## Parti Geometrie drawing

Urheberrechtlich geschütztes Material

### Scales

Before you start any drawing you first decide how large the drawings hove 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 thrs and still draw the object in its netural 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 cleerty. In either case it will be necessary to draw the object to scale' The scale must depend on the size of the obtect. 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 draughtsman 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 (R.F.) The representative fraction 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, a representative fraction of J 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 R.F. is 1 mm 1 mm 1

A cartographer (a map draughtsman) has to work with some very large scales. He mey have to find, for instance, the R.F. for a acale of 1 mm - 5 km. In this case the R.F.

Wl 5km ° 5x1000x1000 ~ 5000000 Plain Scales

There are two types of scales, plain and diagonal. The plain scale is used for simple scales, scales that do not have many sub divisions

When constructing any scale, the first thing to decide is the length of the scele. The obvious length is a little longer then the longest dimension on the drawing. Fig. 1/1 shows a very simple scale of 20 mm - 100 mm. The

Fig. 1/1 Plain scale 10 mm » 100 mm or 1 mm - 5 mm

largest natural dimension <s 500 mm so the total length of the scale ts^S9 mm 0f 100 mm This 100 mm is divided into 5 equal portions, oech 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 F truth 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

Fig 1 /2 shows another plain scale This one would be used where the drawn size would be three times bigger than the natural sore

To construct e plein scale. 30 mm = 10 mm. 50 mm long to read to 1 mm (Fig. 1/2)

Length of scale - 30 x 5 =» 150 mm 1 St division 5 x10 mm

2nd division 10*1 mm

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 thai it is almost impossible. The architect, cartographer and surveyor all have the problem of having to sub-divide into smaller umts 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 pnnciple

Fig 1/3 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 T« the length of AB and line 7-7 is n 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 ^ mm each time. In this way small lengths can be divided into very much smeller lengths, and can be easily picked out.

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### Responses

• helena
How to make a diagonal scaleif it read 30mm represents 1mm?
8 years ago