For computation of included angles, it is recommended that a rough sketch of the traverse be drawn as it gives a better idea for visualization and calculations. By Prof. RD Gupta, MNNIT Allahabad (India) 30 Included Angle = FB of BC – BB of AB B F.B. of DA θ4 A D B.B. of DA 𝜑4 ∠A = 𝜃1 ─ 𝜑4 C θ1 F.B. of AB Included Angle A = FB of next line – BB of previous line = FB of AB – BB of DA = 𝜃1 ─ 𝜑4 Bearings from Included Angles By Prof. RD Gupta, MNNIT Allahabad (India) 31 Calculation of Bearings from Included Angles By Prof. RD Gupta, MNNIT Allahabad (India) 32 Data Given: Included angles and FB of 01 line of the traverse. Bearing (FB) of all the remaining lines of the traverse can be computed either mathematically by making a rough sketch of the traverse or using following formula: FB of the next line = BB of previous line + Included Angle If the value obtained is > 360⁰, then subtract 360⁰. FB of BC = BB of AB + θ = (150 + 180) + 70 = 400⁰ [> 360] = 400⁰ ─ 360 = 40⁰ Local Attraction Local attraction at any station will affect all the magnetic bearings measured at that station by an equal amount, known as Local Attraction at that station. By Prof. RD Gupta, MNNIT Allahabad (India) 35 ✓ Hence, included angle ( 𝛼 ) computed from the affected bearings at any station will always be correct. B A C + 2⁰ + 2⁰ C′ B′ 𝛼 𝛼 Removal of Local Attraction 1. Method of Included Angles 1. Calculate the included angles from known bearings of survey lines of the traverse. 2. The included angles (interior) are not affected by local attraction. Thus, all included angles will be correct angles. ✓ If traverse is a closed traverse, then sum of all the internal angles of the polygon will be (2n – 4) x 90⁰. If sum of computed angles differs, then “Observational and Instrumental Errors” also exists. Now, calculate the correct included angles by distributing this error equally in all the angles. 3. Select a survey line which is unaffected by local attraction (i.e. BB and FB differs by exactly 180⁰). Thus, the bearings of this line will be correct bearings. ✓ If all lines are affected by local attraction, then select the line which differs the least from 180⁰. Correct it by equally distributing the error in FB and BB. Proceed with this survey line. 4. Determine the bearings of all other survey lines starting from the correct bearing of the line of the traverse. By Prof. RD Gupta, MNNIT Allahabad (India) 36 Removal of Local Attraction 2. Method of Correction at Individual Station 1. In this method, correction (local attraction) at each individual station is calculated. 2. From FB and BB of different lines of the traverse, find out the line whose BB and FB differs exactly by 180⁰. Thus, there is no local attraction at both the end stations of this survey line. 3. Hence, all the bearings measured at these two stations will be correct. 4. Start from these survey station(s), and calculate the correct bearings of all the survey lines of the traverse. Compare the computed bearing with the observed bearing at each station of the traverse. This will give you the local attraction (correction) at that station. 5. Correct all the observed bearings at each station by applying the correction computed above. The correction for all the bearings taken at one station will be the same. By Prof. RD Gupta, MNNIT Allahabad (India) 37 Prismatic Compass By Prof. RD Gupta, MNNIT Allahabad (India) 40 Prismatic Compass & its Parts By Prof. RD Gupta, MNNIT Allahabad (India) 41 Prismatic Compass By Prof. RD Gupta, MNNIT Allahabad (India) 42 Taking Observations from Prismatic Compass By Prof. RD Gupta, MNNIT Allahabad (India) 45 Surveyor’s Compass By Prof. RD Gupta, MNNIT Allahabad (India) 46 Surveyor’s Compass & its Parts By Prof. RD Gupta, MNNIT Allahabad (India) 47 ▪ The construction and bearing system of the Surveyor’s compass differs from prismatic compass. ▪ No prism is provided in Surveyor’s compass. ▪ In Surveyor’s compass, reading is taken from the top of glass and under the tip of north end of the magnetic needle directly. Difference between Prismatic & Surveyor's Compass By Prof. RD Gupta, MNNIT Allahabad (India) 50 By Prof. RD Gupta, MNNIT Allahabad (India) 51 Thanks to all of You Any Questions !