Scale lecture of engineering drawing, Lecture notes of Engineering Drawing and Graphics

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L-

ED-ME

Dr. Poonam Kumari

SCALES

A scale is defined as the ratio of the linear dimensions of the

object as represented in a drawing to the actual dimensions

of the same. The proportion by which the drawing of a given

object is enlarged or reduced is called scale of the drawing.

It is not convenient, always, to draw drawings of the object to

its actual size. e.g. Buildings, Heavy machines, Bridges,

Watches, Electronic devices etc. Thus, following scales are used

Enlargement scales Reducing/ Reduction scales Full scale

Scales for the drawing of

small objects needs to be

enlarged

Scales for the drawing of

huge objects needs to be

reduced

Object is drawn on sheet to

its actual size, then its drawn

at full scale.

Format – X:1, X>1, RF>1 Format – 1:Y, Y>1, RF<1 Format – 1:1, RF=

E.g. resistors, screws, gears

for electronics, Ics, transistors

E.g. buildings, bridges,

boilers, ships, aero planes

E.g. spanner, pen, nut bolts

etc.

BIS (SP 46: 2003) recommended scales Intermediate scales can be used in exceptional cases where^. recommended scales can not be applied for functional reasons. LOS (Length of Scale) (mm) All the scales (except the scale of chords) are constructed by drawing a line of length equivalent to the actual distance to be represented. This length is called length of scale (LOS).

LENGTH OF SCALE (LOS)= R.F. X MAX. LENGTH TO BE MEASURED.

Types of scale

• Engineers Scale : The relation between the dimension on the drawing and the actual dimension of the object is mentioned numerically (like 10mm = 15 m).
• Graphical Scale: Scale is drawn on the drawing itself. This takes care of the shrinkage of the engineer’s scale when the drawing becomes old. Types of scales

1. PLAIN SCALES ( FOR DIMENSIONS UP TO SINGLE DECIMAL)

2. DIAGONAL SCALES ( FOR DIMENSIONS UP TO TWO DECIMALS)

3. VERNIER SCALES ( FOR DIMENSIONS UP TO TWO DECIMALS)

4. COMPARATIVE SCALES ( FOR COMPARING TWO DIFFERENT UNITS)

5. SCALE OF CORDS ( FOR MEASURING/CONSTRUCTING ANGLES)

1. PLAIN SCALES ( FOR DIMENSIONS UP TO SINGLE DECIMAL)

2. DIAGONAL SCALES ( FOR DIMENSIONS UP TO TWO DECIMALS)

3. VERNIER SCALES ( FOR DIMENSIONS UP TO TWO DECIMALS)

4. COMPARATIVE SCALES ( FOR COMPARING TWO DIFFERENT UNITS)

5. SCALE OF CORDS ( FOR MEASURING/CONSTRUCTING ANGLES)

TYPES OF SCALES:

= 10 HECTOMETRES

= 10 DECAMETRES

= 10 METRES

= 10 DECIMETRES

= 10 CENTIMETRES

= 10 MILIMETRES

1 KILOMETRE

1 HECTOMETRE

1 DECAMETRE

1 METRE

1 DECIMETRE

1 CENTIMETRE

BE FRIENDLY WITH THESE UNITS.

Plain scales

A plain scale consists of a line divided into suitable number of equal units. The first unit is subdivided into smaller parts.

• (^) The plain scales give only two dimensions, such as a unit and it’s subunit or it’s fraction.
• The zero should be placed at the end of the 1st main unit.
• From the zero mark, the units should be numbered to the right and the sub-divisions to the left.
• The units and the subdivisions should be labelled clearly.
• The R.F. should be mentioned below the scale.

