Pack 12. Surveying processes. Equipment 12.1 Method 12.2 Checklist 12.3 Calculations 12.4

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Rosaline Arnold
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1 Pack 1 Surveying processes Equipment 1.1 Method 1. Checklist 1.3 Calculations 1.4

2 Pack 1 Surveying processes 1.1 Equipment The objective is to measure the height of an inaccessible building using angles. Total station and reflecting prism Spare battery Tripod Wooden peg or surveyors pin Hammer or mallet Sharp metal spike if ground is hard Surveyors chalk 1. Method 1 Set up two pegs parallel to the object to be measured. Ideally place the pegs at least m apart. (The further from the object the greater the distance between the pegs. The angles on the plan should be as near to an equilateral triangle as practical for the greatest accuracy; see the diagram below.) Plan layout of pegs in relation to the object Figure 1.1 Set up and level the instrument (theodolite or total station) over peg A. 3 Target the top of the building to be measured and gently apply the upper and lower clamps. Make fine adjustments with the slow motion screws. 4 Zero the instrument. (This will only apply to the horizontal reading. The vertical reading is set to the zenith as zero and cannot be adjusted.) 5 Take the vertical reading and book it in the appropriate box. Identify the targeted reading and what type of angle reading has been taken. Take and book the other readings on the booking sheet. Pack 1 Surveying processes

3 Table 1.1 Angle Station Target/Comment V or H A Zenith Top of building α1 V Ground level of building α V Pack 1 Surveying processes V = vertical angle, H = horizontal angle. 6 Undo/release the upper clamp and target the base of the building. Apply the upper clamp again and make fine adjustment with the slow motion screw. Take and book the second vertical reading. It is important to include identification on the booking sheet as shown. Zenith 0 1 α 1 α Figure 1. 7 Before taking the horizontal readings check that the horizontal angle is set at zero. If not, press the zero button twice to clear the setting. Now release the lower clamp and rotate the instrument clockwise and target peg B. Book the reading. Ensure it is clearly identified as shown in the diagram. Pack 1 Surveying processes 3

4 Pack 1 Surveying processes 3 Figure 1.3 Take and book the readings. Table 1. Angle Station Target/Comment V or H A Zenith Top of building α1 V Ground level of building α V A H V = vertical angle, H = horizontal angle. 8 If using a total station, place a reflecting prism on a tripod over peg B or place the prism on the top of the peg. Use the electromagnetic distance meter and book the reading. Depending upon the model of total station, the readings will be displayed as sloping dimensions and horizontal dimensions where the instrument has carried out the necessary calculations to provide an accurate length (distance) between the two pegs. If, however, a theodolite has been used, a tape measurement will be required. It should be noted that the tape is likely to sag over a long distance and will have a small effect on the over all height of the building. More importantly the 4 Pack 1 Surveying processes

5 difference in the heights of the pegs should be noted. (If the pegs are, say, more than 300 mm out of level at m apart, the difference in length will be the hypotenuse minus the adjacent see the calculations below.) 10.00m 0.300m Pack 1 Surveying processes Opposite Figure 1.4 Adjacent tan θ = Opposite Adjacent tan θ = Complete the calculation to find the true length. 9 If you have two instruments, set up the second over peg B and target peg A. Apply the lower clamp and zero the instrument. 10 Rotate the instrument and target the building at the same point as previously used. Book the reading. Continue by taking and booking the readings. Table 1.3 Angle Station Target/Comment V or H A Zenith Top of building α1 V Ground level of building α V A H B Top of building B H Lineal between pegs m V = vertical angle, H = horizontal angle. Pack 1 Surveying processes 5

6 Pack 1 Surveying processes 1.3 Checklist 1 Set up two pegs reasonably spaced apart. Set up the instrument over peg A and target the top of the object. 3 Take the vertical angle and book it. 4 Release the clamp and target the base of the object and book the reading. 5 Ensure the instrument has been set at zero horizontally and rotate the instrument clockwise, target peg B and book the reading. 6 Take lineal measurement between pegs A and B and book them. 7 Move the instrument and position it over peg B or use a second instrument. 8 Target peg A and set it at zero. 9 Rotate the instrument clockwise and target the top of the object; book the reading. Zenith Figure Take and book the remaining readings. 1.4 Calculations What information do we currently know? Label each corner of the triangle with upper case letters. 6 Pack 1 Surveying processes

7 Table 1.4 Angle Station Target/Comment V or H A Zenith Top of building α1 V Ground level of building α V Pack 1 Surveying processes A H B Top of building B H Lineal between pegs V = vertical angle, H = horizontal angle. Plan layout of pegs in relation to the object m Figure 1.6 The side opposite the angle is labelled with the corresponding lower case letter. Calculate the angle for corner C. Angle C = 180 ( ) Angle C = Angle C = Pack 1 Surveying processes 7

8 Pack 1 Surveying processes C b C a A m B A 10.50m c B Figure 1.7 Figure 1.8 As there are no right angles, the sine rule should be used. a sin A = b sin B = c sin C The first objective is to calculate the length of side b; therefore use that part of the formula and note the known data. b sin B = c sin C Transpose the formula, placing the unknown on the left of the equals sign and the known on the right: b = c sin C sin B b = sin sin b = m Side b will be the adjacent side in the next calculation. To calculate the height of the building, simple trigonometry can be used. If you cannot remember which set of sides go where, then write the following down: SOH TOA CAH ( sew to a car ) These three formulae only work with right angled triangles: sin θ = Opposite Hypotenuse tan θ = Opposite Adjacent cos θ = Adjacent Hypotenuse 8 Pack 1 Surveying processes

9 What is known? Zenith 0 1 Pack 1 Surveying processes α 1 α Figure 1.9 Take and book the readings. Table 1.5 Angle Station Target/Comment V or H A Zenith Top of building α1 V Ground level of building α V A H B Top of building B H Lineal between pegs m V = vertical angle, H = horizontal angle. Pack 1 Surveying processes 9

10 Pack 1 Surveying processes To calculate the height of the building the space between points 1 and should be divided into two right angled triangles. α 1 β 1 1 Figure 1.10 To calculate the internal angle β1, subtract α1 from90. β1 = ( ) β1 = The adjacent has been previously calculated as m; therefore using the tangent formula the opposite can be calculated. Transpose the formula and enter the known data. tan θ = Opposite 1 Adjacent Opposite 1 = tan θ Adjacent Opposite 1 = tan Opposite 1 = m Calculate the opposite on the lower triangle. To calculate the internal angle β subtract 90 from α: β = ( ) β = α β Figure Pack 1 Surveying processes

11 Opposite = tan Opposite = m Add both Opposite 1 and Opposite to calculate the overall height of the building. Opposite 1 + Opposite = Overall height of building m m = 7.54 m Answer: The overall height of the building is m. Pack 1 Surveying processes Pack 1 Surveying processes 11

Pack 11. Surveying processes. Equipment 11.1 Method 11.2 Using the recorded data to calculate the height of the building 11.3

Pack 11. Surveying processes. Equipment 11.1 Method 11.2 Using the recorded data to calculate the height of the building 11.3 Pack 11 Surveying processes Equipment 11.1 Method 11.2 Using the recorded data to calculate the height of the building 11.3 Pack 11 Surveying processes 11.1 Equipment The objective is to measure the height