Draw Sizer - Geometric Progression
This utility employs geometric progression to compute drawer face
heights. With this technique, heights increase by a constant
multiplicative factor, referred to as the common ratio. For
instance, a common ratio of 1.1 means that each drawer is 1.1 times or
10% larger than the one above it. (See use cases and examples below).
Use case 1: Derive drawer heights given top drawer height, number of drawers, ratio, and drawer spacing. The height of drawer space is computed.
Use case 2: Derive drawer heights given height of drawer space, top drawer height, ratio, and drawer spacing. The number of drawers is computed. The computed overall height will be as close as possible to the input height.
Use case 3: Derive drawer heights (including top drawer) given
height of drawer space, number of drawers, ratio, and drawer spacing.
Width: If the width is not specified, it will automatically be computed to form a golden rectangle in which the ratio of the width to the height is 5/8.
With geometric progression, drawer heights increase by a constant multiplicative factor such that the ratio of consecutive drawer heights is the same. Drawer 1 is to drawer 2 as drawer 2 is to drawer 3, and so on. In other words, each drawer is R times higher than the one above it, where R is the common ratio of the progression.
Example: If the height of the top drawer is 4" and the common ratio is 2, the heights of the next four successive drawers are 8", 16", 32", and 64". Using a more realistic ratio of 1.2, the drawer heights would be 4.8", 5.7", 6.9", and 8.3".
A geometric progression of drawer heights may be quite similar to an arithmetic progression depending on the choice of sizing parameters. The images below illustrate this. The first image depicts a chest of drawers created using an arithmetic progression with an increment of 1.4". It looks quite similar to the second chest of drawers designed using geometric progression with a relatively tame common ratio of 1.2. However, when the ratio is bumped up to 1.5, the heights increase in size much more drastically resulting in the unit shown in the rightmost picture. The lesson here is that you can use either proportioning method to design a nice looking set of drawers - just be careful in your selection of sizing parameters.
Geometric progression can also be used in other furniture design
situations. For example, this technique could be used to proportion the
spacing of stretchers in a table, the stepped front of a sideboard, the
arrangement of decorative molding on a chest or armoire, or even the
arrangement of patterns in a segmented wood turning.
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