# Plane Table Surveying: Methods & Techniques Explained
Hello there! Are you curious about the different methods used in plane table surveying? You've come to the right place! In this article, we will explore the various techniques employed in plane table surveying, providing you with a clear, detailed, and correct understanding of each method.
## Correct Answer
**The primary methods of plane table surveying are Radiation, Intersection, Resection, and Traversing.**
## Detailed Explanation
Plane table surveying is a graphical method of surveying in which field observations and plotting are done simultaneously. It's a relatively quick and less costly method, suitable for small to medium-sized surveys where high precision is not required. The equipment mainly consists of a plane table mounted on a tripod, an alidade (either plain or telescopic), a plumbing fork, a trough compass, and other accessories like drawing sheets, pencils, erasers, etc. Let's dive deeper into the methods:
### What is Plane Table Surveying?
Before we get into the methods, let’s understand what plane table surveying actually involves. Imagine you're creating a map of an area while you're *actually in* that area. That’s the basic idea! You set up a drawing board (the plane table) on a tripod, and using a sighting device (the alidade), you draw lines directly onto a sheet of paper attached to the table. This method is especially useful in areas where detailed maps are needed quickly and where extreme accuracy isn't essential. Think of it like sketching a landscape painting directly from observation, rather than taking a photo and drawing from it later.
### Advantages of Plane Table Surveying
* **Graphical Method:** It's a graphical method, meaning the map is drawn in the field itself, reducing the chances of errors and omissions.
* **Suitability:** Ideal for areas where detail is important, such as mapping of rivers, forests, and irregular terrains.
* **Less Costly:** Requires less equipment compared to other surveying methods.
* **Immediate Results:** The surveyor can check the accuracy of the work on the spot.
### Disadvantages of Plane Table Surveying
* **Not Suitable for All Weather:** Cannot be done during rain or extreme weather conditions.
* **Cumbersome Equipment:** The plane table and accessories can be bulky and difficult to transport.
* **Lower Accuracy:** Less precise compared to theodolite surveying.
* **Limited in Dense Vegetation:** Obstructions can hinder visibility and plotting.
Now, let’s explore the four main methods in detail:
1. **Radiation Method**
2. **Intersection Method**
3. **Resection Method**
4. **Traversing Method**
### 1. Radiation Method
The ***radiation method*** is one of the simplest techniques in plane table surveying. Think of it like drawing spokes radiating from the center of a wheel. In this method, a single point is set up as the *instrument station*, and rays are drawn to various points in the field from this station. The distances to these points are then measured, and the points are plotted along the respective rays at a suitable scale.
Imagine you're standing in the middle of a field and you want to map out the trees around you. You place your plane table in the center, and then use the alidade to draw lines (rays) towards each tree. You then measure the distance to each tree and mark that distance along the corresponding line on your paper. This method is best suited for surveying small areas with points that are directly visible from a single setup.
#### Steps Involved in the Radiation Method
1. **Setup the Plane Table:** Set up the plane table at a convenient location (*the instrument station*) from where all the points to be surveyed are visible.
2. **Orient the Table:** Orient the table so that the plotted direction on the sheet is parallel to the corresponding direction on the ground. Orientation can be done by compass or by back-sighting.
3. **Establish the Initial Point:** Mark the location of the instrument station on the drawing sheet. This point will serve as the origin for all measurements.
4. **Sight and Draw Rays:** Using the alidade, sight each point to be surveyed and draw a corresponding ray on the drawing sheet from the instrument station.
5. **Measure Distances:** Measure the distances from the instrument station to each sighted point using a measuring tape or other distance measuring equipment.
6. **Plot the Points:** Plot the measured distances along the corresponding rays on the drawing sheet, using a suitable scale.
7. **Connect the Points:** Connect the plotted points to complete the survey.
#### Advantages of the Radiation Method
* **Simple and Straightforward:** Easy to understand and implement.
* **Suitable for Small Areas:** Ideal for surveying small areas with clear visibility.
* **Quick:** Can be relatively quick for small surveys.
#### Disadvantages of the Radiation Method
* **Limited Application:** Only suitable when all points are visible from a single station.
* **Not Suitable for Large Areas:** Inefficient for large or complex areas.
* **Accuracy Dependent on Distance Measurements:** Accuracy decreases with increasing distances.
