1. CHAPTER 2 CHAIN SURVEYING Tape Measurements

2. Mapping Details using chain surveying
In chain surveying all ground features (natural or industrial) are located and mapping by measuring lengths using tapes to a selected lines called chain lines .This done by one of two ways:
1- Ties method : Offsets method:
Pole
Building
Pole
Building
Chain lines
offsets
Ties
Ground Details may be located by the method of ties or offsets or a combination of both. The two methods depend on measuring horizontal distances between points and setting Right angles using some of surveying equipments.

3. Chain Surveying Equipments
1- Equipments used for the measurements of lines :
A- The chain
B- Tapes: synthetic, glass fiber, coated steel or plain steel of lengths: 10m,
20m, 30m, 50m . , tapes are more accurate than chain.
C- Invar Tapes: accurate tape made of steel (65%) & Nickel (35%) but they
are very expensive .
2- Equipments used for making right angles :
A- The cross staff:
B- Site square: consists of two telescopes, their lines of
sight at 90º .

4. C- The optical square: There are two types:
mirrors & prism
3- Other equipments:
a- Ranging Rods: 2m, 2.5m, 3m long & painted red and white each 0.5m with a pointed steel shoe.
b- Arrows: 40cm long & 3- 4 mm in diameter.
c- Pegs: wooden (square or circular cross-section) & steel
d- Plumb Bob: a metallic cone object used to erect vertical lines.
e- Clinometer & Abney level: used to measure the inclination angle of slope lines.

5. Processes in Chain Surveying
1- Ranging and measurement of lines:
a- Level ground.
b- Uniformly Sloping Ground.
c- Uneven Ground (non-uniformly sloping ground): using stepping process.
2- Setting out right angles:
A- Dropping a perpendicular from a point to a line:

6. B- Setting out a perpendicular to a line from a specific point:
1- Using the optical square.
2- The equilateral triangle method.
3- Pythagoras theorem method.

7. Plan of Mapping details using chain surveying
1-Reconnaissance: The surveyor should visit the area to be mapped in order to:
a- Notice the shape of the area, the existing details and draws a reasonable sketch of the area showing all details such as roads, buildings, fences, electric poles, ….etc.
in addition to the approximate north direction.
b- Choose the most suitable location for the survey station which form the chain lines,
the following points should be taken into consideration when choosing survey stations:
1- chain lines should form well-conditioned triangles with internal angles is between 30º
and 120º .
2- chain lines should be chosen as close as possible to the mapping details.
3- It should be possible to see at least two other survey stations from each station.
4- The number of chain lines should be kept to a minimum, but enough to locate all details.
5- Survey station should be chosen in away such that check lines is available.
6- Survey Station should be chosen on firm ,easy to reach grounds.

8. 2- Booking the measurements
20cm.
1.50cm
15cm

9. 3- Plotting the details:
a- Choose the appropriate scale
b- If you are drawing the map manually, using a pencil to draw the chain lines on a transparent paper, in order to center the drawing on the final map sheet.
c- Try to make the north direction pointing towards the top of the sheet.
d- Offsets and ties are plotted systematically in the same order in which they were measured and booked.
e- After finishing the drawing by pencil, the plan is taken to the site and checked.
Accuracy of Measurements:
A good draughtsman can plot a length to within 0.20 mm.
(0.20mm on a map of scale 1:500 represents 10cm on the ground).
(0.20mm on a map of scale 1:100 represents 2cm on the ground).
As a result ,measuring a line to 1 cm accuracy is practically sufficient for such scales.

10. Chaining Obstacles 1-Vision obscured, Chaining possible:
2- Vision Possible, Chaining Prevented:
A- Measurements can be made around the obstacle:
AB = AC + EF + DB
AB = AG + KL + HB

11. B- The width of obstacles is greater than tape length:
Case a:
HG = FD .FG /ED
= CG × FG / (EC – FG)
Case b:
The unknown distance FH
Is equal to JG which can
easily measured
Case c:
EG = CE × EF / ED

12. 3-Both Chaining and Vision prevented:
GD = FC × GA / FA
HE = FC × HA / FA
ED is the missing part of AB
Length AB = AD + DE + EB
DE = HJ
MN = 2 CD

13. ERRORS IN CHAIN SURVEYING
1- Blunders (Mistakes).
2- Systematic errors:
a- Temperature correction : Ct = ( T1 – T0 ) L
is the coefficient of thermal expansion of steel per 1º C
T1 = is the field temperature.
T0 = is the temperature under which the tape is calibrated
L = is the length of the line
b- Sag correction: Cs = -W²L / 24 P² or = - w² L³ / 24 P²
W = the total weight of the section of tape located between supports.
w = weight per meter of tape
L = the interval between supports
P = the tension on the tape
Ex : calculate the sag correction for :
a- A 100 ft steel tape weighting 2 ib and supported at the ends only with a 12 Ib pull
b- A 30 m steel tape weighting kg/m and supported at 0, 15, 30m points under a tension of 5 kg.
Solution
a- Cs = -W²L / 24 P² = - (2² × 100 ) / ( 24 × 12² ) = ft
b- Cs = - 2 ( w² L³ / 24 P²) = -2 (( ² × 15² ) / (24 × 5² )) = m.

14. Cp = the elongation of the tape of length L in m.
c- Tension correction: Cp = (P1 – P0 ) × L / AE
Cp = the elongation of the tape of length L in m.
P1= the applied tension
P0= the calibration tension
A = the cross-sectional area of the tape in cm²
E = the modulus of elasticity of the tape material (for steel E= 29,000,000
ib/in² ).
d- Length correction: Cl = ( la – l0 ) L / l0
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.