Scales - ecivilengineering.com

SCALES Chapter -2
Scales
Definition- The proportion by which actual size of object is enlarged or reduced on drawing is called
scale.
Use of scale1. To draw full /reduced/enlarged size of drawing.
2. To measure the length (distance, dimension).
3. To set off dimension.
Representative fraction (R.F) or scale factor- The ratio of drawing size of an object to actual size of
the object in same unit (in linear dimension only) is termed as representative fraction. Examplesa) For showing 45km length on ground by 15cm long line R.F =15cm / 45 X 105cm = 1 / 3 X 105
b) For showing 16km2 Area on ground by 4cm2 area on map R.F =√(4cm2 / 16 X 1010cm2)= 1/2 X
105 i.e. in liner dimension unit only similarly in case of volume take cube root.
Types of scaleA. Based on R.F R.F = 1 Full size scale (i.e. drawing size = actual size of object)
2) R.F < 1 Reducing scale (i.e. drawing size < actual size of object)
3) R.F > 1 Enlarged scale (i.e. drawing size > actual size of object)
1)
Note: The scale or R.F of a drawing is given usually below the drawing. If the scale adopted is
common for all drawings on that particular sheet, then it is given commonly for all figures under the
title of sheet. It is represented by the scale and RF as Scale: - 1cm=100cm or 1:100 and by
RF=1/100 or 1:100 etc.
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SCALES Chapter -2
B. Based on Uses 1)
2)
3)
4)
5)
6)
7)
Plain Scale.
Diagonal scale.
Comparative Scale.
Vernier scale.
Scale of Chord.
Isometric Scale.
Logarithmic Scale.
Will be discussed in later sheets.
Note: When an unusual proportion is to be adopted and when the readymade scales are not
available then the required scale is to be constructed on the drawing sheet itself. To construct the
scale the data required are
1) The R.F of the scale
2) The units which it has to represent i.e. millimeters or centimeters or meters or kilometers in M.K.S
or inches or feet or yards or miles in F.P.S
3) The maximum length which it should measure. If the maximum length is not given, some suitable
length can be assumed.
The maximum length of the scale to be constructed on the drawing sheet (i.e. capacity) = (R.F) X
(maximum length the scale should measure)
4) This should be generally of 15 to 20 cm length.
1) Plain ScalePlain scale read or measures up to two units or a unit and its sub-division, for example centimeters
(cm) and millimeters (mm).When measurements are required up to first decimal, for example 2.3 m
or 4.6 cm etc.
Plain scale consists of a line divided into number of equal main parts (i.e. main unit) and the first
main part is sub-divided into smaller parts (i.e. sub- unit). 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 subdivisions or smaller parts towards left. Give the names of the units and sub-units below clearly.
Indicate below the length of the scale (LOS) and its R.F clearly and name of the scale at top of the
scale.
Example: A drawing’s 5cm long line represents 50cm on the ground. Determine R.F and draw plain
scale to measure up to 100cm and show a length of 54cm on the scale.
Solution: Calculations1) The scale has to represent centimeter and 10 centimeters; hence it is a Plain scale.
2) Calculate R.F from given data i.e. R.F = 5cm / 50cm = 1 / 10.
3) Maximum length to read is 100cm from this calculate the length of scale (LOS) i.e. LOS =
(R.F) X (maximum length the scale should measure) = (1/10) X (100) = 10cm.
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SCALES Chapter -2
ConstructionDraw a straight line of 10cm length and divide into 10 equal parts. Divide again first part into 5 equal
parts. Give numbers as shown. To represent 54cm, take 5 main parts to represent 50cm and 2 small
parts to represent 4cm. Give names as A and B so that the distance between A and B is 54cm as
shown.
PLANE SCALE
Fig. 2.1
Note: Assume height of the plain scale as 1 cm or 2cm or 2.5cm etc. according to your suitability.
2) Diagonal ScaleThree simultaneous units or one unit and up to 0.01 (i.e. second decimal place) can be represented
by diagonal scale. For example: decimeters (dm), centimeters (cm) and millimeters (mm) or miles,
furlongs and yards etc. and measurements like 2.35dm or 4.68km etc. can be represented by this
kind of scale.
