Draw Sizer - Hambridge Proportioning

This utility employs the Hambridge proportioning technique to generate a smooth (some would even say "natural") progression of drawer heights that are in balance with the width of the drawer unit.
 

Inputs may be specified as numbers or fractions (ex: 36.5 or 36 1/2)

Use case 1: Derive drawer heights given number of drawers and width. The drawer space height is computed.

Use case 2: Derive drawer heights given number of drawers and height of drawer space. The width is computed.

Use case 3: Derive drawer heights given width and height of drawer space. The number of drawers is computed.

See also:
Arithmetic progression, and Geometric progression.

 
The Underlying Math

With the Hambridge technique, a reference square is first formed whose width is equal to the width of the drawer face. Picture this square positioned underneath the drawer unit. A series of "root" rectangles are then progressively formed in which the length of each rectangle equals the square root of the sum of squared width plus squared length of the previous rectangle. In other words, the length of each rectangle equals the diagonal of the previous rectangle (the reference square represents the first rectangle).

If we assume a width of 1, the first rectangle length is the square root of two (1.41), the second is the square root of 3 (1.73), the third is the square root of 4 (2), and so on. To get the width of a particular rectangle, you subtract the length of the previous rectangle from the length of the rectangle of interest. In designing a chest of drawers, the rectangle width would represent the height of each drawer.

This all makes a lot more sense if you have diagrams to guide you through the process (see recommended reading below). But, simply put, drawer heights are computed as follows:

The bottom drawer has a height of [(square root of 2) - 1] times the
drawer width.

The second drawer from the bottom has a height of [(square root of 3) - (square root of 2)] times drawer width.

The nth drawer has a height of [(square root of n+1) - (square root of n)] times drawer width.

One of the interesting aspects of Hambridge proportioning is that the change in progressive drawer sizes tends to level out after 6 drawers or so. If you go much beyond 6 drawers, the drawers may look a bit "compressed" in height.

Recommended Reading:

The book Measure Twice Cut Once by Jim Tolpin describes a drafting method for generating a Hambridge progression using a scale drawing and a compass. The method involves swinging a series of arcs with the compass to establish the height of each drawer. Working with the geometry in this manner makes it easier to grasp the underlying math.

Designing Furniture: From Concept to Shop Drawing : A Practical Guide by Seth Stem and Laura Tringali also provides a good overview of Hambridge proportioning as well as furniture proportioning systems in general.  Note that this book is now of out of print but you may be able to borrow a copy from your local library.

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