Monday, June 24, 2013

Plane Table Surveying

In this method of surveying a table top, similar to drawing board fitted on to a tripod is the main instrument. A drawing sheet is fixed on to the table top, the observations are made to the objects, distances are scaled down and the objects are plotted in the field itself. Since the plotting is made in the field itself, there is no chance of omitting any necessary measurement in this surveying. However the accuracy achieved in this type of surveying is less. Hence this type of surveying is used for filling up details between the survey stations previously fixed by other methods.
In this chapter, accessories required, working operations and methods of plane table surveying are explained. At the end advantages and limitations of this method are listed.

 Plane Table and its Accessories

The most commonly used plane table is shown in Fig. 14.1. It consists of a well seasoned wooden table top mounted on a tripod. The table top can rotate about vertical axis freely. Whenever necessary table can be clamped in the desired orientation. The table can be levelled by adjusting tripod legs.
The following accessories are required to carry out plane table survey:
1. Alidade
2. Plumbing fork with plumb bob.
3. Spirit level
4. Trough compass
5. Drawing sheets and accessories for drawing.






Alidade

It is a straight edge ruler having some form of sighting device. One edge of the ruler is bevelled and is graduated. Always this edge is used for drawing line of sight. Depending on the type of line of sight
there are two types of alidade:
(a) Plain alidade (b) Telescopic alidade
Plain Alidade: Figure 14.2 shows a typical plain adidate. A sight vane is provided at each end of the ruler. The vane with narrow slit serves as eye vane and the other with wide slit and having a thin wire at its centre serves as object vane. The two vanes are provided with hinges at the ends of ruler so that when not in use they can be folded on the ruler. Plain alidade is not suitable in surveying hilly areas as the inclination of line of sight in this case is limited.





 Telescopic Alidade: It consists of a telescope mounted on a column fixed to the ruler [Fig. 14.3].
The line of sight through the telescope is kept parallel to the bevelled edge of the ruler. The telescope is provided with a level tube and vertical graduation arc. If horizontal sight is required bubble in the level tube is kept at the centre. If inclined sights are required vertical graduation helps in noting the inclination of the line of sight. By providing telescope the range and the accuracy of line of sight is increased.

Plumbing Fork and Plumb Bob
Figure 14.4 shows a typical plumbing fork with a plum bob. Plumbing fork is a U-shaped metal frame with a upper horizontal arm and a lower inclined arm. The upper arm is provided with a pointer at the end while the lower arm is provided with a hook to suspend plumb bob. When the plumbing fork is kept on the plane table the vertical line (line of plumb bob) passes through the pointed edge of upper arm. The plumb bob helps in transferring the ground point to the drawing sheet and vice versa also.

Spirit Level
A flat based spirit level is used to level the plane table during surveying (Fig. 14.5). To get perfect level, spirit level should show central position for bubble tube when checked with its positions in any two mutually perpendicular direction.

Trough Compass
It consists of a 80 to 150 mm long and 30 mm wide box carrying a freely suspended needle at its centre (Ref. Fig. 14.6). At the ends of the needle graduations are marked on the box to indicate zero to five degrees on either side of the centre. The box is provided with glass top to prevent oscillation of the needle by wind. When needle is centred (reading 0–0), the line of needle is parallel to the edge of the box. Hence marking on the edges in this state indicates magnetic north–south direction.

Drawing Sheet and Accessories for Drawing
A good quality, seasoned drawing sheet should be used for plane table surveying. The drawing sheet may be rolled when not in use, but should never is folded. For important works fibre glass sheets or paper backed with thin aluminium sheets are used.
Clips clamps, adhesive tapes may be used for fixing drawing sheet to the plane table. Sharp hard pencil, good quality eraser, pencil cutter and sand paper to keep pencil point sharp are other accessories required for the drawing work. If necessary, plastic sheet should be carried to cover the drawing sheet from rain and dust.

