FUNDAMENTALS OF SURVEYING : Scales represented ways

Scales can be represented in following ways:

1.      Engineer’s Scale:

One cm on plan or map represents some whole number of meters on ground. For example: 1 cm = x m

2.      Representative Fraction:

1 unit of length on plan or map represents some number of same unit lengths on ground.

Distance on the plan or map(same unit)

Representative Factor =_______________________________

distance on the ground (same unit)

 

Larger the denominator of RF smaller is the scale. 3. Graphical Scale:

 Numerical scales may not give accurate result if the sheet or paper shrinks. However if graphical scale is also drawn. It will shrink proportionately and the distances on map can be found accurately.

 A line is drawn on the plan or map so that its distance corresponds to convenient unit of length on the ground.

 Hence, graphical scales are always shown on maps. Types of scales:

Scales may be classified as ,

1. Plain Scale               2. Diagonal Scale        3. Chord Scale            4. Vernier Scale

1.    Plain Scale:

A plain scale is one on which it is possible to measure two successive dimensions only such as meters - decimeters, cm – mm, etc.

2.    Diagonal Scale:

On a diagonal scale it is possible to measure three successive dimensions such as meters – decimeter - centimeters, yards – feet – inches, etc.

3.    Scale of Chords:

A scale of chord is used to measure & to set out angles without using a protractor. It is rectangular in shape & has graduations from 0⁰ to 90⁰.

4.    The Vernier:

 It is invented in 1631 by Pierre Vernier.

 It is a device used for measuring the fractional part of one of the smallest division on a graduated scale.

> The divisions ofVernier are just little smaller or little large than the main scale divisions.

> The least count ofVernier or fineness of reading is equal to the difference between the smallest division on main scale & smallest division on Vernier.

> Vernier carries index mark which forms the zero of the Vernier. Single Vernier:

When the graduations of main scale are numbered in one direction only, it is called single Vernier. (Extending in one direction only)

Double Vernier:

When graduations of main scale are marked in both the directions it is called double Vernier, extending in both directions having its index marked in the middle.

Whether it is single or double Vernier is classified as

a) Direct Vernier                                          b) Retrograde Vernier

a)   Direct Vernier:

> In direct Vernier, smallest division on vernier is shorter than the smallest division on main scale. > It increases or extends in the same direction as that of main scale.

> Construction of direct vernier is such that n divisions of vernier are equal to ( n - 1) divisions on

main scale.

Let

V = value of one smallest division on vernier,

S = value of one smallest division on main scale

n = number of divisions on vernier

So as per construction n n1

Least Count, LC= S-V = S

n

> Thus, least count is the ratio of one main scale value division to the number of divisions on vernier.

b)   Retrograde Vernier:

> Retrograde vernier is one which extends or increases in opposite direction as that of the main scale.

> Smallest division of vernier is longer that the smallest division of main scale.

> Construction ofretrograde vernier is such that n divisions of vernier are equal to n +1 divisions of main scale.

So as per construction, nV=(n+1)S

Least Count, LC=V-S = S

n