Weisbach triangle (1).pptx

Weisbach triangle (1).pptx

• 1.
  Apparatus: Straight wires,Plumb bob, theodolite, measuring tape, ranging rod etc. Aim: Plumb plane azimuth is obtained from the surface and correct azimuth of the underground reference line can be calculated from underground observation.
• 2.
  Theory • Method ofsurveying by which surface survey and Underground survey are connected to the same base. • Methods - Based on the conditions at the mine: 1. Direct traversing through adits or drifts 2. Shaft plumbing methods: I. One wire in each of the two shafts II. Method of Weisbach triangles III. Methods of Weisbach quadrilateral 3. Optical method 4. Magnetic methods 5. Gyro-Theodolite method
• 3.
  • To determinerelative positions of underground workings. • To fix the boundary of the mine for limiting the extent of underground workings. • To fix positions of surface structures as per plans. • To mark river, lake, pond, etc. on mine plans. • To select suitable sites for proposed pits, drifts, or boreholes to connect with underground workings. Accuracy: The permissible angular error for correlation is ± 2 minutes of arc.
• 4.
  Maximum accuracy isobtained by having: 1. The angle at (T), i.e. angle BTA, as small as possible. Normally the angle is between two and ten minutes. 2. The length TB as short as possible. This would normally be the minimum focussing distance of the theodolite. 3. The distance between the wires AB as long as possible. 4. The length of the backsight, TR, should be as long as possible, preferably greater than 20 metres. Weisbach Triangle method: In Weisbach method the theodolite is set up slightly out of line forming a small triangle with the two wires. This triangle is known as Weisbach Triangle and the azimuth of the line joining the two wires is found by solution of the triangle so formed.
• 5.
  Procedure: • Hang twostraight steel wires (X and Y) from surface to underground with suspended heavy plumb to avoid oscillation of wires. • The line joining X and Y is called plumb plane. • Cross section of steel wires should be 2mm2 and tensile strength 200 kg/mm2. • Weight of plumb bob usually selected as H/3 Where H is depth of plumbing in meters. X Y Cheese weight
• 6.
  Procedure of weisbachtriangle method: i. Hang the wires in accordance with (3) above. ii. Establish a temporary station at (T). Set up the theodolite at (T). iii. Read the interior angle BTR. Three readings on each face should be observed to eliminate any errors due to residual swing in the plumbline. iv. Read the interior angle ATR in the similar manner and the difference between the two angles is obtained to get correct value of angle BTA v. All the distances in the triangle are then measured as accurately as possible, normally to the nearest millimeter. The distance BT is also measured. The distance AT should equal distance AB + distance BT when angle BTA is small.
• 8.
  vi. The theodoliteis next set up at R and the angle TRS is observed and the distances RS and distance RT are also carefully observed. vii. Solve the Weisbach triangles to establish a bearing datum. The sine rule is normally used, sin∠BAT = BT AB sin ∠BTA However,when the angles are less than 0°25’. ∠BAT = BT AB ∠BTA Once angle BATis known the bearing of lines AT and AB can be easily determined. viii. The angle BT’A can be calculated and the azimuth of TR’ can be estimated. Finally by measuring the angle T’R’S’ the azimuth of underground base line R’S’ can be deduced.
• 9.
  Discussions:
• 10.
  • Steel wiresshould be straight. • There should be no oscillations of steel wires. • Distance of theodolite station and near wire should be minimum for example 4.5 to 7 ft. • For accuracy ∠BTA/∠TBA should be less than unity it means ∠BTA should be as minimum as possible. • Plumbing wire : Steel wire such as piano wire, Bronze wire. • Plumb bob : Weight of plumb bob should be between one half and one third of breaking strength of the plumbing wire. The plumb bob is used straighten kinks, reduce vibrations and stabilise the system quickly. • Dampening drum : The plumb bob is placed in drum filled with water or light oil to limit its movement. Precautions