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I am trying to understand the math behind any given router bit (for instance a 5/8", 14 degree or 3/4", 7 degree), the depth of cut that one should expect to set it at to produce a tight joint, and the thickness of the wood it can be used on.

I like to avoid traditional dimension lumber in my projects, but the above has been the source of many BTU's and I'm curious if anyone has this figured out. Manufacturers are great at specific dimensions and profiles, but thats only a beginning.

Thanks in advance for your responses.
 

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There are several basic rules we follow, a good example is when cutting a dado joint we cut half the thickness of the wood. For 3/4" thickness we would set our depth for 3/8". In 1/2" thickness a 1/4" depth. This method keeps the majority of the strength of the wood intact and yet provides a strong joint not likely to pull apart. By using a dovetail bit we gain additional strength through mechanical advantage. It is not just the glue holding the joint together, it is the shear strength of the wood itself working with the glue. By shear strength I mean the amount of pressure required to pull the wood apart. As far as why this angle or that goes, some engineer figured out that 7 degrees was the overall best choice and most followed this example. We know from hand cut dovetails that most any angle will work. As for how to make a tight joint, the less space or slop in the joint the better. If you really need a full explanation on the math I'm afraid you will need to speak with an engineer. I can only provide the practicle, real world explanation.
 
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