Angelo Filomeno

www.angelofilomeno.com

In these lectures we will cover : ◦ The role of linear measurement

◦ Equipment

◦ Procedures and rules

◦ Errors

◦ Applications of linear measurement

Simply the measurement of distance :

New building site -

how big is it?

50.5 metres

50.5 metres

27.9

metres 2

7.9

met

res

Pacing (1:100)

Optical range finder (1:300)

Trundle wheel (1:500)

Stadia tacheometry (1:1000)

Taping or chaining (1:10,000)

Electronic distance measurement (1:50,000)

Equipment is fairly cheap (except EDM) Equipment is easy to maintain and adjust (!) Distances are easy to measure Very accurate results can be achieved (with care) Measurement line needs to be unobstructed Errors occur and need to be managed or minimised

Tape must always be straight

Tape must not be twisted

Use chaining arrows for intermediate points

Tape horizontally if possible

Tape on the ground if possible

Slope taping needs to be reduced

Catenary taping requires correction

Step taping suits some applications

obstruction

measured distance required distance

measured distance required distance

For example :

s = 30.589 m

q = 2.5o

DH = 1.334 m

then

h = 30.589 cos(2.5)

h = 30.560 m To calculate the horizontal distance :

h = s cosq or h = (s2 - DH2)1/2

q

horizontal distance = h

DH

Or….

s = 30.589 m

DH = 1.334 m

then

h = (30.5892 - 1.3342)1/2

h = 30.560 m

required (horizontal) distance

measured distance required distance

required distance

Blunders ◦ mistakes and gross errors

Systematic errors ◦ repeated size and sign

◦ affect accuracy

Random errors ◦ small and usually undetectable (noise)

◦ affect precision

These error types

apply to any

measurement technique used in

surveying…

Temperature correction

L = L +L.c.DT

where :

L is the corrected distance

L is the measured distance

c = 1.15 x 10-5 m/oC (for a steel band)

DT = Tactual - Tstandard

Standardisation ◦ The tape is not of “true” length

lengthassumed

lengthmeasuredxLL

A standardised tape is normally kept in reserve and the working tape often compared to this to ensure that measurements taken in the field are correct.

Comparison must be made at the standard temperature, pressure and tension.

Any discrepancy between the working tape and the standard is recorded and all measurements taken with working tape are corrected to take account of this discrepancy.

0 5 10 15 20

0 5 10 15 20

Standard tape/band

Stretched Working tape/band

Discrepancy

True Distance =

yDiscrepanclengthtapedards

lengthtapedardsceDiscorded

__tan

__tantan_Re

Example A 30m steel band used for recording a survey is compared to a standard 30m band held at the appropriate standard temperature and tension. With the two 30m marks held together it is found that the working tape shows a reading of 55mm in line with the zero mark on the standard. If one of the survey lines was recorded as 120.056m what is the true length of the surveyed line? Apply logic: When the working tape reads 29.945m (30m -55mm) then the true distance is 30m. If we cut the tape at this length of 29.945m we could use this as an accurate representation of 30m. We could see how many times this cut length of tape needed to be stretched out to measure the recorded distance of 120.056 (120.056 29.945 = 4.00921). Now every time we stretch out this cut length we are really measuring out a true distance of 30m. So the true overall distance is equal to 4.00921 times 30m = 120.276m. or Apply Formula: True Distance = 120.056 x 30m / (30m - 55mm)

= 120.056 x 30/(29.945)

= 120.056 x 1.00184 = 120.276m

Catenary (sag) ◦ A suspended tape will measure too long

where :

M is the mass per unit length (0.011 kg/metre)

g is gravity (9.8 metre/sec2)

T is the tension (50 Newton)

is the slope angle

22

32

cosT24

L)Mg(LL

Tension ◦ Tape length will depend on applied tension

Slope ◦ Distances must always be reduced to horizontal

Dimensions of building features

Block dimensions

Location and size of site features

Setting out for construction

Clearances and tolerances

road

wid

th

building setbacks building dimensions

side boundary clearances

underground services

block dimensions

e.g. Buildings, Spoil Heaps, Hills

PROBLEM:

Survey Line is AB. Cannot take straight measurement through obstruction.

SOLUTION:

Set up point D and point E intervisible from A and B.

Locate point C as the point which is on line AD and line EB. (Set up ranging rods at A, B, E, and D. Line up another ranging rod between A and D and move it along line AD until it also lines up with points E and B.)

Record the distances AC,CB, EC, CD and ED.

Use Similar Triangles to calculate the distance AB.

i.e. DABC DECD

Hence and thus

CD

ED

AC

AB AB

ED

CDAC

AB

BC

ED

CENote that the following is also true:-

OBSTRUCTION

A

B

E

D

C

A linear survey for the above situation gave the following information:- AC =48.00m CD = 16.00m BC = 51.00m CE = 17.00m ED = 19.3.00m Find the length of the survey line AB.

e.g. River, Motorway

PROBLEM:

Survey Line is AB. Cannot take straight measurement across obstruction.

SOLUTION:

Set up point D as offset from AB at point A. (Offset means a line at right angle to the main survey line)

Set up an intermediate point E between D and B but accessible from the survey area.

Locate point C as an offset from survey line AB. (Easiest method is to stretch tape from E to line AB and swing arc with tape. The lowest reading on the tape will occur when line CE is at right angle to line AB.)

Record the distances AC, AD and CE.

Use Similar Triangles to calculate the distance AB.

i.e. DABD DDEF

AB

AD

FE

FDHence and thus

but remember FE =AC and FD =AD –CE, so

ABFE

FDAD

ABAC

AD CEAD

A

C

B

D

E

F

river

A linear survey for the above situation gave the following information:- AC = 20.00m AD = 18.00m CE = 12.00m Find the length of the survey line AB