# Plans and Maps

As stated in the definition of surveying, the objective of measurements is to show relative positions of various objects on paper. Such representations on paper are called plan or map.

A plan may be defined as the graphical representation of the features on, near or below the surface of the earth as projected on a horizontal plane to a suitable scale.

However, since the surface of the earth is curved and that of the paper is plane, no part of the earth can be represented on such maps without distortion. If the area to be represented is small, the distortion is less and large scale can be used. Such representations are called plans. If the area to be represented is large, small, scales are to be used and distortion is large.

Representations of larger areas are called maps. Representation of a particular locality in a municipal area is a plan while representation of a state/country is a map. There is no exact demarcation between a plan and map.

## Scales

It is not possible and also not desirable to make maps to one to one scale. While making maps all distances are reduced by a fixed proportion. That fixed proportion is called scale of the map.

Thus, if 1 mm on the paper represents 1 metre on the ground, then the scale of the map is 1 mm = 1 m or 1 mm = 1000 mm or 1:1000.

To make scale independent of the units it is preferable to use representative factor which may be defined as the ratio of one unit on paper to the number of units it represent on the ground.

Thus 1 mm = 1 m is equivalent to RF = 1/1000

Apart from writing scale on map, it is desirable to show it graphically on it. The reason is, over the time, the paper may shrink and the scaling down the distances from map may mislead.

The graphical scale should be sufficiently long (180 mm to 270 mm) and the main scale divisions should represent one, ten or hundred units so that it can be easily read. The scale of a map is considered as

**large**if it is greater than 1 cm = 10 m i.e., RF > 1/1000,**intermediate**if it is between RF = 1 1000 and 1/10,000,**small**if RF < 1/10,000.

In general, scale selected should be as large as possible, since it is not possible for human eye to distinguish between two points if distance between them is less than 0.25 mm.

The recommended scales for various types of surveys are as shown in Table 1.

# Types of Graphical Scales

The following two types of scales are used in surveying:

(i) Plain Scale (ii) Diagonal Scale.

## Plain Scale

On a plain scale it is possible to read two dimensions directly such as unit and tenths. This scale is not drawn like ordinary foot rule (30 cm scale). If a scale of 1:40 is to be drawn, the markings are not like 4 m, 8 m, 12 m etc. at every 1 cm distance. Construction of such a scale is illustrated with the example given below:

**Example**: Construct a plain scale of RF = 1/500 and indicate 66 m on it.

**Solution**. If the total length of the scale is selected as 20 cm, it represents a total length of 500 × 20 = 10000 cm = 100 m.

Hence, draw a line of 20 cm and divide it into 10 equal parts. Hence, each part corresponds to 10 m on the ground. First part on extreme left is subdivided into 10 parts, each subdivision representing 1 m on the field. Then they are numbered as 1 to 10 from right to left as shown in Fig. 1.

If a distance on the ground is between 60 and 70 m, it is picked up with a divider by placing one leg on 60 m marking and the other leg on subdivision in the first part. Thus field distance is easily converted to map distance.

IS 1491—1959 recommends requirements of metric plain scales designated as A, B, C, D, E and F as shown in Table 2. Such scales are commonly available in the market. They are made of either varnished cardboard or of plastic materials. Such scales are commonly used by surveyors and architects.

## Diagonal Scale

In plain scale only unit and tenths can be shown whereas in diagonal scales it is possible to show units, tenths and hundredths. Units and tenths are shown in the same manner as in plain scale.

To show hundredths, principle of similar triangle is used. If AB is a small length and its tenths are to be shown, it can be shown as explained with Fig. 2 below.

Draw the line AC of convenient length at right angles to plain scale AB. Divide it into 10 equal parts. Join BC.

From each tenth point on line AC draw lines parallel to AB till they meet line BC.

Then line 1–1 represent 1/10^{th} of AB, 6–6 represent 6/10^{th} of AB and so on.

Figure 3 shows the construction of diagonal scale with RF = 1/500 and indicates 62.6 m.

IS 1562—1962 recommends diagonal scales A, B, C, and D as shown in Table 3.

## Units of Measurements

According to Standards of Weights and Measurements Act, India decided to give up FPS system used earlier and switched over to MKS in 1956. In 1960 System International (SI units) unit was approved by the conference of weights and measures.

It is an international organisation of which most of the countries are the members. In this system also unit of linear measurement is metre. However, in this system use of centimeters and decameters are discouraged. Of course major difference between MKS and SI is in the use of unit of force.

In MKS unit of force is kg-wt (which is commonly called as kg only) while in SI it is newton. The recommended multipliers in SI units are given below

- Giga unit = 1 × 10
^{9}units - Mega unit = 1 × 10
^{6 }units - Kilo unit = 1 × 10
^{3}units - unit = 1 × 10
^{0 }units - Milli unit = 1 × 10
^{–3}unit - Micro unit = 1 × 10
^{–6}unit

Commonly used linear units in surveying are kilometre, metre and millimetres. However centimetre is not yet fully given up.

For measuring angles sexagesimal system is used. In this system:

- 1 circumference = 360°
- 1 degree = 60′ (minutes of arc)
- 1 minute = 60″ (seconds of arc)