Sonny, tell your idiot engineer to stick to his line of expertise.
There is a ton of information on this phenomenon that started as soon as sawmills began to sell planed wood. So maybe a couple of hundred years ago....
To overly simplify, a board foot is the size of the board BEFORE it was planed or smoothed. So a 1X6 was a board that began as 1" thick, and 6" wide. However, to make it convenient, you began to be able to buy planed boards from the mill. Planing decreased the thickness on each side and the edges, so the sizes you see now reflect the fact that the wood has been processed to a consistent size, or its finished size.
However, the mill still cut it 1"X6" so they would have enough material on the board to smooth it. You didn't think you would get that extra material free, right? So you are charged for the board itself when rough, as well as the convenience of smoothed faces. To drive that home, go to a real hardwood lumber store (NOT HD) and ask for a 1X6. They should ask you "nominal (unplaned) or smooth?". If rough, you can take the board home and plane it yourself. Make to your own smooth boards to your dimensions using nominally sized lumber.
As far as quarters go... think about it. Maybe since it's Thanksgiving, think of an pie as an inch to visualize it. With that in mind, think of one quarter of a pie as "a quarter of a pie". So to extrapolate, if you have one quarter of an inch, then you have..... wait for it..... here it comes..... one quarter of an inch!
So 4 quarters would be..... one inch! Five quarters would be..... an inch and a quarter. Eight quarters would be two inches, etc. Just count the quarters on your tape and you will have it.
IME, the quarter system of describing wood sizes is used only to describe thickness of rough (nominal) lumber. It is not used to determine width. You won't find an lumber man that asks you if you want 4/4 (four quarters) by 24/4 (24 quarters) by 400/4.
You should also know that unless it is in a specific purpose lumber, nominal sizes almost always refer to hardwoods, not softwoods.
Some engineers are pretty bright fellows, but this one sounds brand new. Show him this to help educate him as to how BF is calculated, and after that DAGS the key words.
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out the highlighted words in this book, page 216. "Understanding Wood" (to me) is the absolutely undisputed king of reference books on all things wood.
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