Sub-title: Manipulation of scale expressions.
Several recently posted iQuestions suggest a need for some guidance regarding scale expressions.
Principal types
Two principal methods of expressing scale exist in the world of drafting. These are the metric method that is almost always in the form of a unit-less ratio of the form n:nn... resulting in expressions such as 10:1, 5:1, 1:1, 1:2, 1:5, 1:40, 1:100, … and the imperial method most commonly of the form n'':n...' (or yds, ch, ml, … ) resulting in expressions such as 1/8'' = 1', ¼'' = 1', 1'' = 1' 1''=15'. 1'' = 10ch … .
All of these express the relationship between the size of a drawing and the size of a real-life object.
The imperial system makes a statement that on first reading is not logically correct as there is NO equality between the two sides. However it is an accepted practice to express the size relationship in this way and if we read the “=” sign as a shorthand form for “represents” then the expression makes perfect logical sense.
The metric system avoids this anomaly by using unit-less numbers in a ratio expression and if units are applied to them it is understood that the same units are used on both sides of the expression – unless specifically stated otherwise (e.g. 1 mm: 5m) ; and that practice is not the norm.
Conversion between forms
Modern CAD systems are generally based on a decimal (read “metric”) foundation and it therefore becomes necessary at times to express an imperial scale as a ratio to properly work between the two.
Remember the “ same units used on both sides of the expression” comment above and all should be well for the conversion.
To change 1'' = 1' we simply modify the expression without changing its value so that the size relationship between the two sides remains true and the unit identifiers are no longer needed.
1'' = 1' can be expressed as 1'' represents 12'' (12 inches to the foot) which can then be expressed as 1:12.
1” = 10' can be expressed as 1'' represents 120'' which can then be expressed as 1:120.
1/8'' = 1' can be expressed as 1 fraction represents 96 fractions (12inches x 8 fractions per inch) which can then be expressed as 1:96.
… … …
Expressions equivalent to a ratio
A scale ratio can itself be expressed in a number of different forms.
1:10 expresses the same relationship value as ...
1/10 expresses the same relationship value as ...
1 divided by 10 expresses the same relationship value as...
0.1 x the size of … .
That is in the case of the above example they all express the fact that there is a one tenth relationship between the first and second of two items that are being compared for size – the drawing and the represented object.
Similarly 1/8'' = 1' converts to 1:96 converts to 1/96 converts to 1 divided by 96 converts to 0.010417 correct to six decimal places. (Rounding of excessively long decimal values should always be such that the necessary degree of accuracy for purpose is achieved -- not necessarily six places.).
And a 5:1 ratio converts to 5/1 converts to 5 divided by 1 converts to 5 as a decimal number value.
One important point to remember with DraftSight is that when setting custom (non-standard) scales for viewports in paper space you need either the n/nnn form of the ratio or the decimal equivalent of the scale ratio to be able to set a specific scale via the properties palette. Entering the n:nnn form is currently not accepted.
When it is necessary to return a decimal equivalent of a scale ratio to the original ratio form, simply divide the number that is to appear on the left by the decimal value and then round the result to the nearest whole number to obtain the value on the right. For example:
0.1 represents 1:1/0.1 or 1:10.
Similarly 0.010417 represents 1:1/0.010417 represents 1:95.9969281 or 1:96.
You can always verify the result by doing the reverse calculation in the same manner to that described under "Conversion between forms" above.
Have fun with your manipulations!
[User of DS (Free) V1R2.1 on Windows 7 Home Premium.]9 Oct 2012, 14:32 (NZ standard time)
