Selecting and Constructing a Site Plan Scale
A survey group must plot a rectangular campus 360 m by 240 m on an A3 sheet measuring 420 mm by 297 mm. A 15 mm margin is required on all sides, and a 60 mm by 40 mm title block sits in the bottom-right corner. The group first considers RF 1:1000, then 1:1250. A graphic scale must be long enough to measure at least 300 m and must be read to the nearest 1 m without calculation. One student draws a plain linear scale with 50 mm divisions and claims it reads to 1 m; another writes “RF = 1:100” on a drawing that was actually plotted at 1:1000. The sheet also needs room for dimension lines, a north arrow and a legend. The group wants a scale decision that can be defended at the examination and on site.
1. Compare 1:1000 and 1:1250 for this sheet, allowing for margins and the title block. Recommend one with calculations.
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The available drawing area is 420 − 30 = 390 mm wide and 297 − 30 = 267 mm high, but the 60 × 40 mm title block removes part of the bottom-right corner. At 1:1000 the plan is 360 mm × 240 mm. It fits the raw 390 × 267 mm area, but leaves only 30 mm horizontally and 27 mm vertically. Dimension lines, the north arrow and the title block will crowd the plan, and a small plotting error can push the drawing into the margin. At 1:1250 the plan is 360000/1250 = 288 mm by 240000/1250 = 192 mm. It leaves 102 mm horizontally and 75 mm vertically, which is enough for dimensions, legend and title block. The recommended scale is therefore 1:1250. The decision is based on usable space, not merely on whether the bare outline fits.
2. Design a diagonal scale for 1:1250 that measures 300 m and reads to 1 m. Give the RF, scale length, major divisions, subdivision and diagonal construction.
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RF = 1:1250, so 1 mm on the sheet represents 1250 mm = 1.25 m on the ground. A scale 300 m long is 300000/1250 = 240 mm on paper. Draw a 240 mm line and divide it into six equal major parts, each representing 50 m and measuring 40 mm. Subdivide the first major part into five equal parts, each representing 10 m and measuring 8 mm. Construct a rectangle on the scale, about 30–40 mm high, and divide its left-hand vertical into ten equal parts. Draw the diagonals in the subdivided first part. A horizontal distance of one small subdivision is 8 mm = 10 m; crossing one of the ten vertical divisions along the diagonal reads 10/10 = 1 m. Thus the scale reads to 1 m without calculation. A plain linear scale with 50 mm divisions cannot do this, because its smallest division represents 62.5 m at this RF.
3. A student writes RF 1:100 on a plan plotted at 1:1000. Quantify the error for a 36 m wall and explain why the graphic scale still matters.
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At 1:1000, a 36 m wall is 36000/1000 = 36 mm long. At 1:100 it would be 36000/100 = 360 mm, ten times longer. If the plan was actually plotted at 1:1000 but labelled 1:100, anyone using the stated RF will read every distance ten times too small: the 36 mm line will be interpreted as 3.6 m instead of 36 m. The graphic scale must be drawn for the same RF as the plan. If the scale bar was constructed for 1:1000 but is labelled 1:100, measuring against the bar also gives a tenfold error. The RF and the scale bar are two statements of the same ratio; changing one without the other destroys the drawing. The correct label for a 1:1000 plan is RF = 1:1000, and a 36 m wall must measure 36 mm.