KYTurner,

You aren’t taking it on faith. You’re taking it from me and I have more experience in multi-generation laminations than, well, anyone that I know of.

I learned about MGL from reading the wonderful book from Clarence Rannefeld named Laminated Designs in Wood. Clarence was a mathematician and a good woodworker. His book has inspired many segmenters and woodturners but with the utmost respect for him, I can honestly say that nearly everything in his book was wrong. He had drawings that showed 1st, 2nd and 3rd generations of designs using 30, 45 and 60 degrees and although his designs were great, I could never duplicate one using my software until I made a coding mistake one day where I thought I was using saw kerf of 1/8” while I was actually using a saw kerf of 0” and guess what - I could then make all of his designs. The 2/3rds of his book that were designs were all impossible to make using a table saw.

He actually showed all of his formulas and his most complicated formula was the one that calculated the amount of lineal laminate needed if you input all of the data from the generations used to make the design. It was fun to try to duplicate his results using a scientific calculator but sadly, his formulas came up with results that were nowhere near what was actually needed to make the design. It was then that I decided that his very extensive formula was simply the wrong approach.

Using SketchUp to duplicate the the process of making the design using actual measurements, I found a relationship between 1st and 2nd generations, 2nd and 3rd generations, etc., and finally a radial process.

It’s trivial to start with a laminated board and use trigonmetry to determine how much lineal laminate you need, including saw kerfs, to make x number of repeating units. The only variable that changes between the generations is the angle and that, too, is trivial using trigonometry. Using the relationship between 1st and 2nd generations, you can quickly determine how many 1st generation repeating units you need to make that number of 2nd generation RUs at which time you get to use the simple formula of calculating lineal laminate required to make that many 1st generation RUs.

The same approach lets you start with 4th generation RU that needs x number of 3rd generation RUs which needs x number of 2nd generation RUs which needs x number of 1st generation RUs and finally the simple formula to calculate lineal laminate from that number of 1st generation RUs. It works every time.

The only time this will not work is if the angle you want to use is extreme such as anything more than 60 degrees. I’ve never seen anyone use more than 60 degrees for a cutting angle, though.

Lloyd