## scale

Scale in surveying is a ratio between a distance on the map or drawing to the distance on the surveyed ground.

It has no measuring unit because any ratio never has any measuring unit.

There are the following types of** **scale in surveying.

- Plain Scales.
- Diagonal Scales.
- Comparative or Corresponding Scales.
- Venire Scales.
- Scales of Chords.

**Plain Scale**

The plain scale is used to read in two dimensions only such as units and tenth and hundreds, meters and decimeters, Meters to kilometers and hectometers, etc.

The scale often consists of two lines about 3mm apart, the top one being thinner than the bottom. The whole length is divided into equal parts or units, the first of which sub-divided into smaller parts or subunits of the used unit. The primary and secondary divisions are drawn normal to the two lines and are made about 1.5 mm projection on the top line.

If you want to convince in reading, it would not involve any arithmetic calculation in measuring distance on a map. Therefore, the main division should represent one, tens, or hundreds of units.

**Note:**

Avoid the common mistake of laying down centimeters and dividing the left-hand centimeters into 3 parts and numbering the others 3, 6,9,12, etc. such a scale is inconvenient for taking direct distance and would include unnecessary counting.

**Diagonal Scale**

The diagonal scale is used when it is required to read in the three different dimensions like units, tenths and hundreds, centimeters, decimeters, and meters, etc. there is a reading deficiency in plane scale which overcome by this scale.

The principle of making a diagonal scale is based upon the fact that triangles have their like side proportional and is explained below.

Refer to the bellow figure, suppose a short line AB is required to be divided into 10 equal parts.

Draw a line BC of any length normal to AB and divide it into 10 equal parts. Join the AC line and draw 1-1′, 2-2′, 3-3′, etc. which should be parallel to AB.

It is showing clearly that the triangles CBA, C-1-1’, C-2-2’ etc. are similar.

**Corresponding or Comparative Scale**

When given the scale of plain reads in certain measurements and it is required to prepare a new scale for the same plan to read in some other measurement like R.F. of both scales remains the same, then the new scale would be called the comparative or corresponding scale. The comparative or corresponding scale had the benefit of taking measurements directly from the plan in the required units without any work of calculation.

**How to make a comparative scale**

To prepare the required scale, take a 25 cm long line to represent a length of 25*24=600m. Divide this line into 6 equal parts, every part reading to 100m. Now the extreme left part divide into 10 super parts while each is representing 10m.

Then this extreme left erect a perpendicular to the scale line and divide it into 10 equal parts of a length. Draw lines parallel to the scale line through each of these points to complete the scale as below

Corresponding Diagonal Scale, 1 cm = 24 m, corresponding to 1 in. = 200ft.

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**Vernier Scale**

It is a device that is used for determining the fractional parts of the smallest division the main scale with more accuracy than it can be done by simply estimating by eye. It has a small scale called vernier scale which moves with the graduated edge along the graduated edge of a longer fixed scale which is called the main scale. The scale may be either curved or straight.

**The Scale of Chords**

The scale of chords used to make different angles and to make measurements of angles of any magnitude with high degree accuracy. It is generally marked on the rectangular protector or on a simple ordinary boxwood scale, how to make this scale is given below.

Draw an MN line of suitable length. At N, draw a normal or perpendicular NT to MN. With N as center and radius NM, draw an arc MP cutting NT at P. and then arc MP or the chord MP subtends an angle of 90 degrees at the center N.

Divide the MP arc into 18 equal parts. Every part, therefore, subtends at N an angle of = 5°. Then with M as a center turn down the divisions to 18 the line MR and complete the scale as shown in the picture. Then MR is the desired scale of chords to measure up to 5°.

It should be noted that the distance from M to each division on the scale is the chord of the angle containing that number of degrees e.g. M-30 is equal to the chord of 30° degree and M-60 is equal to the chord of 60° degree and so on. The chord of 60° (i.e. the distance M- 60) always remains equal to the radius MN.