Chapter – 9 .
Contour
1. Definition
2. Contour interval, horizontal equivalent and contour index
3. Factors governing contour interval
4. Characteristics of contour
5. Methods of contouring
6. Contour interpolation and methods of contour interpolation
7. Uses of contour maps
9.1 Definition
Contour An imaginary line on the ground surface joining the points of equal elevation is
known as contour. In other words, contour is a line in which the ground surface is
intersected by a level surface obtained by joining points of equal elevation. This line on
the map represents a contour and is called contour line.
For ex a contour of 90 m indicates that all the points on this line have RL of 90 m.
Similarly, in a contour of 89 m all the points have RL of 89 m and so on.
9.1 Definition
A map showing contour lines is known as Contour map. A contour map gives an idea of
the altitudes of the surface features as well as their relative positions in plan serves the
purpose of both, a plan and a section.
The process of tracing contour lines on the surface of the earth is called Contouring.
PURPOSE OF CONTOURING
i. For preparing contour maps in order to select the most economical or suitable site.
ii. To locate the alignment of a canal so that it should follow a ridge line.
iii. To mark the alignment of roads and railways so that the quantity of earthwork both
in cutting and filling should be minimum
iv. For getting information about the ground whether it is flat, undulating or
mountainous.
v. To find the capacity of a reservoir and volume of earthwork especially in a
mountainous region.
vi. To trace out the given grade of a particular route.
vii. To locate the physical features of the ground such as a pond depression, hill, steep
or small slopes.
9.2 Contour Interval, Horizontal equivalent and Contour Index
Contour Interval
The constant vertical distance between two consecutive contours is called the contour
interval. For ex, a map indicates contour lines of 90 m, 89m, 88 m and so on, the contour
interval is 1m.This interval depends upon the following factors:
• The nature of the ground (i.e. Whether flat or steep)
• The scale of the map
• Accuracy
• Time of cost
Common value of contour interval
• Contour intervals for flat ground are generally small , e.g.. 0.25 m, 0.5 m, 0.75 m
• The contour interval for a steep slope in a hilly area is generally greater, e.g.. 5 m, 10 m,
15 m, etc.
• Again, for a small scale map, the interval may be of 1m, 2 m, 3 m, etc.
• Contour interval is kept large up to 2 m for projects such as highways and railways,
whereas it is kept as small as 0.5 m for measurement of earthwork, building sites, dams,
etc.
• It is desirable to have a constant contour interval for a particular map.
9.2 Contour Interval, Horizontal equivalent and Contour Index
9.2 Contour Interval, Horizontal equivalent and Contour Index
9.3 Factors governing contour interval
The survey leader has to decide an appropriate contour interval for his project before
start of survey work. The following factors govern the selection of contour interval for a
project:
S.No Factor Select High CI like 1m, 2m, 5m or more Select Low CI like 0.5m, 0.25m, 0.1m
or less
1 Nature of ground If the ground has large variation in levels, If the terrain is fairly level
for instance, hills and ponds
2 Scale of the map For small scale maps covering a wide area For large scale maps showing details of
of varying terrain a small area
3 Extent of survey For rough topographical mapmeant for For preparation of detailed map for
initial assessment only execution of work
4 Time and If less time and resources areavailable If more time and resources are
resourcesavailable available
9.3 Horizontal Equivalent
The least horizontal distance between the consecutive contours is called horizontal
equivalent.
It depends on the slope of the ground surface.
9.4 Characteristics of contour
1.Contour lines must close, not necessarily in the limits of the plan.
2.The horizontal distance between any two contour lines indicates the amount of slope
and varies inversely on the amount of slope.
3.Widely spaced contour indicates flat surface.
4.Closely spaced contour indicates steep slope ground.
9.4 Characteristics of contour
5. Equally spaced contour indicates uniform slope.
6.Irregular contours indicate uneven surface.