### 2. Intersection Method
The ***intersection method***, also known as the graphical triangulation method, is used to locate the position of a point by sighting it from two known stations. Think of it as two people pointing at the same object from different locations; where their lines of sight intersect is where the object is located. In this method, the plane table is set up at two different stations, and rays are drawn towards the point to be located from both stations. The point is then located at the intersection of the two rays.
Imagine you want to map the location of a tree that's too far to reach easily. You set up your plane table at one point and draw a line towards the tree. Then, you move to another point, set up your table again, and draw another line towards the tree. The point where these two lines cross on your paper represents the tree's location. This method is especially useful for locating inaccessible points or points at a considerable distance.
#### Steps Involved in the Intersection Method
1. **Select Two Stations:** Choose two stations (A and B) from which the point to be located (C) is visible. The distance between A and B should be known or measurable.
2. **Set Up at the First Station (A):** Set up the plane table at station A and orient it. Mark station A on the drawing sheet.
3. **Sight and Draw Ray from A:** Using the alidade, sight the point C and draw a ray from station A towards C on the drawing sheet.
4. **Set Up at the Second Station (B):** Move the plane table to station B and orient it. Mark station B on the drawing sheet based on the measured distance and direction from station A.
5. **Sight and Draw Ray from B:** Using the alidade, sight the point C and draw a ray from station B towards C on the drawing sheet.
6. **Locate the Point (C):** The point C is located at the intersection of the two rays drawn from stations A and B.
#### Advantages of the Intersection Method
* **Locating Inaccessible Points:** Useful for locating points that cannot be directly measured or accessed.
* **Long Distances:** Suitable for locating points at considerable distances.
* **No Distance Measurement to the Point:** Only the distance between the two stations needs to be measured accurately.
#### Disadvantages of the Intersection Method
* **Requires Two Setups:** Needs setups at two different stations, increasing the time and effort.
* **Accuracy Dependent on Intersection Angle:** Accuracy decreases if the angle of intersection is too acute or too obtuse.
* **Not Suitable for Dense Areas:** Can be difficult in areas with many obstructions.
### 3. Resection Method
The ***resection method*** is used to determine the location of the plane table station itself by sighting known points. This is like knowing where you are by looking at landmarks on a map. In this method, the plane table is set up at an unknown station, and rays are drawn towards at least three known points (points whose locations are already plotted on the drawing sheet). The intersection of these rays, after applying certain corrections, determines the location of the plane table station on the drawing sheet.
Imagine you're lost in a park and you have a map with some key landmarks marked on it. You set up your plane table and, using the alidade, draw lines towards those landmarks. By carefully adjusting your table and drawing lines that intersect correctly, you can figure out exactly where you are on the map. This method is particularly useful when you need to establish a new survey station and you know the locations of some surrounding points.
There are several methods to perform resection, including:
* **Two-Point Problem:** Requires sightings to two known points.
* **Three-Point Problem:** Requires sightings to three known points. This is the most common method.
#### Steps Involved in the Three-Point Problem (Resection)
1. **Set Up at the Unknown Station (P):** Set up the plane table at the unknown station P. This station's location is to be determined.
2. **Orient by Estimation:** Roughly orient the table by compass or by estimation. This initial orientation is crucial for the next steps.
3. **Sight the First Known Point (A):** Sight one of the three known points (A) and draw a ray back along the direction of A. The plotted location of A on the sheet is *a*.
4. **Sight the Second Known Point (B):** Sight another known point (B) and draw a ray back along the direction of B. The plotted location of B on the sheet is *b*.
5. **Sight the Third Known Point (C):** Sight the third known point (C) and draw a ray back along the direction of C. The plotted location of C on the sheet is *c*.
6. **The Triangle of Error:** The three rays will usually not intersect at a single point, forming a small triangle called the *triangle of error*. The correct location of the instrument station will be within or near this triangle.
7. **Adjust and Repeat:** Adjust the orientation of the table and repeat the process of sighting and drawing rays until the triangle of error is reduced to a negligible size, or the three rays intersect at a single point. Various graphical solutions (like Bessel's method or Lehmann's rules) can be used to find the exact location.
