Download - Lecture 4 Tape Corrections
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8/15/2019 Lecture 4 Tape Corrections
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Department of Geodetic EngineeringTraining Center for Applied Geodesy and Photogrammetry GE 10 – General Surveying I
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Department of Geodetic EngineeringTraining Center for Applied Geodesy and Photogrammetry GE 10 – General Surveying I
At the end of the lecture, the student should beable to: –
Identify, enumerate and apply correctly the rulesand general statement for tape corrections – Discuss the causes of errors in taping and carry
out corresponding corrections
– Determine equations to apply for each tapecorrection
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Department of Geodetic EngineeringTraining Center for Applied Geodesy and Photogrammetry GE 10 – General Surveying I
I. Rules in Tape CorrectionsA. Measuring with a tapeB. Laying out distances using a tapeC. General Statement
II. Corrections to TapeA. Tape not of standard lengthB. SlopeC. Alignment
D. TemperatureE. TensionF. SagG. Wind
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Department of Geodetic EngineeringTraining Center for Applied Geodesy and Photogrammetry GE 10 – General Surveying I
Rules in Tape CorrectionsFirst Rule:
When a line is measured with a tape that is“TOO LONG” , corrections are ADDED
Second Rule:
When laying out a length with a tape that is“TOO LONG”, corrections are SUBTRACTED
Third Rule:
When a line is measured or laid out with a tape thatis “TOO SHORT”, corrections applied are opposite of 1 st and2nd rules
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Department of Geodetic EngineeringTraining Center for Applied Geodesy and Photogrammetry GE 10 – General Surveying I
GENERAL STATEMENT“When measuring with tape
TOO LONG , ADD;
TOO SHORT , SUBTRACT.
Do the r ever se when laying out .”
Rules in Tape Corrections
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Department of Geodetic EngineeringTraining Center for Applied Geodesy and Photogrammetry GE 10 – General Surveying I
Corrections to Tape
1. Due to tape not of standard length2. Due to Slope
3. Due to Alignment
4. Due to Temperature
5. Due to Tension
6. Due to Sag7. Due to Wind
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Department of Geodetic EngineeringTraining Center for Applied Geodesy and Photogrammetry GE 10 – General Surveying I
Often due to imperfections in their manufacture,stretching or wear
Also due to constant use of tapes becomingworn, kinked, and improperly repaired whenbreaks occurred.
Corrections may vary from few millimeters orcentimeters
Tape Not of Standard LengthCorrections to Tape
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Department of Geodetic EngineeringTraining Center for Applied Geodesy and Photogrammetry GE 10 – General Surveying I
Corr = Correction per tape length
TL = True or Actual Length
NL = Nominal Length of tape
Tape Not of Standard LengthCorrections to Tape
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Department of Geodetic EngineeringTraining Center for Applied Geodesy and Photogrammetry GE 10 – General Surveying I
CL = Corrected length of the line to be measured or laid out
ML = length measured or laid out
Corr = Correction per tape length (TL-NL)TL = True or Actual Length per tape length
NL = Nominal Length of tape
NL
MLCorr MLCL
Tape Not of Standard LengthCorrections to Tape
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Department of Geodetic EngineeringTraining Center for Applied Geodesy and Photogrammetry GE 10 – General Surveying I
The length of line AB measured with a 50-m tape is465.285 m. The tape used is found out to be 0.016 mtoo long. Determine the correct length of AB.
ANS: CL = 465.434 m
Tape Not of Standard LengthCorrections to Tape
Example
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Department of Geodetic EngineeringTraining Center for Applied Geodesy and Photogrammetry GE 10 – General Surveying I
When distances are measured along a slope, the equivalent
horizontal distance may correspondingly be determined by applyingan approximate or exact slope correction
Due to SlopeCorrections to Tape
hC sd
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Department of Geodetic EngineeringTraining Center for Applied Geodesy and Photogrammetry GE 10 – General Surveying I
3
42
82 s
h
s
hC
h
s
hC h 2
2
cos1 sC h
Gentle Slopes (30%)
Ch = slope correction = s-dh = Delev between ptss = measured slope distanced = equivalent Horizontal distance
hC sd
Due to SlopeCorrections to Tape
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Department of Geodetic EngineeringTraining Center for Applied Geodesy and Photogrammetry GE 10 – General Surveying I
Slope distances AB and BC are measured with lengths 76.52 mand 84.94 m, respectively. The differences in elevation are30.55 m for points A and B, and –20.60m for points B and C.Determine the combined slope correction for line AC assumingslopes are gentle , steep and very steep . Finally, calculate thecorrected horizontal distance AC for each slope type.
