INTRODUCTION TO SCALE :
Scales are made of wood, steel, celluloid plastic, or cardboard. 15 cm long and 2 cm wide or 30 cm long and 3 cm wide level scales are in Common use.
They are ordinarily around 1 mm thick. However, a 15 c.m. long and 2 c.m. wide scale is considered a Standard length of scale. By using scale, small components can be drawn with the same size as the components are actually.
A 150 mm long pen or 175 mm long pencil may be shown by a drawing of 150 mm length or 175 mm length respectively.
Drawings of the same size as the objects are called full-size drawings and ordinary full-size scales are generally used to draw such drawings.
A scale is determined by the ratio of the dimensions of an element as represented in a drawing to the actual dimensions of the same element. This is called R.F. or Representative Fraction of Scale.
The scales are generally classified as :
(1) Plain scales (2) Diagonal scales (3) Vernier scales (4) Comparative scales (5) Scale of chords.
However, Plain scales, Diagonal scales, and Vernier scales are mainly used in engineering.
Comparative scales & scale of chords are less used applications in technical fields.
Least count of Plain scale = 0.5 mm.
Least count of the Diagonal scale = 0.01 mm.
Least count of Vernier scale = 0.02 mm.
[ N.B. Least count is a minimum distance or length that can be measured by a scale. ]
For engineering drawings or technical drawings, plain scale and diagonal scale are mainly required and both types of scale also have a huge application in mechanical engineering drawing.
Vernier scale is mainly used in technical or engineering workshops. So, basically, here in this chapter, we will discuss the Plain Scales and Diagonal Scales only.
Definition of Scale :
It is an instrument used to measure the length of an element or the shortest distance between two points.
Some Technical Terms Frequently Used To Draw A SCALE :
1. Representative Fraction (R.F.) :
It is the ratio between the size or length of an element in the drawing with the actual size or length of the element. Ex. 1:2, 1:4, 1:50, 2:1, 4:1, 50:1 etc. It is the most important relation to figure out the length of the scale or to construct a scale.
In the production sector, it is also termed as Scale Factor or Scale Ratio during manufacturing or after completion of a workpiece.
2. Reducing Scale :
In a scale, if Representative Fraction (R.F) is less than unity or 1, it is termed a Reducing Scale. Ex. 1:2, 1:4, 1:8, 1:50, 1:5000 etc.
For drawing large objects like houses, buildings, bridges, large machine parts, transformers, power plants, etc. a reducing scale is frequently used.
3. Enlarging Scale :
In a scale, if a Representative Fraction (R.F) is greater than unity or 1, it is termed an Enlarging Scale. Ex. 2:1, 4:1, 8:1, 50:1, 5000:1 etc.
For drawing small objects or very small objects such as screws, nuts, bolts, threads, parts of watches, etc. an enlarging scale is frequently used.
4. Full-Size Scale or True Scale :
In a scale, if Representative Fraction (R.F) is equal to 1 or unity then the scale is termed as a Full-Size scale or True scale.
That means, if a drawing is drawn with the actual lengths of an object, it is said to be a full-scale drawing or true-scale drawing and the R.F would be in this case 1:1.
HOW TO DRAW A PLAIN SCALE :
Following rules should be maintained when we draw any plain scale.
1. A plain scale consists of a line divided into a suitable number of divisions or Main Divisions (A division is equal parts of that line or scale as per requirement). This is how main divisions are drawn on a plain scale
The first division is further subdivided into smaller equal parts, as per requirement. This is how sub-divisions are drawn on a scale.
A plain scale can represent a maximum of two units. Ex. Metres & Decimetres, Centimetres & Millimeters, etc., or a single unit.
2. The zero should be placed at the end of the first division from the left-hand side. See the figure in the examples below.
3. From the zero mark, the divisions should be numbered to the right sequentially, and sub-divisions are also numbered to the left in proper sequence. See the figure in the examples below.
4. The names of the units of division and sub-division should be stated clearly below at the respective ends of the scale. See the figure in the examples below.
5. Always provide dimensions for drawing length or scale length below the scale and the actual length of the object or actual dimensions should be provided above the scale. See the figure in the examples below.