#### Lehmann’s Rules for Adjusting Orientation (Resection):
Lehmann's rules provide guidelines for determining the approximate location of the plane table station within the triangle of error and adjusting the table's orientation accordingly. These rules are based on the relative positions of the known points and the triangle of error.
* **Rule 1:** If the station sought (P) lies outside the triangle formed by the three known points (A, B, C), the plane table station is on the side of the rays from the two farthest points.
* **Rule 2:** If the station sought (P) lies inside the triangle formed by the three known points (A, B, C), the plane table station is on the side of the ray from the middle point.
* **Rule 3:** If the station sought (P) lies on the great circle through any two points, the plane table station is on the opposite side of the ray from the third point.
By applying these rules, a surveyor can systematically refine the orientation of the plane table until the triangle of error converges to a point, representing the true location of the instrument station.
#### Advantages of the Resection Method
* **Self-Location:** Allows determining the station's location using known points.
* **Useful in Difficult Terrain:** Suitable for areas where direct measurements are difficult.
* **Flexibility:** Can be used to establish new stations quickly.
#### Disadvantages of the Resection Method
* **Complex Procedure:** Requires careful orientation and adjustments.
* **Triangle of Error:** The presence of the triangle of error can complicate the process.
* **Requires Known Points:** Depends on the availability of accurately plotted known points.
### 4. Traversing Method
The ***traversing method*** is used to survey a series of connected lines or a route. Think of it as walking a path and mapping it as you go. In this method, a series of connected lines (a traverse) is established, and the plane table is set up at each station along the traverse. At each station, the directions of the next station and other details are plotted. This method is similar to compass traversing but with the advantage of graphical plotting in the field.
Imagine you're mapping a hiking trail through a forest. You set up your plane table at the starting point and draw a line towards the next point along the trail. You then move to that point, set up your table again, and draw a line towards the following point. By continuing this process, you can create a map of the entire trail. This method is ideal for surveying long, narrow areas like roads, rivers, or pipelines.
#### Steps Involved in the Traversing Method
1. **Establish the Traverse Stations:** Select a series of connected stations along the route to be surveyed.
2. **Set Up at the First Station:** Set up the plane table at the first station and orient it. Mark the station on the drawing sheet.
3. **Sight and Draw to the Next Station:** Using the alidade, sight the next station in the traverse and draw a ray on the drawing sheet.
4. **Measure the Distance:** Measure the distance to the next station using a measuring tape or other equipment.
5. **Plot the Next Station:** Plot the next station on the drawing sheet based on the measured distance and direction.
6. **Move to the Next Station:** Move the plane table to the next station and orient it, often by back-sighting the previous station.
7. **Repeat:** Repeat steps 3-6 until the entire traverse is surveyed.
#### Advantages of the Traversing Method
* **Suitable for Long, Narrow Areas:** Ideal for surveying roads, rivers, and pipelines.
* **Flexibility:** Can follow any route, making it versatile for various terrains.
* **Progressive Plotting:** The map is created progressively as the survey advances.
#### Disadvantages of the Traversing Method
* **Cumulative Errors:** Errors can accumulate along the traverse, reducing overall accuracy.
* **Requires Multiple Setups:** Needs setups at each station, which can be time-consuming.
* **Checking Accuracy:** Closing errors need to be checked and adjusted to maintain accuracy.
### ### Key Concepts
* ***Alidade:*** A sighting device used to draw lines of sight.
* ***Orientation:*** Setting the plane table so that the lines on the drawing sheet are parallel to the corresponding lines on the ground.
* ***Instrument Station:*** The location where the plane table is set up.
* ***Rays:*** Lines drawn on the drawing sheet representing lines of sight.
* ***Triangle of Error:*** A small triangle formed by the intersection of rays in the resection method, indicating the need for adjustments.
* ***Back-Sighting:*** Sighting a previously surveyed point to orient the plane table.
## Key Takeaways
* Plane table surveying is a graphical method where field observations and plotting are done simultaneously.
* The main methods are Radiation, Intersection, Resection, and Traversing.
* The Radiation method is simple and suitable for small areas with clear visibility.
* The Intersection method is used to locate points by sighting them from two known stations.
* The Resection method determines the station's location by sighting known points.
* The Traversing method is used to survey a series of connected lines or a route.
I hope this detailed explanation has given you a comprehensive understanding of the different methods used in plane table surveying. Happy surveying!
