EEC3523 Engineering Surveying

Chapter 3 : Linear Surveying

Contents

2.1 Definition

2.2 Linear Measurement Techniques

2.3 Procedure in Linear Surveying

2.4 Plotting the Survey

Definition

Linear Surveying

• A method of surveying which carried out by

measuring only the length of lines.

• No angular measurements are made at all.

• A survey makes use of the principles of geometry.

• The simplest possible geometric figure is a

triangle.

Linear Measurement Techniques

2.2.1 Equipment

Instruments required on a linear survey include :

Rules and tape (folding rule, steel tapes, synthetic tapes, etc.)

Ranging pole or ranging rod.

Marking arrow.

Linear Measurement Techniques

2.2.1 Equipment

Folding rule

Linear Measurement Techniques

2.2.1 Equipment

Steel tapes

Linear Measurement Techniques

2.2.1 Equipment

Ranging Pole – used for sightings.

Linear Measurement Techniques

2.2.1 Equipment

Marking Arrow

Linear Measurement Techniques

2.2.2 Party Organization

At least two surveyors are required to measure a long line.

Leader’s job is to pull the tape in the required direction and mark each tape length.

A known number of arrows and ranging rod are carried by the leader.

The follower’s job is to align the tape and count the tape lengths.

Linear Measurement Techniques

2.2.3 Inclined Lines Measurements

When any measured distance is to be shown on a plan, the horizontal distance is required and any inclined distance must be converted to its horizontal equivalent before plotting.

Trigonometrically, by measuring the inclined distance and angle of inclination, the horizontal distance can be calculated.

Linear Measurement Techniques

2.2.3 Inclined Lines Measurements Inclinometer or clinometer is used to measure

angle of slope.

Linear Measurement Techniques

2.2.3 Inclined Lines Measurements An alternative method of obtaining horizontal

measurements is without using angle-measuring, which is known as step taping.

Station 1

Station 2

D1

D2

D3

Drop arrow or plumbed ranging rods

Linear Measurement Techniques

2.2.3 Inclined Lines Measurements For step taping, three persons are required : a

leader, a follower and an observer.

• Follower holds end of tape against rod(s);

• Leader holds tape horizontally;

• Observer estimates horizontal position of tape, ensuring right-angled step(s) is formed.

• Leader reads the tape.

Linear Measurement Techniques

2.2.3 Inclined Lines Measurements Step tapping

• Less accurate and more difficult to carry than other method where horizontal distances are obtained directly.

• Considerable tension is required to straighten a tape and avoid sagging.

• Only be used as a last resort where slopes are short and fairly steep.

2.2 Linear Measurement Techniques

2.2.4 Errors in Taped Measurements No matter how carefully any line is measured, all

taped measurements are subjected to error(s).

2.2 Linear Measurement Techniques

2.2.4 Errors in Taped Measurements Gross errors

• Arise from inexperience, carelessness or lack of concentration of the surveyors.

• Misreading the tape graduations – 6 metres and 40 millimetres is 6.040 m, not 6.400 m;

• Miscounting the number of tape lengths – lose count of lengths;

• Booking errors – record wrong measurement, etc.

2.2 Linear Measurement Techniques

2.2.4 Errors in Taped Measurements Constant errors

• Occur no matter how often a line is measured and checked.

• The error will always be of the same sign for any tape for any given set of circumstances.

• Misalignment – measurements taken are not in straight line between two end stations, resulting in greater value.

2.2 Linear Measurement Techniques

2.2.4 Errors in Taped Measurements Constant errors

• Standardization

• It is important, before commencing a survey that the measuring instrument being used is exactly the right length.

• It must be compared with some standard length, probably a new tape kept solely for the purpose.

• If a tape is not standard, it will give a wrong measurement.

• If a tape has stretched, the resultant measurement will be shorter than the correct measurement.

2.2 Linear Measurement Techniques

2.2.4 Errors in Taped Measurements Constant errors

• Standardization

• The correction to measured length is found from the formula below :

c = ( L – l ) per tape or chain length

where :

c is correction;

L is actual length of tape;

l is nominal length of tape.

2.2 Linear Measurement Techniques

2.2.4 Errors in Taped Measurements Accidental or Human errors

• Arises from defects of human sight and touch.

• e.g., marking various tape or chain lengths, when estimating readings on a tape when it does not quite coincide with a graduation mark.

• Tend to be compensatory and have relatively little significance at this level of surveying.

