Top 4 Methods of Surveying with the Plane Table |Plane Table Surveying |Surveying

Methods of surveying with the plane table may be classified under four distinct heads viz: 1. Radiation 2. Intersection 3. Traversing 4. Resection.

Method # 1. Radiation (Fig. 6.5.):

In this method, the plane table is set up at only one station and the points to be plotted are located by radiating rays from the instrument-station to the points and plotting to scale the respective distances along the rays.

This method is suitable for the survey of small areas which can be commanded from a single station. This is rarely used for making a complete survey hut is useful in combination with other methods for surveying- detail within a tape length from the station.

Procedure:

(i) Select a point P such Unit all the points to be located are visible from it.

(ii) Set up and level the table at P and clamp it.

(iii) Select a point p on the sheet and make it vertically above P on the ground by the use of U-frame. The point p thus represents on the sheet the station P on the ground.

(iv) Mark the direction of the magnetic meridian with the trough compass in the top comer of the sheet.

(v) With the alidade touching p, sight the various points A, B, C, etc. to be located and draw radial lines towards them along the fiducially edge of the alidade.

(vi) Measure the radial distance PA, PB, PC etc. with tape or by stadia wires (if the alidade is telescopic).

(vii) Plot the distances to scale along the corresponding rays. Join the points a, b, c, etc. on the sheet.

Method # 2. Intersection (Fig. 6.6.):

In this method, the positions of the points are fixed on the sheet by the intersection of the rays drawn from two instrument-stations. The line joining these stations is termed as base line. The only linear measurement required in the method is that of the base line.

This method is largely employed for locating detail and for locating the points to be used subsequently as instrument stations. This may also be used for plotting the distant and inaccessible objects, the broken boundaries of the river etc. It is much suitable for surveying hilly country where it is difficult to measure the horizontal distances.

Procedure:

(i) Select two point A and B so that all points to be plotted are visible from both of them and no triangle formed by joining any point to be located and the end points of the base line is bad conditioned.

(ii) Set up and level the plane table at station A and mark a suitable point a on the paper so that it is vertically above the instrument station A on the ground.

(iii) Mark the direction of the magnetic meridian on the top corner of the sheet by means of a trough compass.

(iv) With the alidade centered on the point a, sight the station B and other points 1, 2, 3 etc. to be plotted and draw rays towards them. Mark the respective lines by letters b and 1, 2, 3 etc. to avoid confusion.

(v) Measure the base line AB accurately with a steel tape and cut off AB to scale along the ray drawn from a to B, thus fixing the position b on the sheet of the station B on the ground.

(vi) Shift the instrument and set it up and level at B, so that the point b is exactly above the point B on the ground.

(vii) Orient the table by placing the alidade along ba, tuning the table until the line of sight strikes A, and then clamp it.

(viii) With the alidade pivoted on b, draw rays sighting towards the same objects. The intersections of these rays with the respective rays from a determine the positions of the objects 1, 2, 3 etc. on the sheet.

Alternative Method:

After selecting the suitable base line, measure it accurately and plot it on the sheet before setting up the table over A. Then level and centre the table over A so that the plotted line ab lies above the base line AB on the ground. This may be done by placing the alidade along ab and sighting towards B. Then proceed as explained above.

Method # 3. Traversing (Fig. 6.7.):

This is the main method of plane tabling and is similar to that of compass or theodolite traversing. It is used for running survey lines of a closed or open traverse. The detail may be located by offsets taken in the usual manner or by the radiation or by intersection method of plane-tabling.

Procedure:

(i) Select the traverse stations A, B, C etc.

(ii) Set up the table over one of them say A. Select the point a suitably on the sheet. Level and centre the table over A.

(iii) Mark the direction of the magnetic meridian on the top corner to the sheet by means of the trough compass.

(iv) With the alidade touching a, sight B and draw the ray.

(v) Measure the distance AB and scale off ab, thus fixing the position of b on the sheet, which represents the station B on the ground.

