linear measurments

8/13/2019 Linear Measurments

1/34

LinearMeasL1_2008: 1ELS/DC/MH

Linear Measurement

one of the fundamental measurements in

surveyingdepending on the type of instruments used,

there are three basic methods of determining

distance:Direct

Indirect and

Electronic


2/34


Direct Method

- using tapes and accessories to measure the distance


3/34


Indirect Method

- using optical means (i.e. stadia or tacheometry) to measure the

distance. Height can also be determined using this method.


4/34


Electronic Method

A B C

ReflectorEDM

- using an instrument known as Electromagnetic Distance

Measuring (EDM) instrument to measure distance


5/34


6/34


METHODS OF MEASUREMENT

Pacing:

a rapid means of approximately checking more precise

measurements of distanceused on reconnaissance surveys

relative precision around 1/100 to 1/200

distance = individual pace distance x number of pace

Odometer:

Distance = number of revolutions of the wheel x circumferenceof the wheel

Optical: Stadia or Tacheometryinvolves measuring the interval between the stadia hairs as

shown on a leveling staff held vertically at a point

Distance = (UH LH) x 100


7/34


Types of Tapes

Taping

involves direct measurement of the distance withtapes which are graduated in metres, decimetres,centimetres and sometimes in millimetres

the most popular nominal length is 30 m, but 50 m

and 100 musually reeled up in either boxes or open-reel frames.

Four kinds of tapes are used:

1)Synthetic/Fibre-Glass Reinforced Tape2)Steel/Plastic Composite Tape

3) Steel Tapes

4)Invar tapes


8/34


Synthetic/Fibre-Glass Reinforced

Tape

made of fibre-glass

coated with P.V.C..hard-wearing, durable

and water proof.

materials can easily be

stretched when tension is

applied.

used for measurements

that do not need to behighly precise


9/34


Steel/Plastic Composite Tape

thin steel strip coated with

P.V.C. is used.more precise than the

fibre-glass tape because

the steel strip inside can

be well-controlled to givea uniform dimension

temperature and tension

variations can becorrected.


10/34


Steel Tapes

made from high-quality

steel which is thicker andheavier than steel/plastic

composite tape

more precise and more

stable

nominal length:

temperature = 20C and

applied tension between 50N to 80 N

printed on the zero end of

tape


11/34


Invar Tape

most precise tape

made from an alloy of36% nickel and 64% iron

low coefficient of

expansion (only 1/13 that

of steel tape)

Disadvantages:

soft and weak

price is ten times more

expensive than steel tape


12/34


Ancillary Equipment (1)


13/34


Ground Taping or Surface Chaining

taping on smooth or level ground

Minimum of two people are required of whom one is the leaderandthe other is the follower.

When making a measurement, the leaderperforms the followingfunctions:

holds the tape reel and move towards the distant point;

sets the direction of travel; and

does the booking.The followerperforms the following:

holds the zero end of the tape precisely against the ground mark; and

sometimes, helps to define the straight line.

Notes:

To avoid mistakes, holding zero and taking the reading should be donesimultaneously.

When the follower has brought the zero end of the tape against theground point, he has to shout "GOOD!" or "READY!" to indicate to the

leader that tape reading can be taken. If not, he has to remain silent.


14/34


15/34


Ground Taping or Surface Chaining

taping on smooth or level ground

at least 3 or 4 readings should be taken for each

leg to ensure reliability of measurementdifferent "zero" point should be used for eachreading, e.g.. first reading starts with 0, second

reading starts with 0.100, etc., to avoidsystematic error.

difference between the leader and the "zero" ofthe follower gives the distance

mean of all the individual measurements gives amore accurate result and will eliminate most ofthe gross errors in linear measurement


16/34


Sloping Ground: Step Chaining

Point A

Point B

Distance AB = S1 + S2 + S3


17/34


Slope Distance : Height

Difference & Slope Angle

Point A

Point B

L

h

Distance AB = L2 (h)2 OR Distance AB = L * cos a


18/34


Errors in Taping

Sources of Error

Instrumental Error :

tape is not standardized, chaining arrow or ranging pole is not

properly plumbed

Human Error:

reading or recording error, insufficient tension etc. Natural Error:

tape being influenced by temperature, wind and gravity

Precision

Using fraction to indicate the relative precision of the measureddistance, the numerator should be set to 1 while the denominator

should be as large as possible.

