Determining Spot Heights from Contours

Transcription

1 Determining Spot Heights from Contours In the last section we looked at drawing contours from your grid observations. As highlighted it is a useful tool to allow you to conduct feasibility studies. As builders you may do this a few times but it is more likely your regular encounter with contour lines will be when you are given drawings to price. You are likely to be given a site plan to price a project. Contours on the plan will indicate the heights of the land. From this you will determine the cut and fill requirements and form a price accordingly. To determine ground levels from a contour drawing it is simply a reverse of what we did in the lesson above. From the contour drawing we recreate the grid. Step 1 On our contoured drawing were place an even grid. Grid size is IMPORTANT. You must use a scale ruler and select a dimension that is, 1. Relevant- A grid size of 100 metres will be too large and no reliable quantities will be determined later. 2. Ease Select a grid size that will make your later calculations easier when you need to do the volume calculations e.g. uses a grid size of say 10m x 10m instead of 13m x 13m. Draw the grid as described and this time lightly draw in the grid lines. 1

2 Step 2 Identify grid intersections that the contour lines pass through

3 Step 3 Method 1 Select a grid intersection between contour lines and use the following formula to interpolate the grid spot heights. Spot Height = Higher Contour ((Higher Contour Lower Contour)) x (Distance from Higher Contour to Grid Distance between Contours)) Note Distance from Higher Contour to Grid is Distance from Higher Contour to Grid heading towards the lower contour. For example at grid B3 the spot height may be determined as follows Distance between Contours = 29mm (Note- while it is important to use a scale when setting the grid, it is not important when interpolating as was displayed when we developed the contour drawing above. The Grids are used for volume calculations later) Spot Height = Higher Contour ((Higher Contour Lower Contour)) x (Distance from Higher Contour to Grid Distance between Contours)) Spot Height = ( ) x = = x

4 Step 3 Method 2 Select a grid intersection between contour lines and use the following method to interpolate the grid spot heights. In our example we will use grid B3. 1. Determine the height difference between the two contours e.g = Determine the distance between the two contour lines. The distance measured must be along the grid line passing through the grid intersection (Scale is not important for the same reason outlined above). In this case = 29mm 3. Determine the amount of fall per mm measured on the plan mm = m Therefore for every 1mm actually measured along the grid line there is a decrease of m in vertical height. 4. Measure the distance from the highest contour to the required grid intersection. It is important that this is measured along the same line as the previous measurement. In this case = 18mm 5. Determine the actual difference in height from the highest contour to the grid intersection x 18mm = Subtract the answer in point 5 (0.124) from the highest contour value ( ) = This RL of the grid intersection B3 = mm 45mm 72mm 98mm x

5 Step 4 Repeat the process described above for each grid intersection. For example grid points C2 to F2 may be done in this manner. Distance between Contour & along Grid 2 = 125mm (Note that may change for you depending what scale the document is printed at) Method 1 Using the formula Spot Height = Higher Contour ((Higher Contour Lower Contour)) x (Distance from Higher Contour to Grid Distance between Contours)) C2 = ( ) x = D2 = ( ) x = E2 = ( ) x = E2 = ( ) x = Method 2 1. Determine the height difference between the two contours e.g = Determine the distance between the two contour lines. The distance measured must be along the grid line passing through the grid intersection (Scale is not important for the same reason outlined above). In this case = 125mm 3. Determine the amount of fall per mm measured on the plan mm = m Therefore for every 1mm actually measured along the grid line there is a decrease of m in vertical height. 4. Measure the distance from the highest contour to the required grid intersection. It is important that this is measured along the same line as the previous measurement. In this case the measurements are a. 18mm b. 45mm c. 72mm 5

6 d. 98mm 5. Determine the actual difference in height from the highest contour to the grid intersections. a. 18mm x m = b. 45mm x m = c. 72mm x m = d. 98mm x m = Subtract the answer in point 5 (0.124) from the highest contour value ( ). a. Grid C2 = = b. Grid D2 = = c. Grid E2 = = d. Grid C2 = = mm 45mm 72mm 98mm x x x x x mm 6

