Which of the following scales may NOT give accurate measurements of a plan drawn on a paper, due to shrinkage after few years?
📝 Detailed Explanation: The Problem of Paper Shrinkage
Paper, as a material, is dimensionally unstable. Over time, it is affected by environmental factors like changes in temperature and humidity, which cause it to shrink or expand. This physical change poses a significant problem for the accuracy of maps and plans.
Understanding the Types of Scales
- Representative Fraction (R.F.): This is a numerical ratio (e.g., 1:100 or 1/100) that expresses the relationship between a distance on the map and the corresponding distance on the ground. It is unitless. For example, R.F. 1:100 means 1 cm on the map represents 100 cm (or 1 meter) on the ground.
- Engineer's Scale: This is also a numerical scale, but it is expressed in terms of different units (e.g., 1 cm = 10 m). It is essentially another way of stating the R.F.
- Graphical Scale: This is a line or bar drawn directly on the map and subdivided into units (like meters or kilometers) that are proportional to the map's scale.
Why Numerical Scales Fail with Shrinkage
When the paper shrinks, all the drawn features on it, including lines, boundaries, and symbols, become smaller. However, the numerical scales (R.F. and Engineer's scale) do not change because they are just text or ratios written on the map.
If you use a standard ruler to measure a distance on the shrunken map and then use the original R.F. (e.g., 1:100) to calculate the ground distance, your result will be incorrect. The measured map distance will be smaller than it should be, leading to an underestimation of the actual ground distance.
Why the Graphical Scale Remains Accurate
The graphical scale is the solution to this problem. Because it is a physical line drawn on the map, it shrinks and expands at the same rate as the rest of the map.
When you take a measurement from the shrunken map (perhaps using dividers) and compare it directly to the shrunken graphical scale, the ratio remains correct. The measurement tool and the map have been altered proportionally, canceling out the error caused by shrinkage. This is why a graphical scale should always be included on any official map or plan.
💡 Key Concepts for Students
- Dimensional Stability: Be aware that physical media like paper are not perfectly stable. Professional practice must account for potential material distortion over time.
- Numerical vs. Graphical: Understand the fundamental difference. Numerical scales (R.F., Engineer's scale) are abstract ratios, while a graphical scale is a physical representation that lives with the map.
- Preserving Accuracy: The primary reason for including a graphical scale on a drawing is to ensure that accurate measurements can be taken from it, regardless of paper shrinkage or distortion from copying.