Notations and Applications in Scale Drawings

The art of Technical Drawing for engineers, architects and other disciplines is expected to comply with conventions set out in the Australian Standards, in particular, the Australian Standard AS 1100. In this way, the symbols and styles used are kept reasonably uniform within the country and internationally.

For our immediate purpose, we are concerned with scaling in drawings.

In a scale drawing, an object is represented in a way that reflects, in two dimensions and restricted size, the important features of the object. The essential principle in scaling is that angles are preserved and lengths are held in proportion. Thus, the size usually changes but the shape is maintained in the drawing.

This is the same idea as is encountered in the study of similar figures in geometry. Recall that, in the case of triangles, preserving the same angles in two triangles guarantees that the corresponding sides will be in the same proportions, and also keeping the sides in proportion ensures that the angles are preserved.

However, for polygons of more than three sides, one ot these conditions does not guarantee the other and we need to make sure both that angles are preserved and that the corresponding sides are in the same proportion in order to be sure that two figures are similar.

 

Proportions are indicated by a scale notation $a:b$a:b, meaning a distance of $a$a units in the drawing represents $b$b units in the real object. For example, $1:100000$1:100000 means $1$1 centimetre on the drawing is equivalent to $100000$100000 centimetres (or $1$1 kilometre) in the thing being represented. A scale like this would be typical of a map.

For smaller objects, like a house, the scale might be more like $1:100$1:100 or $1:200$1:200. The precise scale is chosen by the person making the technical drawing to ensure that the representation of the object fits comfortably onto the sheet of paper being used.

Notice that units are not used in a scale. This is because the same unit, whatever it might be, applies to both sides of the proportion.

Examples

Example 1

An object that is rectangular when viewed from above is to be represented on an A3 sheet. The dimensions of the object are $5.2$5.2m by $3.4$3.4m and an A3 sheet is $420$420mm by $297$297mm. What scale could be chosen for the drawing?

Converted to millimetres, the object's dimensions are $5200$5200 and $3400$3400. Since $5200$5200 divided by $13$13 is $400$400, which is less than $420$420, and $3400$3400 divided by $13$13 is less than $297$297, the drawing would fit on the page if a scale of $1:13$1:13 was chosen. However, this would only leave a margin of $10$10mm at each end for the long dimension and so, it may be better to choose, say, $1:15$1:15 so that the drawing would have dimensions $\frac{5200}{15}$520015​ and $\frac{3400}{15}$340015​. That is, $347$347mm by $227$227mm.

Example 2

A scale drawing of a building has windows in a wall $35$35mm apart. The scale is $1:150$1:150. How far apart, in millimetres, are the windows in the building?

According to the scale, $1$1mm in the drawing represents $150$150mm in the building. So, $35$35mm represents $35\times150=5250$35×150=5250mm in the building.

 

Example 3

Example 4

Example 5