FUNDAMENTALS OF SURVEYING : Contour

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 1^lar 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 + — — + O_n) d

Area = 1

(O + O₂ +O₃ +— —+ O_n)

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 [A_o + A_n+ 2(A + A₂+ — — + An—1)]

Prismoidal formula or simpsons rule:

h

V= [A + A_n+ 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.

Symbol	Description	Symbol	Description
	Village (open)		Telephone Line
	Church		Electric Power Line
	Temple		Railway, Broad Gauge Double Line
	Mosque		Bridge carrying Railway over Road
	Idgah		Metalled Road
	Burial-Ground		National Highway
	Boundary pillar		UN-Metalled Road
	Aerodrome		Level Crossing
	Well		Foot Path with Bridge, Culvert

	Well		Foot Path with Bridge, Culvert
	Swamp or Marsh with Cultivation		( Road or Railway ) Embankment
	Lake with		Orchard / Garden / Plantation
	a)Defined Limit
	b)Fluctuating Limit c)Embankment
	Single Line Stream		Trees
	a) Perennial		a) Scattered
	b) Non-Perennial		b) Surveyed
	Canal with Navigation Lock and Road		Bench Mark
	Aqueduct with Road Alongside		Triangulation Station
	Earthwork Dam		Broken or Rocky Ground
	Masonry dam with Road		Contours