Linear Measurement
one of the fundamental measurements in
surveying
depending on the type of instruments used,
there are three basic methods of determining
distance:
™Direct
™Indirect and
™Electronic
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Direct Method
- using tapes and accessories to measure the distance
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Indirect Method
- using optical means (i.e. stadia or tacheometry) to measure the
distance. Height can also be determined using this method.
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Electronic Method
- using an instrument known as Electromagnetic Distance
Measuring (EDM) instrument to measure distance
EDM
A
ELS/DC/MH
Reflector
B
C
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Comparisons
Method
Instrument
Precision
Usage
Direct
Tape
1/500 to
1/30000
General distance
measurement, baseline
measurement
Indirect
Theodolite
or Level
1/300 to
1/20000
Topographic survey,
general traversing
1/10000 to
1/300000
Trilateration, General
distance measurement
Electronic EDM or
Total
Station
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METHODS OF MEASUREMENT
Pacing:
™a rapid means of approximately checking more precise
measurements of distance
™used 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 circumference
of the wheel
Optical: Stadia or Tacheometry
™involves measuring the interval between the stadia hairs as
shown on a leveling staff held vertically at a point
™Distance = (UH – LH) x 100
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Types of Tapes
Taping
™involves direct measurement of the distance with
tapes which are graduated in metres, decimetres,
centimetres and sometimes in millimetres
™the most popular nominal length is 30 m, but 50 m
and 100 m
™usually reeled up in either boxes or open-reel frames.
Four kinds of tapes are used:
1)Synthetic/Fibre-Glass Reinforced Tape
2)Steel/Plastic Composite Tape
3) Steel Tapes
4)Invar tapes
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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 be
highly precise
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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 give
a uniform dimension
temperature and tension
variations
can
be
corrected.
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Steel Tapes
made from high-quality
steel which is thicker and
heavier than steel/plastic
composite tape
more precise and more
stable
nominal length:
™ temperature = 20°C and
™ applied tension between 50
N to 80 N
printed on the zero end of
tape
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Invar Tape
most precise tape
made from an alloy of
36% 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
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Ancillary Equipment (1)
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Ground Taping or Surface Chaining –
taping on smooth or level ground
Minimum of two people are required of whom one is the leader and
the other is the follower.
When making a measurement, the leader performs the following
functions:
™ holds the tape reel and move towards the distant point;
™ sets the direction of travel; and
™ does the booking.
The follower performs 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 done
simultaneously.
™ When the follower has brought the zero end of the tape against the
ground 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.
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Ground Taping or Surface Chaining –
taping on smooth or level ground
Leader
Follower
Surveyor - directing the alignmnet
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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 measurement
different "zero" point should be used for each
reading, e.g.. first reading starts with 0, second
reading starts with 0.100, etc., to avoid
systematic error.
difference between the leader and the "zero" of
the follower gives the distance
mean of all the individual measurements gives a
more accurate result and will eliminate most of
the gross errors in linear measurement
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Sloping Ground: Step Chaining
Distance AB = S1 + S2 + S3
Point A
Point B
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Slope Distance : Height
Difference & Slope Angle
Distance AB = √ L2 – (Δh)2 OR Distance AB = L * cos a
Point A
L
α
Δh
ELS/DC/MH
Point B
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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 measured
distance, the numerator should be set to 1 while the denominator
should be as large as possible.
Precision = (error in distance) / total measured distance
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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 : distance
must be reduced to Principal Datum of Hong
Kong
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Calibration (Standardization)
Prior to any measurement, the servicing tape, i.e.
tape to be used, must be calibrated with a
standard 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
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Correction for Temperature
variation
Correction = L * α * (tm - ts)
where
L = measured length
α = coefficient of expansion, (0.000 012 per oC for
steel and 0.000 000 9 per oC for invar)
tm = temperature at measurement
ts = temperature at standardization
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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 handle
L = length measured
A = cross-sectional area of the tape
E = Young's modulus, from 200 to 250 kN/mm2
Pm = tension at measurement
Ps = tension at standardization
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Correction For Slope
if the slope distance has to be converted to the
horizontal distance, then either Δh, the height difference
between end-points, or the angle a, the angle of
elevation (or depression), must be measured.
If height difference Δh is measured, the correction will be
⎛ h2 ⎞
⎜⎜ ⎟⎟
⎝ 2L ⎠
If slope angle a is known correction = L - L cos a = L
( cos a - 1)
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Correction for Sag
When the tape is suspended, as in catenary
taping, the unsupported part will sag giving an
observed reading which will be too great.
correction =
w 2 L3
24 p 2
w = unit weight of tape
p = tension applied to the tape
L = length measured
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Reduction to Mean Sea Level
Correction = L - L'
R×L
= L−
H +R
ELS/DC/MH
=
H × L + R× L − R× L
H +R
=
H × L
H + R
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Example
A 50 m steel tape which had previously been
standardized in catenary at a tension of 10 kg and at a
temperature 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,
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Example
where
Mean radius of the earth = 6370 Km
Mass of tape = 0.021 kg/m
Cross-sectional area of the tape = 3.21 mm2
Young's modulus
E = 2.2 * 105
Coefficient of expansion α = 12 * 10-6/oC
N/mm2
Solution :
Temperature, C = L * α * (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
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Example
Tension, C = L * (tm - ts) / AE
= (49.9915 * (8 - 10) * 9.81) / 2.2 * 105 * 3.21)
= -0.0014 m
2
3
2 3
0
021
49
9915
×
.
.
1
1
w
L
(
) (
) ⎡− 1 + 1 ⎤
⎡
⎤
Sag, C =
=
−
+
⎢⎣ 82 102 ⎥⎦
24
24 ⎢⎣ Tm2 Ts 2 ⎥⎦
= -0.0129 m
Mean Sea Level,
H×L
C=
H+R
308 × 50
=
308 + 6370,000
= -0.0024 m
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Example
No.
1
2
3
4
5
6
Types of Correction
Standard
Temperature
Slope
Tension
Sag
Mean Sea Level
+
0.0050
0.0050
-0.0224
-0.0174
0.0030
0.0027
0.0014
0.0129
0.0024
0.0224
Correct length = 49.9915 - 0.0174 = 49.9741 m
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Obstacles
When both end points are invisible from
intermediate points on the line:
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Obstacles Obstructing Chaining
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Obstacles Obstructing Both
Chaining and Ranging
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Perpendicularity (Offsets)
P
P
B
Chain
Line
Chain
Line
A
A
Q
B
Q
Q
15m
9m
A
Chain Line
P
12m
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Cross Staff
Cross Staff
Chain line
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