Understanding Horizontal Equivalent and Contour Interval in Surveying

This question asks us to evaluate four statements related to fundamental concepts in surveying and map interpretation: horizontal equivalent and contour interval. Let's break down each statement to determine its correctness.

Analyzing Statement i: Horizontal equivalent between two contour lines is always constant.

The horizontal equivalent is the horizontal distance between two consecutive contour lines on a map. It represents the horizontal distance covered for a change in elevation equal to the contour interval. This distance is directly related to the slope of the ground. If the ground is steep, the contour lines will be close together, resulting in a small horizontal equivalent. If the ground is gentle, the contour lines will be far apart, resulting in a large horizontal equivalent. Therefore, the horizontal equivalent is not constant; it varies with the slope.

Statement i is incorrect.

Analyzing Statement ii: Horizontal equivalent may be zero for a vertical cliff.

A vertical cliff is a feature where the ground rises or falls vertically. When contour lines are drawn for a vertical cliff, they would theoretically coincide or overlap completely on the map because there is no horizontal distance covered for the change in elevation. In such a case, the horizontal distance between consecutive contour lines on the map is zero. Hence, the horizontal equivalent for a vertical cliff is zero.

Statement ii is correct.

Analyzing Statement iii: Contour interval should be inversely proportional to the scale.

The contour interval is the constant vertical distance between any two successive contour lines. It represents the difference in elevation between these lines. The choice of contour interval depends largely on the scale of the map, the purpose of the survey, and the nature of the terrain. For maps with a larger scale (which show more detail over a smaller area, like 1:100 or 1:500), a smaller contour interval (e.g., 0.5 m or 1 m) is typically used to depict minor variations in elevation accurately. For maps with a smaller scale (which show less detail over a larger area, like 1:50,000 or 1:100,000), a larger contour interval (e.g., 10 m or 20 m) is used. This relationship shows that as the scale increases (denominator decreases), the contour interval decreases, and vice versa. This is an inverse relationship.

Statement iii is correct because for a larger scale map (smaller denominator), a smaller contour interval is needed, and for a smaller scale map (larger denominator), a larger contour interval is used.

Analyzing Statement iv: For detailed design work, large contour interval is taken.

Detailed design work, such as designing roads, buildings, or drainage systems, requires precise information about the ground's elevation. A large contour interval means that the map shows elevation changes only at larger vertical increments (e.g., every 5 meters or 10 meters). This level of detail is insufficient for intricate design work where even small changes in slope and elevation are critical. For detailed design work, a small contour interval (e.g., 0.25 m, 0.5 m, or 1 m) is necessary to provide a fine resolution of the terrain's shape and elevations.

Statement iv is incorrect.

Conclusion

Based on the analysis of each statement, statements ii and iii are correct.

Therefore, the correct option includes statements ii and iii.

Revision Table: Key Surveying Terms

Additional Information: Factors Affecting Contour Interval Selection

The selection of the appropriate contour interval for a topographic map is a crucial decision in surveying and mapping. Several factors influence this choice:

• Scale of the Map: As discussed, a larger map scale generally requires a smaller contour interval to show sufficient detail. A smaller map scale requires a larger contour interval to avoid overcrowding of contour lines.
• Nature of the Terrain: In flat or gently sloping areas, a small contour interval is needed to depict subtle changes in elevation. In hilly or mountainous terrain with steep slopes, a larger contour interval might be used to prevent contour lines from merging, though key details in flatter areas would still need appropriate representation.
• Purpose of the Survey/Map: The intended use of the map is a primary factor. For detailed engineering design, site planning, or quantity estimation, a small contour interval is essential. For general planning, reconnaissance surveys, or small-scale regional maps, a larger contour interval is acceptable.
• Available Time and Funds: Conducting a survey for a smaller contour interval requires more field work and data processing, which increases time and cost.
• Clarity and Readability: The contour interval should be chosen such that the contour lines are not too close (causing clutter and illegibility) or too far apart (missing important terrain features).

Understanding the relationship between these factors and the contour interval, as well as the concept of horizontal equivalent, is key to correctly interpreting and using topographic maps in surveying and engineering.