WHAT ARE SCALES ? SCALES AND THEIR USES , PLANE AND DIAGONAL SCALES ,architectural scales and theory related to it .

1. Scales
Ar. Surashmie Kaalmegh
Asisstant Professor
LAD College , Nagpur

3. Reading scales

4. SCALES Usually the word scale is used for an instrument used for
drawing straight lines.
But in an Engineer’s/ designers language
scale means :--
the proportion or ratio between the
dimensions adopted for the drawing and
the corresponding dimensions of the object.
 It can be indicated in two different ways.
 Eg . The actual dimensions of the room ---- 10m x 8m cannot be adopted on the
drawing.
 In suitable proportion the dimensions ---- reduced in order to adopt conveniently on the
drawing sheet.
 If the room is represented by a rectangle of 10cm x 8cm size on the drawing sheet
that means the actual size is reduced by 100 times.
 Representing scales: The proportion between the drawing and the object can be
represented by two ways as follows:
a) Scale: - 1cm = 1m or 1cm=100cm or 1:100
b) Representative Fraction: - (RF) = 1/100 (less than one) .
i.e. the ratio between the size of the drawing and the object.

5. There are three types of scales depending upon
the proportion it indicates as : --
 1 .. Reducing scale: When the dimensions on the drawing are smaller
than the actual dimensions of the object. It is represented by the scale and
RF as
Scale: - 1cm=100cm or 1:100 and by RF=1/100 (less than one)
2. Full scale: Some times the actual dimensions of the object will be
adopted on the drawing then in that case it is represented by the scale and
RF as
Scale: - 1cm = 1cm or 1:1 and by R.F=1/1 (equal to one).
3. Enlarging scale: 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 by scale and RF as
Scale: - 10cm=1cm or 10:1 and by R.F= 10/1 (greater than one)

6. Big objects :

7. Small objects:

8. Scale drawing
 A drawing in which the figure drawn is
an exact representation of the original
object except for size.
 The change in size is done using
equal intervals or a scale.
 A scale diagram of an object is in the
same proportion to the object itself.
 If a diagram is smaller than the
object, it is a reduction ,If it is larger, it
is an enlargement
 The number of times the size of the
diagram is enlarged or reduced is
called the scale factor.
The Eiffel Tower is approx. 300 yds.
It is about 4.5 in. in the drawing
and using the scale 1:2800, its
height is found to be 4.5
2800 = 12,600 in., or 1050 ft, or
350 yd.
The precise height of the Eiffel
Tower is 348.53 yards with the
antenna that was added in 1994.

9. Scales and their constructions:
 To construct the scale the data required is :
1) the R.F of the scale
2) The units which it has to represent i.e. millimetres
or centimetres or metres or kilometres 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 = R.F X maximum length the scale should
measure.
•This should be generally of 15 to 20 cms length.
Need : When an unusual proportion is to be adopted and
when the ready made scales are not available then
the required scale is to be constructed on the drawing sheet itself.

10.  REPRESENTATIVE FACTOR (R.F.) = DIMENSION OF DRAWING
DIMENSION OF OBJECT
i.e . = LENGTH OF DRAWING
ACTUAL LENGTH
LENGTH OF SCALE = R.F. * MAX. LENGTH TO BE MEASURED
The scale 3/32 in. = 1 ft, expressed fraction- ally, comes to 3/32 = 12, or 1/128
&

11.  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.

14.  The scale 3/32 in. = 1 ft, expressed fractionally,
comes to 3/32 = 12, or 1/128

16.  The following two types of scales are used :
(i)Plain Scale
(ii) Diagonal Scale.
 Plain Scale
On a plain scale it is possible to read two
dimensions directly such as unit and tenths.
 This scale is not drawn like ordinary foot rule (30
cm scale).
 If a scale of 1 : 40 is to be drawn, the markings are
not like 4 m, 8 m, 12 m etc. at every 1 cm
distance.
 Construction of such a scale is illustrated with the
example given below:

21.  Example : Construct a plain scale of RF = 1 /500 and indicate
66 ms. on it.
 Solution. If the total length of the scale is selected as 20 cm,
it represents a total length of 500 × 20 = 10000 cm = 100 m.
Hence, draw a line of 20 cm and divide it into 10 equal parts.
Hence, each part correspond to 10 m on the ground. First
part on extreme left is subdivided into 10 parts, each
subdivision representing 1 m on the field. Then they are
numbered as 1 to 10 from right to left as shown in Fig. 11.6. If
a distance on the ground is between 60 and 70 m, it is picked
up with a divider by placing one leg on 60 m marking and the
other leg on subdivision in the first part. Thus field distance is
easily converted to map distance.

25. Diagonal Scale
 In plain scale only unit and tenths can be shown
whereas in diagonal scales it is possible to show
units, tenths and hundredths. Units and tenths are
shown in the same manner as in plain scale.
 To show hundredths, principle of similar triangle is
used.
 If AB is a small length and its tenths are to be
shown, it can be shown as explained with Fig. on
next slide.

26. Diagonal scales
 Draw the line AC of convenient length at right
angles to plain scale
AB. Divide it into 10 equal parts. Join BC. From
each tenth point on line AC
draw lines parallel to AB till they meet line BC.
 Then line 1–1 represent 1 / 10th
of AB, 6–6
represent 6 / 100th
of AB and so on.
 Figure shows the construction
of diagonal scale with RF = 1 / 500 and indicates
62.6 m.

27. Principles of diagonal scales

28. Division of lines

29. Division of lines

30. Measures of Length
1 foot (ft.
or ')
= 12 inches (in. or ")
1 yard (yd.) = 36 inches (in.)
1 yard (yd.) = 3 feet (ft.)
1 mile (mi.) = 5,280 feet (ft.)
1 mile (mi.) = 1,760 yards (yd.)

