River Direction, Intervisibility and a School Site on a 1:50,000 Sheet
The extract covers a 10 km by 10 km area of hill country on a 1:50,000 sheet; each grid square is 2 cm and represents 1 km, and the contour interval is 20 m. A river enters the area at grid 4125 (380 m) and leaves at grid 4431 (340 m). A road runs north–south along easting 43, crossing the river at the bridge at grid 4427 (350 m). Spot heights are 512 m at 4625, 468 m at 4526, 428 m at 4024 and 386 m at 4130. Settlement is mapped at 4522 and at 4820, the second described as scattered. Between northings 22 and 27, contours are closely spaced near 4124 and widely spaced near 4228. The straight-line distance from the bridge at 4427 to the spot height at 4625 is about 2.8 km, and the 468 m spur at 4526 lies on the straight line between them.
1. State the direction in which the river flows and give two pieces of map evidence for your answer.
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The river flows northward, toward increasing northing.
Evidence 1 - heights along the channel. Where the river enters the extract at 4125 the height is given as 380 m; where it leaves at 4431 the height is 340 m. Water flows from higher to lower ground, so the fall of 40 m over the distance between those two points is in the direction of increasing northing. The bridge height of 350 m at 4427 fits between the two and confirms the gradient.
Evidence 2 - contour behaviour on tributaries. The closely spaced contours near 4124 indicate steep valley sides where a tributary descends from the higher ground to the south and west, and the values on the intervening contours decline northward as they approach the main channel. A common error is to assume that because the highest ground (512 m) is in the north-east, the river must flow southward; that confuses the position of the summit with the direction of the valley floor.
A check is worthwhile: 40 m of fall over roughly 6.7 km of channel gives a gradient of about 1 in 168, a gentle but consistent lowland-to-valley-floor stream, which matches the wide contour spacing near 4228.
2. Decide whether an observer standing at the spot height of 512 m at 4625 can see the bridge at 4427. Show your reasoning.
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Do not answer from the heights alone; compare the line of sight with the ground between.
The observer is at 512 m, the target at 350 m, and the horizontal separation is about 2.8 km. The 468 m spur at 4526 lies on the straight line between them, at approximately the midpoint, so the critical question is whether the line of sight clears the spur.
Assuming a uniform slope, the height of the line of sight at the midpoint is the mean of the two end heights:
(512 + 350) ÷ 2 = 431 m.
The spur stands at 468 m, which is 37 m above the line of sight at that point. The ground therefore intercepts the line and the bridge is not visible; the profile is convex from the observer's side, with the spur forming the horizon.
A useful refinement: raising the observer's eye by 10 m on a tower lifts the line of sight at the midpoint by only about 5 m, to 436 m, still well below 468 m. A much taller structure, or moving the observer to the 512 m summit's northern shoulder, would be needed before the bridge came into view.
3. A secondary school is to serve the settlements at 4522 and 4820. Compare site 4624 (on a spur, 470 m, 300 m from the road) with site 4721 (flat, 430 m, 900 m from the road) and recommend one.
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Compare the two sites criterion by criterion rather than choosing on one attribute.
Site 4624 lies on a spur at 470 m, only 300 m from the road. Its advantage is direct road access with minimal new track. Its disadvantages are serious for a school: a spur is a narrow, steep-sided site, so a level playing field and future classrooms require cut-and-fill and retaining walls, which raises capital cost and creates landslide risk in a monsoon climate; water supply on a ridge may be difficult; and the site is close to 4522 but roughly 3 km from the scattered settlement at 4820, so half the catchment walks furthest.
Site 4721 is flat at 430 m and roughly central, about 2 km from each settlement. Flat land is cheaper to build on, allows a field and later expansion, and is better drained by the surrounding slopes than a ridge. Its weakness is the 900 m gap to the road, which needs a graded access track - but that is a modest, once-only cost against the recurring disadvantages of a steep site.
Recommendation: 4721, with a properly drained access track, provided a site investigation shows no flood risk or seasonal waterlogging and land tenure can be secured. If the flat land proves waterlogged or is unavailable, 4624 becomes acceptable only with engineered retaining works.