# A Valley of Rolling Hills is an Example of _____

## CHAPTER iii – ELEMENTS OF TOPOGRAPHY

iii.1 Slopes
3.2 Elevation of a point
3.iii Contour lines
3.iv Maps

## iii.1 Slopes

3.ane.i Definition
3.1.two Method of expressing slopes
3.1.iii Cross slopes

### 3.1.1 Definition

A gradient is the rise or autumn of the country surface. It is important for the farmer or irrigator to identify the slopes on the land.

A slope is easy to recognize in a hilly expanse. Start climbing from the foot of a hill toward the peak, this is called a rise slope (see Fig. 46, black pointer). Go downhill, this is a falling slope (see Fig. 46, white pointer).

Fig. 46. A rising and a falling slope

Flat areas are never strictly horizontal; there are gentle slopes in a seemingly apartment area, just they are often hardly noticeable to the naked eye. An accurate survey of the land is necessary to identify these so called “flat slopes”.

### 3.ane.2 Method of expressing slopes

The slope of a field is expressed as a ratio. It is the vertical distance, or deviation in height, between 2 points in a field, divided by the horizontal distance between these 2 points. The formula is:

….. (14a)

An instance is given in Fig. 47.

Fig. 47. The dimensions of a slope

The slope can also be expressed in per centum; the formula used is so:

….. (14b)

Using the same measurements shown in Fig. 47:

Finally, the slope can be expressed in per mil; the formula used is then:

….. (14c)

with the figures from the aforementioned example:

NOTE:

Slope in ‰ = slope in % x 10

QUESTION

What is the slope in pct and in per mil of a field with a horizontal length of 200 thousand and a superlative difference of ane.5 chiliad between the peak and the lesser?

Field slope in ‰ = field slope in % x ten = 0.75 x ten = 7.5‰

QUESTION

What is the difference in height betwixt the top and the bottom of a field when the horizontal length of the field is 300 m and the slope is 2‰.

thus: height difference (m) = 0.002 x 300 m = 0.6 m.

The following tabular array shows a range of slopes commonly referred to in irrigated fields.

 Slope % ‰ Horizontal 0 – 0.2 0 – two Very flat 0.ii – 0.5 2 – five Flat 0.v – i 5 – 10 Moderate one – 2.5 10 – 25 Steep more 2.5 more than 25

Fig. 48b. A flat slope

### 3.1.iii Cross slopes

Place a volume on a table and lift one side of it 4 centimetres from the table (Fig. 49a). Now, tilt the book sideways (half-dozen cm) so that only one corner of it touches the table (Fig. 49b).

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Fig. 49a. Main slope

Fig. 49b. Principal gradient and cantankerous slope

The thick pointer indicates the direction of what can be called the primary slope; the thin pointer indicates the management of the cross slope, the latter crosses the direction of the main slope.

An illustration of the master gradient and the cantankerous slope of an irrigated field is shown in Fig. fifty.

Fig. 50. The main slope and cross slope of an irrigated field

## 3.2 Elevation of a point

3.2.1 Definition
3.two.2 Bench mark and hateful sea level

### 3.2.ane Definition

In figure 51, betoken A is at the pinnacle of a concrete span. Any other point in the surrounding expanse is college or lower than A, and the vertical distance betwixt the two can be adamant. For example, B is college than A, and the vertical altitude between A and B is 2 chiliad. Point C, is lower than A and the vertical distance between A and C is 1 m. If bespeak A is chosen every bit a reference indicate or datum, the elevation of any other betoken in the field can be defined as the vertical distance between this indicate and A.

Fig. 51. Reference point or datum “A”

Thus, the peak or superlative of B, in relation to the datum A, is 2 k and the elevation of C, likewise related to the datum A, is i m.

As a reminder that a bespeak is above or below the datum, its acme is prefixed by the sign + (plus) if it is in a higher place the datum, or – (minus) if it is below the datum.

Therefore, in relation to the datum A, the summit of B is +ii g and the elevation of C is -1 m.

### three.2.ii Bench mark and mean ocean level

A bench marker is a permanent marking established in a field to use every bit a reference point. A bench marking can exist a concrete base in which an atomic number 26 bar is fixed, indicating the exact place of the reference point.