2.2 Linear Measurement Techniques

Example 2.1

Calculate the corrected plan length of line AB measured in 3 sections as follows :

Line AB Section 1 Section 2 Section 3

Measured length 36.50 19.26 52.77

Angle of slope 2° 3.5° 5°

2.2 Linear Measurement Techniques

Solution 2.1

Corrected Section 1 :

36.50 × cos 2° = 36.478 m

Corrected Section 2 :

19.26 × cos 3.5° = 19.224 m

Corrected Section 3 :

52.77 × cos 5° = 52.569 m

Corrected line AB = 36.478 + 19.224 + 52.569

= 108.271 m

2.2 Linear Measurement Techniques

Example 2.2

A line AB is measured using a tape of length 20 m and is found to be 65.32 m long. When checked against a standard, the tape was found to be 50 mm too long. Calculate :

(a) the correction to the length AB.

(b) the correct length of AB.

2.2 Linear Measurement Techniques

Solution 2.2A line AB is measured using a tape of (nominal) length 20 m and is found to be 65.32 m long. When checked against a standard, the tape was found to be 50 mm too long.

Tape of (nominal) length, l = 20.00 m

If tape is 50 mm too long, actual length of tape, L = 20.00 + 0.05 m

= 20.05 m

AB = 65.32 m

2.2 Linear Measurement Techniques

Solution 2.2

(a) Correction to the length AB, cAB :

Number of times tape is used = 65.32 ÷ 20

= 3.266

∴ Tape is used 3.266 times.

c = ( L – l ) per tape or chain length

c = 20.05 – 20.00

= +0.05 m

cAB = 3.266 x (+0.05 )

= +0.1633 m

2.2 Linear Measurement Techniques

Solution 2.2

(b) the correct length of AB.

Corrected AB = 65.32 + 0.1633

= 65.4833 m

2.3 Procedure in Linear Surveying

The principle of linear surveying is to divided the area into a number of triangles, all the sides of which are measured.

Reconnaissance survey :

• Working from the whole to the part.

• Formation of well-conditioned triangles.

• Good measuring conditions.

• Permanency of the stations.

• Referencing the stations.

• Obstruction to measuring.

• Intervisibility of stations.

• Check measurements or tie lines.

2.3 Procedure in Linear Surveying

Conducting a survey.

• Surveying the framework.

• Offsetting.

Recording the survey.

• Referencing the survey.

• Booking the details.

2.3 Procedure in Linear Surveying

Reconnaissance survey

Upon arriving at a site, a survey team’s first task is to make a reconnaissance survey of the area.

The team simply walks over the area with a view to establishing the best sites for survey stations.

Working from the whole to part.

• This is a fundamental rule of all survey operations.

• The area to be surveyed is treated as a whole; and is broken down into several triangles (trilateration - a measurement of three sides).

2.3 Procedure in Linear Surveying

Reconnaissance survey

Formation of well-conditioned triangles.

• The triangles into which area is broken should have no angle less than 30° nor greater than 120°. (These are minimum conditions).

• The ideal figure is an equilateral triangle and every effort should be made to have triangles whose angles are all around 45° to 75°.

2.3 Procedure in Linear Surveying

Reconnaissance survey

Good measuring conditions.

• All of the lines of survey must be accurately measured.

• Lines, that are going to be physically easy to measure, are selected.

• Roads and paths are usually constructed along even gradients and present good measuring conditions.

2.3 Procedure in Linear Surveying

Reconnaissance survey

Permanency of stations.

• The survey stations may have to be used at some future date when setting-out operations take place.

• Therefore, the stations

may have to be of a

permanent nature.

• Marks must be sited in

places that do not

inconvenience anyone.

• Never place mark(s) on roads or paths that may block off traffic as obstacles.

2.3 Procedure in Linear Surveying

Reconnaissance survey

Permanency of stations.

2.3 Procedure in Linear Surveying

Reconnaissance survey

Referencing the stations.

• When the stations have to be used again, it is wise to position them such that they can be found easily.

• Each station should be referenced to nearby permanent objects like fence posts, gates, bus stops, lamp standards, etc.

• Such permanent objects are known as referencing stations.

2.3 Procedure in Linear Surveying

Reconnaissance survey

Obstructions to measuring.

• Obstacles like pond, river or railway cutting will present a considerable problem to measurement.

• They should be avoided if at all possible.

Intervisibilty of stations.

• It is necessary to be able to see only from any one station to the other two stations of any triangle.

• An attempt should be made to see as many stations as possible from any one station.

2.3 Procedure in Linear Surveying

Reconnaissance survey

Check measurements or tie lines.

• Before a survey is complete, check measurements must be made.

• A check line is a dimension that will prove the accuracy of part, of all, of a survey.

• In the figure presented in the following slide, line CF is measured to check for triangles ABD, BCD, and ADF.

• On completion of the plotting, the scaled distance of this line must be agree with its actual measured length.