PROBLEM NO.2:- In a map a 36 km distance is shown by a line 45 cms long. Calculate the R.F. and construct a plain scale to read kilometers and hectometers, for max. 12 km. Show a distance of 8.3 km on it. CONSTRUCTION:- a) Calculate R.F. R.F.= 45 cm/ 36 km = 45/ 36. 1000. 100 = 1/ 80, Length of scale = R.F. max. distance = 1/ 80000 12 km = 15 cm b) Draw a line 15 cm long and divide it in 12 equal parts. Each part will represent larger division unit. c) Sub divide the first part which will represent second unit or fraction of first unit. d) Place ( 0 ) at the end of first unit. Number the units on right side of Zero and subdivisions on left-hand side of Zero. Take height of scale 5 to 10 mm for getting a look of scale. e) After construction of scale mention it’s RF and name of scale as shown. f) Show the distance 8.3 km on it as shown. KILOMETERS HECTOMETERS

8KM 3HM

R.F. = 1/80,

PLANE SCALE SHOWING KILOMETERS AND HECTOMETERS

PLAIN SCALE

PROBLEM NO.3:- The distance between two stations is 210 km. A passenger train covers this distance in 7 hours. Construct a plain scale to measure time up to a single minute. RF is 1/200,000 Indicate the distance traveled by train in 29 minutes. CONSTRUCTION:- a) 210 km in 7 hours. Means speed of the train is 30 km per hour ( 60 minutes) Length of scale = R.F. max. distance per hour = 1/ 2,00,000 30km = 15 cm b) 15 cm length will represent 30 km and 1 hour i.e. 60 minutes. Draw a line 15 cm long and divide it in 6 equal parts. Each part will represent 5 km and 10 minutes. c) Sub divide the first part in 10 equal parts,which will represent second unit or fraction of first unit. Each smaller part will represent distance traveled in one minute. d) Place ( 0 ) at the end of first unit. Number the units on right side of Zero and subdivisions on left-hand side of Zero. Take height of scale 5 to 10 mm for getting a proper look of scale. e) Show km on upper side and time in minutes on lower side of the scale as shown. After construction of scale mention it’s RF and name of scale as shown. f) Show the distance traveled in 29 minutes, which is 14.5 km, on it as shown. PLAIN SCALE

MIN 10 0 10 20 30 40 50 MINUTES

R.F. = 1/

PLANE SCALE SHOWING METERS AND DECIMETERS.

KM 5 2.5^0 5 10 15 20 25 KM

DISTANCE TRAVELED IN 29 MINUTES. 14.5 KM

Diagonal scales

6. Since the triangles are similar; 1΄1 = 0.1 AB, 2΄2 = 0.2AB, …. 9΄9 = 0.9AB.
7. Gives divisions of a given short line AB in multiples of 1/10 its length, e.g. 0.1AB, 0.2AB, 0.3AB, etc.

R.F. = 1 / 40,00,

DIAGONAL SCALE SHOWING KILOMETERS.

100^50 0 100 200 300 400

10 9 8 7 6 5 4 3 2 1 0 KM KM KM 569 km 459 km 336 km 222 km PROBLEM NO. 4 : The distance between Delhi and Agra is 200 km. In a railway map it is represented by a line 5 cm long. Find it’s R.F. Draw a diagonal scale to show single km. And maximum 600 km. Indicate on it following distances. 1) 222 km 2) 336 km 3) 459 km 4) 569 km SOLUTION STEPS: RF = 5 cm / 200 km = 1 / 40, 00, 000 Length of scale = 1 / 40, 00, 000 X 600 X 10^5 = 15 cm Draw a line 15 cm long. It will represent 600 km.Divide it in six equal parts.( each will represent 100 km.) Divid e first division in ten equal parts.Each will represent 10 km. Draw a line upward from left end and mark 10 parts on it of any distance. Name those parts 0 to 10 as shown.Join 9th^ sub-division of horizontal scale with 10th^ division of the vertical divisions. Then draw parallel lines to this line from remaining sub divisions and complete diagonal scale. DIAGONAL SCALE

10 9 8 7 6 5 4 3 2 1 0 CENTIMETRES MM CM R.F. = 1 / 2. DIAGONAL SCALE SHOWING CENTIMETERS.