6. The R.F. of the scale (e.g. R.F. = 1: 4) should be always mentioned below of
the scale. See the figure in the examples below.
Now see examples :
Ex. 1. Construct a scale of 1: 4 to show centimetres and long enough to measure up to 5 decimetres. Show 3.7 decimetres on the scale.
[ Observation: First of all, we should have to read the question very carefully and understand the whole meaning very clearly! Here, in the above question, we need to show two units on the scale i.e. decimeters and centimeters. So, we should draw a plain scale, whether it is clearly mentioned in the question or not. ]
Solution :
Given data,
R.F. of scale = 1:4
Maximum Length required to be measured = 5 dm.
Therefore, length of scale = R.F. × Max. length to be measured
= 1/4 × 5 dm.= 1/4 × 5 × 10 cm.
= 12.5 cm.
Assuming, main divisions of scale = 5
and,
number of subdivisions in a division = 10.
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The above example is a solution to the given problem of the plain scale. Now, diving into details how can we actually draw this plain scale.
First of all, draw a scale of 12.5 cm. as shown above. Here, we are assuming the width of the scale is 3 mm.
(The width of plain scale may vary in drawing from 3 mm. to 25 mm. depending upon our assumption )
Now, another assumption is required to take regarding the divisions of scale.
As we need to show decimeters (1×10 cm) & centimeters on the scale, it is very much essential to find out 1 decimeter on the scale, unless we never find out centimeters on the scale.
As we've already found out the scale length in the drawing is 12.5 cm. Its equivalent actual length is 5 decimeters.
So, if we divide 12.5 cm. into 5 nos. of divisions( 12.5 ÷ 5 = 2.5 cm. ) then each division(i.e. 2.5 cm.) on the scale will be equivalent to 1 decimetre of actual length.
So now assuming, the divisions of scale are 5 nos. & we need to divide the total scale length into 5 nos. of equal divisions in our drawing as shown in the above drawing.
The next step is to find out the centimeter on the scale & for this, we need to draw subdivisions on the scale. For this, we need to divide the First Division(2.5 cm.) from the left-hand side into 10 nos of equal sub-divisions on the scale. (See above drawing)
Remember, 1 division of scale = 2.5 cm. & It is equivalent to 1 decimetre(1×10 cm.) of actual length.
So, if we divide 1 division into 10 nos. of equal subdivisions then we get,
Length of subdivision on the scale =
(2.5 ÷ 10) cm. = 0.25 cm. = 2.5 mm. This 2.5 mm. scale length is equivalent to 1 cm. of the actual length.
So, every subdivision length is 2.5 mm. on the scale and if there are 10 nos. of equal subdivisions, then (2.5 mm ×10 ) = 2.5 cm & this is the total length of a division of scale which is equivalent to 1 decimetre of the actual length.
Now we can show the actual 3.7 decimeters length on the scale as shown in the above drawing.
So, this is how we can draw a plane scale while maintaining the rules and help of simple assumptions, equations, and calculations.
N.B. Shading or Filling on a scale drawing is not mandatory as it completely depends upon our assumptions for giving a better visual effect of the scale.
HOW TO DRAW A DIAGONAL SCALE :
Following rules should be maintained when we draw any diagonal scale.
1. A diagonal scale consists of a line divided into a suitable number of Main Divisions (A main division is equal parts of that line or scale as per requirement).
The first main division is further subdivided into smaller equal parts, as per requirement ( This is how sub-divisions are drawn on a diagonal scale ).
Small sub-divisions are also further divided into very small equal parts following diagonal law. This is how further sub-divisions or further subunits are drawn on a diagonal scale.
A diagonal scale can represent a maximum of three units. Ex. Metres & Decimetres and Centimetres, Decimetres & Centimetres and Millimeters etc.
2. The zero should be placed at the end of the first division from the left-hand side. See the figure in the examples below.
3. From the zero mark, the main divisions should be numbered to the right sequentially, sub-divisions are also numbered to the left in proper sequence.
And furtherly sub-divisions or further subunits are numbered vertically to the left-hand side width of the diagonal scale. See the figure in the examples below.
