Topographic surveying
A topographic survey records the shape of the land and the things on it. Heights are measured at many points by levelling or satellite receivers. Points of equal height are joined by contour lines. The vertical gap between two neighbouring contours is the contour interval. Close contours mean a steep slope; wide gaps mean a gentle slope.
Route surveying
A route survey is done for roads, canals, railways and pipelines. First a long strip of land is studied, then the best line is chosen, then the centre line is marked with pegs, usually every 100 m or 30 m. The distance of each peg from the start is its chainage. Levels along the line give a longitudinal profile to choose slopes.
Construction surveying
A construction survey (setting out) transfers the design on paper to the ground. Corner pegs of a building are placed from the plan. To check a corner is square, the two diagonals of a rectangle must be equal (or use the 3-4-5 rule). Levels are also marked so floors and drains have the right height and slope.
River surveying
A river survey measures width, depth and bank levels. A rope or tape is stretched across the river; at points along it the depth is measured with a rod or echo sounder (soundings). Together they give the cross-section of the river. Water level and flow speed are noted. This helps design bridges, intakes and flood walls.
Forest surveying
A forest survey maps the boundary and finds how much wood there is. It is too big to count every tree, so we use sample plots (for example circles of fixed area). Trees in the plots are counted and measured for height and girth. The average per plot is multiplied up to the whole area.
Key formulas and definitions
- Contour interval = height difference between two neighbouring contours
- Chainage of a peg = distance from the start of the route
- Diagonal of rectangle = square root of (length squared + width squared)
- Cross-section area is about the sum of (width of strip x mean depth)
- Trees in forest = trees per plot x (forest area / plot area)
Worked examples
1. A hill has contours at 100 m, 110 m and 120 m. What is the contour interval?
110 - 100 = 10 m.
2. Pegs are placed every 100 m starting at 0+000. What is the chainage of the 6th peg (the first is at 0)?
The 6th peg is 5 gaps from the start: 5 x 100 = 500 m.
3. A building is 7 m by 4 m. Find each diagonal when the corners are square.
Diagonal = square root of (49 + 16) = square root of 65 = 8.06 m.
4. A river is 12 m wide. Depths taken at the middle of four equal strips (3 m each) are 1.2, 2.0, 1.6 and 0.8 m. Estimate the cross-section area.
Mean depths x width: 3 x (1.2 + 2.0 + 1.6 + 0.8) = 3 x 5.6 = 16.8 m2.
5. Three circular plots of 100 m2 each contain 12, 9 and 15 trees. The forest is 4 hectares (40000 m2). Estimate the trees.
Average = (12 + 9 + 15) / 3 = 12 trees per 100 m2. Number of plot-areas in forest = 40000 / 100 = 400. Trees = 12 x 400 = 4800.
Common mistakes
- Thinking contour lines can cross each other. Different heights never cross (except on a cliff).
- Measuring only one diagonal when setting out a building. Check both.
- Taking depth only at the middle of a river. Many points are needed.
- Using one or two sample plots in a forest. More plots give a better estimate.