Engineering Drawing II Scale Development
Representative Fraction Representative fraction (RF) is the ratio of the length in scale to the actual length.
Mathematically, RF = Length in scale ÷ Actual Length
Why RFs are used? To present a figure of a relatively larger object in a small sheet of paper.
To present a figure of a relatively smaller object in a relatively larger sheet of paper.
Examples of Uses of RFs In drawing maps In drawing road locations In drawing house plans In presenting enlarged figures of microscopic objects; i.e. bacterial cells, amoebas etc.
Significance of RF values RF greater than 1 Used in presenting enlarged figures of relatively small objects. RF less than 1 Used in presenting reduced figures of relatively larger objects.
Different Types of Scales Plain Scale: • • • •
It is simply a line which is divided into a suitable number of equal parts, first of which is sub-divided into small parts. It is used to represent either two units or a unit and its fraction. Such as m and dm. Used where the required scale divisions are relatively big. Easier to use for its simplicity.
Diagonal Scale • • • •
It is used to represent either three units of measurements. Such as m cm and dm Used where the required scale divisions are relatively small. Provides much accuracy. Complex to construct and use.
Construction of Plain Scales Example 1 The distance between Dhaka and Feni is 175 km. A passenger train covers the distance in 5 hours and 50 minutes. Construct a plain scale to measure time up to a single minute and corresponding distance. RF is 1/200000. Also indicate the distance covered by the train in 28 minutes.
Construction of Plain Scales (Contd.) Step 1: Check the RF to select unit Here, RF = 1/200000 i.e. 1 cm = 200000 cm or, 1 m = 200000 m or, 1 ft = 200000 ft etc. Our objective is to develop a 6” or 15 cm scale for a fair presentation. Here the distance is given in km. So we can take 1 km = 200000 km. But we can not draw a scale with such a big unit in a small sheet of paper. If we look for a smaller unit, we can take 1 cm = 200000 cm (2 km) easily and a 15 cm scale can show a 30 km distance. Moreover, km and cm can be related easily.
Construction of Plain Scales (contd.) Step 2: Solve the problem In these sort of problem, relationship between distance and time needs to be presented in a scale. Therefore, calculation of velocity is required. Velocity = Distance ÷ Time = 175 km ÷ 350 minutes = ½ km/minute So, the train travels 1 km in 2 minute.
Construction of Plain Scales (contd.) Step 3: Decide on Scale Type & Divisions Now, you may take ….. 2 major divisions of 7.5 cm (15 km in 30 minutes) or, 3 major divisions of 5 cm (10km in 20 minutes) or, 5 major divisions of 3 cm (6km in 12 minutes) or, 6 major divisions of 2.5 cm (5km in 10 minutes) As you need to show the distance covered by the train up to a single minute, it is better to select the number of major divisions to limit the fractioning of a division to minimum for simplicity & neatness. The last choice is ideal and can be easily drawn.
Construction of Plain Scales (contd.) Step 4: Draw the Scale
Construction of Diagonal Scales Example 1 Construct a scale of RF=1/2000 to read 300 meters to 1 meter. Also show 135 meters in the scale. Step 1: Check the RF to select unit As you need to measure the distance in meter unit, you can take 1 cm = 2000 cm (i.e. 1 cm = 20 m) In that case 300 meters will be 15 cm in our scale. We know that, RF = Length in scale ÷ Actual Length or, Length in scale = RF X Actual Length. So, the scale length for your actual 300 m will be, = (1/2000) X (300X100) = 15 cm
Construction of Diagonal Scales (contd.)
Step 2: Solve the problem
In these problem, there is nothing extra to calculate. You have completed the necessary calculations in the previous step. Step 3: Decide on Scale Type & Divisions This is an important part. You may take …. 2 major divisions of 7.5 cm (150m) or, 3 major divisions of 5 cm (100m) or, 5 major divisions of 3 cm (60m) or, 6 major divisions of 2.5 cm (50m) If you choose the last option to construct a scale with smaller divisions and try to show 1 m, then you need to divide a 2.5 cm major division into 50 minor divisions !!! ABSOLUTELY IMPOSSIBLE ! ! ! In such cases, you need to construct a diagonal scale.
Construction of Diagonal Scales (contd.) Step 4: Calculate to Draw Diagonal Scale If you draw a scale with 3 major division, then your one major division represents 100 m and the minor division have to show 1 m. Now 100 ÷ 1 = 100. You need to draw a diagonal grid and the (no. of rows X no. of columns) has to be 100. You may take … 10 rows & 10 columns or, 4 rows & 25 columns or, 25 rows & 4 columns or, 2 rows & 50 columns or, 50 rows & 2 columns or, 100 rows & 1 column or, 1 row & 100 columns (It will be a plain scale !!!) You should choose the first option, because it is not easy to divide your 5 cm major division into 25 or 50 or 100 minor divisions !!!
Construction of Diagonal Scales (contd.) Step 5: Draw the Scale
Construction of Diagonal Scales (contd.) Example 1 A car runs at 40 miles/hour. Construct a diagonal scale with RF=1/1584000 to read directly the position of the showing time interval of 3 minutes. Also show the distance traveled by the car in 1 hour & 42 minutes in the scale.
Construction of Diagonal Scales (contd.) Step 1: Check the RF to select unit Here, RF = 1/1584000 i.e. 1 cm = 1584000 cm or, 1 m = 1584000 m or, 1 ft = 1584000 ft or, 1 inch = 1584000 inch etc. Our objective is to develop a 6” or 15 cm scale for a fair presentation. Here the velocity is given in mph. So we may take 1 ft = 1584000 ft. But we can not draw a scale with such a big unit in a small sheet of paper. If we look for a smaller unit, can take 1 inch = 1584000 inch easily.
Construction of Diagonal Scales (contd.) Step 2: Solve the problem Now let us check the length of scale that represents 40 miles (the distance traveled by the car in an hour) according to RF. 40 miles = 40 X (1760 X 3 X12) inch = 2534400 “ According to RF, Actual 40 miles is (2534400 ÷ 1584000) or 1.6”. So in the scale, 1.6” is the distance traveled by the car in 1 hour (i.e. actually 40 miles). If you draw a 6.4” (1.6”X4) scale, it will show the distance covered by the car in 4 hours. The scale will be around 6” also and it will be fair enough !!!
Construction of Diagonal Scales (contd.) Step 4: Calculate to Draw Diagonal Scale Now your scale’s each major division represents the distance covered by the car in 1 hour and you need to divide it into it’s minor divisions to show the distance traveled by the car per 3 minutes. So,… 60 ÷ 3 =20 You need to draw a diagonal grid and the (no. of rows X no. of columns) has to be 20. You may take … 4 rows & 5 columns or, 5 rows & 4 columns or, 2 rows & 10 columns or, 10 rows & 2 columns or, 20 rows & 1 column or, 1 row & 20 columns (It will be a plain scale !!!) You should choose the second option, because it is relatively easy to divide your 1.6” major division into 4 minor divisions of 0.4”.
Construction of Diagonal Scales (contd.) Step 5: Draw the Scale