1. Surveying Chain Surveying
Faculty of Applied Engineering and Urban Planning
Civil Engineering Department
Surveying
First Semester 2010/2011
Chain Surveying
Part V: Errors
Lecture 8- Week 5

2. Revision Chaining Obstacles Vision is obscured, Chaining is Possible
Vision Possible, Chaining is Obscured
Both of Vision and Chaining are Obscured

3. Vision is Possible, Chaining is Obscured

4. Vision is Possible, Chaining is Obscured
From the similar triangles
EDF, FGH

5. Vision is Possible, Chaining is Obscured

6. Vision is Possible, Chaining is Obscured

7. Both of Vision and Chaining are Obscured
Random Line

8. Both of Vision and Chaining are Obscured
Prolonged Line

9. Both of Vision and Chaining are Obscured
A-Method

10. Both of Vision and Chaining are Obscured
A-Method

11. Errors in Chaining
Types of Errors:
Blunders
Systematic
Random Errors

12. Blunders Mistakes caused by human carelessness Omitting Measurement
Misreading the chainage (14 m 16 m)
Erroneous Booking (32.14 >> 23.14)

13. Systematic Errors Their source and effect are known Temperature Ct
Sag Cs
Tension Cp
Length Errors due to Wear and Tear Cl
Cc = Ct + Cs + Cp + Cl

14. Systematic Errors Temperature Correction Ct Ct = 0.0000116 (T1 – To) L
( ) thermal expansion coeff.
for steel per 1oC
T Field Temp.
To Temp. under which tape is calibrated
L Length of Line

15. Systematic Errors
Sag Correction

16. Systematic Errors or W Total weight between supports
Sag Correction or
W Total weight between supports
w weight per meter
L Interval between supports
P Tension on the tape

17. Systematic Errors
Calculate the sag correction for a 30 m steel tape weighing kg/m and supported at 0, 15 and 30 points under a tension of 5 kg.

18. Systematic Errors
Calculate the sag correction for a 100 ft steel tape weighting 2 Ib and supported at the ends only with a 12 Ib pull
Cs = -W²L / 24 P² = - (2² × 100 ) / ( 24 × 12² )
= ft

19. Systematic Errors

20. Systematic Errors Cp Elongation of tape P1 Applied Tension
Tension Correction
Cp Elongation of tape
P1 Applied Tension
Po Calibrated Tension
A Cross-Sectional Area
E Modulus of Elasticity

21. Systematic Errors Cl Length Correction la Actual Length of Tape
lo Nominal Length of Tape
L Length of Measured Line

22. Systematic Errors
Length Correction

23. Systematic Errors
Ex: A line is measured with a tape believed to be 100 ft long which gives a length of ft . On checking ,the tape is found to measure ft . What is correct length of the line ?
Solution
la = ft , l0 = 100 ft , L = ft
Cl = ( – 100 ) × / 100 = ft
correct length = ft = ft.

24. Random Errors
Error can be minimized by making several measurements and then calculating the average

25. Example
The tape has a mass of kg/m and a cross-sectional area of 3.24 mm2. It was standardized on the flat at 20°C under a pull of 89 N.
The coefficient of linear expansion for the material of the tape is /oC, and Young's modulus is 20.7 x 104 MN/m2.
Station length (m) Temp. (oC) Tension (N) I
Determine the absolute length of the survey line.

26. Example
Station L L3

27. Example

28. Example
= m

29. Exercises
The slope distance between two points was measured to be ft. the difference in elevation between the two ends of the line was found to be Compute the horizontal distance.
Two edges of an axis of a road deflect by an angle = 90. using a tape of length = 30m, ranging rods, pegs, arrows and an optical square, show how to connect those lines by a circular curve of a radius = 26m. Give the solution for the two cases when the center of the curve can be reached and when the center cannot be reached due to the existence of an obstacle such as a building.

30. Exercises
A four-sided land parcel. ABCDA has a building inside it, which obscure vision along the diameters AC and BD. Describe a simple way to indirectly measure these diameters. Assume that the internal angles of the land parcels are different from 90.
A line is measured along a long gentle slope using a 20m tape. The gradient of the line is measured with an Abney level and found to be ’ . The slope distance is recorded as m. The length of the tape was found to be only 19.96m. Calculate the correct horizontal length of the line.

31. Questions?!