32. Kilometre, Hectometre, Decametre, Metre, Decimetre, Centimetre, Millimetre

34. SCALES Problems :
Plain Scales.
1Construct a plain scale of 1½ times full size to read up to 60mm.
2.Construct a plain scale of 1:200, to give a maximum reading of 60m
and a minimum reading of 0.5m.
3.The 50mm mark on a dipstick for measuring palm oil content of a drum
represents three quarters of a litre.Design your own dipstick for measuring
up to 6 litres of the content of the container.
4.Draw a plain scale of 40mm to 1m to read to 3m
5.To draw a plain scale of 50mm to 1km to read to 3km.
6.Construct a plain scale of 50mm equal to 300mm to read to 10mm up
to 1200mm.
7.Construct a plain scale of 30mm = 10mm, 50mm long to read to 1mm.
Diagonal Scales.
1.Construct a diagonal scale of 50mm to 1km to read to 3km in
Decameters and decimeters.
2.Construct adiagonal scale of 3:2 to read up to 300mm.
3.Construct a diagonal scale to measure lengths up to 100mm to an
accuracy 0f 0.1mm.
4.Construct a diagonal scale of 1:50 (20mm represents 1000mm or 1
meter) to give readings to an accuracy of two decimal places.
.5.Construct a diagonal scale of 1:10,000 (100mm to 1km) to read up to
3km, to an accuracy of two

35.  6.Construct a diagonal scale of 1 /4full size to read up to 5dm in
cm and mm.
 7.Construct a diagonal scale of twice full size to read upto 6cm in
mm and tenths of a mm.
 8.Construct a diagonal scale of 25mm to represent 1m, capable of
reading one-hundredth of a meter, up to amaximum of 5m. Mark
on the scale two points A and B such that AB = 3.72m.
 9.Construct a diagonal scale of cm to read up to 11cm in mm and
tenths of a mm.
 10.Construct a diagonal scale of twice full size to read up to 6cm
in mm and 1 / 10ths
of a mm.
 11.Construct a diagonal scale of 3cm equal to 1m to read up to
4m in dm and cm.
 12.Construct a diagonal scale of 1 /4 th full size to read up to 5dm
in cm and mm.
 13.Construct a diagonal scale of 30mm equal to 1m 4m long to
read to 10mm.
 14.Construct a diagonal scale of 50mm equal to 1mm, 3mm long
to read 0.01mm.
 15.Construct a diagonal scale of 40mm to represent 1m to read
down to 10mm to cover a range of 5m.

36.  16.Construct a diagonal scale of 25mm equal to 1m which can be
used to measure m and 10mm up to 8m.Use the scale above to
construct a quadrilateral abcd. Base ab = 4m720mm, bc =
3m530mm, ad =4m170mm, angles abc = 1200, adc = 900
 . Measure, to the nearest 10mm, the vertical height of
thequadrilateral and the lengths of the diagonals.
 17.Construct a diagonal scale of ten times full size to show mm and
tenths of a mm to read to a maximum of 20mm.Using the scale
above, construct a triangle abc with ab = 17.4mm, bc = 13.8mm and
ac = 11mm.18.Construct a diagonal scale, 50mm = 1mm, 3mm long
to read to 1 /100th
 0f a mm.19.Construct a diagonal scale, 30mm = 1m, 4m long to read
to 10mm.20.Construct a diagonal scale of20mm = 10mm, 60mm
long to read to 0.1mm.21.Construct a diagonal scale of 1:1000 that
is accurate to two decimal places to give a maximum reading
of 300m.22.A science department at school requires a suitable scale
for measuring lengths of steel rod, toa maximumlength of 200mm.
The scale should be accurate to within 0.1mm. Construct the scale.

37. Parallel Dimensions
Dimensioning

38. Dimensioning types:
Combined dimensions
Dimensioning small objects
Chain dimensions

40. Spherical dimensions

41.  ANY REGULAR POLYGON WITH A GIVEN
LENGTH OF SIDE : To draw a nine-sided regular
polygon with length of side equal to AB, first extend
AB to C, making CA equal to AB. With A as a center
and AB or CA) as a radius, draw a semicircle as
shown. Divide the semicircle into nine equal
segments from C to B, and draw radii from A to the
points of intersection. The radius A2 is always
the second side of the polygon. Draw a circle
through points A, B, and D. To do this, first erect
perpendicular bisectors from DA and AB. The point
of intersection of the bisectors is the center of the
circle. The circle is the circumscribed circle of the
polygon. To draw the remaining sides, extend the
radii from the semicircle as shown, and connect the
points where they intersect the circumscribed circle.
Besides the methods described for constructing any
regular polygon, there are particular methods for
constructing a regular pentagon, hexagon, or
octagon

42.  ANY REGULAR
POLYGON ON A GIVEN
INSCRIBED CIRCLE The
method (dividing the
circumference into equal
segments) can be used to
construct a regular polygon
on a given inscribed
circle. In this case,
however, instead of
connecting the points of
intersection on the
circumference, you draw
each side tangent to the
circumference and
perpendicular to the
radius at each point of
intersection,

43.  REGULAR PENTAGON IN A
GIVEN CIRCUMSCRIBED
CIRCLE : Draw a horizontal
diameter AB and a vertical
diameter CD. Locate E, the
midpoint of the radius OB. Set a
compass to the spread between
E and C, and, with E as a center,
strike the arc CF. Set a compass
to the spread between C and F,
and, with C as a center, strike the
arc GF. A line from G to C
forms one side of the
pentagon. Set a compass to GC
and lay off this interval from C
around the circle. Connect the
points of intersection