Plane table surveying can be performed using one of several methods, which include radiation, traversing, intersection, and resection. The choice of method depends on factors such as the visibility between stations, the feasibility of making necessary measurements, and the availability of data required to accurately locate the instrument station. At each survey station, in addition to drawing rays that assist in determining future points, nearby details are often fixed through the radiation method.
To help visualize the process, capital letters like A, B, and C are used to represent ground points, while lowercase letters such as a, b, and c denote their corresponding plotted positions on the drawing sheet.
Before diving into the details of each method, it is important to understand a few key terms used in plane table surveying:
Fore Sight: A fore sight refers to the ray drawn from the instrument station towards the sighted station. This line is based on the plotted location of the instrument station and extends towards the station being observed.
Back Sight: A back sight involves aligning the alidade along a previously plotted line between the current instrument station and another known station. The table is rotated until the line of sight bisects the known station, which establishes the back sight for the survey.
Resector: A resector is used when a known station is sighted, and a line is drawn through its plotted location towards the instrument station. This helps in positioning the instrument station accurately in the survey.
(i). Radiation Method
The Radiation Method in plane table surveying is used to plot detail points by radiating lines from a single instrument station. This method is particularly suitable for surveying small areas where all necessary points can be observed from a central location. Though rarely used for complete surveys, it is often combined with other methods, such as traversing, to efficiently plot details close to the instrument station.
Principle of the Radiation Method
The Principle of the Radiation Method is based on geometrical similarity, where the positions of various ground stations are plotted using proportional relationships between the distances measured on the ground and the corresponding distances drawn on the plan.
Let’s consider a situation where A is the instrument station, and B, C, and D are other ground stations that need to be plotted. From the position a on the drawing (corresponding to station A), rays are drawn towards stations B, C, and D, resulting in lines ab, ac, and ad. The ground distances AB, AC, and AD are then reduced to a uniform ratio, denoted by K, which is the scale of the survey.
This relationship can be expressed as:
AB/ab = AC/ac = AD/ad = K
This proportionality ensures that the triangles formed by points A, B, and C on the ground and their corresponding points a, b, and c on the map are geometrically similar. Since the triangles ABC and abc are similar, the following relationship holds:
Thus, the line bc on the drawing is a scaled version of the line BC on the ground, and this principle ensures that all plotted points maintain their correct relative positions and distances according to the chosen scale.
Procedure of the Radiation Method
To carry out the radiation method, follow these steps:
Setting up the Plane Table:
Set up the plane table at a suitable, commanding station, ensuring it is accurately centered and leveled.Plotting the Instrument Station:
Choose a position for the station on the drawing paper (denoted as point A) in a convenient location that aligns with the layout of the area being surveyed.Transferring the Station Point:
Using a plumbing U-fork, transfer the station point from the drawing paper to the ground to allow for future setups at the same location.Drawing the Magnetic North:
Clamp the table securely and use a magnetic compass to draw the north-south direction on the drawing sheet.Sighting Detail Points:
Place the alidade at the plotted location of the instrument station (point a) and pivot it to sight other points in the area (such as B, C, D, etc.). Draw rays along the alidade’s fiducial edge toward each of these points.Measuring and Plotting Distances:
Measure the ground distances to each point by direct chaining and plot these distances to scale on the corresponding rays. If the ground is sloped, apply slope corrections and plot the equivalent horizontal distances.Finishing the Plan:
Conventional symbols are drawn for various details, and the drawing is inked for clarity and permanence.
Application and scope of the Radiation Method
This method is highly efficient when all points of interest are visible and accessible from the instrument station. In practice, the method is most effective for surveying small areas, particularly when creating large-scale plans. For increased precision over longer distances, a tacheometer can be used to measure distances instead of direct chaining.
While the radiation method is rarely used for full-scale projects, it is valuable for plotting nearby details and is often combined with traversing to map areas within the length of a survey chain from the instrument station.
(ii). Intersection Method (Graphic Triangulation)
The Intersection Method in plane table surveying is a graphical technique used to determine the location of detail points by intersecting rays drawn from two known stations. This method is particularly useful in situations where direct linear measurements are impractical due to large distances, inaccessible locations, or uneven terrain. It is commonly referred to as Graphic Triangulation because it relies on the geometric principle of constructing triangles to locate points.
Principle of the Intersection Method
Let A and B represent two ground points that are a known distance apart. Their positions are plotted as a and b on the plane table. The plane table is first set up at station A and oriented by aligning the alidade along the line ab and sighting toward B. Once the table is oriented, a ray is drawn from a toward the unknown point C. The table is then moved to station B, centered over the ground mark, and reoriented by sighting back toward A. A second ray is drawn from b toward C, intersecting the first ray. The intersection of these two rays gives the location c of the point C on the drawing, using the same scale as that used for plotting AB.
