How To Scale A Metric Drawing To English

Normally the word scale is used for an instrument used for drawing straight lines. Only really in Engineer's language calibration means the proportion or ratio betwixt the dimensions adopted for the cartoon and the respective dimensions of the object. It can be indicated in two dissimilar ways. Example: The actual dimensions of the room say 10m x 8m cannot be adopted on the cartoon. In suitable proportion the dimensions should be reduced in society to adopt conveniently on the drawing canvas. If the room is represented by a rectangle of 10cm x 8cm size on the drawing sheet that means the actual size is reduced past 100 times.

Representing scales : The proportion between the drawing and the object can be represented by ii ways every bit follows:

a) Scale: - 1cm = 1m or 1cm=100cm or 1:100

b) Representative Fraction : - (RF) = one/100 (less than one) i.e. the ratio between the size of the cartoon and the object.

There are three types of scales depending upon the proportion it indicates as

1. Reducing scale : When the dimensions on the cartoon are smaller than the actual dimensions of the object. It is represented by the scale and RF as

Calibration: - 1cm=100cm or 1:100 and by RF=1/100 (less than ane)

two. Full scale : Some times the bodily dimensions of the object will be adopted on the drawing so in that case information technology is represented by the scale and RF as

Scale: - 1cm = 1cm or i:1 and past R.F=1/one (equal to i).

three. Enlarging calibration : In some cases when the objects are very small like inside parts of a wrist watch, the dimensions adopted on the drawing will be bigger than the actual dimensions of the objects then in that case it is represented past scale and RF every bit

Scale: - 10cm=1cm or 10:ane and by R.F= 10/1 (greater than one)

Notation: The calibration or R.F of a drawing is given unremarkably below the drawing. If the scale adopted is common for all drawings on that detail sail, and so it is given unremarkably for all figures nether the title of canvass.

i.7 Types of Scales and their constructions:

When an unusual proportion is to be adopted and when the prepare fabricated scales are not available and so the required scale is to be constructed on the drawing sheet itself. To construct the scale the data required is i) the R.F of the calibration 2) The units which it has to represent i.eastward. millimetres or centimetres or metres or kilometres in M.K.S or inches or feet or yards or miles in F.P.Southward) The maximum length which information technology should measure. If the maximum length is not given, some suitable length tin be causeless.

The maximum length of the calibration to be constructed on the cartoon canvas =

R.F X maximum length the scale should measure.

This should exist generally of 15 to 20 cms length.

Tabular array: Metric Units Table: FPS Units

1 Kilometre (km) =10 Hecta metres (hm) 1 Mile =8 Furlongs

one Hectametere(hm) =10 Decametres(dam)or 0.1km one Furlong =220 Yards

1 Decametre(dam) =10 Metres (m) or 0.1hm 1Yard =iii Feet

1 Metre(m) =10Decimetres(dm) or 0.1dam 1 Feet =12 Inches

1 Decimetre(dm) =x Centimetres(cm) or 0.1m

1 Centimetre(cm) =10 Millimetres (mm) or 0.1dm

The various types of scales used in practice are 1. Plain scales, 2. Diagonal scales, iii. Vernier scales, iv. Comparative scales and 5. Scale of chords.

1.vii.1 Plain Scales: Plain scales read or mensurate upto two units or a unit and its sub-partitioning, for example centimetres (cm) and millimetres (mm). When measurements are required upto first decimal, for case ii.3 m or iv.6 cm etc. It consists of a line divided into number of equal main parts and the first main part is sub-divided into smaller parts. Mark zero (O) at the end of the first main part. From zero mark numbers to the main parts or units towards right and give numbers to the sub-divisions or smaller parts towards left. Give the names of the units and sub-units below clearly. Indicate below the proper noun of the scale and its R.F clearly.

The construction of the plain scale is explained below by a worked case.