A bench mark tin can also be a permanent object on the farm, such every bit the pinnacle of a concrete structure.

In near countries the topographical departments have established a national network of bench marks with officially registered elevations. All bench marker heights are given in relationship to the one national datum plane which in general is the mean body of water level (MSL) (see Fig. 52).

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Fig. 52. A bench mark (B.M.) and hateful sea level (G.South.L.)

EXAMPLE

In Figure 52, the tiptop of point A in relation to the bench mark (BM) is 5 metres. The BM elevation relative to the hateful sea level (MSL) is 10 thousand. Thus, the elevation of point A relative to the MSL is 5 1000 + 10 yard = 15 m and is called the reduced level (RL) of A.

QUESTION

What is the reduced level of point B in Figure 52.

The peak of B relative to BM = 3 chiliad

The top of BM relative to MSL = 10 one thousand

Thus, the reduced level of B = 3 thousand + 10 yard = 13 one thousand

QUESTION

What is the difference in elevation between A and B? What does information technology correspond?

The difference in peak betwixt A and B is the reduced level of A minus the reduced level of B = xv chiliad – 13 m = two thou, which represents the vertical distance between A and B.

## 3.3 Contour lines

A contour line is the imaginary horizontal line that connects all points in a field which have the same peak. A contour line is imaginary but can be visualized by taking the example of a lake.

The h2o level of a lake may move upwards and downwardly, only the water surface e’er remains horizontal. The level of the water on the shore line of the lake makes a contour line because it reaches points which are all at the aforementioned height (Fig. 53a).

Fig. 53a. The shore line of the lake forms a contour line

Suppose the water level of the lake rises 50 cm in a higher place its original level. The contour line, formed by the shore line, changes and takes a new shape, at present joining all the points 50 cm higher than the original lake level (Fig. 53b).

Fig. 53b. When the water level rises, a new profile line is formed

Contour lines are useful means to illustrate the topography of a field on a flat map; the height of each contour line is indicated on the map so that the hills or depressions can exist identified.

## iii.4 Maps

3.four.one Description of a map
3.four.2 Interpretation of contour lines on a map
3.4.iii Mistakes in the contour lines
iii.four.4 Calibration of a map

### 3.4.1 Description of a map

Fig. 54 represents a three-dimensional view of a field with its hills, valleys and depressions; the contour lines take too been indicated.

Fig. 54. A three-dimensional view

Such a representation gives a very adept idea of what the field looks similar in reality. Unfortunately, it requires much skill to describe and is almost useless for the designing of roads, irrigation and drainage infrastructures. A much more accurate and convenient representation of the field, on which all data referring to topography can be plotted, is a map (Fig. 55). The map is what y’all see when looking at the three-dimensional view (Fig. 54) from the top.

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### 3.4.ii Interpretation of profile lines on a map

The arrangement of the profile lines on a map gives a direct indication of the changes in the field’s topography (Fig. 55).

Fig. 55. A two-dimensional view or map

In hilly areas, the contour lines are close together while they are wider apart on flat slopes. The closer the contour lines, the steeper the slope. The wider the profile lines, the flatter the slopes.

On a hill, the contour lines grade circles; whereby the values of their elevation increase from the edge to the centre.

In a depression, the contour lines also form circles; the values of their elevation, nevertheless, decrease from the border to the eye.

### three.4.3 Mistakes in the contour lines

Contour lines of different heights can never cantankerous each other. Crossing countour lines would mean that the intersection indicate has two different elevations, which is impossible (meet Fig. 56).

Fig. 56. Wrong; crossing profile lines

A contour line is continuous; there can never be an isolated slice of contour line somewhere on the map, equally shown in Effigy 57.

Fig. 57. Wrong; an isolated piece of profile line

### 3.four.4 Scale of a map

To be complete and actually useful, a map must have a defined scale. The scale is the ratio of the altitude betwixt two points on a map and their real distance on the field. A calibration of one in 5000 (one:5000) ways that i cm measured on the map corresponds to 5000 cm (or converted into metres, fifty one thousand) on the field.

QUESTION

What is the real distance between points A and B on the field when these ii points are 3.5 cm apart on a map whose scale is 1 to 2 500? (see Fig. 58)

Fig. 58. Measuring the distance between A and B