In the triangles abc (on the plane table) and ABC (on the ground):
- ∠ bac = ∠ BAC (by construction)
- ∠ abc = ∠ ABC (by construction)
Thus, the remaining angles are also equal, making the two triangles abc and ABC similar. As a result, the sides of the triangles are proportional:
where k is a constant of proportionality (the scale factor). Therefore:
- ab = k × AB
- ac = k × AC
- bc = k × BC
This demonstrates that the sides AC and BC of the triangle ABC have been reduced in the same proportion as AB, ensuring that the point C is accurately plotted on the plane table at the same scale as the base line AB.
Procedure of the Intersection Method
To apply the intersection method in the field, follow these steps:
Selection of Stations:
Select two stations, A and B, that are intervisible and accessible. Measure the distance AB directly, or use known coordinates if available.Plotting the Base Line:
Plot the base line AB on the plane table at the desired scale, keeping the overall layout of the area in mind.Set Up at Station A:
Set up the plane table at station A, centering it over the ground point and ensuring that the line ab is aligned with the actual ground line AB.Sighting and Drawing Rays:
Using the alidade, sight station B and draw the line ab. Then, sight the required detail points (such as point C) and draw a ray from a toward C.Shift to Station B:
Move the plane table to station B and set it up again, centering the table. Orient the table by aligning the alidade along line ba and sighting back to A.Drawing Rays from B:
From station B, sight the same detail points (e.g., C) and draw corresponding rays from b. The intersection of the rays from A and B gives the location of point C.
Suitability and Applications of the Intersection Method
The intersection method is suitable for surveying large or inaccessible areas, where direct measurements are either impossible or impractical due to uneven terrain or obstacles. It is often used for plotting broken boundaries, as well as for mapping mountainous regions.
This method is especially useful when distance measurements between points are too large or difficult to measure. The method’s accuracy relies on the proper alignment and intersection of rays from multiple points, which can be improved by using more than two intersecting rays. For accurate results, the angles formed by the intersecting rays should ideally be between 30° and 120° to ensure well-conditioned triangles.
The Intersection Method is widely used in large-scale surveys, including by the Survey of India, due to its ability to map extensive areas with minimal error accumulation, limited only to the scale of the base line plotting.
(iii). Traversing Method
The Traversing Method is a technique used in plane table surveying, similar to compass and theodolite traversing. In this method, the plane table is set up at each successive station, and a foresight is taken to the next station. The distance between stations is either measured directly or obtained through intersecting rays. Traversing is particularly useful for surveying elongated areas, such as roads, railways, or forested regions where large open views are scarce.
Principle of the Traversing Method
The principle of traversing is similar to that of the radiation method, with the key difference being that in the radiation method, observations are made to all surrounding points near the station, while in the traversing method, observations are limited to subsequent stations where the surveyor will set up the plane table. The plane table traverse is typically carried out in a closed circuit or originates and closes on known or resected points.
Procedure of the Traversing Method
To perform a plane table traverse, follow these steps:
Reconnaissance:
Survey the area to select a sufficient number of stations, ensuring they are far enough apart, visible to one another, and practical for measuring distances between them.Setting up at Station A:
Set up the plane table over the starting station A and transfer its ground location to the drawing sheet using a U-fork.Orientation of the Table:
Orient the plane table so that the general layout of the area is covered. This can be done approximately by visual estimation.Draw Magnetic North:
Mark the magnetic north on the drawing sheet using a compass.Sighting the Next Station:
With the alidade placed at the plotted point a (the assumed location of A), sight the next station B. Draw a ray toward B along the edge of the alidade.Measure Distance AB:
Measure the distance AB accurately in the field, then plot the corresponding distance ab on the drawing sheet using the chosen scale.Shift to Station B:
Move the plane table to station B and set it up so that the ray ab passes vertically above the ground point B.Reorient the Table:
Place the alidade along the ray ba and rotate the table until station A is sighted again. Clamp the table in this position.Plotting the Next Station (C):
Pivot the alidade at b, sight the next station C, and draw a ray toward it. Measure the distance BC and plot the corresponding distance bc on the drawing sheet.Repeat the Process:
Continue setting up the plane table at subsequent stations, orienting the table at each station by sighting back to the previous station and plotting the new station on the sheet. Repeat this process until all stations are traversed.
Suitability of the Traversing Method
The Traversing Method is particularly well-suited for surveying narrow strips of land, such as roads, railways, or areas with limited visibility, such as forested regions. It is also useful when surveying magnetically disturbed areas, where other plane table methods, like radiation or intersection, may be impractical. The traversing method works best for large-scale surveys because longer rays are required for orientation. It may not be suitable for small-scale plotting, where shorter distances are hard to represent accurately on the drawing sheet.