 Working Operation

After fixing the table top to the stand and drawing sheet to the table, the following operations are to be
carried out before map making:
1. Centering
2. Levelling
3. Orientation.
14.2.1 Centering
Centering is the process of setting the plane table on the point so that its plotted position is exactly over the position on the ground. This is achieved by moving the legs of the tripod and checking the position of the point on the ground and on the paper with the help of plumbing fork and plumb bob.
14.2.2 Levelling
The level of the plane table should be ensured in two positions of spirit level which are at right angles to each other. The legs of tripod are moved radially or along the circumference to adjust the plane table and get levelled surface.
14.2.3 Orientation
Orientation is the process of setting plane table over a station such that all the lines already plotted are parallel to corresponding lines on the ground. Accuracy of plane table survey mainly depends upon the
accuracy of orientation of plane table at each station point. It can be achieved by any one of the following methods:
(a) using trough compass
(b) by back sighting
(c) by solving two point or three point problems.
The first two methods are commonly used while the third method is used occationally. The third method is explained under the article methods of plane tabling by resection.
(a) Orientation Using Trough Compass: When the survey work starts, the plane table is set on first station and the table is oriented by rough judgement such that the plotted position of the area falls in the middle portion of the paper. Then the table is clamped and the north direction is marked on right hand side top corner of drawing sheet. Trough compass is used to identify north direction. This orientation is to be maintained at all subsequent stations. After centering and levelling the table trough compass is kept along the marked north direction and the table is rotated to get freely suspended magnetic needle centred. After achieving it the table is clamped.
This method of orientation is considered rough, since the local attraction to magnetic needle affects the orientation. This method is used as preliminary orientation and finer tuning is
made by observing the already plotted points.
(b) Orientation by Back Sighting: It is the commonly used method in plane table surveying.
After completing surveying from plane table set at A, if table is to be shifted to next station B, a line is drawn from the plotted position of station A towards station B. Then distance AB is measured, scaled down and plotted position of station B is obtained. Then table is shifted to station B, centred, levelled. Then keeping alidade along BA, station A is sighted and the table is clamped. Thus the orientation of the table is achieved by back sighting. Orientation may be checked by observing already plotted objects.

 METHOD OF PLANE TABLING



The following four methods are available for carrying out plane table survey:
1. Radiation
2. Intersection
3. Traversing
4. Resection.
The first two methods are employed for locating details while the other two methods are used for locating position of plane table station on drawing sheet.
14.3.1 Radiation
After setting the plane table on a station, say O, it is required to find the plotted position of various objects A, B, C, D ….. . To get these positions, the rays OA, OB, OC ….. are drawn with soft pencil (Ref. Fig. 14.7). Then the distances OA, OB, OC ….., are measured scaled down and the positions of A, B, C ….., are found on the drawing sheets.
This method is suitable for surveying small areas and is convenient if the distances to be measured are small. For larger areas this method has wider scope, if telescopic alidade is used, in which the distances are measured technometrically.

Intersection
In this method the plotted position of an object is obtained by plotting rays to the object from two stations. The intersection gives the plotted position. Thus it needs the linear measurements only between the station points and do not need the measurements to the objects. Figure 14.8 shows the method for locating objects A and B from plane table positions O1 and O2.

This method is commonly employed for locating:
(a) details
(b) the distant and inaccessible points
(c) the stations which may be used latter.
14.3.3 Traversing
This is the method used for locating plane table survey stations. In this method, ray is drawn to next station before shifting the table and distance between the stations measured. The distance is scaled down and next station is located. After setting the plane table at new station orientation is achieved by back sighting. To ensure additional checks, rays are taken to other stations also, whenever it is possible. Figure 14.9 shows a scheme of plane table survey of closed area. This method can be used for open traverses also.

