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CHAPTER 5

PLANE TABLE SURVEYING

Table

Plumbing fork

Alidade

Tripod

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OBJECTIVES

1. Describe the plane table and accessories

2. Explain temporary adjustment of plane table

3. Explain the different methods to locate points with plane table.

4. Explain the two-point problem and its solution

5. Explain the three-point problem and its solution

6. Explain the likely errors and precautions to be taken

7. List the advantages and disadvantages of plane tabling.

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AGENDA

Plane Table and Accessories

Setting up

Plane Tabling Methods

Two-point and three-point problems

Errors in Plane tabling

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PLANE TABLE

Plane table is of well-seasoned wood 450 to 750 mm size.

Table has a ball and socket arrangement to level and can be screwed on to a tripod.

Drawing sheet can be fixed with pin or tape.

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ALIDADE

Alidade of two types – Plane

Alidade as shown.

Metallic rule with a fiducial

edge for marking.

Two frames attached at

ends.

Eye vane has a slit to sight

objects.

The other vane, object vane

with a fine hair or wire for

bisecting objects.

• Plane Alidade

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TELESCOPIC ALIDADE

Heavy metal rule tow which

a frame is attached.

This frame supports the

telescope providing a

very accurate line of

sight.

A spirit level on the rule

helps to level the table.

It can also take inclined line

of sight to objects low or

high.

• Telescopic Alidade

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TELESCOPIC ALIDADE

Composite instrument of telescopic alidade and Beaman

arc with compass and spirit level

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SPIRIT LEVEL

A spirit level is required to ensure levelling the table surface.

The spirit level can be place in two perpendicular directions and levelled.

A circular level can also be used.

• Spirit Level

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MAGNETIC COMPASS

A magnetic needle in a rectangular box is

generally used.

By turning the box placed on the table, the

needle is made to read zero.

A line drawn along the edges of the box

gives the magnetic meridian

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MAGNETIC COMPASS

• Trough compass

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PLUMBING FORK

A folded frame with a hook

and a plumb bob at the

lower limb makes up the

plumbing fork.

The upper frame is placed

on the sheet with its

pointed end at a point

marked as station.

The tripod legs are adjusted

to bring the plumb bob

over the station mark. Plumbing fork

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PLANE TABLE SURVEY

Setting up the Plane Table

1. Setting up over a station

2. Levelling

3. Centering

4. Orienting

BACK

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SETTING UP

The Plane Table is screwed on to a tripod. Adjust the tripod legs for a comfortable height.

The plane table is levelled using spirit level.

Centering is done if the station mark is already on the drawing sheet. This is done using the plumbing fork and adjusting the tripod legs.

If the station is not marked, mark the station point using the plumbing fork on the sheet as well as on ground.

Mark the magnetic meridian using the trough compass at a convenient place on the sheet.

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ORIENTING THE TABLE

The table first set up at A.

The line ab is drawn on

table after sighting the

ranging rod at B using the

alidade.

The instrument is shifted

and set up at B

Keep the alidade along ba

and sight the ranging rod

at A.

The table is now oriented.

By backsighting

BACK

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PLANE TABLING METHODS

Radiation method

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PLANE TABLING METHODS

Intersection method

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PLANE TABLING METHODS

Traversing

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PLANE TABLING METHODS

Resection is a method of orienting the table.

The objective is to plot the station occupied by the

table rather than plotting other points.

After resection, the station occupied by the table is

obtained on the sheet in correct orientation.

The two-point and three-point problems are

resection methods.

BACK

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TWO-POINT PROBLEM

The two-point problem can be stated as:

“To find the position a on the table of the

station A occupied by the table, given the

accurately plotted positions, p and q, of

two stations P and Q, visible from the

instrument station and by not occupying

these two stations.”

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Procedure -Two point Problem

1. Plot the points P and Q two well defined

points whose positions are plotted on

map as p and q.

2. An auxiliary station B is selected at a

suitable position. The table is setup at B

and levelled and oriented by eye position.

It is then clamped.

3. Touching the alidade p and q the points P

and Q are bisected and rays are drawn.

The rays will bisect at b. 23

Procedure – Contd..

4. Alidade is centred on b ranging rod A is

bisected and a ray is shown.

5. A point a1 is marked on the ray.

6. Shift the table and centred on A with a1

just over A. It is levelled and oriented by

back sighting.