Principle of diagonal scale: Small divisions of short lines are obtained by the principle of diagonal
division. To divide a given line AB into small divisions in multiples of 1/10 its length for example
0.1AB; 0.2AB etc. as shown below-
Fig. 2.2
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i) Draw AB of given length
ii) At one end, say at B draw a line perpendicular to AB.
iii) Mark 10 equal divisions by taking some convenient length starting from B and ending with C.
iv) Give numbers from 9, 8, 7----1 as shown.
v) Join C to A and from 9 to 1, draw parallels to AB, cutting AC at 9′, 8′, ------ 1′ etc.
vi) From the similar triangles 1′1C, 2′2C ------- 9′9C and ABC, C5=(1/2)BC=0.5BC and
5′5=(1/2)AB=0.5AB. Similarly 1′1=0.1AB, 2′2=0.2AB etc.
Thus each horizontal line below AB will be shorter by (1/10)AB, giving lengths in multiples of 0.1AB.
Example: A drawing’s 20cm long line represents 10m on the ground. Draw scale to read up to 1cm
and long enough to represent 6m.Show a length of 3.56m on the scale.
Solution: Calculations1) The scale has to represent cm, dm and m; hence we should opt diagonal scale.
2) Calculate R.F from given data i.e. R.F ={(20)cm /(10 X 100)cm} = 1 / 50.
3) Maximum length to read is 6m from this calculate the length of scale (LOS) i.e. LOS = (R.F) X
(maximum length the scale should measure) = (1/50) X (6 X 100) = 12cm.
ConstructionDraw a line AB of 12 cm and construct a rectangle on it, by taking AD 5cm as shown. Divide AB into 6
equal parts and number them from second part starting with 0 to 5 towards right side to indicate
meters (m). Divide 0A into 10 equal parts, each part represents a decimeter (dm). Divide AD into 10
equal parts, each part represents one centimeter (cm). Join diagonals as shown.
To mark 3.56m, take it as sum of 3.50m and 0.06m. On the plain scale take 3.5m and on the diagonal
at 5 up to 6 parts diagonally which is equal to 0.06m, giving a total of 3.56m as shown by MN.
DIAGONAL SCALE
Fig. 2.3
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Note: Assume the height of the diagonal scale AD as 5cm for dividing it into 10 equal parts
conveniently.
3) Comparative ScaleComparative scale is a pair of scales having same R.F but graduated in different units. On a map if
distance is shown in kilometer and meter it is possible to show it easily in millimeter and centimeter
by use of this scale. Comparative scales can be constructed as plain scales or diagonal scales
depending upon the requirement. They can be drawn separately or one over other.
Example: On a railway map, an actual distance of 36 miles between two stations is represented by a
10 cm long line. Draw a plain scale to show a mile, and which is long enough to read up to 60 miles.
Also draw a comparative scale attached to it to show a kilometer and read up to 90 km. Take 1 mile
= 1609 meters.
Solution: Calculations1) Calculate R.F from given data i.e. R.F = {(10) cm /(36 X 1609 X 102)cm} = 1 / 579240.
2) Calculate length of scale (LOS) i.e. LOS (miles) = (R.F) X (maximum length) = (1/579240) X (60
X 1609 X 102) = 16.67 cm and LOS (kilometer) = (R.F) X (maximum length) = (1/579240) X (90
X 105) = 15.54 cm.
Construction1) Draw a 16.67 cm long plain scale to represent 60 miles. Make its divisions and sub-divisions
so that its least count is 1 mile.
2) Draw another plain scale attached to it as shown, 15.54 cm long to represent 90 km. Make
its divisions and sub-divisions so that its least count is 1 km.
3) Write the main unit and second unit of both the scales. Also write its R.F.
Comparative Scale
Fig. 2.4
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4) Vernier ScaleA Vernier scale consists of a primary scale and a vernier. The primary scale is a plain scale fully
divided into minor divisions. Similar to Diagonal scale, Vernier scale is used for measuring up to
second decimal.
The graduations on the vernier are derived from those on the primary scale. Least count (LC) is the
minimum distance that can be measured.
Forward Vernier / Direct Vernier Scale:
MSD>VSD; LC = MSD-VSD
Backward Vernier / Retrograde Vernier Scale:
VSD>MSD; LC = VSD - MSD
Vernier Scale Concept:
1) Length A0 represents 10 cm and is divided in to 10 equal parts each representing 1 cm.
2) B0 = 11 (i.e. 10+1) such equal parts = 11 cm.
3) Divide B0 into 10 equal divisions. Each division of B0 will be equal to 11/10 = 1.1 cm or 11
mm.
