Measurement of Horizontal Distances
the distance between two points means the horizontal distance
Methods of Linear Measurements
Pacing
Mechanical Devices
Taping*
Tachymetric
Photogrammetric*
Electronic Distance Measurement (EDM)*
Distance by Pacing
Pacing ◦ Consists of counting the number of steps, or paces, in a required distance
Length of a pace varies with different persons
Pace Factor = Distance Average No. of Steps
1 Pace (Toe to Toe)
1 Pace (Heel to Heel)
1 Stride (2 Paces or Double Step)
1 Stride (2 Paces or Double Step)
Distance by Mechanical Devices
This method can often be used to advantage on preliminary surveys where precise distances are not necessary
For low precision surveys or for quick measurements
Odometer & Measuring Wheel converts the number of revolutions
of a wheel of known circumference to a distance.
Distance by Photogrammetric
Photogrammetry ◦ Measurement of images on a photograph
◦ Photographs taken from an aircraft with the axis of the camera pointed vertically towards the terrain photographed
Distance by EDM
These devices send out a beam of light or high-frequency microwaves from one end of a line to be measured, and directs it toward the far end of the line.
A reflector or transmitter-receiver at the far end reflects the light of microwave back to the instrument where they are analyzed electronically to give the distance between the two points.
Distance by EDM
Distance by Tachymetric
Based on the optical geometry of the instruments employed; indirect method of measurement
1. Stadia Method ◦ Factors:
Refinement with which the instrument was manufactured
Skill of observer
Length of measurement
Effects of refraction
Distance by Tachymetric
1. Stadia Method
CKsD
D = horizontal distance K = stadia interval factor of the instrument s = difference between the upper and lower stadia hair reading C = stadia constant
Distance by Tachymetric
2. Subtense Bar Method
α α/2
D (Horizontal Distance)
S/2
S/2
S
Theodolite or Transit
2-m Long Subtense Bar
Left Target Mark
Right Target Mark
D
STan
2/)2/(
)2/(
2/
Tan
SD
)2/()2/(
1
Cot
TanD
Since S=2.00m
D = horizontal distance α = angle subtended by the targets
Illustrative Problem
1. A stadia rod held at a distant point B is sighted by an instrument set-up at A. The upper and lower stadia hair readings were observed as 1.50m and 0.80m, respectively. If the stadia interval factor is 100, and the instrument constant is 0, determine the length on line AB.
2. The following subtended angles were read on a 2m long subtense bar using a transit: 0°55’45”, and 0°10’50”. Compute the horizontal distance from the transit to each position of the bar.
Distance by Taping
Most common method of measuring or laying out horizontal distances
Consists of stretching a calibrated tape between two points and reading the distance indicated on the tape
a. Steel Tape b. Meter c. Marking Pins d. Clamp Handles e. Range Pole f. Plumb bobs
Taping Corrections
• Incorrect Tape Length
• Slope
• Temperature
• Pull (Tension)
• Sag
• Alignment
• Wind
Incorrect Tape Length
A systematic error occurs when incorrect length of a tape is used.
The true length of a tape can be obtained by comparing it with a standard tape or distance.
An error caused by incorrect length of a tape occurs each time the tape is used.
When measuring,
•If the tape is long, add the correction.
•If the tape is short, subtract the correction.
Incorrect Tape Length
Measured Distance A 100m B
AB is measured using 2 tape lengths
But, the tape length is actually 50.02m (Tape is too long)
So AB is actually: 2(50.02) = 100.04m
Must add a correction of 2(0.02) = 0.04m
Incorrect Tape Length
Measured Distance A 100m B
AB is measured using 2 tape lengths
But, the tape length is actually 49.98m (Tape is too short)
So AB is actually: 2(49.98) = 99.96m
Must subtract a correction of 2(0.02) = 0.04m
Incorrect Tape Length
When laying out,
•If the tape is long, subtract the correction.
•If the tape is short, add the correction.
Incorrect Tape Length
Layout Distance (construction surveys)
A 100m B
The distance between A and B must be 100m.