Ch: gentle = 8.596 m, steep = 8.876 m , very steep = 8.899 m
DAC: gentle = 152.864 m, steep = 152.584 m, very steep = 152.561 m
Example
Due to SlopeCorrections to Tape
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Department of Geodetic EngineeringTraining Center for Applied Geodesy and Photogrammetry GE 10 – General Surveying I
Linear error due to inaccuracy in alignment of a tape
Similar to the effect of slope
Easier to control and smaller in magnitude
Generally least important among different tapecorrections
Due to AlignmentCorrections to Tape
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Department of Geodetic EngineeringTraining Center for Applied Geodesy and Photogrammetry GE 10 – General Surveying I
Change in the length of the tape due to variations intemperature
Occurs when measurements are taken attemperatures above or below the standard temperatureof the tape
Correction is usually small and negligible
Proportional to the number of tape lengths
Due to TemperatureCorrections to Tape
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Department of Geodetic EngineeringTraining Center for Applied Geodesy and Photogrammetry GE 10 – General Surveying I
st T T kLC
Ct = Correction due to change in temperature
k = coefficient of linear expansion (steel = 0.0000116/ 0C)
L= length of line measured
T = temperature of tape at time of measurements
Ts = standard temperature of tape (usually 20 0C)
Due to TemperatureCorrections to Tape
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Department of Geodetic EngineeringTraining Center for Applied Geodesy and Photogrammetry GE 10 – General Surveying I
A steel tape is known to be 50 m long at 20 0C. The tape wasused to measure a line 532.28 m long at 35 0C.
Determine:
a) Whether the tape is “too short” or “too long”
b) Ct per tape length
c) Ct total
d) Corrected length of line
Too Long!
0.0087 m
0.0926 m
532.373 m
Example
Due to TemperatureCorrections to Tape
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Department of Geodetic EngineeringTraining Center for Applied Geodesy and Photogrammetry GE 10 – General Surveying I
Arises whenever the pull applied is different from thestandard tension used in calibration
A function of:Difference between applied and standard pulls
Measured length
Cross-sectional area of the tapeModulus of elasticity of the tape material
Due to TensionCorrections to Tape
C i T
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Department of Geodetic EngineeringTraining Center for Applied Geodesy and Photogrammetry GE 10 – General Surveying I
AE
L P P C S M
P
CP = Correction due to incorrect pull applied on the tape (m)
E = modulus of elasticity of the tape material (kg/cm 2)
L= length of line measured (m)PM = pull applied to the tape during measurement (kg)
PS = standard pull applied to the tape (kg)
A = cross-sectional area of the tape (cm 2)
Due to TensionCorrections to Tape
C i T
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Department of Geodetic EngineeringTraining Center for Applied Geodesy and Photogrammetry GE 10 – General Surveying I
A 30-m steel tape weighing 1.45 kg is of standard length under apull of 5 kg, supported for full length. A line 938.55 m long wasmeasured using the tape with a steady pull of 10 kg.
If E = 2.0x10 6 kg/cm 2 and unit weight of steel is 7.9x10 -3 kg/cm 3,determine:
a) cross-sectional area of the tape
b) total C P
c) Correct length of line
= 0.061 cm 2
= +0.038 m
= 938.588 m
Due to TensionCorrections to Tape
Example
C ti t T
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Department of Geodetic EngineeringTraining Center for Applied Geodesy and Photogrammetry GE 10 – General Surveying I
Occurs when tape supports are only at its ends orat the 2 points measured
Will sag because of its own weightTape takes the form of a catenary between points
of supports
Similar to electric or telephone wires which swingsloosely between two posts
Due to SagCorrections to Tape
C ti t T
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Department of Geodetic EngineeringTraining Center for Applied Geodesy and Photogrammetry GE 10 – General Surveying I
CS = Correction due to sag (m)
w = weight of tape per unit length (kg/m)
L= interval between supports or unsupported length of tape (m)
P = tension or pull applied on the tape (kg)
2
32
24 P
LwC
S
Note: The effect of sag always shortens the tape.
Due to SagCorrections to Tape
Corrections to Tape
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Department of Geodetic EngineeringTraining Center for Applied Geodesy and Photogrammetry GE 10 – General Surveying I
A 50-m steel tape weighs 0.04kg/m and is supported at itsendpoints and at the 8-m and 25-m marks. While measuring aline, a pull of 6 kg is applied to the tape. Determine the following:
a) CS for each span
b) Total C S
c) Correct distance between tape ends
CS1 = 0.0009m; C S2 = 0.0091m; C S3 = 0.0289m
= 0.0389 m
= 49.9611 m
Due to SagCorrections to Tape
Example
Corrections to Tape
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Department of Geodetic EngineeringTraining Center for Applied Geodesy and Photogrammetry GE 10 – General Surveying I
Caused by wind blowing perpendicular to thedirection of taping
Wind moves the middle and unsupported portion
of the tape to one side of the line measured
Similar to the effect of sag but is usually much less
Preferable not to undertake any taping workduring windy days
Due to WindCorrections to Tape
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Department of Geodetic EngineeringTraining Center for Applied Geodesy and Photogrammetry GE 10 – General Surveying I
Sources
Davis, R.E., et. al (1981). Surveying: Theory andPractice. USA: McGraw-Hill, Inc.
La Putt, J.P. (2007). Elementary Surveying. Philippines:National Book Store.
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Department of Geodetic EngineeringTraining Center for Applied Geodesy and Photogrammetry GE 10 – General Surveying I