Solution:
Architect's scale
From Wikipedia, the free encyclopedia. http://en.wikipedia.org/wiki/Architect%27s_scale
An architect's scale is a specialized ruler. It is used in making or measuring from reduced scale drawings, such as blueprints. It is marked with a range of calibrated scales (ratios).
The scale was traditionally made of wood but for accuracy and longevity the material used should be dimensionally stable and durable. Today they are now more commonly made of rigid plastic or aluminium. Depending on the number of different scales to be accommodated architect's scales may be flat or shaped with a cross-section of an equilateral triangle.
United States and Imperial units
In the United States, and prior to metrification in Britain, Canada and Australia, architect's scales are/were marked as a ratio of x inches-to-the-foot. For example one inch measured from a drawing with a scale of "one-inch-to-the-foot" is equivalent to one foot in the real world (a scale of 1:12) whereas one inch measured from a drawing with a scale of "two-inches-to-the-foot" is equivalent to six inches in the real world (a scale of 1:6).
Typical scales used in the United States are:
- Full scale, with inches divided into sixteenths of an inch
The following scales are generally grouped in pairs using the same dual-numbered index line:
- three-inches-to-the-foot (1:4) / one-and-one-half-inch-to-the-foot (1:8)
- two-inches-to-the-foot (1:6) / one-inch-to-the-foot (1:12)
- three-quarters-inch-to-the-foot (1:16) / three-eighths-inch-to-the-foot (1:32)
- one-half-inch-to-the-foot (1:24) / one-quarter-inch-to-the-foot (1:48)
- one-eighths-inch-to-the-foot (1:96) / one-sixteenths-inch-to-the-foot (1:192)
From http://www.tpub.com/content/engineering/14069/css/14069_75.htm
Below are the standard scales on an architects scale ruler. Notice that all scales except the 16th scale are actually two scales that read from either left to right or right to left. When reading a scale numbered from left to right, notice that the numerals are located closer to the outside edge (top of the ruler). On scales that are numbered from right to left, the numerals are located closer to the inside edge (middle of the ruler).
Architect’s scales are “open” divided (only the main divisions are marked throughout the length) with the only subdivided interval being an extra interval below the 0-ft mark. These extra intervals are divided into 12ths. To make a scale measurement in feet and inches, lay off the number of feet on the main scale and add the inches on the subdivided extra interval. However, notice that the 16th scale is fully divided with its divisions being divided into 16ths. Now let’s measure off a distance of 1 ft 3 in. to see how each scale is read and how the scales compare to one another. Since the graduations on the 16th scale are subdivided into 16ths, we will have to figure out that 3 in. actually is 3/12 or 1/4 of a foot. Changing this to 16ths, we now see we must measure off 4/16ths to equal the 3-in. measurement. Note carefully the value of the graduations on the extra interval, which varies with different scales. On the 3 in. = 1 ft scale, for example, the space between adjacent graduations represents one-eighth in. On the 3/32 in. = 1 ft scale, however, each space between adjacent graduations represents 2 in.
The diagram illustrates some simple examples such as 1 foot and 3 inches.
Example with fractions:
For a harder example let’s look closer at the ¾ (left) and 3/8 (right) scale on the ruler. For this example we will use the 3/8 scale. Reading from right to left 0, 1 (14 on ¾ scale), 2, 3 (12 on ¾ scale) etc. Each of the larger marks are 3/8 units in length (which could be feet, inches, etc. depending on your major unit of measurement). The further graduated portion of the ruler on the far right side (from 0 marking to last mark before 3/8) is divided into 12 equal divisions. 12 equal divisions are used so you can easily measure fractional portions of the unit.
Example: Need to mark of 3 5/8” on the 3/8 scale. The 3” mark is 13 mark from the right hand 0 mark. To get 5/8” we use the further graduations on the far right side. There are a total of 12 markings (looking from 0 to the right). To represent 5/8” we need to mark of 5/8 of 12 (5/8 * 12). [5/(2*4)] * (3*4) = (5*3)/2 = 15/2 = 7 ½ . In order to mark off 5/8” on the 3/8 scale we move to mark 7 and half way to mark 8 for 7 ½ . See diagram below.
Attached a diagram which may help to explain the 5/8 of 12 . I used an applet from http://www.arcytech.org/java/fractions/fractions.html to create the attached illustration. :
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