Precision = (error in distance) / total measured distance


19/34


Corrections in Taping

First of all, the field tape must be calibrated and

corrected for slope. In addition,For precision of 1/5000 or above : apply

temperature, tension and sag corrections

For precision of 1/50 000 or above : distancemust be reduced to Principal Datum of Hong

Kong


20/34


Calibration (Standardization)

Prior to any measurement, the servicing tape, i.e.

tape to be used, must be calibrated with astandard length, i.e. baseline, or a more precise

tape. Measurements made with a tape found to

be in error can be corrected using the formula:True distance = Actual length of tape

Measured distance Nominal length of tape


21/34


Correction for Temperature

variation

Correction = L * * (tm - ts)where

L = measured length

= coefficient of expansion, (0.000 012 per oC forsteel and 0.000 000 9 per oC for invar)

tm = temperature at measurementts = temperature at standardization


22/34


Correction for Tension Variation

Correction = L * (tm - ts) / AE

where

F = force applied or change in tension, measured

by a spring balance or a tension handleL = length measured

A = cross-sectional area of the tape

E = Young's modulus, from 200 to 250 kN/mm2Pm = tension at measurement

Ps = tension at standardization


23/34


Correction For Slope

if the slope distance has to be converted to the

horizontal distance, then either

h, the height differencebetween end-points, or the angle a, the angle of

elevation (or depression), must be measured.

If height difference h is measured, the correction will be

If slope angle a is known correction = L - L cos a = L

( cos a - 1)

L

h

2

2


24/34


Correction for Sag

When the tape is suspended, as in catenary

taping, the unsupported part will sag giving anobserved reading which will be too great.

correction =

w = unit weight of tape

p = tension applied to the tape

L = length measured

2

32

24 p

Lw


25/34


Reduction to Mean Sea Level

Correction = L - L'

=

=

=

RH

LRL

+

RHLRLRLH

+

+

RH

LH

+


26/34


Example

A 50 m steel tape which had previously been

standardized in catenary at a tension of 10 kg and at atemperature of 20oC was found to be 0.005 m too long. It

was used to measure the first 50 m bay of a base line.

Determine the correct length of the bay reduced to mean

sea level from the following data:The recorded length was 49.9915 m when it was

measured in catenary at a temperature of 15oC and at a

tension of 8 kg. The difference in height between

supports was 0.52 m and the base was 308 m above

mean sea level,


27/34


Example

where Mean radius of the earth = 6370 Km

Mass of tape = 0.021 kg/mCross-sectional area of the tape = 3.21 mm2

Young's modulus E = 2.2 * 105 N/mm2

Coefficient of expansion = 12 * 10-6/oC

SolutionSolution :Temperature, C = L * * (tm - ts)

= 49.9915 * 12 * 10-6 * (15 - 20) = -0.0030 m

Slope, C = -h2/2L = (0.52)2 / 2 * 49.9915 = -0.0027 m


28/34


Example

Tension, C = L * (tm - ts) / AE

= (49.9915 * (8 - 10) * 9.81) / 2.2 * 105 * 3.21)= -0.0014 m

Sag, C= +

w L

Tm Ts

2 3

2 2

24

1 1 ( ) ( )=

+

0 021 49 9915

24

1

8

1

10

2 3

2 2

. .

= -0.0129 m

= -0.0024 m

C = H L

H R

+

=

+

308 50

308 6370 000,Mean Sea Level,


29/34


30/34


ObstaclesWhen both end points are invisible fromintermediate points on the line:


31/34


Obstacles Obstructing Chaining


32/34


Obstacles Obstructing Both

Chaining and Ranging


33/34


Perpendicularity (Offsets)

P

Chain

Line

A

B

Q

P

Chain

LineA B

Q

Q

12m

15m9m

A P

Chain Line


34/34


Cross Staff

Chain lineCross Staff

linear measurments

Documents