SCALES Engineering Drawing
Scales
Definition- The proportion by which actual size
of object is enlarged or reduced on drawing is called scale.
Use of scale-
1. 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. Examples-
a)
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 scale-
A. Based on R.F -
1) 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)
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.
B. Based on Uses
-
1) Plain Scale.
2) Diagonal scale.
3) Comparative Scale.
4) Vernier scale.
5) Scale of Chord.
6) Isometric Scale.
7) Logarithmic Scale.
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Will be
discussed in later sheets.
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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 Scale-
Plain 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 sub-divisions 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: Calculations-
1) 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.
Construction-
Draw 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 Scale-
Three
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
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: Calculations-
1) 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.
Construction-
Draw 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
Note: Assume the
height of the diagonal scale AD as 5cm for dividing it into 10 equal parts
conveniently.
3) Comparative Scale-
Comparative
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: Calculations-
1) 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.
Construction-
1) 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
4) Vernier Scale-
A 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
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: Calculations-
1) Length of Scale (LOS) =
(1/25) X (4 X 100) = 16 cm Construction-
1) 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 chords-
Scale of cords is very helpful in measuring
angles without help of protector.
Method of Construction:
1) Draw AB
and erect perpendicular at B.
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: Construction-
1) Following
the above discussed steps draw fig. 2.7.
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”
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)
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