lecture 4 tape corrections

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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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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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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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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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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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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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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Corr = Correction per tape length

TL = True or Actual Length

NL = Nominal Length of tape



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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



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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


Example


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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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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



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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



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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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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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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)



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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



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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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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)


C i T


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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


Example

C ti t T


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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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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.


Corrections to Tape


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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


Example

Corrections to Tape


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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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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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lecture 4 tape corrections

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