7.Approximately concentric closed contours with
decreasing values towards centre indicate a pond.
8. Approximately concentric closed contours with
increasing values towards centre indicate hills
9.4 Characteristics of contour
9. Contour lines with U-shape with convexity towards lower ground indicate ridge.
10.Contour lines with V-shaped with convexity towards higher ground indicate valley.
11. Contour lines generally do not meet or intersect each
other. If contour lines are meeting in some portion, it shows
existence of a vertical cliff.
9.4 Characteristics of contour
12. Contours of different elevations cannot cross each other. If
contour lines cross each other, it shows existence of
overhanging cliffs or a cave.
13. The steepest slope of terrain at any point on a contour is
represented along the normal of the contour at that point.
14.Contours do not pass through permanent structures such as
buildings
15.A contour line must close itself but need not
be necessarily within the limits of the map.
9.5 Methods of contouring
There are mainly two methods of locating contours:-
(1)Direct Method and (2) Indirect Method.
Direct Method:
In this method, the contours to be located are directly traced out in
the field by locating and marking a number of points on each
contour. These points are then surveyed and plotted on plan and
the contours drawn through them.
This method is employed only for small area where superior accuracy is demanded.
The method of locating contours directly consists of horizontal and vertical control.
The horizontal control for a small area can be exercised by a chain or tape and a large
area by compass, theodolite or plane table. For vertical control either a level and staff
or a hand level may be used.
9.5 Methods of contouring
Indirect Method:
Indirect methods are less expensive, less time consuming and less tedious as compared
wit the direct methods. These methods are commonly employed in small scale survey of
large areas. This method is most commonly used in engineering survey, while
interpolating it is assumed that slope between two adjacent points is uniform. There are
three different ways of employing the indirect methods of contouring
• (i) Grid Method
• (ii) Cross-Sectional Method
• (iii) Radial line method or Tachometric method
9.5 Methods of contouring
Indirect Method:
Grid method
If the area is not large, it is divided into a grid
or series of squares. The grid size may vary
from 5m x 5 m to 25 m x 25 m depending
upon the nature of the ground, the contour
interval and the scale of the map. The grid
corner are marked on the ground and spot levels
of these corners are then determined by normal
method of leveling using a level. The grid is
plotted to the scale of the map and the spot
levels of the grid corners are entered, the
contours of desired values are then locked by
interpolation. This method is very suitable for a
small open area where contour are required at a
closed vertical interval
9.5 Methods of contouring
Indirect Method:
Cross section method
In this method, suitable spaced cross –sections are projected on either side of the centre
line of the area. Several points are chosen at reasonable distances on either sides. The
observations are made in the usual manner with a level. The cross-section lines are
plotted to the scale, the points on these lines are marked and reduced levels are entered.
The contours of desired values are then located by interpolation. This method is suitable
for road, railway and canal survey.
9.5 Methods of contouring
Indirect Method:
Radial line method or Tachometric
method
In this method, a number of radial lines are
set out at known angular interval (i.e. 15 0
or 30 0) at each station. The point are
selected on a line depend on the nature of
the ground surface. Instead of the level, a
tachometer may be used. The observations
are taken on the staff stations and elevations
and distances are then calculated. A traverse
and radial lines are plotted to the scale RLs
of the point entered. The contour of desired
values are then located by interpolation .
This method is convenient in hilly area.
9.5 Methods of contouring
Comparison of direct and Indirect methods of contouring
Direct Method Indirect Method
Most accurate but slow and tedious Not so accurate but rapid and less tedious
Expensive Reasonable cost
Not suitable for hilly area Suitable for hilly area
During the work calculations can be done Calculations are not required in the field
Calculation can not be checked after Calculation can be checked as and when
contouring required
Suitable for small project requiring high accuracy, Suitable for large project requiring moderate to
e.g. layout of building, factory, structural low accuracy, e.g. layout of highway, railway,
foundations, etc. canal, etc.
