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Surveying is the science of determining the relative positions of points on or near the Earth's surface. Among various surveying techniques, Plane Table Surveying stands out for its simplicity and directness. It is a graphical method where the surveyor plots the map simultaneously while measuring the field, enabling real-time map creation.
Imagine you want to draw a map of a small park. Instead of taking measurements and then returning to the office to plot the map, plane table surveying allows you to set up a drawing board right in the field and plot points as you measure them. This immediate visualization helps in quick decision-making and reduces errors.
In civil engineering, plane table surveying is especially useful for small to medium-sized areas where detailed maps are required quickly, such as construction sites, road alignments, and property boundaries.
Before diving into the methods, it is crucial to understand the equipment involved and how to set it up correctly for accurate surveying.
To begin surveying, the plane table must be set up properly:
Correct setup is essential to ensure that the plotted points correspond accurately to their real-world locations.
The Radiation Method is the simplest and most commonly used method in plane table surveying. It involves plotting points by drawing rays from a single station point to various survey points.
Here's the basic idea: You set up the plane table at a station point, orient it correctly, and then sight the alidade towards each point you want to plot. You measure the distance to that point on the ground and then mark the corresponding distance along the ray on your drawing sheet.
Why use the radiation method? Because it is fast and efficient when the area is small and all points are visible from a single station. It reduces the need to move the plane table frequently.
The Intersection Method is used when points to be plotted are not visible from a single station or when higher accuracy is needed. It involves taking sightings from two or more known stations and plotting rays from these stations. The point where these rays intersect on the drawing sheet is the location of the unknown point.
This method is particularly useful in dense areas where direct sighting from one station is impossible or obstructed.
The Traversing Method involves setting up the plane table at a series of stations connected by straight lines called traverse lines. At each station, the table is oriented, and points are plotted by radiation or intersection. This method is ideal for surveying long, narrow areas such as roads, canals, or boundaries.
Traversing requires careful marking of station points on the ground and accurate orientation at each station to maintain the continuity and accuracy of the survey.
Let's summarize the typical steps followed in a plane table survey:
Orientation is the process of aligning the plane table so that the directions on the drawing sheet correspond to the actual directions on the ground. Two common methods are:
Back sight method is preferred for higher accuracy as it directly relates to known points.
Once oriented, points are plotted by:
Repeating this for all points ensures a complete and accurate map.
Plane table surveying is widely used in:
Its accuracy depends on proper setup, orientation, and careful plotting. Common sources of error include:
Corrections involve re-leveling, re-orienting, and double-checking measurements.
| Feature | Plane Table Surveying | Chain Surveying | Theodolite Surveying |
|---|---|---|---|
| Field Plotting | Direct plotting in field | Measurements recorded, plotting done later | Measurements recorded, plotting done later |
| Equipment Complexity | Simple | Very simple | Complex and precise |
| Accuracy | Moderate | Low to moderate | High |
| Area Size | Small to medium | Small | Any size |
Points plotted on the plane table map are represented in a coordinate system, usually Cartesian (x, y), where the origin is at a reference station. Coordinates help in calculating distances and angles between points.
The scale relates distances on the map to actual ground distances. For example, a scale of 1:1000 means 1 cm on the map equals 10 meters on the ground.
A plane table is set up at station P. The surveyor measures the following distances and bearings to points A, B, and C:
Using a scale of 1:1000 (1 cm = 10 m), plot the points A, B, and C on the plane table map.
Step 1: Convert ground distances to map distances using the scale.
Step 2: Draw a vertical north line on the drawing sheet representing north at station P.
Step 3: From station P, draw rays at the given bearings (30°, 90°, 150°) measured clockwise from north.
Step 4: Mark points A, B, and C along their respective rays at distances of 5 cm, 7 cm, and 6 cm from P.
Answer: Points A, B, and C are plotted on the map at the correct scaled distances and bearings from station P.
Two plane table stations P and Q are 100 m apart. From station P, the surveyor sights point X at an angle of 45° from the line PQ. From station Q, point X is sighted at 60° from line QP. Using a scale of 1:1000, find the coordinates of point X relative to station P.
Step 1: Set station P at origin (0,0) and station Q at (100,0) on the map (since PQ = 100 m, scaled to 10 cm).