(vi) Locate the nearby details by offsets taken in the usual manner or by radiation and the distant objects by intersection.

(vii) Shift the table and set it up at B, with b over B and orient it by placing the alidade along ba, turning the table until the line of sight strikes A ,and then clamp it.

(viii) With the alidade touching b sight C and draw a ray.

(ix) Measure the line BC and cut off be to scale.

(x) Locate the surrounding detail as before.

(xi) Proceed similarly at other stations, in each case orienting by an each sight before taking the forward sight until all the remaining stations are plotted.

Check:

(i) Intermediate checks should be taken whenever possible. Thus if A is visible from C, the work done up to C can be checked thereby sighting A with the alidade against c and noting if the edge touches a. Similarly other check lines DB, EC etc. can be used to check the work.

(ii) When no other Stations visible from the station occupied, some well-defined object such as a corner of a building, which has been previously fixed on the sheet can be used to check the work.

If the traverse is a closed one, the work can be checked by plotting the starting point say (A) from the last station say (E) of the traverse and finding the closing error, the closing error if any can be adjusted graphically as in compass traversing.

Plane Table and Compass Traversing:

Plane table traversing becomes similar to compass traversing if each orientation is performed only by compass. This is less accurate than back sight orientation particularly if the area to be surveyed is affected by local attraction.

Since the compass errors tend to compensate, however, the method is useful for surveying long narrow strips, and proves rapid when the plane table is set up at alternate stations only. A traverse plane table (a table with a trough compass recessed in (to the board) is sometimes used for such work.

Method # 4 Resection:

This method is used for locating the station points only. The characteristic feature of resection is that the point plotted on the sheet is the station occupied by the table. After stations are fixed, the surrounding detail is located by radiation or intersection?

There are several cases of resection, the simplest one being described below (Fig. 6.8).

As in intersection, this method requires only one linear measurement.

Procedure:

(i) Select a base line AB on the ground. Measure it accurately and plot ab in a convenient position.

(ii) Set up and level the table at B so that b lies vertically above B and orient the table by placing the alidade along ab and turning the table until A is bisected and then clamp it.

(iii) With the alidade touching b, sight the station C which is to be plotted by resection, and draw a ray.

(iv) Estimate the distance BC by judgement only and mark the point c along the ray to represent the approximate position of C.

(v) Shift the table and set it up with c cover C. Orient the table by taking back sight on B and clamp it.

(vi) With the alidade pivoted on a, sight the station A and draw a ray. The point of interaction of this ray and that previously drawn from b gives the required point c, the true position of C.

(vii) Similarly locate other stations if required.

Errors of centering are inevitable in this method but since it is used only for small scale work, the accuracy is not much affected.

The method described above is known as back-ray method as it necessitates a ray drawn from a preceding station to that being occupied, and therefore requires the previous selection of the instrument-station. This is only a particular case of resection.

The more usual cases where no ray has already been drawn to the instrument station are:

1. Two-point problem,

2. Three point problem.

Of these the second is more important

Two-Point Problem:

The two-point problem consists in establishing the position of the instrument -station on the plan by making sights towards two well-defined objects, which are visible from the instrument-station and whose positions have already been plotted on the plan.

In fig. 6.9. A and B are the two well-defined objects; a and b their plotted positions on the plan: C the instrument station and c is its required position on the plan.

Solution:

The of the problem consists in making the correct orientation of the instruments i.e., placing ab exactly to AB, when instruments is set up at C, and then finding c on the plan. For this,

(i) Select a suitable auxiliary point P(a fourth point) so that he angles CAP and CBP are not too small for good intersections at A and B.

(ii) Set up and level the table at P. Orient the table approximately by compass or by placing ab parallel to AB by judgement and clamp it.

(iii) With the alidade centered on a, sight A and draw a ray through a, Similarly with the alidade touching b, sight and draw a ray through b, the two rays intersecting each other p₁, which is the approximate position of the auxiliary station P as the orientation made at P is only approximates.

