Explanation:

• There is a wide variation in sizes for engineering objects. Some are very large (e.g. Aeroplanes, rockets, etc) Some are very small (wristwatch, MEMs components)
• There is a need to reduce or enlarge while drawing objects on paper. Some objects can be drawn to ir actual size. The proportion by which drawing of an object is enlarged or reduced is called scale of drawing.
• A scale is defined as ratio of linear dimensions of object as represented in a drawing to actual dimensions of same. Drawings drawn in same size as objects are called full sized drawing.

Representation Factor (R. F)

$\mathrm{R}.\mathrm{F}=\frac{\mathrm{L}\mathrm{e}\mathrm{n}\mathrm{g}\mathrm{t}\mathrm{h}\mathrm{o}\mathrm{f}\mathrm{a}\mathrm{n}\mathrm{o}\mathrm{b}\mathrm{j}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{o}\mathrm{n}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{d}\mathrm{r}\mathrm{a}\mathrm{w}\mathrm{i}\mathrm{n}\mathrm{g}}{\mathrm{A}\mathrm{c}\mathrm{t}\mathrm{u}\mathrm{a}\mathrm{l}\mathrm{l}\mathrm{e}\mathrm{n}\mathrm{g}\mathrm{t}\mathrm{h}\mathrm{o}\mathrm{f}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{o}\mathrm{b}\mathrm{j}\mathrm{e}\mathrm{c}\mathrm{t}}$

Reducing scale

• An actual length of 5 m of a room is represented by 25 mm length on drawing. Then,
• R.F= distance on drawing/Distance on object = 25 mm/5 m = 1/200
• The scale of drawing is 1:200

Enlarging scale

• An actual length of a typical terminal strip of 10 mm is represented by 50  mm length on drawing. Then,
• R.F. = Distance on drawings / Distance on object = 50 mm/10 mm = 5/1
• The scale of drawing is 5:1

Full scale

• An actual length of an electrical switchboard of length 30 mm, is represented by a 30 mm length on drawing. Then,
• R.F.= Distance on drawing/Distance on object = 30 mm/30 mm = 1/1
• The scale of drawing is 1:1

The distance from 0 on horizontal to point Q is 3 yards. In feet scale, point P lies on 1 feet and in inches scale, point P lies on 10 inches. Hence, length of PQ is 3 yards 1 foot 10 inches.

Minute divisions are accurately measured by using diagonal scales. Diagonal scales are also when three different units of measurements are needed to be measured. With help of se scales, we can get a relation between three different units.

Explanation:

Diagonal Scale:

• A diagonal scale relies on a "diagonal" to divide a small distance into furr equal parts.
• The principle of diagonal scale is based on principle of similar triangles.

Example:

A small distance AB is to be divided into 10 equal parts using a diagonal scale. AB is line to be divided into 10 equal parts.

The diagonal scale is shown in Figure. Side AD is line to be divided into 10 equal parts 1 to 10.

Parallel lines are drawn to AB from points 1,2.....10.

Join one of diagonal AC. Join parallel line cuts diagonal at a,b.....j.

Distance 1 - a is $\frac{1}{10}$th of AB = 0.1 AB

Distance 2 - b is $\frac{2}{10}$th of AB = 0.2 AB

Distance a - i is $\frac{9}{10}$th of AB = 0.9 AB

Distance b - ii is $\frac{8}{10}$th of AB = 0.8 AB

If AB is 1 mm n 1 - a will be 0.1 mm and 2 - b will be 0.2 mm. Similarly a - i will be 0.9 mm and c - iii will be 0.7 mm.

Parallel lines on both sides of diagonal can be considered for measurement.

Additional Information Types of scales are as follows:

1. Plain scale
2. Diagonal scale
3. Vernier scale
4. Comparative scale
5. Scale of chords (for angles) 

The length of scale can be found using ?length of scale = Representative fraction x Maximum length?. To draw drawing R.F (representative fraction), Units to represent (example: meters and centimeter or anor if needed) and maximum length required is essential.

Origin is at 1st division ending. 1st division is made to sub-divisions. From origin, it is divided into divisions on right side and towards left 1st division is divided into sub-divisions. Here it is asked to measure how many divisions do 2 feet takes. It is 2 from origin to left.

Representative factor is calculated as ratio of length of drawing to actual length of drawing it represents. From this formula we get, R.F. = 100 � 25. Hence representative factor is 4:1.

Length of scale = Representative fraction x Maximum length. Length of scale = 3/40 x 100 cm = 7.5 cm. That is to draw a scale for 100 cm with 3/40 R.F. We need to draw a 7.5 cm length line and divide to 10 decimeters.

It is clearly visible that maximum length that can be measured using given scale is 7 feet. The rest twelve inches can be measured. Since 12 inches = 1 foot, we can measure 1 foot in addition to 7 feet. Hence we can measure 8 feet maximum using above scale.

The scale given is 1:5 (reducing scale) that is drawing is made with 1/5th of actual dimensions. So we have to multiply drawing length with 5. 50 mm x 5 =250 mm and 1 cm =10 mm. The actual length in cm is 25.