Have you ever wondered why you found the shape or form of one turning more comfortable or pleasant to look at than another? The reason is called Aspect Ratio. Aspect Ratio can be viewed in several ways, the rule of thirds, the golden mean, the golden triangle, the golden rectangle, and divine proportion. In woodturning, we often use what is called the rule of thirds or an aspect ratio of 1:2.
For a lidded box, you would have a lid that equals 1/3 and a box that equals 2/3’s of the total.
In turning a vase, the widest portion should occur within an area of about 1/3 of the total length, either from the top to the bottom or the bottom to the top.
For bowls, the diameter to the height should be a ratio of 1:2
The other ratio you will find commonly used in woodturning is the Golden Mean 1 to 1.618
The Golden mean states that the ratio of the largest segment to the smallest segment should be the same as the ratio of the largest segment to the whole. This is also known as the Golden Ratio and Divine Proportion. It is often thought to be the ratio used in the human form, hence the name Divine Proportion.
The ratio of the whole line (A) to the large segment(B)
is the same as
the ratio of the large segment(B)to the small segment(C).
___________ B ___________ ________C_______
In other words, A is to B as B is to C.
This occurs only where A is 1.618 … times B and B is 1.618 … times C.
The Golden rectangle
Drawing the Golden Rectangle
1. On a sheet of paper, draw a square. Now find the center of the right side of the square and mark this point A. Place the point of the compass on point A and the pencil of the compass on the top left corner of the square, which is shown as point B. Swing an arc from Point B that extends beyond point A. Draw a straight line up the right side of the square to where it intersects the arc, and this is now point C. This point is the top corner of the Golden Rectangle. Reverse these procedures to draw an arc from the left side center of the square to determine the left top corner of the rectangle.
3. The will result in a rectangle that has a height to width ratio of 1 to 1.618.
The Golden Triangle
The Golden Triangle is based on a five-sided polygon we refer to as a Pentagon. By drawing lines that connect the points of the pentagon, we can discover the most interesting phenomenon. The triangular form that results has sides with the same 1to1.618 ratio as the Golden Rectangle. The Golden Triangle is very useful to us as turners, as it allows us to create well-proportioned forms that don’t fit neatly into the Golden Rectangle.
The Golden Triangle and the golden rectangle have been used by people since ancient times to gauge proportion.
Aspect Ratios in Woodturning
Basic Design Principals
Cold Bend Hardwoods