Resection
This method is just opposite to the method of intersection. In the method of intersection, the plotted position of stations are known and the plotted position of objects are obtained by intersection. In this method the plotted position of objects are known and the plotted position of station is obtained. If a, b and c are the plotted positions of objects A, B and C respectively, to locate instrument station P on the paper, the orientation of table is achieved with the help of a, b, c and then resectors Aa, Bb, Cc are drawn to get the ‘p’ , the plotted position of P. Hence in the resection method major work is to ensure suitable orientation by any one of the methods. The following methods are employed in the method of resection:

(a) by compass
(b) by back sighting
(c) by solving two point problem
(d) by solving three point problem.
(a) Resection after Orientation by Compass: Let a and b be the plotted positions of A and B of two well defined points in the field. Keeping the through compass along north direction marked on the drawing sheet table is oriented on station P, the position of which is to be found on paper. The resectors Aa and Bb [Fig. 14.10] are drawn to locate ‘p’ the plotted position of station point P. This method gives satisfactory results, if the area is not influenced by local attractions. It is used for small scale mapping only.
(b) Resection after Orientation by Back Sighting: Figure 14.11 shows the scheme of resection after orientation by back sighting. From station A, the position of B is plotted as ‘b’ and ray has been taken to station P as ap′. Then plane table is set at P and oriented by back sighting A, line AP is not measured but the position of P is obtained on the paper by taking resection Bb.

(c) Resection after Solving Two Point Problem: The problem of finding plotted position of the station point occupied by the plane table with the help of plotted positions of two well defined points is known as solving two point problem. Figure 14.12 shows the scheme of solving this.

Let A and B be two well defined points like lightening conductor or spire of church, the plotted positions a and b already known. Now the problem is to orient the table at P so that by resection its plotted position p can be obtained. The following steps may be followed to solve this problems:
(i) Select a suitable point Q near P such that the angles PAQ and PBQ are not accute.
(ii) Roughly orient the table at Q and draw the resectors Aa and Bb to get the point ‘q’.
(iii) Draw the ray qp and locate p1 with estimated distance QP.
(iv) Shift the plane table to P and orient the table by back sighting to Q.
(v) Draw the resector Aa to get ‘p’.
(vi) Draw the ray pB. Let it intersect line bq at b1.
(vii) The points b and b1 are not coinciding due to the angular error in the orientation of table. The angle bab, is the angular error in orientation. To correct it,
* Fix a ranging rod at R along ab, * Unclamp the table and rotate it till line ab sights ranging rod at R. Then clamp the table. This gives the correct orientation of the table which was used in plotting the points A and B. (viii) The resectors Aa and Bb are drawn to get the correct plotted position ‘p’ of the station P.
(d) Resection after Solving Three Point Problem: Locating the plotted position of a station point using observations to three well defined points whose plotted positions are known, is called solving three point problem.
Let A, B, C be three well defined objects on the field whose plotted positions a, b and c are known. Now the problem is to locate plotted position of the station point P. Any one of the following methods can be used.
(i) Mechanical (Tracing paper) method,
(ii) Graphical method, or
(iii) Trial and error method (Lehman’s method).
(i) Mechanical Method: This method is known as tracing paper method since it needs a tracing paper. The method involved the following steps [Ref. Fig. 14.13.]
* Set the table over station P and by observation approximately orient the table.
* Fix the tracing paper on the plane table and select P approximately, say as p′. From p′, draw p′ A, p′ B and p′ C. These lines may not pass through the plotted positions a, b and c since the orientation is not exact.
* Loosen the tracing paper and rotate it so that the rays pass through respective points a, b and c. Now prick the point p′ to get the plotted position ‘p’ of the station P.
* Keep the alidade along pa and sight A. Then clamp the table. This is correct orientation.
Check the orientation by observing along pb and pc.
(ii) Graphical Method: The following two graphical methods are available to solve three point problem:
* Bessel’s solution
* Method of perpendiculars.
Bessels Solution: It involves the following steps:
1. Keep the bevelled edge of alidade along ba and sight object at A. Clamp the table and draw
bc′ along the line bc [Fig. 14.14 (a)].
2. Keep bevelled edge of alidade along ab, unclamp the table and sight B. Clamp the table.
Draw line ac intersecting bc′ at d [Fig. 14.14(b)].
3. Keep the alidade along dc and bisect C. Clamp the table [Fig. 14.14(c)]. This gives the
correct orientation.
4. Draw resectors to get ‘p’.
Method of Perpendiculars
This is another graphical method. It involves the following steps [Ref. Fig. 14.15].
1. Draw line ae perpendicular to ab. Keep alidade along ea and turn the table till A is sighted. Clamp the table and draw the ray Bb to intersect the ray Aac at e [Fig. 14.15(a)].
2. Draw cf perpendicular to bc and clamp the table when fcC are in a line. Draw Bb to intersect
Ccf at F [Fig. 14.15(b)].