W E 1.i A iii cm long line represents a length of four.v metres. Extend this line to mensurate upto 30 metres and bear witness on information technology units of metre and five metre. Testify the length of 22 metres on this line. Fig one.x

i) The scale has to represent metre and 5 metres, hence it is a Apparently scale.

ii) Given that 3cm represents iv.5metres or 450cm, Hence 1cm represents 450/three=150cm, hence calibration is 1cm=150cm or 1:150: R.F=1/150

iii) Maximum length to read is 30metres; Length of the scale is 20cm. i.east. (i/150)x30x100 = 20cm

Construction:

Draw a direct line of 20cm length and split up into six equal parts.

Divide again starting time function into 5 equal parts. Give numbers as shown. To represent 22 metres, take 4 main parts to represent xx metres and two small parts to represent 2metres. Give names as A and B so that the distance between A and B is 22 metres as shown.

Note: Assume pinnacle of the plain scale equally i cm.

Construct a plain scale of 1:v to show decimeters and centimeters and to read upto 1 metre. Show the length of vii.4 decimetres on information technology.

i) The scale has to correspond decimetre and 1/10 of decimeter.

ii) Given that the calibration is 1:5 that is R.F=one/5

iii) Maximum length to read is i metre; Length of the calibration=(i/5)x1x100=20cm

Construction:

Draw a straight line of 20cm length and divide into x equal parts.

Divide once again first function into ten equal parts. Give numbers as shown. To correspond seven.four decimetres, take vii main parts to represent 7 decimetres and iv small parts to represen0t 0.4 decimetres. Requite names as A and B so that the distance between A and B is 7.4 decimetres every bit shown.

Diagonal Scales :

Diagonal scales are used to read or measure upto 3 units .

For case: decimetres (dm), centimetres (cm) and millimetres (mm) or miles, furlon

gs and yards etc. This scale is used when very modest distances such equally 0.1 mm are to be accurately measured or when measurements are required upto 2d decimal.

For example: 2.35dm or four.68km etc.

Small divisions of short lines are obtained past the principle of diagonal division, as explained below:

Principle of diagonal scale: To divide a given line AB into pocket-size divisions in multiples of 1/10 its length for example 0.1AB; 0.2AB etc. as shown in

Process:

i) Depict AB of given length

two) At one stop, say at B draw a line perpendicular to AB.

iii) Marker 10 equal divisions by taking some convenient length starting from B and ending with C.

iv) Requite numbers from 9, 8, seven----1 equally shown.

five) Join C to A and from 9 to one, draw parallels to AB, cutting Air conditioning at 9′, viii′, ------ 1′ etc.

vi) From the similar triangles 1′1C, two′2C ------- 9′9C and ABC, C5=(1/two)BC=0.5BC and five′5=(1/2)AB=0.5AB. Similarly 1′1=0.1AB, ii′ii=0.2AB etc

Thus each horizontal line beneath AB volition be shorter by (1/ten)AB, giving lengths in multiples of 0.1AB

: An area of 144 sqcm on a map represents an area of 9 sqkm on the field. Notice the R.F.of the calibration for this map and describe a diagonal scale to evidence kilometers, hectametres and decameters and to measure out upto 5 kilometres. Indicate on the scale a distance of 3 kilometres, 5 hectametres and 6 decametres or 3.56km.

The expanse on the map is 144 sqcm and the surface area on the field is 9 sqkm.

Take square root on both sides. Then 12cm=3 km or Scale is 1 cm= 0.25km or 2.5x10 ⁴ cm; RF=1/(ii.5x10 ⁴ )
Length of the calibration to read upto v km is RF X five km= 1/(2.5x10 ⁴ ) Ten 5x10 ^v =20cm

Structure:

Draw a line AB of twenty cm and construct a rectangle on it, by taking AD 5cm as shown. Divide AB into 5 equal parts and number them from second part starting with 0 to 4 towards right side to indicate kilometers (km). Divide 0A into 10 equal parts, each part represents a hectametre (hm). Divide Advert into x equal parts, each role represents one decametre (dam). Join diagonals as shown.

To mark three.56km, have it equally sum of three.50km and 0.06km. On the manifestly scale accept 3.5km and on the diagonal at 5 upto half-dozen parts diagonally which is equal to 0.06km, giving a total of iii.56km as shown past MN.

Annotation: Assume the peak of the diagonal scale AD as 5cm for dividing it into 10 equal parts conveniently.