Contour:
Contour is a imaginary line
joining points of equal elevation.
Vertical distance between any
two consecutive contours is called “contour interval”
Horizontal distance between any two points on two consecutive contours is known
as “horizontal equivalent”.
Choice of contour interval
depends upon:
1)
The nature ofthe ground
2)
The scale of the map.
3)
The purpose and extent of the survey.
4)
Time
and expense of field and office work. Characteristics of contours:
1)
Two contour lines of different elevations never cross
each other. If they crosses that means point of intersection may have two
different elevations. However contour line can intersect only in case of
overhanging cliff or cave
2)
Contour lines of different elevations con unite to form
one line only in the case ofa vertical cliff.
3)
Contour
lines close together indicates steep slope if they are a part, gentle slope is
there. If contour lines are equally spaced, uniform slope is indicated.
4)
A contour passing through any point is 1lar to
the line of steepest slope at that point.
5)
A closed contour line with one or more higher readings
inside it represents a hill. A closed contour with one or more lower ones
inside it represents a depression without an outlet.
6)
Two contour line having same eleven cannot unite and
continue as one line similarly, single contour cannot split into two lines.
7)
Contour line must close upon itself, though not
necessarily within the limits of map.
8)
Contour
lines cross a watershed or ridge line at right angles. They form curves of U
shape round it with the concave side of the curve towards higher ground
9)
Contour
lines cross a valley line at right angles. They from sharp curves of V – shape
across it with the convex side of the curve towards higher ground.
10)The same contour
appears on either side of a ridge or valley, for the highest horizontal plane
that intersect the ridge must cut it on both sides. Uses of contour maps:
1)
In drawing sections
2)
Determination of intervisibility between two points
3)
Tracing of contour gradients and location of route.
4)
Measurement ofdrainage area.
5)
Calculation ofreservoir capacity
6)
Intersection of surfaces and measurement of earthwork. Areas
& volumes : One of the objective of survey is to find out areas
& volume.
I)
Area by dividing into no of triangles:
Area ofan irrengular triangle can
be calculatede by the following formula.
A= S(S—a)(S—b)(S—c)
S + + a b
c
Where,
a, b & c are sides of a tringle. & =_______ =
half perimeter.
2
II)
Area
using offsets taken from a base line : (offsets at regular interval) a) Mid-ordinate rule
:
d d d d
 |
|
L = nd
|
|
 |
|
|
|
offset is taken at unid pt. of
each divsion
Area = avg. ordinate x length of base
Area = (O1+ O2 + O3 + — — + On) d
Area = 1
(O + O2 +O3 +— —+ On)
n
b) Average ordinate method :
offset is meavred to each of the
points of the dinision of the base line.
 |
L
=
n+1
EO
 |
c) Trapezoidal rule :
- Assumes that area betn two offsets trape zoids.
- This is more accurate than
previous two methods.
 |
A=h 2 [O0+ O,2+2(O1+ O2 + — — +O,2—1)1
d) Simpsons 1/3 rd rule :
- The boundaryy betn the
ordinates is assumed to be parabolic
- Formula is useful when boundary
betn offsets departs covisiderably from straight line.
- Thin formula is applicable when
total no of ordinates are odd i.e. the no of dicisions of area are
even
Area = [
h O + O + X O +
O + O + O + O
6
4 ( 1 5
) 2( 2 4
) ]
0 3
3
Since,
ordinates are even (7 +1 = 8) simpsons rule is applied any upto O6
(odd ordinate) & ( O + O X
6 7 h.
area of lact region is calculated
by 2
III)Meridian
distances :
- The meridian distance
of any points in the point from the reference meridian, measured at right
angles to the meridian.
- The meridian passing through
most westerly station of a traverse is called as reference meridian.
Meridian distance of any line =
meridian dist of preceding line + half the departure of provious line + half
the departure of line itself
Area of closed = m.L travers
- The latitude (L) is taken as
positive if it is northing & negative ifit is southing.
