Week 1 Introduction to Basic Surveying

transcript

A2.2NP1Environmental Practical 1

TOPIC 1

TECHNIQUES IN BASIC SURVEYING

Basic ideas

• Surveying - the creation of a scale representation of the ground surface - is a basic activity in many areas of environmental management.

• A survey will be one of of two types:

– Primary survey - to establish the position of objects in three dimensions when no previous information exists

– Secondary survey - to add extra information to existing data or to measure changes over an interval of time

Basic ideas

• The task of three dimensional position fixing is normally broken into two parts:

Determining plan position

Determining elevation

Basic ideas

• Each of these determinations may be either: absolute - made in terms of a fixed co-ordinate

system

relative - made in terms of local co-ordinates which may later be converted to absolute co-ordinates if required.

• The majority of surveys carried out for environmental management are thus secondary relative surveys

Plan Position Fixing

• The plan position of a station can be established in a number of ways:

By reference to the apparent positions of astronomical objects when viewed from that station

• This method gives the absolute location of the station in terms of latitude and longitude, which can be converted to local systems such as the National Grid.

By the measurement of the angles between lines of sight to the unknown station from other known positions

By the intersection of lines of sight from the unknown station to other objects whose positions are already known

• These two methods both rely on the simple Euclidean geometry of the plane. (Hence the term plane surveying). The first procedure is termed triangulation and the second resection.

BaselineA B

The basic principle of triangulation

Measured angle Measured angle

Unknown position

The basic principle of resection

Measuredangle

Known position

Known positionKnown position

Measuredangle

By measurement of distances between the unknown station and other objects of known positions

• This last method includes a number of particular cases:

measurements of offset distances from a base line.

trilateration - the distance equivalent of triangulation.

tacheometry - an optical method of distance measurement along a known bearing

BaselineA B

The basic principle of trilateration

Measured sideMeasured side

Plane Surveying: Theory

• Plane surveying relies on the basic concepts of Euclidean geometry, and in particular the properties of triangles.

• The most important (for our purposes) of these are:

The internal angles of a triangle sum to 180 The sides of an equilateral triangle are equal

and the internal angles are all 60°

The base angles and opposing sides of an isosceles triangle are equal

60º 60º

The equilateral triangleAll sides equal in lengthAll angles equal (= 60º)

The isosceles triangleTwo sides equal in lengthTwo angles equal

If the respective angles in two triangles are equal then the triangles are similar and their sides are all in the same proportion

If two triangles have two angles and one side equal (or vice versa) then they are congruent and all their other respective angles and sides are equal.

Two triangles are also congruent if all their sides are equal.

Similar triangles have corresponding angles equalbut are of differing size

Conguent triangles are identical

• two angles and one side equal• two sides and one angle equal• all three sides equal

• Congruent triangles are unique - you cannot draw two different triangles from the same set of measurements

• This means that a complete set of survey data must define the positions of objects uniquely.

Any closed polygon can be subdivided into a series of contiguous triangles

• These properties are repeatedly used in the procedure of triangulation in which stations are surveyed in a pattern of contiguous triangles.

Any closed polygon can be subdivided into contiguous triangles

These should be chosen to make as many of the triangles asclose to equilateral as possible

Plane surveying: practical aspects

• In practice, most plane surveys are carried out in a straightforward way following an established sequence:

1. A reconnaisance survey will establish the dimensions of the area, relative levels, significant features, accessibility, obstacles etc

2. Establish an accurate baseline by measurement from existing survey points, natural features, buildings etc. If none are available then the baseline must be fixed by absolute methods.

3. Establish as required any further control points by triangulation or trilateration from the base-line.

4. Incorporate detail by tacheometry, traversing, tape & offset or whatever other method is appropriate.

5. The intermediate stations should where appropriate be cross-checked with the control points by resection and all traverses should be closed at a control point.

6. Inaccessible detail should be incorporated by triangulation or plane tabling from the ends of the baseline.

Baseline

ILLUSTRATION OF THE USE OF OFFSETS

7. If a topographic survey is being undertaken, levelling traverses should be carried out around the survey stations and the baseline tied to the local benchmark by a closed traverse.

8. The use of a theodolite or total station will enable both the position and the elevation of stations to be found simultaneously by combined tacheometry and triangulation or by trilateration

THE “CHAIN” SURVEY

How to establish relative plan positions

Chain survey

• Simplest of all survey techniques

• Relies on linear measurements; slopes >3o require some adjustment to technique

• Usually requires a clear line of sight

• The triangles used should be equilateral or approximately so

Terminology

• Trilateration is the measurement of sides of a triangle

• whereas triangulation refers to the measurement of the angles of the triangle

Basic equipment

• Ranging poles

• Survey pegs and ‘arrows’

• Chain & tape measure or other distance measuring instrument

• Plumb line

• Compass

Chain survey components

• Base line: the longest line

• Chain /survey lines

• Survey stations

• Offset lines

Order of events

• “Range out” survey stations with ranging rods

• Establish base line and measure accurately

• Measure remaining distances between other survey stations

• Measure offset lines whilst measuring between survey stations

Sloping ground

• If the ground slopes by more than about 3°, this must be allowed for in the survey.

• The measured distances are thus slant distances and must be corrected to true horizontal distances.