7.Keep the alidade touching the point p the

point P is bisected and a ray is drawn. The

ray intersects line ba1 at point a1 which

was assumed before. 24

Procedure – Contd.. 8.Keep the alidade on a1 the point Q is

bisected and a ray is drawn. The ray

intersects bq at q1. A triangle is formed,

pqq1( This is the error triangle which

should be eliminated)

9.The alidade is then placed along the line

pq1 and a ranging rod R is fixed at some

distance from the table.

10.Alidade is placed along the line pq and

the table is turned to bisect R

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Procedure – Contd..

10. The table is said to be perfectly oriented.

11.Finally, the alidade cetered on p and q ,

the points P and Q are bisected and rays

are drawn. The rays intersect at a point a.

This would represent the exact position of

the required station A.

12. Station A is marked on the ground.

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THREE POINT PROBLEM

Three point problem is

“Given three visible stations and their plotted positions, to plot the station occupied by the table with the table correctly oriented.”

Methods of Solution

1. Mechanical method (Tracing paper method

2. Graphical method (Bessel’s method)

3. Trial and error method

Graphical Method (Bessel)

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Procedure – Bessel’s method

1. A,B,C stations are three well defined

points which have been plotted as a,b,c.

It is required to locate a station at P.

2. The table is placed at the required station

P and levelled . The alidade is placed

along the line ca and the point A is

bisected. The table is clamped.

3. With the alidade centred on c , the point

B is bisected and a ray is drawn.

(I Position) 29

Contd...

4. Again the alidade is placed along the line

ac and the point C is bisected and the

table is clamped.

5. With the alidade, touching the position a,

the point B is bisected and a ray is drawn.

Let this ray intersects the previous ray at a

point (II Position)

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Contd...

6. The alidade is placed along the line db,

and the point B is bisected. At this position

the table is perfectly oriented. Now the

rays Aa, Bb, Ca are drawn. These rays

must meet at the point P, which is required

point.

7. The point is transfered to the ground by

U frame or U fork.

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TRACING PAPER METHOD

Procedure – Tracing paper method

1The table is placed at P and levelled. A

tracing paper is fixed on the map and a

point p is marked on it.

2. With the alidade centred on P, the points

A, B, C are bisected and the rays are

drawn. The rays will not pass through the

points a,b,c.

3. Now the tracing paper is removed and

moved over the map such a way that , the

three rays at a time pass through the

positions a, b, c.

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• The point p is picked with a pin to give a

impression p on the map. p is the required

point on the map. The tracing paper is

removed.

• Alidade is centred on p and the rays are

drawn towards A, B, C. These rays must

pass through the points a,b,c.

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TRIAL AND ERROR METHOD

Lehmann’s method

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TRIAL AND ERROR METHOD

Procedure

1. Set up the plane table at S. The station S should be such that P,Q and R do not subtend very acute angles at S.

2. Orient the table approximately.

3. Now keeping the alidade at s, draw the three rays to P, Q and R. They will not intersect at a point but form a triangle of error.

4. Select a new position of s and draw again the three rays. A new triangle of error, but smaller, will be formed.

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TRIAL AND ERROR METHOD

Lehmann’s Rules:

1. If S is outside the great triangle PQR, then s

will be outside triangle of error. If S is inside

PQR, triangle of error will be inside PQR and s

will be inside the triangle of error.

2. The position of s will be such that its distance

from pP,qQ and Rr will be proportional to

distance of S from P,Q,R.

3. S will lie on the same side of pP,qQ and rR.

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ERRORS

1. Table not levelled.

2. Table not oriented.

3. Wrong placement of alidade.

4. Inaccurate bisection of objects.

5. Improper clamping.

6. Lines not accurately drawn.

7. Inaccurate scaling and plotting

8. Expansion/contraction of paper.

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ADVANTAGES

1. Faster method

2. No field book

3. Errors in field book avoided.

4. Suitable for small scale maps.

5. Object representation accurate.

6. Inexpensive and simple to use.

7. Suitable for filling in detail.

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DISADVANTAGES

1. Too many accessories.

2. Heavy and cumbersome equipment.

3. Not very accurate.

4. No field notes and hence no calculations possible.

5. Not suitable for rainy areas.

END