For areas where direct line-of-sight between stations is interrupted or where measurements over long distances are impractical, the Traversing Method provides a reliable alternative for mapping such terrain. Plane table traversing can also be suitably employed for surveying an area magnetically disturbed.
(iv). Resection Method
The Resection Method in plane table surveying involves determining the location of the station occupied by the plane table by drawing rays from stations whose positions are already plotted on the sheet. This method is also called the Interpolation Method or Fixing Method because it involves interpolating the position of the occupied station using already known locations.
The resection process works by drawing rays from two or more known points to the station whose location needs to be determined. When the orientation of the table is correct, these rays will intersect at a point, marking the position of the unknown station. Since precise orientation is difficult to achieve using only a magnetic compass, various methods are used to ensure accurate orientation. These methods include:
- Back Ray Method
- Three Points Method
- Two Points Method
- Box Compass Method
1. Back Ray Method
In the Back Ray Method, the table is oriented by laying the alidade along a line drawn from the previously known station. The location of the unknown occupied station is then found by drawing a ray from another known station on the sheet, ensuring the rays intersect at a favorable angle.
Procedure of Back Ray Method
Set up at Station B:
Assume two ground stations A and B with their positions a and b already plotted on the sheet. Set up the plane table over station B. Place the alidade along ba and rotate the table until station A is sighted, then clamp the table.Sight and Draw Ray to Station C:
Pivot the alidade at b and sight station C. Draw a ray from b towards C, extending the ray beyond the alidade.Move to Station C:
Shift the table to station C and set it up. Ensure the plane table is centered and leveled over the ground point.Reorient the Table at Station C:
Place the alidade along cb and rotate the table until station B is sighted, ensuring the line bc is vertically aligned with ground point C.Draw Ray from Station C to A:
Pivot the alidade at c and sight station A. Draw a ray towards A that intersects the previously drawn ray from B. The intersection point provides the required location of station C.
Suitability of Back Ray Method
The Back Ray Method is particularly useful when a prominent landmark, such as a temple spire or chimney, is available in the center of the surveyed area. After setting up the plane table at each subsequent station, the location of the station can be determined by drawing rays from the known points. This method is also suitable for large-scale surveys where long rays can be used. The accuracy of the survey largely depends on how well the table is initially oriented.
Precautions of Back Ray Method
To ensure accuracy while using the Back Ray Method, the following precautions should be taken:
Accurate Centering:
The actual plotted position of the station on the sheet must be centered over the corresponding ground station, not just the center of the table. Even a minor centering error, such as 30 cm, can introduce a significant orientation error, particularly in shorter rays.Careful Selection of Stations:
The forward station should be clearly marked with a wooden peg before drawing the forward ray. Similarly, the back station should be marked by transferring its position vertically below the plotted location using a U-fork before leaving the station.Marking Forward Ray on Both Edges:
The forward ray should be drawn using both edges of the alidade to ensure more precise orientation of the table at the next station.Consistent Use of Alidade Edge:
Always use the same side of the alidade for drawing rays to maintain consistency in measurements and avoid errors.
2. Three Point Method of Resection
The Three Point Method is used in plane table surveying to determine the location of the occupied station on the sheet by sighting three known points (stations). The three points should already be plotted on the sheet, and the table is oriented by ensuring the rays drawn from these points intersect at a common point. This method is practical for finding the location of the table without visiting the reference points.
Following are the methods to Achieve Orientation by Three Point Method of Resection:
(i) Mechanical (or Tracing Paper) Method.(Only this is explained here)
(ii) Graphical Method.
(iii) Trial and Error Method or Lehmann’s Method.
Mechanical (or Tracing Paper) Method
This method is employed to determine the location of the instrument station using a piece of tracing paper, making it suitable for detail surveying but not for establishing control points.
Let A, B, and C be three known ground stations whose locations on the sheet are represented by a, b, and c, respectively. The station P is the unknown location of the plane table, which is represented by p on the sheet.
Procedure of Mechanical Method:
Set Up the Plane Table:
- Place the plane table over the station P, which is the location to be determined. The table is roughly oriented using a magnetic compass or by eye judgment.
Fix the Tracing Paper:
- Attach a piece of tracing paper large enough to cover the plotted locations of A, B, C, and P on the sheet.
- Mark a temporary point p′ on the tracing paper to represent the unknown station P.
Sight and Draw Rays:
- Using the alidade, pivot around p′ and sight the known points A, B, and C one by one.
- Draw rays from p′ to A, B, and C, labeling them as p′A, p′B, and p′C on the tracing paper.
Adjust the Tracing Paper:
- Remove the tracing paper from the table and shift it on the sheet so that the lines p′A, p′B, and p′C pass through the known plotted points a, b, and c on the sheet.