Step 2: From P, draw a ray at 45° to the line PQ (positive x-axis).
Step 3: From Q, draw a ray at 60° to the line QP (which points left, so the angle is 180° - 60° = 120° from positive x-axis).
Step 4: Find the intersection of the two rays.
Equation of ray from P (origin): \( y = x \) (since 45°)
Equation of ray from Q (10 cm, 0): slope = \(\tan 120^\circ = -\sqrt{3}\)
Equation: \( y = -\sqrt{3}(x - 10) \)
Step 5: Solve for intersection:
\( x = y \)
\( y = -\sqrt{3}(x - 10) \)
Substitute \( y = x \):
\( x = -\sqrt{3}(x - 10) \)
\( x = -\sqrt{3}x + 10\sqrt{3} \)
\( x + \sqrt{3}x = 10\sqrt{3} \)
\( x(1 + \sqrt{3}) = 10\sqrt{3} \)
\( x = \frac{10\sqrt{3}}{1 + \sqrt{3}} \approx \frac{10 \times 1.732}{1 + 1.732} = \frac{17.32}{2.732} \approx 6.34 \text{ cm} \)
\( y = x = 6.34 \text{ cm} \)
Step 6: Convert back to ground distance:
\( x = 6.34 \times 10 = 63.4 \text{ m}, \quad y = 63.4 \text{ m} \)
Answer: Point X is located at (63.4 m, 63.4 m) relative to station P.
A plane table traverse survey is conducted with stations A, B, and C. The distance AB is 80 m and BC is 60 m. The bearing of AB is 0° (north), and the angle at B between AB and BC is 90°. Using a scale of 1:1000, plot the traverse and find the coordinates of station C relative to A.
Step 1: Plot station A at origin (0,0).
Step 2: Draw line AB vertically upwards (north) with length 8 cm (80 m scaled).
Step 3: Station B is at (0, 80 m).
Step 4: At B, draw a 90° angle to AB. Since AB is north, BC will be towards east.
Step 5: Plot BC as 6 cm (60 m scaled) towards east from B.
Step 6: Coordinates of C relative to A:
Answer: Station C is located at (60 m, 80 m) relative to station A.
During a plane table survey, the table was not properly oriented at station P, causing a 5° error in all plotted bearings. If the distance to point A from P is 40 m, estimate the maximum positional error on the map due to this orientation error. Use a scale of 1:1000.
Step 1: The positional error \( e \) due to angular error \( \Delta \theta \) at distance \( d \) is approximately:
\[ e = d \times \sin(\Delta \theta) \]
Step 2: Calculate \( e \):
\( d = 40 \text{ m}, \quad \Delta \theta = 5^\circ \)
\( e = 40 \times \sin 5^\circ = 40 \times 0.0872 = 3.49 \text{ m} \)
Step 3: Convert to map distance:
\( e_{map} = \frac{3.49}{10} = 0.349 \text{ cm} \)
Answer: The maximum positional error on the map is approximately 0.35 cm.
You need to survey a rectangular plot measuring 120 m by 80 m. If your drawing sheet size allows a maximum length of 24 cm, determine a suitable scale for the plane table map and calculate the map length corresponding to the 80 m side.
Step 1: Determine scale based on the longer side (120 m) fitting into 24 cm.
\[ \text{Scale} = \frac{\text{Map length}}{\text{Ground length}} = \frac{24 \text{ cm}}{120 \text{ m}} \]
Convert 120 m to cm: 120 m = 12,000 cm
\[ \text{Scale} = \frac{24}{12000} = \frac{1}{500} \]
Step 2: Calculate map length for 80 m side:
\( 80 \text{ m} = 8000 \text{ cm} \)
\[ \text{Map length} = \text{Scale} \times \text{Ground length} = \frac{1}{500} \times 8000 = 16 \text{ cm} \]
Answer: Use a scale of 1:500. The 80 m side will be plotted as 16 cm on the map.
When to use: At the start of each station setup to ensure accurate plotting.
When to use: When surveying small plots or when quick mapping is required.
When to use: During multi-station surveys to maintain continuity and accuracy.
When to use: When measuring angles between points to improve precision.
When to use: Every time the plane table is set up to maintain accuracy.
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