4) Difference between 1 part of A0 and one part of B0 = 1.1 cm -1.0 cm = 0.1cm or 1 mm.
Fig. 2.5
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Example: Draw a Vernier scale of R.F. = 1/25 to read up to 4 meters. On it show lengths 2.39 m and
0.91 m.
Solution: Calculations1) Length of Scale (LOS) = (1/25) X (4 X 100) = 16 cm
Construction1) Draw a 16 cm long line and divide it into 4 equal parts. Each part is 1 meter. Divide each of
these parts in to 10 equal parts to show decimeter (10 cm).
2) Take 11 parts of dm length and divide it in to 10 equal parts (i.e. use of Retrograde /
Backward Vernier). Each of these parts will show a length of 1.1 dm or 11 cm (* if we make
use of direct or forward vernier instead of retrograde or backward vernier than in that case
we need to take (n-1) i.e. 9 parts of dm length and divide that in to 10 equal parts, each part
showing 0.9 dm or 9 cm of length).
3) To measure 2.39 m, place one leg of the divider at A on 99 cm mark and other leg at B on 1.4
mark (i.e. AB = 0.99 + 1.4 = 2.39).
4) To measure 0.91 m, place the divider legs at C and D (i.e. CD = 0.8 +0.11 = 0.91).
Vernier Scale
Fig. 2.6
5) Scale of chordsScale of cords is very helpful in measuring angles without help of protector.
Method of Construction:
1) Draw AB and erect perpendicular at B.
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2) With AB radius draw arc with center B cutting AB at C. With same radius cut arc from C as
center, cutting at D.
3) Divide AB into six equal parts by trial & error method. With same distance divide arc AC into
18 equal parts. With centre A & radius =cut point on the arc draw the arc as shown in figure
below. Write 0-90 on the arc AC and also on line AB.
4) It can measure minimum up to 5Degrees. Scale of Chords is shown in Fig. 2.5. We need to
make sufficient practice of dividing lines into equal parts.
Scale of Chords
Fig. 2.7
Example: Construct a scale of chords showing 50 divisions and with its aid set-off an angle of 350.
Solution: Construction1) Following the above discussed steps draw fig. 2.7.
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2) Draw a line PQ equal to AB of the scale of chords. With center P and radius AB, draw an arc
PR.
3) With center Q and radius equal to 00-350 chord length, draw an arc to intersect arc QR at
point S. Join PS. This /_SPQ represents 350.
Scale of Chords
Fig. 2.8
“GOD CREATED THE EARTH WE MADE IT COMFORTABLE”
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EXERCISE
CLASS WORK:
1. On a survey map the distance between two places, 1 Km apart, is represented by 2.5 cm
Construct a plain scale to measure up to 6 Km. Find the R.F. and indicate a distance of 4 Km
and 6 Hm, 3.9 km.
2. Construct a diagonal scale to read maters, decimeters & centimeters for of 1/25 and long
enough to measure up to 4 meters. Show on it a length of 0.89 in, 2.67 m. and 3.44 m.
3. The distance between Kota and New Delhi is 450 km. Its equivalent distance on a railway
map measures only 15 cm what is the RF? Draw a diagonal scale to show hundreds of
kilometers, tens of kilometers and kilometers. Indicate on the scale the following distance
A) 525Km B) 313 Km C) 209 Km.
4. Construct a vernier scale to read meters, decimeters and centimeters and long enough to
measure up to 6 meters when one meter is represented by 2.5 cm. Find R.F. and show on it
a distance of 4.33 m & 2.37 m.
5. Construct a scale of chords and graduate it. With the help of scale construct angles of 28°
and 129°.
HOME ASSIGNMENT
1. A room of 1000m3 volume is represented by a block of 125cm3 volume Find R.F. and
construct a plain scale to measure up to 30 m. Show a distance of 18 m on this scale.
2. A drawing is drawn in inch units to a scale of 3/8 full size. Draw the scale showing 1/8 of
an inch division and to measure up to 16 inches. Construct a comparative scale showing
centimeters and millimeters and long enough to measure up 'to 40 centimeters. Show on it
distance 2 and 5/8 inch and 14 cm and 6 mm.
3. A rectangular plot of land area 0.45 hectare is represented on a map by a similar
rectangle of 5 cm2. Find the R.F. of the scale of the map. Also draw a scale to read up to
single meters from the map. The scale should be long enough to measure up to 400 meters.
Show on it a distance of 328m, 97m and 109m (1 hectare= 10000m2)