3. Join cf drop bp perpendicular to ef to get the plotted position ‘p’.
4. Orient the table such that pbB are in a line. Clamp the table to place it in correct orientation.
Resections Aa and Cc may be used to check the orientation.
Trial and Error Method
This method is also known as ‘triangle of error method’ and ‘Lehman’s Method’. It involves the following steps:
1. Set the table over point P and orient the table approximately, just by observation.
2. Draw the rays aA, bB and cC [Fig. 14.16]. If the orientation was perfect, the three rays would have intersected at a single point, i.e. at point ‘p’. Otherwise a triangle of error is formed.
3. To eliminate the triangle of error an approximate position, ray p′, is selected near the triangle
of error. Then keeping alidade along p′a object A is sighted and the table is clamped. Draw the resectors cC and bB to check the orientation.
4. Above step is repeated till triangle of error is eliminated.

Lehman presented the following guidelines to select ‘p′’ so that triangle of error is eliminated quickly.
Rule 1: The distance of point sought ‘p’ is in the same proportion from the corresponding rays as the distance of those from the plane table station.
Rule 2: The point sought ‘p’ is on the same side of all the three resectors.
Defining the triangle ABC on the field as great triangle and the circle passing through them as great circle, from the above two rules of Lehman, the following sub-rules may be drawn [Ref. Fig. 14.17].

* If ‘P’ lies within the great triangle, the point ‘p’ is within the triangle of error (p1 in the Fig. 14.17).
* If the plane table station P lies outside the great triangle the point sought ‘p’ is outside the triangle of errors (p2).
* If the ‘P’ is on the great circle, the correct solution is impossible (p3 and p4).
* If ‘P’ is outside the great circle, ‘p’ is nearer to the intersection of rays to the nearest two points (P5).
* If point P is outside the great circle and the two rays drawn are parallel to each other the point sought is outside the parallel lines and on the same side of the three rays (P6).

ERRORS IN PLANE TABLE SURVEYING

The errors may be grouped into the instrumental and personal errors.

 
Instrumental Errors

1. The surface of plane table not perfectly plane.
2. Bevelled edge of alidade not straight.
3. Sight vanes of alidade not perfectly perpendicular to the base.
4. Plane table clamp being loose.
5. Magnetic compass being sluggish.
6. Drawing sheet being of poor quality.
Personal Errors
1. Centering errors
2. Levelling errors
3. Orientation errors
4. Sighting errors
5. Errors in measurement
6. Plotting errors
7. Errors due to instability of tripod.

ADVANTAGE AND LIMITATIONS OF PLANE TABLE SURVEY 

Advantages are

1. Possibility of omitting measurement is eliminated.
2. The surveyor can compare the plotted work in the field then and there only.
3. Irregular objects are plotted more accurately, since they are seen while plotting.
4. Booking errors are eliminated.
5. Local attractions do not influence the plotting.
6. No great skill is required to produce satisfactory maps.
7. Method is fast.
8. No costly instruments are required.

Limitations are
1. Survey cannot be conducted in wet weather and rainy days.
2. Plane table is cumbersome and heavy to carry.
3. It needs many accessories.
4. It is less accurate.
5. Reproduction of map to different scale is difficult.

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