Toposheet reasoning: gradient, intervisibility and siting a check dam on a described extract
A practice toposheet extract covers 5 km × 5 km at 1:50,000 (the extract measures 10 cm × 10 cm). A stream rises near spot height 612 in the north-east and flows south-west to a village tank at spot height 498; measured along the stream course, the distance from the 612 spot to the tank is 6.4 km. West of the stream a ridge runs north–south with spot heights 618 and 605. The village of Bhogaon (spot height 545) lies on the eastern bank, 1.6 km from the stream. Contours are at 20 m intervals. On the western valley side there are about 8 contours in 500 m; on the eastern side about 3 contours in 700 m. Between Bhogaon and ridge point 605 lies a saddle at about 590, roughly midway between them. The tank has a masonry bund 240 m long on its southern side. A metalled road from Bhogaon to the taluka town crosses the stream 2 km downstream of the tank.
1. Calculate the average gradient of the stream from spot 612 to the tank and compare the two valley-side slopes. Express the gradients in three ways.
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Stream gradient (612 → 498):
- Fall = 612 − 498 = 114 m
- Horizontal distance = 6.4 km = 6,400 m
- Ratio = 114 ÷ 6,400 = 0.0178 → 1 in 56
- As a percentage = 1.78%
- Per kilometre = 114 ÷ 6.4 = 17.8 m per km
That is a moderate, graded long profile - typical of a stream that has already cut down through most of its fall, not of a torrent.
Western slope: 8 contours in 500 m = 8 × 20 = 160 m fall in 500 m → 160 ÷ 500 = 0.32 = 32%, i.e. 1 in 3.1. Extremely steep - probably an escarpment or a fault-line scarp.
Eastern slope: 3 contours in 700 m = 60 m in 700 m → 60 ÷ 700 = 0.086 = 8.6%, i.e. 1 in 11.7. Moderate.
Why the contrast matters: the western side has thin soil, rapid runoff, high erosion risk and poor conditions for agriculture - the contour crowding is a warning for deforestation and for any road alignment, which would need a zig-zag or a cutting. The eastern side, where Bhogaon stands, has a gentler slope, deeper soil and is the natural side for cultivation and settlement. Slope, read from contour spacing, explains the location of the village as much as the water supply does.
2. Are Bhogaon (545) and ridge point 605 intervisible? Prove your answer arithmetically.
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Test by comparing the line of sight with the ground at the intervening saddle.
The saddle (590) lies roughly midway between Bhogaon and the ridge point. If it is midway, the straight line joining them would stand at:
(545 + 605) ÷ 2 = 1,150 ÷ 2 = 575 m at that midway point.
The ground there is 590 m, which is 15 m above the line of sight.
Conclusion: Bhogaon and ridge point 605 are NOT intervisible. The saddle blocks the view; the observer at Bhogaon sees the skyline of the saddle, not the ridge point behind it.
Note on the method: because the saddle is 'about midway', a small shift in its position does not overturn the result - the line of sight between 545 and 605 never exceeds 605 m anywhere along the profile, and a 590 m obstruction 15 m above the line is decisive. The check is always the same: interpolate the straight-line height at the obstruction's position and compare it with the contour height there.
Practical consequence: an observer on ridge point 605 cannot see Bhogaon, so a trigonometric station or watchtower on 605 is useless for watching the village; a point on the low spur just east of the saddle, or the higher 618 summit, would be a better observation site. This is the kind of intervisibility reasoning used to site fire lookouts, microwave links and defence posts.
3. Identify the drainage pattern and the stream's stage of development, and choose a site for a check dam, giving reasons against at least one rejected alternative.
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Drainage pattern: dendritic. The stream and its tributaries follow no single structural direction, join at acute angles, and the western scarp produces shorter, steeper right-bank tributaries - an arrangement that reflects the slope and the underlying rock rather than a rectangular joint grid (which would give right-angled, trellised junctions).
Stage: the steep western slope and the 1-in-56 upper long profile indicate a youthful upper course with active downcutting; by the tank and Bhogaon the valley is broader and the gradient gentle, so the middle course is mature - a stream that has cut close to its base level in the lower part while still eroding headward above.
Preferred check-dam site: across the stream about 1–2 km upstream of the road crossing, where the valley is narrow (contours on both banks close together), on a bedrock reach, with a catchment large enough to yield a dependable flow but small enough that the structure is not overwhelmed. A narrow section means a short, cheap wall with a large storage volume per metre of crest.
Rejected alternative: across the stream immediately below the tank bund. The tank's 240 m bund already regulates that reach; a second structure there would double-store the same water, would be fed by water the tank has already released, and would sit on the silted, flat reach where the bed is fine material, not bedrock. It would add cost and siltation risk without adding recharge.
Second rejected option: the steep western tributary - the gradient (1 in 3) is too high and the sediment load too coarse; small gully plugs, not a masonry check dam, belong there.