Introduction
Before you start any drawing you first decide how large the drawings have to be. The different views of the object to be drawn must not be bunched together or be too far apart. If you are able to do this and still draw the object in its natural size then obviously this is best. This is not always possible; the object may be much too large for the paper or much too small to be drawn clearly. In either case it will be necessary to draw the object ‘ to scale ’ . The scale must depend on the size of the object; a miniature electronic component may have to be drawn 100 times larger than it really is, whilst some maps have natural dimensions divided by millions.
There are drawing aids called ‘ scales ’ which are designed to help the draughts person cope with these scaled dimensions. They look like an ordinary ruler but closer inspection shows that the divisions on these scales are not the usual centimetres or millimetres, but can represent them. These scales are very useful but there will come a time when you will want to draw to a size that is not on one of these scales. You could work out the scaled size for every dimension on the drawing but this can be a long and tedious business – unless you construct your own scale. This chapter shows you how to construct any scale that you wish.
There are drawing aids called ‘ scales ’ which are designed to help the draughts person cope with these scaled dimensions. They look like an ordinary ruler but closer inspection shows that the divisions on these scales are not the usual centimetres or millimetres, but can represent them. These scales are very useful but there will come a time when you will want to draw to a size that is not on one of these scales. You could work out the scaled size for every dimension on the drawing but this can be a long and tedious business – unless you construct your own scale. This chapter shows you how to construct any scale that you wish.
The Representative Fraction (RF)
The RF shows instantly the ratio of the size of the line on your drawing and the natural size. The ratio of numerator to denominator of the fraction is the ratio of drawn size to natural size. Thus, an RF of 1/ 5 means that the actual size of the object is five times the size of the drawing of that object.
If a scale is given as 1 mm = 1 m, then the RF is
A cartographer (a map draughtsperson) has to work with some very large scales. They may have to find, for instance, the RF for a scale of 1 mm = 5 km. In this case the RF will be
Plain Scales
There are two types of scale, plain and diagonal. The plain scale is used for simple scales, scales that do not have many subdivisions. When constructing any scale, the first thing to decide is the length of the scale The obvious length is a little longer than the longest dimension on the drawing.
Figure 1 below shows a very simple scale of 20 mm = 100 mm.
Figure 1 below shows a very simple scale of 20 mm = 100 mm.
The largest natural dimension is 500 mm, so the total length of the scale is (500 / 5) mm or 100 mm. This 100 mm is divided into five equal portions, each portion representing 100 mm. The first 100 mm is then divided into 10 equal portions, each portion representing 10 mm. These divisions are then clearly marked to show what each portion represents. Finish is very important when drawing scales. You would not wish to use a badly graduated or poorly marked ruler and you should apply the same standards to your scales. Make sure that they are marked with all the important measurements. Figure 2 shows another plain scale. This one would be used where the drawn size would be three times bigger than the natural size.
Diagonal Scales
There is a limit to the number of divisions that can be constructed on a plain scale. Try to divide 10 mm into 50 parts; you will find that it is almost impossible. The architect, cartographer and surveyor all have the problem of having to subdivide into smaller units than a plain scale allows. A diagonal scale allows you to divide into smaller units. Before looking at any particular diagonal scale, let us first look at the underlying principle.
Figure 3 shows a triangle ABC. Suppose that AB is 10 mm long and BC is divided into 10 equal parts. Lines from these equal parts have been drawn parallel to AB and numbered from 1 to 10.
Figure 3 shows a triangle ABC. Suppose that AB is 10 mm long and BC is divided into 10 equal parts. Lines from these equal parts have been drawn parallel to AB and numbered from 1 to 10.
It should be obvious that the line 5 – 5 is half the length of AB. Similarly, the line 1 – 1 is 1/10 the length of AB and line 7 – 7 is 7/1 the length of AB. (If you wish to prove this mathematically use similar triangles.)
You can see that the lengths of the lines 1 – 1 to 10 – 10 increase by 1 mm each time you go up a line. If the length of AB had been 1 mm to begin with, the increases would have been 1/10 mm each time. In this way small lengths can be divided into very much smaller lengths, and can be easily picked out.
Three examples of diagonal scales follow .
This scale would be used where the drawing is twice the size of the natural object and the draughtsperson has to be able to measure on a scale accurate to 0.1 mm. The longest natural dimension is 60 mm. This length is first divided into six 10 mm intervals. The first 10 mm is then divided into 10 parts, each 1 mm wide (scaled). Each of these 1 mm intervals is divided with a diagonal into 10 more equal parts ( Fig.4 ).
You can see that the lengths of the lines 1 – 1 to 10 – 10 increase by 1 mm each time you go up a line. If the length of AB had been 1 mm to begin with, the increases would have been 1/10 mm each time. In this way small lengths can be divided into very much smaller lengths, and can be easily picked out.
Three examples of diagonal scales follow .
This scale would be used where the drawing is twice the size of the natural object and the draughtsperson has to be able to measure on a scale accurate to 0.1 mm. The longest natural dimension is 60 mm. This length is first divided into six 10 mm intervals. The first 10 mm is then divided into 10 parts, each 1 mm wide (scaled). Each of these 1 mm intervals is divided with a diagonal into 10 more equal parts ( Fig.4 ).
Reference: Kenneth Morling, Geometric and Engineering Drawing
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