2.3 Procedure in Linear Surveying

Reconnaissance survey

Check measurements or tie lines.

2.3 Procedure in Linear Surveying

Reconnaissance survey

Check measurements or tie lines.

2.3 Procedure in Linear Surveying

Conducting a survey

Surveying framework.

• The figure in the previous slide shows is an example of survey layout, consisting of trilateration framework and a series of offsets.

• Various lines are measured using the methods previously described.

• Plan length is required and all gradient must be carefully observed and measured.

• If line BD in previous figure is being measured, a ranging pole should be left at point G, for the purpose of getting a check point and producing check lines AG and CG.

2.3 Procedure in Linear Surveying

Conducting a survey

Offsetting.

• Offsets are short lengths measured to all points of detail from points along the main frame lines.

• The latter points are called chainages.

ObjectOffsets

Chainages

Survey line

2.3 Procedure in Linear Surveying

Conducting a survey

Offsetting.

• Wherever possible, the offsets are measured at right angles to the survey lines with the right angle being judged by eye.

• On average, the naked eye can detect a distance of 0.25 mm on paper during plotting.

• An average person is able to judge a right angle to ±3°.

2.3 Procedure in Linear Surveying

Conducting a survey

Offsetting.

• The oblique offsets are used when the maximum allowable right-angled offset is to be exceeded.

• They provide greater accuracy and are used to fix important details, like corners of a house.

HouseObliqueOffset

Survey line

ObliqueOffset

2.3 Procedure in Linear Surveying

Conducting a survey

Offsetting.

• When a building or wall, etc., lies at an angle to a survey line, it may be desirable to use in line offsets.

• They are similar to oblique offsets but have the advantage that they are measured on the line of the detail feature.

HouseIn lineOffset

Survey line

In lineOffset

2.3 Procedure in Linear Surveying

Conducting a survey

Offsetting.

2.3 Procedure in Linear Surveying

Recording the survey

Referencing the survey.

• The first task in booking is to make a reference sketch of the survey as a whole.

• The sketch is drawn to show the main survey stations in their correct relationship.

• Length is written alongside each lines, together with any gradient values.

• Measurements in the direction of arrows indicate gradients, and are always positive downhill.

2.3 Procedure in Linear Surveying

Recording the survey

Referencing the survey.

2.3 Procedure in Linear Surveying

Recording the survey

Referencing the survey.

2.3 Procedure in Linear Surveying

Recording the survey

Booking the details.

• The details to be surveyed from the main survey lines include the road, hedges, fences, building and stream.

• There are two methods of detail bookings, namely double line method, and single line method.

2.3 Procedure in Linear Surveying

Recording the survey

Booking the details.

• Double line method.

2.3 Procedure in Linear Surveying

Recording the survey

Booking the details.

• Single line method.

2.4 Plotting the Survey

Results of the fieldwork.

Plotting equipment.

Procedure in plotting :

• Orientation

• Rough sketch

• Scale

• Calculation of plain lengths

• Plotting the framework

• Plotting the details

Computer aided design/draughting (CAD)

2.4 Plotting the Survey

Results of the fieldwork

Results are to be plotted

to a suitable scale on

paper.

2.4 Plotting the Survey

Plotting equipment

Paper.

Scale rules.

Compasses.

Others.

2.4 Plotting the Survey

Procedure in plotting Orientation

• Most maps and

plans are drawn

and interpreted

looking north

towards the top

of the paper.

• Top and bottom

of a plotting

material are respectively north

and south.

2.4 Plotting the Survey

Procedure in plotting

Calculation of plain lengths

Line Slope length (m) Angle of inclination (°)

BD 54.33 2.5

BG 30.00 2.5

CG 30.02 2.0

GA 23.06 2.0

AD 19.36 3.0

FE 18.12 4.0

FH 15.43 2.0

2.4 Plotting the Survey

Procedure in plotting

Calculation of plain lengths

Line Plan length (m)

BD 54.33 cos 2.5 = 54.278

BG 30.00 cos 2.5 = 29.971

CG 30.02 cos 2.0 = 30.002

GA 23.06 cos 2.0 = 23.046

AD 19.36 cos 3.0 = 19.333

FE 18.12 cos 4.0 = 18.076

FH 15.43 cos 2.0 = 15.421

Plotting the Survey

Computer aided design/draughting (CAD)

CAD software is used to produce final survey drawings.

AutoCAD from Autodesk and Microstation from Bentley are the most widely used packages.

Simpler, less expensive software such as Design CAD 3DMAX is used too.

End of Chapter 3

Revise…

2.1 Definition

2.2 Linear Measurement Techniques

2.3 Procedure in Linear Surveying

2.4 Plotting the Survey