Two Road Alignments on a 1:50,000 Sheet: Shorter or Gentler?
A candidate is given a Survey of India 1:50,000 sheet with a 20 m contour interval, covering a hilly tract, and is asked to suggest a road alignment from village A, near spot height 312, to village B, near spot height 228. Two alignments are marked in the field notes. Alignment 1 measures 6.4 cm on the map, crosses six contour lines and crosses the same stream twice. Alignment 2 measures 8.2 cm, runs along the crest of a spur, crosses three contour lines and crosses the stream once. Both villages lie inside surveyed settlement areas where contours are not drawn. The sheet shows a causeway symbol where the stream meets the existing road, and a dotted double line running north from B. Estimated earthwork cost is proportional to length plus 1.5 times the cost of every stream crossing. The candidate writes: 'Alignment 1 is better because it is shorter, and the stream flows south because the contours point south.'
1. Compute the average gradient of both alignments and comment on the candidate's use of length alone.
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Scale conversion: at 1:50,000, 1 cm on the map = 0.5 km on the ground.
| Map length | Ground length | Fall (312 - 228) | Gradient | |
|---|---|---|---|---|
| Alignment 1 | 6.4 cm | 3.2 km | 84 m | 84 / 3200 = 1 in 38 (about 2.6%) |
| Alignment 2 | 8.2 cm | 4.1 km | 84 m | 84 / 4100 = 1 in 49 (about 2.05%) |
Comment: both drops are fixed by the two spot heights, so the only variable is length. Alignment 2 is 0.9 km longer - about 28% more - but its average gradient is appreciably gentler.
Why length alone is a weak criterion:
- A road on a 1 in 38 average grade needs more cut-and-fill, more drainage control and heavier maintenance than one at 1 in 49, and may be unusable for loaded vehicles in the wet season.
- The end-to-end figure is an average, not a profile. Alignment 1 crosses six contours against three, so its grade is more uneven - short steep pitches alternating with flat stretches - which the average hides.
- Caveat: both villages sit where contours are not drawn, so the 84 m fall is between spot heights, not between the actual road termini.
2. Correct the candidate's statement about stream direction and explain what a contour V actually indicates.
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The statement is wrong in both its reasoning and its conclusion.
A contour V points up-valley, that is, towards higher ground, because the contour line has to bend upstream to stay at the same elevation as it crosses the valley sides. The stream flows out through the open end of the V, towards lower ground. So if the V apex points south, the ground rises to the south and the stream flows north, not south.
How to check it on this sheet:
- Follow the stream from its source to the causeway and read the spot heights. If the causeway lies at the lower end of the stream's course, the water flows towards the causeway.
- A contour V is a statement about slope, not about flow direction on its own; the two must agree. Where they seem not to, the reading of the V is usually the error.
Practical rider: the causeway symbol is itself information. A causeway is a low, unbridged crossing, liable to be submerged in high water. Any alignment that meets the stream at such a point needs a flood-level check, and Alignment 1, which crosses the stream twice, has two such structures to maintain.
3. Choose an alignment, apply the stated cost rule, and state one assumption on which your choice depends.
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Apply the rule (cost = length in cm + 1.5 x number of stream crossings, in the same arbitrary unit):
- Alignment 1: 6.4 + 1.5 x 2 = 9.4 units
- Alignment 2: 8.2 + 1.5 x 1 = 9.7 units
The cost rule narrowly favours Alignment 1 - by about 3%. That is within the error of measurement on a paper map, so it does not decide the matter.
Recommendation: Alignment 2.
- 3% of notional cost is trivial against the maintenance bill for two stream crossings and a 1 in 38 grade; a rule that prices a crossing at only 1.5 times a unit of length almost certainly undervalues it.
- Running along a spur crest gives natural drainage on both sides and avoids the cut-and-fill that a slope traverse demands.
- Three contour crossings instead of six means a smoother profile, better for the vehicles and for the road's life.
- Longer, gentler alignments also keep the road above flood level for more of its length.
Assumption: that the surveyed settlement areas do not conceal a steep bluff or a built-up obstruction on the Alignment 2 spur. This should be checked on the ground, because contours are omitted inside the settlement.