9.6 Contour interpolation
The process of spacing the contours proportionally between the plotted ground – points
is termed as interpolation of contours .
This becomes necessary in the case of indirect contouring as only the spot levels are
taken in this method. While interpolation of contours the ground between any two points
is assumed to be uniformly sloping.
There are three main methods of interpolation:
• Estimation
• Arithmetical Calculation
• Graphical Method
i) By Estimation:
The position of the contour points between ground - points are estimated roughly using
eye judgment and the contours are then drawn through these points. This is a rough
method and is suitable for small scale maps.
9.6 Contour interpolation
ii) By arithmetical calculation: This is very tedious but accurate method and is used for
small areas where accurate results are necessary. The contours are interpolated as under:
Suppose A and B are two points at a distance of 30 m and the reduced level of A and B
are 25.45m and 27.54m respectively .Taking the contour interval as 1m, 26 and 27 m
contours may be interpolated in between A and B. The difference of level between A and
B is 2.09m.the difference of level between A and 26m,and A and 27m is 0.55mand 1.55
m respectively. Therefore the horizontal distance
𝐷𝐷 𝑑𝑑
between A and 26 m contour =0.55/2.09 x 30m and =
Between A and 27 m contour =1.55/2.09 x 30m. 𝑅𝑅𝐿𝐿2 − 𝑅𝑅𝐿𝐿1 𝑅𝑅𝑅𝑅 − 𝑅𝑅𝐿𝐿1
These distances are then plotted to scale on the map
Use of straight line equation or similar triangle principle
D=distance between two points A & B (known)
d= distance from points A to required contour
RL= RL of contour to be interpolated (known)
RL1 = RL of point A (known)
RL2= RL of point B (known)
9.6 Contour interpolation
ii) By Graphical method : Graphical method of
interpolation is simpler as compared to
arithmetical method and also the results obtained
are accurate. Out of several graphical methods,
the most common is as given below:
As shown in the fig. suppose the contour interval
is 5m, then on a piece of tracing cloth, a number
of parallel lines spaced at 0.5 m (usually 1/10th
of the contour interval) are drawn. Every tenth
line being made thick.
Suppose it is required to interpolate contours
between two points A and B of elevation 51.5m
and 62.5m respectively
9.6 Contour interpolation
ii) By Graphical method :
If the bottom line represents an elevation of 50m. Then
the successive thick lines will represent 55m, 60m and
65m, etc. Place the tracing cloth so that the point A is on
the third line from the bottom, now move the tracing
cloth until B is on the fifth line above the 60m thick line.
The intersection of the thick lines 1 and 2 representing
elevations of 55m and 60 m and the line AB give the
position of the points on the 55m and 60m contours
respectively and are pricked through on the plan with a
pin.
9.6 Contour interpolation
DRAWING THE CONTOUR LINES
Contour lines are drawn as fine and smooth free hand curved lines. Sometimes they are
represented by broken lines .They are inked in either in black or brown colour. A drawing
pen gives a better line than a writing pen and French curves should be used as much as
possible .Every fifth contour is made thicker than the rest.
The elevation of contours must be written in a uniform manner, either on the higher side
or in a gap left in the line .When the contour lines are very long, their elevations are
written at two or three places along the contour .In the case of small scale maps, it is
sufficient to figure every fifth contour.
8.7 Uses of contour maps
1. A contour map furnishes information regarding the features of the ground , whether it is
flat, undulating or mountainous.
2. From a contour map , sections may be easily drawn in any direction
3. Intervisibility between two ground points plotted on map can be ascertained
4. It enables an engineer to approximately select the most economical or suitable site for an
engineering project such as a road, a railway, a canal or a pipe line etc.
5. A route of a given grade can be traced on the map.
6. Catchment area and capacity of a reservoir may be determined from the contour map.
7. Contour map may be used to determine the quantities of earth work.
