Scales (Plain and Diagonal)

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1 Building Careers. Transforming Lives Scales (Plain and Diagonal) Prepared By : Er. Rahul Mehra (Asst. Professor) (Mechanical Engineering Department)

2 SCALES Usually the word Scale is used for an instrument used for drawing straight lines. But actually in Engineer s language A scale is defined as the proportion by which we either reduce or increasestheactualsizeoftheobjectonadrawing.or Scale means the proportion or ratio between the dimensions adopted for the drawing and the corresponding dimensions of the object. Example: The actual dimensions of the room say 10m x 8m cannot be adopted on the drawing. In suitable proportion the dimensions should be reduced in order to adopt conveniently on the drawing sheet. If the room isrepresentedbyarectangleof10cmx8cmsizeonthedrawingsheetthat meanstheactualsizeisreducedby100times. Similarly, For Small Screw Thread or Nut, The actual dimension is very small (assume 10mm length for screw thread) so it is not clear in the drawing sheet if you draw in the ratio 1:1, So you need to enlarge the size for better understanding of the object. You assume 100mm in the drawing sheet.itmeanstheactualsizeisenlargedby10times.

3 Types of Scales 1) Types of Scales which indicates the Proportion or Ratio a) Full Size Scales b) Reducing Scales c) Enlarging Scales 2) TypesofScaleswhichisusedfortheMeasurement (Scales indicating the ratio or proportion is helping for the measurement) a) Plain Scales b) Diagonal Scales c) Comparative Scales d) Vernier Scales e) Isometric Scales f) Scale of Chords

4 Representative Fraction(R.F) and Length of Scale (LOS) It is defined as the ratio of Drawing Size of the object to its Actual size of the object is called Representative Fraction or R.F USE FOLLOWING FORMULAS FOR THE CALCULATIONS IN THIS TOPIC. A REPRESENTATIVE FACTOR (R.F.) = = DIMENSION ON DRAWING SHEET ACTUAL DIMENSION OF OBJECT LENGTH ON DRAWING SHEET ACTUAL LENGTH OF OBJECT = = V V 3 AREA OF DRAWING ACTUAL AREA VOLUME AS PER DRWG. ACTUAL VOLUME B LENGTH OF SCALE (LOS) = R.F. X Maximum Length to be Measured.

5 Different Units of Measurement Table: Metric Units Table: 1 Kilometre (km) = 10 Hectometres (hm) 1 Hectometre (hm) = 10 Decametres(dam)or 0.1km 1 Decametre(dam) = 10 Metres (m) or 0.1hm 1 Metre(m) = 10Decimetres(dm) or 0.1dam 1 Decimetre(dm) = 10 Centimetres(cm) or 0.1m 1 Centimetre(cm) = 10 Millimetres (mm) or 0.1dm

6 Types of Scales (According to Proportion or Ratio) There are three types of scales depending upon the proportion it indicates as 1) Full scale: Some times the actual dimensions of the object will be adopted on the drawing sheet then in that case it is represented by the scaleandrfasscale:-1cm=1cmor1:1andbyr.f=1/1(equaltoone). 2) Reducing scale: When the objects are very bigger like Buildings, Roads, Ships, Bridges, Machine Parts etc. then the dimensions adopted on the drawing sheet 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). Example:-1:2,1:5,1:10,1:100,1:500,1:1000,1:100000etc. 3) Enlargingscale: Insomecaseswhen theobjectsareverysmalllikeinside parts of a wrist watch, screw thread, small gears, nuts etc. the dimensions adopted on the drawing will be bigger than the actual dimensionsoftheobjectstheninthatcaseitisrepresentedbyscaleand RFasScale:-10cm=1cmor10:1andbyR.F=10/1(greaterthanone). Example:- 2:1, 5:1, 10:1, 100:1, 500:1, 1000:1, 50000:1 etc. 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 isgivencommonlyforallfiguresunderthetitleofsheet.