Transfer the Location:
- Prick through the point p′ on the tracing paper to transfer the location of P onto the sheet as p, which is the determined position of the station.
Orientation of the Table:
- Align the alidade along the longest ray, typically pa (assuming A is the farthest point).
- Rotate the plane table until the ground station A is sighted.
Verification:
- Pivot the alidade about the locations b and c and draw rays from stations B and C. These rays should pass through the point p. This step verifies the accuracy of the orientation of the table.
Note:
- The precision of this method depends on the accuracy with which the rays are drawn from the assumed position p′ on the tracing paper.
- The method is effective for detail points but is not suitable for establishing control points due to the potential for minor errors.
3. Two Point Problem
The Two Point Problem involves determining the location of the plane table’s station by sighting to two well-defined points, whose locations have already been plotted on the sheet.
Consider two known ground points A and B, with their locations represented on the sheet as a and b. The task is to determine the location of the unknown station C, which will be represented as c on the sheet
Procedure of Two Point Problem
Select an Auxiliary Point:
- Choose an auxiliary point D on the ground so that CD (the distance from C to D) is approximately parallel and roughly equal to AB by eye judgment.
Initial Orientation:
- Set up the plane table over the point C and roughly orient it so that the plotted points a and b are parallel to their corresponding ground points A and B.
- Clamp the table in position.
Plot the Point C (1st Position):
- Using the alidade, pivot about a and sight towards A, then pivot about b and sight towards B. Draw rays from a and b, and their intersection gives the first approximation of the location c.
- Transfer this approximate point c to the ground using a U-fork and fix a wooden peg at the point.
Sight the Auxiliary Point D:
- Pivot the alidade about c and sight the auxiliary station D, drawing a ray from c towards D.
Shift to Station D (2nd Position):
- Move the table to station D and accurately orient it using the back ray method. Ensure that the ray cd passes vertically over the ground point D.
- Once the table is oriented, pivot the alidade about a and b and draw resectors (rays back towards A and B). These resectors should intersect along the line drawn from C.
Adjust for Orientation:
- If the resectors do not intersect correctly, pivot the alidade at the point of intersection of the rays drawn from C to A. Sight station B and draw a ray to cut the line cb at b′ (an adjusted location for b).
Fix a Point on the Line of Sight:
- Align the alidade along the line ab′ and choose a distant point E on the line of sight.
- Now, align the alidade along ab and rotate the table until point E is again sighted. Clamp the table in position.
Plot the Correct Location of C:
- Pivot the alidade about a and b again, drawing resectors to intersect at d.
- Pivot about d and draw a ray towards C.
Shift Back to Station C (3rd Position):
- Move the table back to station C and orient it using the back ray method.
- Pivot the alidade about a and b again and draw rays from these points. The intersection of the rays from D will give the accurate location of station C.
Suitability of Two Point Problem
- The accuracy of this method depends on the proper selection of the auxiliary station D, which should be on a line approximately parallel to AB, and CD should be roughly equal to AB.
- Although this method can be useful, it requires setting up the table at two different stations, which can make it time-consuming and less efficient. Therefore, it is not always the most reliable method for high-precision work.
4. Orientation by Compass Method
This method involves orienting the plane table using a magnetic compass, allowing the user to determine the location of a new station by sighting two known points, without needing to rely solely on sighting or triangulation.
Procedure for Orientation by Compass Method
Select a Base Line:
- Choose a base line AB, and measure it accurately.
- Plot points a and b on the sheet in a convenient location.
Set Up the Table at Station A:
- Set up the plane table at station A, and ensure that the location a on the sheet is centered directly over the ground mark at A.
- Level the table properly.
Orient the Table Using the Alidade:
- Place the alidade along the plotted line ab.
- Rotate the table until station B is sighted through the alidade.
- Once B is sighted, clamp the table in position.
Align the Magnetic Compass:
- Place the magnetic compass on the table, and rotate the compass until the magnetic needle points along the north-south axis.
- Draw a line along the longer side of the compass to represent the magnetic north-south direction.
Move to Station C:
- Shift the plane table to the next station C, and level the table as before.
Use the Compass to Orient the Table:
- Place the compass in the same marked position on the table.
- Rotate the table until the magnetic needle rests in the north-south direction (matching the line drawn at station A).
- Clamp the table once it is correctly oriented.
Plot the New Station C:
- Pivot the alidade about points a and b and draw resectors (rays) to intersect at c.
- The point c is the required location of the new station C.
Suitability of Compass Method
- This method is useful in areas that are free from magnetic disturbances (such as areas without large metal objects or electrical interference).
- It is also best suited for surveys conducted on a relatively small scale, as large-scale surveys may introduce greater errors due to compass inaccuracy.
- For accurate results, the magnetic compass should be in perfect working order, free from external magnetic influences.