• This requires that the vertical angle between the stations is known

Ground distance determined

Sloping ground

• For an approximate survey, it may be sufficient to step up or downhill using a series of horizontal and vertical lines

• If the drop is measured at the same time, some estimate of the slope profile can be obtained

Chain surveying (“stepping”)

Sloping ground

• If stepping is not appropriate, more sophisticated methods must be used to measure the slant distance and the vertical angle simultaneously

• Requires optical sighting equipment: usually either a clinometer, Abney level or theodolite

Basic levelling in chain surveys

Correcting for horizontal distance:the “hypotenusal allowance”

correction factor = xy - yz

= xy(1 - cosa)

LEVELLING

How to destermine relative elevations

Levelling: accounting for slopes

Unlike chain surveys, levelling surveys account directly for slope and incorporate this data into the whole measurement exercise

AIMS:• to determine height differences between

two points• to determine elevations for sections

• The elevation of a station can be established by:

inclined line of sight from chain survey stations

levelling from another point of known height

by inclined tacheometry

• Levelling is the more accurate method but is also the slower. Modern instruments are capable of cm accuracy under normal conditions over distances of 100’s metres.

• The keys to successful levelling lie in the setting up of the instrument, in the closure of the traverses and in the careful recording (booking) of the results.

• Inclined tacheometry relies on the combined measurement, by theodolite, of the slant distance to the new station and the angle relative to the horizontal.

• The elevation change and horizontal distance can then be found by simple trigonometry.

• The accuracy of the method, using normal instruments, is around 10’s cms in 100’s metres.

Direct levelling

• Most typical form used

Relies upon:

• a horizontal line of sight, also termed “the line of collimation”

• a fixed datum level

Measurements to be taken

• Backsight

• Foresight

• Intermediate sights

Booking your results

The “rise and fall” method

• This method records the relative change in level between successive stations

• The changes are converted to the reduced level of each station

• The reduced level is relative to the local datum

Booking the results

• The method relies on recording your results in a survey book in a standard format

• This allows you to check your work and to identify any errors systematically

Reduced levels

The change of level is 2.312m - 2.533m = -0.221m

2.533m

Datum line: 100.522m(from OS Benchmark)

2.312 m

The reduced level of point B is 100.301m

The absolute (datum) level of point A is 100.522m

Backsight Interm.Foresight Rise Fall R.L. DistanceRemarks

2.312 100.5220.221 100.301

Rise and fall booking

Point A

Point B

-2.533

Transfer of level

The new change of level is 1.674m - 1.631m = + 0.043m

1.631m

1.674 m

The absolute level of point C is 100.344m

At the next stage, B becomes the backsight and C is the new foresight

2.312 100.522- 0.221 100.301

Rise and fall booking (cont)

Point A

Point B-

2.5331.6741.631 + 0.043 100.344 Point C

• Continuing this process, suppose we end up with a set of results as follows:

• This will enable us to check our working

2.312 100.522- 0.221 100.301

Rise and fall booking (cont)

Point A

Point B

2.5331.6741.631 + 0.043 100.344 Point C2.504

3.0102.413

0.9562.0162.718

+ 1.548+ 0.994

-0.305

101.892102.886

102.581

11.913

9.854 2.585

- 0.526

- 0.526 102.581

- 100.5222.059 2.059 2.059 CHECKS

Using an intermediate sight

• Sometimes we wish to include a specific feature but it is not convenient to set up a new instrument position for this

• The solution is to take a sighting onto the staff when it is placed on this feature - this is called an intermediate sight

Intermediate sight

The new change of level is 1.674m - 2.988m = -1.314m

2.988m

The absolute level of the intermediate point C is 98.987m

The intermediate sight is taken at the base of the channel between B and C

Intermediate sight 1.674m

2.312 100.522- 0.221 100.301

Rise and fall booking (intermediate sight)

Point A

Point B-

2.5331.674

1.631 + 0.043 100.344 Point C

2.988 channel-1.314 98.987

Next FS

Optical distance measurement

• It is often convenient to use the levelling instrument itself to calculate the distance between the instrument and staff positions

• This is done using the stadia lines that are visible in the viewfinder

• These are arranged such that the distance to the staff is 100x the stadia interval that is read on the staff between the two lines

• This procedure is known as tacheometry

Tacheometry

The viewfinder:

Stadialines

Multiply vertical distance by 100to obtain horizontal distance

Inclined tacheometry

• If the ‘level’ can be swung in a vertical arc, the distance up an inclined sight line can be obtained.

• If the vertical angle is also measured, the slant distance can be converted to give both the change in height and the true horizontal distance.

Inclined tacheometry

Change of height

Tacheometric distance

Measured angle

True horizontal distance

The theodolite

• If such an instrument can also be swung in a horizontal arc, and the angle of rotation can be measured, we are able to determine the angles of the sight lines between stations.

• This allows both trilateration and triangulation with the same instrument.

• Such a versatile instrument exist and is called a theodolite.

Summary

• Chain surveys are suited to planimetric surveys on low slopes. They rely upon trilateration.

• Levelling is used where terrain is more uneven. Levelling surveys often use tacheometry to fix station positions.

• A theodolite survey permits levelling, tacheometry or triangulation as required.

Week 1 Introduction to Basic Surveying

Documents