The mathematics will help but it is not enough; you must be experienced to make such an operation, no "chuck-it-and-chance-it" philosophy. By this reason the so called "Super Z" or "Swiss" ferrule has been favored by many since its introduction in the 40´s. Compared to the "Leonard – type" or "Payne type" ferrule it is shorter and so occupies less of the bamboo blank - but at the cost of a much bulkier construction ( see pictures ).
On a short three-piece rod a set of Super Z´s could be considered, but in general there is no need for a shorter ferrule than the original "step down" type. You don´t gain much; as long as You use ferrules the stiffening problem is there , and a few millimeters less impact won´t do much. To me the slender look of the traditional ferrule, almost flush to the blank, gives a rod that elegance look you should expect from a fine rod so I use them exclusively.
I never make any other. The minor advantage of a shorter ferrule is so slight that you can decide what kind of ferrule to use by esthetical preferences. "Truncated" ferrules are shortened versions of the two. Stay away from them!
By their short construction the momentum by casting makes them slip easily (if not pinned).
Ferrules are foremost made from nickel silver. Commercial ferrules are soldered together from matching pieces of tubing, while independent rod makers often make them from solid bars.
The ferrule itself was normally made from one piece of brass tubing that fit into another piece of larger dimensions. That arrangement called for a "step" of 1mm !!!, whichnormally meant stepping down the taper of the tip ferrule station accordingly.
To reduce weight titanium ferrules would be an option, but unlike nickel silver and brass titanium isn't self-lubricating, causing stuck ferrules.