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Here's a program which displays potential log sawing patterns for band milling.
Background & Techniques
One form of band mill is the horizontal band saw, probably the most common type for small individual sawmills and serious hobbyists. I recently cut a large red oak for firewood but was so impressed with its beauty that I'm considering joining the "serious hobbyist" ranks. I've been browsing the web reading forums and viewing online videos from manufacturers, etc., half hoping that the desire will pass if I wait awhile. These mills mount the bandsaw on a carriage which slides over the log on rails. The saw is adjustable up and down to control the depth of cut and the log is physically turned to saw a different side. There seem to be a number of different strategies for sawing and this program explores my understanding of a few of them. One strategy is cut boards from all four sides of a log to leave a rectangular "cant" or large beam. Having never actually operated or even seen one of these mills, I made some guesses about the parameters and implemented the math and graphics to calculate and display the resulting boards. Three strategies have been implemented so far. Each takes as input:
The sawing strategies are:
For sawing cants, it seems that cutting from the edges of the cant to the edge of the log would maximize the board widths obtained, but I'm not sure f this is feasible. The option is included to saw boards in either direction, "bark to cant" or "cant to bark".
Two other strategies I've seen mentioned online, but haven't implemented yet, are "Box" sawing where the log is turned 90 degrees after each board is cut, and "Quarter" sawing where the log is quartered and boards are cut from each quarter turning the flitch 90 degrees clockwise then counter clockwise after each board.
It also seems that logs with elliptical cross sections should be considered in the real world. Adding major and minor diameters would be a straightforward enhancement.
I look forward to getting feedback from viewers with real sawing experience.
Non-programmers are welcome to read on, but may want to jump to bottom of this page to download the executable program now.
The math required to determine the length of a horizontal line (the saw blade) which intersects a circle (the log) at a given distance from the top edge is a straightforward application of Pythagorean Theorem, see WidthFunc for the code.
The tricky part was making our rectangular boards fit within the log. If we are cutting from top to bottom in the upper half of the log, the top edge of the board will determine its width, in the bottom half of the log the bottom edge of the board will determine the width. In cutting cants, the board may be cut from the outside of the log toward the center or from the cant surface toward the outside of the log which complicates the determination of which surface of the determines the usable width. After spending a day or more trying to handle all of the permutations, I finally capitulated and just always calculate maximum width of both the top and bottom board surface and use the smaller as the width of that board. All of this applies to the on-edge boards cut from the left and right if we just replace "top" and "bottom" references with "left" and "right". Remember that the band saw only cuts horizontally and these "on-edge" boards are actually cut from the top and bottom after rotating the log by 90 degrees.
Procedure "Makeboards" handles the iteration between "Start" and "Stop" distances from the top or left edge, incrementing by the specified board thickness "Thick, plus blade thickness (Blade) for each board. If Stop is smaller than Start, the boards are generated upwards or towards the left edge. Dimensions and location of generated baords are displayed in Memo1, the TMemo that initially holds the introductory text. They are displayed by calls to procedure DrawBoard which scales the board size and location using the ScaleIt function with a pixels per inch scaling factor, Scale, generated when the "Saw it" button is clicked. Drawboard used the TImage, Image1, to display rectangles representing the generated boards. The log outline is generated by a call to the DrawLog procedure during the setup when the SawBtn is clicked.
Addendum June 17, 2010: Version 1.1 corrects a couple of minorl problems:
Suggestions for Further Explorations
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