(iv) With the alidade pivoted on p₁, sight c and draw a ray estimate the distance PC by judgement and cut off p₁C₁ to scale equal to the estimated distance PC, c₁ being the approximate position of C.

(v) Shift the table and set it up and level at C with c₁ over C. Orient the table by placing the alidade along c₁p₁ and turning it until P is bisected. Then clamp the table.

(vi) With the alidade against a, sight A, and draw a ray through a intersecting the line p₁c₁ in c₂. With the alidade centered on c₂, sight B and draw a ray through c₂. This ray will pass through b, provided the initial orientation at P was correct. But since the orientation at P as well as at C was only approximate, the ray will not pass through b.

Let the point of intersection of the rays c₂B and p₁b be b₁ which represents B. Thus ap₁, c₂ b₁ represents APCB. But since ab is the true representation of AB and ab₁ is the desired position of AB on the plan, the error of orientation is the angle between ab and ab. This error can be eliminated by rotating the table through this angle.

To do this: 

a. Place the alidade along ab₁ and fix a ranging rod R at a great distance from the table in the line ab₁ produced.

b. Then place the alidade along ab and turn the table until the ranging rod R is bisected. Clamp the table, ab is thus made parallel to AB and the orientation is correct.

c. To find the true position of C place the alidade against a, sight A and draw a ray through a. Similarly with the alidade touching b sight B and draw the ray through b. The point of intersection (c) of these two rays on the plan is the true representation of the station-point (C) on the ground.

Three-Point Problem:

The three-point problem consists in establishing the position of the instrument-station on the plan by making sights towards three well-defined objects, which are visible from the instrument station and whose positions have already been plotted on the plan.

Suppose A, B and C are three well-defined objects; a b and c their plotted positions on the plan; P is the instrument station and p is its required position on the plan.

Solution:

The solution of the problem consists in making the correct orientation of the instrument i.e., placing ab parallel to AB and bc parallel to BC when the instrument is set up at P, and then finding p on the plan.

The problem may be solved:

1. By Mechanical Method.

2. By Graphical Method.

3. By Trial and Error Method.

1. Mechanical Method. (Fig. 6. 10, a and b):

It is also known as tracing paper method.

(i) Set up the table at P and orient it as nearly in its proper position as possible by compass or by placing ab and be respectively parallel to AB and BC by judgement and clamp it.

(ii) Stretch a sheet of tracing paper over the plane table sheet and select a point p₁ on the tracing paper to represent approximately the station P. (Fig. 6.10 a).

(iii) With the alidade pivoted on p₁ sight A, B and C successively and draw rays towards them.

(iv) Then unfasten the tracing paper and move it over the plane table sheet until the three rays simultaneously pass through a, b and c. Then prick through the point p₁ on the sheet with a fine needle point. The point so obtained is the required point p (fig. 6.10 b).

(v) Remove the tracing paper, unclamp the table and orient it by placing the alidade along pa and turning the board until A is bisected. As a check, sight the points B and C with the alidade centered on b and c respectively, and draw the rays. These rays should pass through p if the work is correct. If not a small triangle of error is formed which can be eliminated by the trial and error method.

2. Graphical Method:

Of the several graphical methods, Bessel’s method of inscribed quadrilateral is the simplest and is commonly used.

Bessel’s Method:

(i) (Fig 6.11a). Set up and level the instrument at P. Place the alidade along the line ca and turn the table until A is sighted, such that a is towards A. Clamp the table. With the alidade touching c, sight B and draw a ray cB.

(ii) (Fig. 6.11, b). Unclamp the table. Place the alidade along ac and turn the table until C is bisected such that c is towards C and then clamp the table. With the alidade centered on a, sight B and draw a ray aB, intersecting the previously drawn ray cB in the point d.

(iii) (Fig. 6.11, c). With the alidade along db, turn the table until B is sighted, and then clamp it. The table is now in correct orientation and p must be lie on bd and also on Aa and Cc.

(iv) With the alidade pivoted on a, sight A and draw a ray through a intersecting the ray bd in p. which represents the instrument station P.

