Weeelllllll, the 1/4 bottom isn't optional and the formula is for each bottom cutting the correct width. You know, all it is, is a way to express where the resultant soil force vector is on the plow. When you add up the individual soil force vectors of each bottom you get the resultant vector. I read a IH plowing book from 1952 and the formula was expressed a different way.
Here's my explanation: The soil force vector is located about 1/4 the width to the right of the shin, so 3/4*14=10.5" on the front bottom from the furrow wall in this case. The 2nd bottom would be at 10.5+14=24.5 and the third bottom would be at 24.5+14=38.5. Then you just average those numbers: a three bottom is easy, the center of those three vectors is at 24.5" from the furrow wall. For a two bottom it would be (10.5+24.5)/2=17.5" from the furrow wall. Or, 0.5(2*14)+0.25*14=17.5".
And, once again, this is a starting point. The actual resultant soil force vector, or point of load, will change depending on moldboard design, plowing depth, speed, and soil conditions.
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Today's Featured Article - Gatherin of the Orange - by Rick Nikolich. In July of 1998 I was talking to fellow Allis Chalmers collector Mike Schilling about the annual "Gathering of The Orange" AC show coming up in August of 1999. He got this wild idea that we should get a convoy of AC tractors and drive them from Charlotte, Michigan 105 miles to LaGrange, Indiana.
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