## Lef

View at B

Fig. 18 If some views are not in strict "projection" the direction of view should be shown by lettered arrows. This can save space compared with Fig. 13.

tern is particularly useful when we need to show the section of an object, a matter dealt ยป.with later.

A second, and possibly obvious exception is when an object is so large that views must be spread over two or more drawings. In such a case the view indicators should also carry the drawing number on which the view will appear.

### An interesting example

I have included Fig. 19 just to show you what can be done with very simple projection methods. The object is to produce a set of three true views of a matchbox standing on one of its corners. The procedure is shown on the drawing; we start at I with the normal upright position. At II we have tilted it on the lower edges, the front elevation (A) retaining the true lengths of. At III we have taken the plan view of II and turned it through an angle, and derived the other views from it. Finally, at IV the end elevation of has been cocked over at an angle and the other views projected from it as described in the caption. Try it for yourself - even freehand sketching with a suitable box to look at and see how you get on. Incidentally, don't be alarmed if some of the views seem to turn themselves inside out now and then. This is a not uncommon optical illusion inherent in these oblique views

### Other forms of representation

The projections we have looked at are what is known as orthographic. That means that if, for example, a cube is drawn the face will show all lines at their true length and all angles at their true value. However, we can see only one face at a time, and for some people the use of several views does seem to make it difficult for them to visualise the overall shape of the object. We can, of course, revert to the artistic pictorial representation (see in Fig. 2 for example) but this needs some skill as an artist, not given to many of us. Some geometrically valid form of pictorial representation had to be found.

The oldest form of these is, perhaps, the use of perspective. This approximates very nearly to the eye's view of the object, and assumes that all lengths set down on the drawing are proportional to their distance from imaginary vanishing points at the implied horizon. Contrary to supposition, it is possible for such representations to be scaled from - indeed, they must be scaled TO to make the drawing - but it is difficult and very time-consuming. For this reason true perspective drawings are used, in engineering examples, only for display purposes, possibly in sales literature.

In isometric projection, three of the faces can be seen on the one view. To enable lengths to be truly scaled the object must be angled so that the lengths of all edges of an ideal cube still appear to be the same length. See Fig. 20. The cube has been rotated on its vertical axis through 45 degrees, and at the same time tilted forward through an angle of 35 degrees 15 seconds. The measured lengths of each side are the same, and will be 0.8165 (square root of 2/3) of their true lengths. The angles XOY, XOZ and YOZ which are 90 degrees on the actual cube appear as exactly 120 degrees on the drawing. With this type of representation, of course, all circles will appear as ellipses as seen at (b) in Fig. 20. (This applies to all oblique or pictorial types of view.) While isometric views were, at one time, always drawn with

1. Box is drawn square on one end.

2. Box tilted on one end 3-7. "a" ia all true dimension. In "b" width only is true. Draw "a" first, set off true width in "b" and project from "a" for foreshortened lengths, "c" is completed by projection from "a" and "b".

3. Box now turned through 30 deg. still on edge 3-7. Draw "d" from view "c" as this is still of the same dimensions. Project heights from "a" to "f" and widths from "d". Complete "e" by projection from T and "d".

4. Box turned on corner 3. "g" is dimensionally similar to "e" but tilted to right. Draw "g" from "e" by measurement. Project "h" from "g" and T, "k" from "g" and "h". (Note - "k" is inverted plan).

Fig. 19 An exercise in projection. The view at 4 is obtained from that at 1 with the minimum of measurement.

scales which allowed for the ratio mentioned above it is now common practice to draw the view using 'true lengths'; this simply makes the drawing 22 per cent larger. The system is not used a great deal these days, as it looks all wrong and is slow in execution.

Isometric has now been replaced by the trimetric system. This involves arranging the three planes of the ideal cube to be