(v) As a check, centre the alidade on c and bisect C and draw a ray through c. The ray Cc should now pass through p, if the work is correct.

Note:

In the first two steps, instead of sighting through a and c and drawing rays towards B, any two of the points may be used and the rays drawn towards the signal corresponding to the third, which is then sighted in the third step.

3. Trial and Error Method:

It is also known as triangle of error method. In this method, the position of the station-point on the sheet is found by trial. It is quick and accurate method.

Set up and level the instrument and orient it as nearly possible by compass or by judgement. Within the alidade touching a, b and c, sight A, B and C respectively and draw rays Aa, Bb and Cc. As the table is not correctly oriented, these rays will not pass through one point, but will form a small triangle known as triangle of error.

By repeated trials, this triangle is eliminated so that the three rays Aa, Bb and Cc pass through one point, which is the required point (p). The position of this point can be estimated from the triangle of error by the application of Lehmann’s Rules.

The triangle formed by joining the ground points A, B and C is called the great triangle, while the circle passing through these pointy is known as the great circle.

Lehmann’s Rules:

(i) The distance of the point p from each of the rays Aa, Bb and Cc is in proportion to the distance of A, B and C from P respectively.

(ii) When looking in the direction of each of the distant points A, B and C, the point p will be found on the same side of the three rays Aa, Bb and Cc i.e., it is either to the left or to the right of each of the three rays. (Figs. 6.12, 6.13 and 6.14).

(iii) It follows from the above two rules that if the instrument station P lies outside the great triangle ABC, the triangle of error falls outside abc and the required point p is outside the triangle of error (fig 6.13 and 6.14).

Similarly if the station P lies within the great triangle ABC, the triangle of error falls inside the triangle abc and the point p must within the triangle of error (Fig. 6.12).

Although the above rules suffice for the solution of the problem, yet two more rules are given for assistance;-

(iv) When the station-point P is outside the great circle, the point p is always on the same side of the ray drawn to the most distant point as the intersection (e) of other two rays (Fig. (6.13).

(v) When the station-point P is outside the great triangle ABC, but inside the great circle i.e., within one of the three segments of the great circle, formed by the sides of the great triangle, the ray drawn towards the middle point lies between the point p and the intersection (e) of the order two rays (fig. 6.14).

After estimating the position of the point p by applying the above rules, orient the table by placing the alidade along the line joining p and one of the points a, b or c and turning the table until the corresponding point on the ground is bisected. Then sight the other two stations and draw rays.

These rays will pass through p if the estimated position of p has been corrected. If not, another but smaller triangle of error will be formed. Assume a new position of p with reference to the new triangle of error, and repeat the orientation. Repeat the process until the correct position of p is established.

Strength of Fix:

The relative position of A, B, C and P has an important influence on the accuracy with which the position of point (p) can be fixed. The position of the required point (p) becomes indeterminate. If the instrument station (P) lies anywhere on the circumference of the great circle passing through A, B and C, as the three rays will intersect at one point even through the table is not correctly oriented.

For other positions of P, they will not pass through one point unless the table is oriented, but will either form a triangle or error or two of them may be parallel and intersected by the third. In such cases the accuracy with which the position of station P is fixed varies with different positions of P relatively to A, B, and C. The accuracy of fix is also termed as strength of fix.

The strength of fix is good when:

(i) P is within the triangle ABC.

(ii) The middle station B is much nearer than the others, and

(iii) Of the two angles subtended at P, one is small and the other is large, provided the points subtending the small angle are not too near each other.

The strength of fix is bad when:

(i) Both angles subtended at P are small, and

(ii) P is near the circumference of the great circle.

Practical Utility of Resection:

The methods of resection, particularly the three-point problem, provide a great advantage of saving the necessity of selecting and plotting the forward station in advance. The surveyor has entire liberty to choose stations best suited to him for taking detail. He is dependent only upon the visibility of three well-defined objects already plotted from the station to be occupied and not upon the position of the previous instrument-station.