7 Types of Scales (According to the measurement) Plain Scales :Plain scales read or measure up to two units or a single unit and its sub-division. For example centimetres (cm) and millimetres (mm). When measurements are required up to first decimal, for example 2.3 m or 4.6 cm etc. Steps to Draw Plain Scale:- 1. It consists of a line (LOS) divided into number of equal main parts. 2. The first main part is sub-divided into smaller parts. 3. Mark zero (O) at the end of the first main part. 4. From zero, mark numbers to the main parts or units towards right and give numbers to the sub-divisions or smaller parts towards left. 5. Give the names of the units and sub-units below clearly. Indicate below the name of the scale and its R.F clearly.

8 Continues.. DiagonalScales :Diagonalscalesareused toread ormeasureuptothree units.adiagonalscaleisused whenvery minutedistancessuch as0.1mm etc. are to be accurately measured or when measurements are required in threeunitsoruptoseconddecimal. For example: decimetres (dm), centimetres (cm) and millimetres (mm) or 2.35dm or 4.68km etc.

9 Plain Scale Questions PROBLEM NO.1:- Draw a scale 1 cm = 1m to read decimeters, to measure maximum distance of 6 m. Show on it a distance of 4 m and 6 dm. PROBLEM NO.2:- In a map a 36 km distance is shown by a line 45 cm 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. 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.

10 Diagonal Scale Questions 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 PROBLEM NO.5:- A rectangular plot of land measuring 1.28 hectors is represented on a map by a similar rectangle of 8 sq. cm. Calculate RF of the scale. Draw a diagonal scale to read single meter. Show a distance of 438 m on it. 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. Show the distance of 13.4cm on it.

11 Plain Scales Problems

12 PLAIN SCALE:- This type of scale represents two units or a unit and it s sub-division. PROBLEM NO.1:- Draw a scale 1 cm = 1m to read decimeters, to measure maximum distance of 6 m. Show on it a distance of 4 m and 6 dm. CONSTRUCTION:- a) Calculate R.F.= DIMENSION OF DRAWING DIMENSION OF OBJECT PLAIN SCALE R.F.= 1cm/ 1m = 1/100 Length of scale = R.F. X max. distance = 1/100 X 600 cm = 6 cms b) Draw a line 6 cm long and divide it in 6 equal parts. Each part will represent larger division unit. c) Place ( 0 ) at the end of first unit. Number the units on right side of Zero. (0,1,2,3,4,5) (1part = 1meter) d) Sub divide the first part which will represent second unit or fraction of first unit. d) Mark the subdivisions on left-hand side of Zero (0,1,2,...10). (1part = 1Decimeter) 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 4 m 6 dm on it as shown. 4 M 6 DM METERS DECIMETERS R.F. = 1/100 PLANE SCALE SHOWING METERS AND DECIMETERS.

13 PROBLEM NO.2:-In a map a 36 km distance is shown by a line 45 cm 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/ = 1/ 80,000 Length of scale = R.F. X max. distance = 1/ X 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) Place ( 0 ) at the end of first unit. Number the units on right side of Zero. (0,1,2,3 11) (1part = 1 KM) d) Sub divide the first part which will represent second unit or fraction of first unit. d) Mark the subdivisions on left-hand side of Zero. (0,1,2,..10)(1part = 1 HM) 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. PLAIN SCALE 8KM 3HM 10 5 HECTOMETERS KILOMETERS R.F. = 1/80,000 PLANE SCALE SHOWING KILOMETERS AND HECTOMETERS

14 PROBLEM NO.3:- The distance between two stations is 210 km. A passenger train covers this distance in7hours.constructaplainscaletomeasuretimeuptoasingleminute.rfis1/200,000indicatethedistance traveled by train in 29 minutes. CONSTRUCTION:- a)210kmin7hours.meansspeedofthetrainis30kmperhour(60minutes) PLAIN SCALE Lengthofscale=R.F. X max.distanceperhour =1/2,00,000 X 30km =15cm b)15cmlengthwillrepresent30kmand1houri.e.60minutes. Drawaline15cmlonganddivideitin6equalparts.Eachpartwillrepresent5kmand10minutes. c)subdividethefirstpartin10equalparts,whichwillrepresentsecondunitorfractionoffirstunit. Each smaller part will represent distance traveled in one minute. d)place(0)attheendoffirstunit.numbertheunitsonrightsideofzeroandsubdivisions onleft-handsideofzero.takeheightofscale5to10mmforgettingaproperlookofscale. e)showkmonuppersideandtimeinminutesonlowersideofthescaleasshown. Afterconstructionofscalementionit srfandnameofscaleasshown. f)showthedistancetraveledin29minutes,whichis14.5km,onitasshown. DISTANCE TRAVELED IN 29 MINUTES KM KM KM SINGLE MIN TEN R.F. = 1/100 PLANE SCALE SHOWING METERS AND DECIMETERS. MINUTES