But, the tape length is actually 50.02m (Tape is too long)
2 tape applications: 2(50.02) = 100.04m
Must subtract a correction of 2(0.02) = 0.04m
Incorrect Tape Length
Layout Distance (construction surveys)
A 100m B
The distance between A and B must be 100m.
But, the tape length is actually 49.98m (Tape is too short)
2 tape applications: 2(49.98) = 99.96m
Must add a correction of 2(0.02) = 0.04m
Incorrect Tape Length
TL = actual length of tape Cl = total correction to be applied to
the measured length or length to be laid out
CL = corrected length of the line to be
measured or laid out ML = measured length or length to be
laid out NL = nominal length of tape
l
l
CMLCL
NL
MLCorrC
NLTLCorr
Incorrect Tape Length
Illustrative Problem
1. A rectangular lot was measured using a 50-m steel tape which was found to be 0.025m too short. If the recorded length and width of the lot are 180.455m and 127.062m, respectively, determine the following:
a. Actual dimension of the lot.
b. Error in area introduced due to the erroneous length of tape.
Due to Slope
s
hCh
2
2
Gentle Slope (s < 20%)
3
42
82 s
h
s
hCh
Steep Slope (20% < s < 30%)
)cos1( sCh
Very Steep Slope (s > 30%)
s = measured slope distance between points A and B
h = difference in elevation between A
and B d = equivalent horizontal distance
AC Ch = slope correction
hCsd
Illustrative Problem
2. Slope distance AB and BC measures 300.50m and 650.01m, respectively. The differences in elevation are 15.00m for point A and B, and 20.05m for point B and C. using the approximate slope correction formula for gentle slopes, determine the horizontal length of line ABC. Assume that line AB has a rising slope and BC a falling slope.
Due to Temperature
)( 12 TTkLCt
k= coefficient of linear expansion or the amount of change on length per unit length per degree change in temperature L = length of the tape or length of line measured T2 = observed temperature of the tape at the time of measurement T1 = temperature at which the tape was standardized
For steel: k = 0.0000116/°C Standard Temperature = 20 °C
A temperature higher or lower than the standard temperature causes a change in length
If T2 > T1, +Ct (too long); otherwise, - Ct
Illustrative Problem
3. A steel tape with a coefficient of linear expansion of 0.0000116/°C is known to be 50m long at 20°C. The tape was used to measure a line which was found to be 656.29m long when the temperature was 40°C. Determine the following:
a. Temperature correction per tape length
b. Temperature correction for the measured line
c. Correct length of the line
Due to Pull / Tension
p
p
CLL
AE
LPPC
'
)( 12
Cp= total elongation in tape due to pull or the correction due to incorrect pull applied on the tape (m)
P2 = pull applied to tape the during
measurement (kg) P1 = standard pull (kg) L = measured length of line A = cross-sectional area of the tape
(sq. cm) E = modulus of elasticity (kg/cm2) L’= corrected length of the measured
line (m)
If Pm > Ps, too long; otherwise, too short
Illustrative Problem
4. A heavy 50-m tape having a cross-sectional area of 0.05cm2 has been standardized at a tension of 6.0kg. If E=2.10x106 kg/cm2, determine the elongation of the tape if a pull of 15kg is applied.
Due to Sag
• A steel tape not supported along its entire length sags in the form of a catenary curve
• Because of sag the horizontal distance is less than the graduated distance between tape ends
• Sag can be reduced by applying great tension, but not eliminated unless the tape is supported throughout
Due to Sag
2
2
2
32
24
24
P
LWC
P
LwC
s
s
Cs= correction due to sag or the difference between the tape reading and the horizontal distance between supports (m)
w = weight tape per unit length
(kg/m) W = total weight of tape between
supports (kg) L = interval between supports or the
unsupported length of tape (m) P = tension or pull applied on the
tape (kg)
Illustrative Problem
5. A 50-m steel tape weighing 0.035kg/m is constantly supported at mid-length and its end points, and is used to measure a line AB with a steady pull of 6.5kg. If the measured length of AB is 1200.00m, determine the following:
a. Correction due to sag between supports and for the whole tape length
b. Total sag correction for the whole length measured
c. Correct length of line AB
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