Double Meridian Distance (DMD)
DMD ofa line is equal to the sum
ofthe meridan distance ofthe two extremities.
DMD of any line = DMD of
preceding line
+ departure of proceding line
+ departure of line itself.
|
Area,
|
A = ML
1 ( )
2
|
Steps to find area by MD/DMD
1)
Find
MD/DMD of each survey line.by taking eastwared departures
positive & westward as negative.
2)
Multiply
MD/DMD of each line by its latitude, taking nothward latitude as positive &
southen as negative.
3)
If
M.D. are used then a bove algebric sum gives areas oftraverse & if DMD’s
are used then half of the above algebric sum given area of traverse.
IV)Area from
co-ordinates:
 |
Here, it is copuplsory to
calculate the independent co-ordinates of all the point
Example 12.5 Punmia
Planimeter :
An instrument which measures the
area of plan or map of any shape very accurately.
- Areas betn curved boundaries an
a plan or map can be found by planimeter.
- Amsler polur planimeter is
most communly used.
- The error involved in the
planimeter measurement are accidental and are mainly due to the
inability ofthe observer to
follow exact boundary ofthe figure with the tracing point.
Zero circle or circle
of correction :
The circle round the
clrcumference of which ifthe tracing point is moved, the wheel will simply.
slide (without rotation) an the
paper without anyy change in the reading.
Measurement of volume
:
End are formula or
trapezoodal formula
h
V=2 [Ao + An+
2(A + A2+ — — + An—1)]
Prismoidal formula or
simpsons rule:
h
V= [A + An+ 4x odd + 2x even] 2 o
- Namber of cross-sections
should be odd. i.e no of strips should be even.
- If there are even number of
sections then last strip must be treated separately.
Prismoidal correction:
- Prismoidal correction is equal
to the diffreance betn the volumes calculated by end area formula
& prismoidal formula.
- Correction is always
substractive & it is always substracted from the volume calcilaed by end
area formula or trapezoidal
formula.
Level Section :
C =
L8
P
8 Slope
L = contant distbetn section.
Curvature Correction:
The prismoidal & end area formula were derived an
the assumption that the end sections are in parallel planes.
When center line of embankment
or cutting is curved in plan, it is common ptactice to calculate the volume as
if the end sections are in patallel planes and apply the aorrection for
curvature
L b
2 2
C =____ (
W 1
W h _______
— 2
) ( + )
c 6 R 2
S
b= bottom width of cutting or top
width of embankment
The correction is positive (negative) ifthe centroid
of the volume and the center of the curvature are to the opposite (same) side
of center line.
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Symbol
|
Description
|
Symbol
|
Description
|
|
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Village
(open)
|
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Telephone
Line
|
|
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Church
|
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Electric Power Line
|
|
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Temple
|
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Railway,
Broad Gauge
Double Line |
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|
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|
|
|||
|
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Mosque
|
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Bridge
carrying Railway over Road
|
|
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Idgah
|
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Metalled Road
|
|
|
Burial-Ground
|
|
National Highway
|
|
|
|||
|
|
Boundary
pillar
|
|
UN-Metalled Road
|
|
|
Aerodrome
|
|
Level Crossing
|
|
|
|||
|
|
Well
|
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Foot
Path with Bridge,
Culvert |
|
|
Well
|
|
Foot
Path with Bridge,
Culvert |
|
|
Swamp
or Marsh
with Cultivation |
|
(
Road or Railway )
Embankment |
|
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Lake with
|
|
Orchard
/ Garden /
Plantation |
|
a)Defined Limit
|
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b)Fluctuating Limit c)Embankment
|
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Single Line Stream
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Trees
|
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a) Perennial
|
a)
Scattered
|
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b) Non-Perennial
|
b)
Surveyed
|
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Canal
with
Navigation Lock and Road |
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Bench Mark
|
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Aqueduct
with
Road Alongside |
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Triangulation Station
|
|
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Earthwork Dam
|
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Broken
or Rocky
Ground |
|
|
Masonry
dam with
Road |
|
Contours
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