Correct Length Calculation from Wrong Scale Measurements

When measurements are taken using a scale different from the intended or original scale, it's essential to correct these measurements to determine the true correct length of the line. This situation often arises in surveying and drafting when a map or drawing might have an effective scale that deviates from its nominal or labeled scale, or when a measuring instrument with an incorrect scale is used.

Understanding Representative Fraction (RF)

• The Representative Fraction (RF) is a way to express the scale of a map or drawing. It is the ratio of a distance on the map to the corresponding actual distance on the ground. For example, an RF of 1/1000 means 1 unit on the map represents 1000 units on the ground. A smaller denominator indicates a larger scale (e.g., 1/50 is a larger scale than 1/100).
• The RF of wrong scale refers to the representative fraction of the scale that was actually used to measure the length, or the effective scale of the drawing if it has undergone changes like shrinkage or expansion.
• The RF of correct scale refers to the representative fraction of the scale that the drawing or map should ideally be, or the true scale to which the original drawing was intended.

Formula for True Correct Length

To find the true correct length of a line when it has been measured using a wrong scale, the following formula is applied:

\(\rm correct \ length = \frac{RF\ of\ wrong\ scale}{RF\ of\ correct \ scale} \times Measured \ length\)

Explanation of Formula Components

• \(\rm correct \ length\): This is the actual or adjusted length of the line that accounts for the error introduced by using the wrong scale. It represents what the length should truly be under the correct scale conditions.
• \(\rm RF\ of\ wrong\ scale\): This is the representative fraction of the scale that was used for taking the measurement.
• \(\rm RF\ of\ correct\ scale\): This is the representative fraction of the scale that should have been used, or the true scale of the map/drawing.
• \(\rm Measured\ length\): This is the length observed or read directly from the measurement using the wrong scale.

This formula acts as a correction factor. It adjusts the raw measured length based on the ratio of the RFs of the wrong and correct scales, thereby yielding the accurate length that corresponds to the true or intended scale of the drawing or line.