7 Step 5 Sometimes the point required is not between contours but between a contour and the edge of the drawing. A x A Grid Point B5 This point is not between 2 contours. It is between a contour and the edge of the drawing. In all previous interpolation exercises we have assumed that the ground level is found in a straight line between the 2 contour lines. We can review this principle by determining the height of Grid Point B4. Spot Height = Higher Contour ((Higher Contour Lower Contour)) x (Distance from Higher Contour to Grid Distance between Contours)) = (( ) x (12/30)) = =

8 30mm 48 mm Grid Spot Height mm We can also look at this graphically in Section A-A. Spot Height RL Located on straight line between contours Contour RL RL RL RL Contour Section A-A Plan View Excerpt We use this principle to determine the spot height at the edges of the drawing. If we look at Section A-A again the straight line between the and contours can be extended to the edge of the drawing to Grid Point B5. Spot Height RL Located on straight line between contours Contour RL RL RL RL Grid Point B Contour Section A-A Plan View Excerpt We can use our formula from the previous example Spot Height = Higher Contour ((Higher Contour Lower Contour)) x (Distance from Higher Contour to Grid Distance between Contours)) In this case the distance from the Higher Contour to Grid will be larger than the Distance between the contours. Distance between Contours = 30 Distance from Higher Contour to Grid Point = 48 We can determine the spot height for Grid B5 as follows = (( ) x (48/30)) = =

9 55mm -35mm x x Now lets look at Grid Point F1, it is located on the edge of the drawing. Distance between contours = 55mm Distance from Higher Contour = -35mm (It is important to enter the distance as a negative as it is directional i.e. heading away from the lower contour) We can determine the spot height for Grid F1 as follows Spot Height = Higher Contour ((Higher Contour Lower Contour)) x (Distance from Higher Contour to Grid Distance between Contours)) Note Distance from Higher Contour to Grid is Distance from Higher Contour to Grid heading towards the lower contour. = (( ) x (-35/55)) = (-0.140) = =

10 x x x The above example was used in a prelude to the next discussion. As builders on many occasions from contour drawings you need to determine the ground levels adjacent to proposed structures. In the following page we have a proposed garage to be built on a property with an existing house on it. 10

11 Scale 1:200 N

12 The first item to consider is what is the contour interval? The interval is 0.5m. The next task is what is the existing ground level at the 4 corners of the garage? South West Corner This South West corner of the Garage is located between the Contour and the Contour. We can calculate the ground level at this point by using the same formula we used previously, Spot Height = Higher Contour ((Higher Contour Lower Contour)) x (Distance from Higher Contour to Feature Distance between Contours)) When measuring the distance between the contours in this situation you should measure as close as possible in the direction of fall in the land. This is at 90 to the contours along the dotted line. Higher Contour = Lower Contour = Distance from Higher Contour to Feature = 35mm Distance between Contours = 45mm Spot Height = (( ) x (35 45) Spot Height = Spot Height = South East Corner Higher Contour = Lower Contour = Distance from Higher Contour to Feature = 30mm Distance between Contours = 60mm x Spot Height = (( ) x (30 60) Spot Height = Spot Height =

13 North East Corner This part of the building is not between 2 contours but located between a contour and the edge of the drawing. We can use the method outlined previously. Higher Contour = Lower Contour = Distance from Higher Contour to Feature = 60mm Distance between Contours = 40mm x Spot Height = (( ) x ( ) Spot Height = Spot Height = Spot Height = As mentioned before interpreting contours is not an exact science. You need to use judgement when determining contours. In this example the spot height calculated was 0.750m above the contour. The contour interval is 0.500m so you would expect the contour between the spot height location and the contour. If you remember in your field day you conducted your grid survey at the edge of the grided area i.e. the fence line. It would be unlikely that the survey was not conducted to the fence line. It is common practice to leave some spot heights at the edges of a drawing to assist you to clarify these issues. In this case you should reject your answer and suspect that the land plateaus and adopt a spot height of say North West Corner x X Higher Contour = Lower Contour = Distance from Higher Contour to Feature = 48mm Distance between Contours = 50mm x X Spot Height = (( ) x (-48 50) Spot Height = Spot Height = Spot Height =