PROBLEM NO.6:. Draw a diagonal scale of R.F. 1: 2.5, showing centimeters and millimeters and long enough to measure up to 20 centimeters. SOLUTION STEPS: R.F. = 1 / 2. Length of scale = 1 / 2.5 X 20 cm. = 8 cm. 1.Draw a line 8 cm long and divide it in to 4 equal parts. (Each part will represent a length of 5 cm.) 2.Divide the first part into 5 equal divisions. (Each will show 1 cm.) 3.At the left hand end of the line, draw a vertical line and on it step-off 10 equal divisions of any length. 4.Complete the scale as explained in previous problems. Show the distance 13.4 cm on it. 13 .4 CM

DIAGONAL

SCALE

COMPARATIVE SCALES : These are the Scales having same R.F. but graduated to read different units. These scales may be Plain scales or Diagonal scales and may be constructed separately or one above the other.

EXAMPLE NO. 7 :

A distance of 40 miles is represented by a line 8 cm long. Construct a plain scale to read 80 miles. Also construct a comparative scale to read kilometers upto 120 km ( 1 m = 1.609 km ) SOLUTION STEPS: Scale of Miles : 40 miles are represented = 8 cm 80 miles = 16 cm R.F. = 8 / 40 X 1609 X 1000 X 100 = 1 / 8, 04, 500 CONSTRUCTION: Take a line 16 cm long and divide it into 8 parts. Each will represent 10 miles. Subdivide the first part and each sub-division will measure single mile. Scale of Km : Length of scale = 1 / 8,04,500 X 120 X 1000 X 100 = 14. 90 cm CONSTRUCTION : On the top line of the scale of miles cut off a distance of 14.90 cm and divide it into 12 equal parts. Each part will represent 10 km. Subdivide the first part into 10 equal parts. Each subdivision will show single km. 10 5 0 10 20 30 40 50 60 70 MILES 10 0 10 20 30 40 50 60 70 80 90 100 110 KM 5 R.F. = 1 / 804500 COMPARATIVE SCALE SHOWING MILES AND KILOMETERS

EXAMPLE NO. 9 : A car is traveling at a speed of 60 km per hour. A 4 cm long line represents the distance traveled by the car in two hours. Construct a suitable comparative scale up to 10 hours. The scale should be able to read the distance traveled in one minute. Show the time required to cover 476 km and also distance in 4 hours and 24 minutes.

COMPARATIVE

SCALE :

SOLUTION: 4 cm line represents distance in two hours , means for 10 hours scale, 20 cm long line is required, as length of scale.This length of scale will also represent 600 kms. ( as it is a distance traveled in 10 hours) CONSTRUCTION: Distance Scale ( km) Draw a line 20 cm long. Divide it in TEN equal parts.( Each will show 60 km) Sub-divide 1st^ part in SIX subdivisions.( Each will represent 10 km) At the left hand end of the line, draw a vertical line and on it step-off 10 equal divisions of any length. And complete the diagonal scale to read minimum ONE km. Time scale: Draw a line 20 cm long. Divide it in TEN equal parts.( Each will show 1 hour) Sub-divide 1st^ part in SIX subdivisions.( Each will represent 10 minutes) At the left hand end of the line, draw a vertical line and on it step-off 10 equal divisions of any length. And complete the diagonal scale to read minimum ONE minute. 10 5 0 kM kM (^) (^60 ) 60 120 180 240 300 360 420 480 540 (^60 01 2 3 4 5 6 7 8 ) HOURS MIN. 10 5 0 DISTANCE SCALE TO MEASURE MIN 1 KM KILOMETERS TIME SCALE TO MEASURE MIN 1 MINUTE. 4 hrs 24 min. ( 264 kms ) 476 kms ( 7 hrs 56 min.)

Vernier scales

1. Similar to Diagonal scale, Vernier scale is used for measuring up to second decimal.
2. A Vernier scale consists of (i) a primary scale and (ii) vernier.
3. The primary scale is a plain scale fully divided in to minor divisions. Subdivision on main scale is called main scale div.
4. The graduations on the vernier are derived from those on the primary scale. Subdivision - vernier scale division (VSD).
5. Vernier is auxillary scale above main scale whose length can be more or less by fixed amount than that of main div. Least count (LC) It is the minimum distance that can be measured precisely by a given vernier scale.