15 Diagonal Scale Problems

16 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 DIAGONAL SCALE 1. Draw a line 15 cm long. It will represent 600 km. Divide it in six equal parts.( each will represent 100 km). 2. Divide first division in ten equal parts. Each will represent 10 km. 3. Draw a line upward from left end of any dimension and mark 10 parts on it of same distance. 4. Name those parts 0 to 10 as shown. 5. Join 9 th sub-division of horizontal scale with 10 th division of the vertical divisions. 6. Then draw parallel lines to this line from remaining sub divisions and complete diagonal scale. Then Show distances. 569 km 459 km 336 km 222 km KM KM R.F. = 1 / 40,00,000 DIAGONAL SCALE SHOWING KILOMETERS. 100 KM

17 PROBLEM NO.5: A rectangular plot of land measuring 1.28 hectors is represented on a map by a similar rectangle of 8 sq. cm. Calculate RF of the scale. Draw a diagonal scale to read single meter. Show a distance of 438 m on it. SOLUTION : 1 hector = 10, 000 sq. meters 1.28 hectors = 1.28 X 10, 000 sq. meters = 1.28 X 10 4 X 10 4 sq. cm 8 sq. cm area on map represents = 1.28 X 10 4 X 10 4 sq. cm on land 1 cm sq. on map represents = 1.28 X 10 4 X 10 4 / 8 sq cm on land 1 cm on map represent = 1.28 X 10 4 X 10 4 / 8 cm = 4, 000 cm 1 cm on drawing represent 4, 000 cm, Means RF = 1 / 4000 Assuming length of scale 15 cm, it will represent 600 m. DIAGONAL SCALE 1. Draw a line 15 cm long. It will represent 600 m. Divide it in six equal parts. ( each will represent 100 m.) 2. Divide first division in ten equal parts. Each will represent 10 m. 3. Draw a line upward from left end of any distance and mark 10 parts on it of same distance. 4. Name those parts 0 to 10 as shown. Join 9 th sub-division of horizontal scale with 10 th division of the vertical divisions. 5. Then draw parallel lines to this line from remaining sub divisions and complete diagonal scale. 438 meters M M R.F. = 1 / 4000 M DIAGONAL SCALE SHOWING METERS.

18 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. Show the distance of 13.4cm on it. SOLUTION STEPS: R.F. = 1 / 2.5 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 of any distance and on it mark10 equal divisions of same length. 4.Complete the scale as explained in previous problems. Show the distance 13.4 cm on it. DIAGONAL SCALE 13.4 CM MM CM CENTIMETRES R.F. = 1 / 2.5 DIAGONAL SCALE SHOWING CENTIMETERS.

19 Thank You

SIMILARLY IN CASE OF TINY OBJECTS DIMENSIONS MUST BE INCREASED FOR ABOVE PURPOSE. HENCE THIS SCALE IS CALLED ENLARGING SCALE. FOR FULL SIZE SCALE R.

SIMILARLY IN CASE OF TINY OBJECTS DIMENSIONS MUST BE INCREASED FOR ABOVE PURPOSE. HENCE THIS SCALE IS CALLED ENLARGING SCALE. FOR FULL SIZE SCALE R. DIMENSIONS OF LARGE OBJECTS MUST BE REDUCED TO ACCOMMODATE ON STANDARD SIZE DRAWING SHEET.THIS REDUCTION CREATES A SCALE OF THAT REDUCTION RATIO, WHICH IS GENERALLY A FRACTION.. SUCH A SCALE IS CALLED