I'm not sure that Brent's math is as wrong as you may be suggesting. My assumption is that Brent is using something like an A572 which is a high-strength low alloy steel which has better corrosion properties and more strength than A36 which you mentioned, and which has a tensile yield strength in the 60,000 psi range.
Brent said,"That is 11,250 lbs per linear inch for 3/16th plate. Multiply that by the 96 inches in the side of one of my twin keels." And in that regard, something like A572-60 that was 3/16 thick would have a tensile yield strength around 11,250 lbs per linear inch. (60,000*3/16= 11,250) His arithmetic is essentually correct.
The problem is one of how the is applying that math relative to proper engineering principles contained in Brent's metaphoric description of:
"That is 1.08 million pounds per side, times four keels sides.
How are you going to break that with a boat under 20,000 lbs?"
This metaphor assumes that the loads are shared by both keels equally and that the loads are solely in tension. Neither is likely to be present or likely to relate to the actual failure mode of the keel.
The more probable failure modes for a frameless keel connection would more likely be some mix of buckling of the keel sides in compression (skinny column failure), sheer where the keel sides try to cut through the hull plate (as you noted in your comments), or bending of the hull skin perhaps coupled with lamellar tearing near where the hull meets the keel since the hull plate would be in bending due to the large lever arm formed by the depth of the keel and the narrower width of the keel root being resisted in bending by comparably thin plate.
But beyond that I also want to touch on Brent's Herreshoff reference.
I am not sure that its clear which Herreshoff Brent is referring to, but by and large all of the Herreshoffs were consumate engineers. Nat Herreshoff and Herreshoff Manufacturing developed their own formulas for many of the calculations involved in properly engineering a boat. At a time when boats were 'engineered' by rules of thumb, Nat did his own scientific research and developed his own formulas based on his research. And he used these formulas to design some of the most sohisticatedly engineered designs in that era. He later boiled those down into his own set of widely used rules of thumb, but these were heavily based on proper engineering based methodologies.
L. Francis began his carreer working with Nat as a designer at Herreshoff Manufacturing but did the majority of his apprenticeship working beside Starling Burgess and Frank Payne at Burgess, Swasey & Paine in Boston. Burgess was one of the most creative, multi-discipline, engineering-oriented designer/ inventors of his day. Burgess was a brilliant mathematician who was able to do high level scientific research, then develop mathematic equations to explain the observations and ultimately literally wrote the book on a wide range of early 20th aeronautical engineering applications.
In yacht design, Burgess literally developed sophisticated formulas that replaced the crude rules of thumb which preceeded his time. Starling Burgess working with Glenn Curtiss was key to the design of the first successful seaplane (only a few years after the Wright Bros first flight), he designed three America's Cup winning defenders, he designed the first successful aluminum masts, he designed many of Buckminster Fuller's so called Dymaxion inventions (car and house being most notable), (and designed 'Little Dipper' for Bucky, one of the most beautiful little cutters of all time), as a kid in the late 1800's he designed one of the first light weight machine guns, he also is thought to have possibly/probably designed the Times New Roman font, wrote poetry, and novels, and produced world class paintings.
And L. Francis learned his trade at Starling's side and along side of Frank Payne as well. And Frank Payne was no slouch either when it came to sophisticated engineering. There was nothing even slightly shoddy about L. Francis's math or engineering skills.
But of all the Herreshoffs', L. Francis would be the only one that I could imagine who might write negative comments about engineering formula. I can imagine that since L. Francis was known for writing things that he thought sounded good and doing just the opposite. (Like advising adult sailors that they had an obligation to take children sailing and teach them the ways of the sea, when L. Francis notoriously hated kids and hated being around them.) So, if L. Francis was dismissive of the crude formulae of the day, it was only because he and his close life long friends, Starling and Frank, were beyond the quick and dirty engineering methods that he decried.
Sidney Dewolf Herreshoff was a graduate from MIT in engineering. 'nuf said. He used the numbers. Halsey Herrshoff has an undergraduate degree from Webb Instutute and a masters from MIT, I have to figure that he uses the numbers as well.
Please, lets try to keep the historic references close to what is actually known about these people.
Jeff, my view on this came out of the formula for calculating bridge impact or impact on structures, as well as knowing that Brent said "mild steel" and looking at a photo of a BS boat, I can see the steel in it looks pretty ugly, and the whole thing looks pretty cheap. The problem with Brent's calculations are multiple, but the main one is that he is not working with the whole picture, his 1.8 million PSI calculation is not going to work out like it seems it might. First you have to remember that he may or may not be working with the steel you mention, my guess is that he is not, simply because it would be expensive, and his costs that he has quoted were dirt cheap. The second is that the 3/16 is on edge, now that might seem like you could multiply things out and come up with a higher number, but if I am remembering right you should not do that, because of point loading. I think, and I may be wrong, that you would actually be increasing the shear load on the hull by having the edge being like a knife or a metal shear...
The real issue is the impact forces being way above what he thinks they will be, somewhere on the upside of 250,000 psi or more, and probably a lot more, I hate to admit it but I have such a headache right now that I cannot do the math without a blackboard and chalk. You might look here and see if you can do it for us, the formula is right here. I was trying to read over it again, and I will get back to it, but the force is going to be far more than you would think.
Guide Specifications and Commentary for Vessel Collision Design of Highway ... - Aashto - Google Books