4. The names of the units of main divisions, sub-divisions, or subunits and further sub-divisions should be stated clearly below at the respective ends of the scale. See the figure in the examples below.
5. Always provide dimensions for drawing length or scale length below the scale and the actual length of the object or actual dimensions should be provided above the scale. See the figure in the examples below.
6. The R.F. of the scale (e.g. R.F. = 1: 4) should be always mentioned below of
the scale. See the figure in the examples below.
Now see examples :
Ex. 2. Construct a scale of 1: 50000 to show decametres long enough to measure up to 5 kilometers. Show 3.56 km on the scale.
[ Observation: First of all, we should have to read the question very carefully and understand the whole meaning very clearly! Here, in the above question, we need to show three units on the scale i.e. Kilometre, Hectametre (as 3.56 km = 3 kilometers and 56 hectometres), and Decametre. So, we should draw a diagonal scale, whether it is clearly mentioned in the question or not. ]
Solution :
Given data,
R.F. of scale = 1:50000
Maximum Length required to be measured = 5 km.
Therefore, length of scale = R.F. × Max. length to be measured
= 1/50000 × 5 km.= 1/50000 × 5 × 1000 ×100 cm.
= 10 cm.
Assuming, main divisions of scale = 5
and,
number of subdivisions in a division = 10
and also,
number of further sub-divisions in a subdivision = 10
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The above example is a solution to the given problem of diagonal scale. Now, diving into details how can we actually draw this diagonal scale.
First of all, draw a diagonal scale of 10 cm. in length as shown above. Here, we are assuming the width of the diagonal scale is 25 mm.
(The width of the diagonal scale may vary in drawing from 25 mm. to 40 mm. depending upon our assumption )
Now, another assumption is required regarding the divisions of the diagonal scale.
As we need to show kilometers (1×10 hm) & decametre on the scale, it is very much essential to find out 1 km on the scale, unless we never find out hectometre (hm) and decimetre(dm) on the scale.
As we've already found out the scale length in the drawing is 10 cm. concerning its equivalent actual length of 5 km.
So, if we divide 10 cm. into 5 nos. of divisions (10 ÷ 5 = 2 cm.) then each division (i.e. 2 cm.) on the scale will be equivalent to 1 km of actual length.
So now assuming, the main divisions of the diagonal scale are 5 nos. & we need to divide the total scale length into 5 nos. of equal divisions in our drawing as shown in the above drawing.
The next step is to find out the hectometre on the diagonal scale unless we are never able to find out the decametre on the diagonal scale. For this reason, we need to draw subdivisions on the diagonal scale. For this, we need to divide the First Division (2 cm.) from the left-hand side into 10 nos of equal sub-divisions on the diagonal scale. (See above drawing)
Remember, 1 division of scale = 2 cm. & It is equivalent to 1 kilometer (1×10 hm.) of actual length.
So, if we divide 1 division into 10 nos. of equal subdivisions then we get,
Length of subdivision on the scale = (2 ÷ 10) cm. = 0.2 cm. = 2 mm. This 2 mm. scale length is equivalent to 1 hecta meter (hm.) of the actual length.
Now, we need to equally divide these subdivisions into 10 nos. As we know, 1 hectometre = 10 decametres. So, we need to further subdivide that diagonal scale based on diagonal law with the method of dividing a straight line into any number of equal parts.
Therefore, Length of Furtherly Subdivision = (length of subdivision ÷ 10) = ( 2 ÷ 10 )mm = 0.2 mm.
Therefore, 0.2 mm. on the diagonal scale is equivalent to 1 decametre of actual length.
So, every furtherly subdivision is 0.2 mm and every subdivision length is (0.2 × 10 = 2 mm.) on the diagonal scale and if there are 10 nos. of equal subdivisions, then (2 mm ×10 ) = 2 cm & this is the total length of a main division of diagonal scale which is equivalent to 1 kilometer of the actual length.
Now, we can show the actual 3.56 kilometers length on the diagonal scale as shown in the above drawing.
So, this is how we can draw a diagonal scale while maintaining the rules, and help of simple assumptions, equations, and calculations.
N.B. Shading or Filling on a scale drawing is not mandatory as it completely depends upon our assumptions for giving a better visual effect of the scale.