scales: basics , plain and diagonal
TRANSCRIPT
Scales
Ar. Surashmie Kaalmegh Asisstant Professor LAD College , Nagpur
Reading scales
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.
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)
Big objects :
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.
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.
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
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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.
The scale 3/32 in. = 1 ft, expressed fractionally, comes to 3/32 = 12, or 1/128
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:
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.
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.
Diagonal scales Draw the line AC of convenient length at right
angles to plain scaleAB. Divide it into 10 equal parts. Join BC. From each tenth point on line ACdraw 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 constructionof diagonal scale with RF = 1 / 500 and indicates 62.6 m.
Principles of diagonal scales
Division of lines
Division of lines
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.)
Kilometre, Hectometre, Decametre, Metre, Decimetre, Centimetre, Millimetre
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 3m5.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
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.
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.
Parallel Dimensions
Dimensioning
Dimensioning types:
Combined dimensions
Dimensioning small objects
Chain dimensions
Spherical dimensions
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
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,
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
