The maximum error (mm) on the drawing should not be greater than ______
Maximum Permissible Error Formula
To ensure field errors do not exceed the plotting accuracy, surveyors use the following check. The error on the drawing (E), derived from a potential error on the ground, must not be greater than 0.25 mm.
[ (l sinθ) / S ] ≤ 0.025 cm
E ≤ 0.25 mm
Where:
- l = Length of the line/offset being measured on the ground.
- θ = Angular error in laying out the direction.
- S = Denominator of the map's scale (e.g., for a scale of 1:1000, S = 1000).
📝 Detailed Explanation: Plotting Accuracy
This question deals with the concept of plotting accuracy, which is the limit of how precisely a point or line can be physically drawn and distinguished on a map or plan. It's a fundamental principle in cartography and technical drawing.
The Standard Limit: 0.25 mm
The widely accepted standard for the smallest accurately plottable distance is 0.25 mm. This value is based on the resolving power of the average human eye.
- Any detail smaller than 0.25 mm is difficult for a person to distinguish clearly without magnification.
- A point plotted with a fine pencil tip will have a diameter of roughly this size.
- Attempting to plot details with an error smaller than this is impractical, as the graphical error (the thickness of the lines themselves) would mask the detail.
⚙️ Practical Implications for Surveying
This 0.25 mm limit has a direct impact on how surveys are conducted and what scale is chosen for a map.
Choosing a Scale
The scale of the map must be chosen so that the smallest feature to be shown on the ground can be represented by at least 0.25 mm on the map. For example, if the smallest object to be surveyed is 1 meter wide, the scale must be large enough to make 1 meter on the ground at least 0.25 mm on the drawing.
Field Measurement Precision
The accuracy of the fieldwork must be consistent with the plotting accuracy. The total error from field measurements, when translated to the map's scale, should not exceed the 0.25 mm plotting limit.