The geometry of the nakago (tang) is very important as the assembly of the knife hinges on the correct form and construction of the tang. Viewed from the spine, the thickest part of the blade is at the machi (notches) and there is a distal taper towards the tip of the blade and towards the tip of the tang.
For the blade, this provides the most strength at the most critical point (the stress at the blade-handle junction is mediated and distributed by the habaki, but that is more physics for another post) and for the tang allows for a tight but removable fit to the wood core of the tsuka (handle).
As a follow up to the post on the Aizu Shintogo Kunimitsu Tanto Kata, I wanted to add some information about the rest of the geometry of the classical tanto form. A kata is a documentation of the outline but leaves much lacking in terms of creating a three-dimensional blade. Fortunately there are some fairly standard practices to use as a starting point, dictated mainly by functional requirements, but also by traditional aesthetics.
Tang Profile
As seen in the kata, the profile of the nakago should consist of straight lines converging gently from the machi towards the nakago tip. The munemachi is generally just slightly deeper than the ends of the peaks of the iori spine bevels. The tip of the tang can be one of several shapes but slightly rounded is common and has a nice aesthetic.
Edges of the Tang
The nakago-no-ha (edge of the tang) should be about 2mm all the way from machi to tip, maintaining a constant thickness from where it first leaves the blade at the hamachi. This provides a flat surface to sit against the wood and allows the habaki to slide on evenly. It is normal for the nakagoha to be slightly undersized in tanto depending on the blade geometry, whatever the thickness at the hamachi will set the size for the rest of the edge. Antiques are often seen with thinning under the habaki as polishing thins the blade over the centuries.
The nakago-no-mune (spine of the tang) will taper slightly, it should automatically as the blade bevel angle continues back along the tang from the 2mm wide nakago-no-ha towards the nakago-no-mune. On blades such as yoroi-doshi with extreme distal taper, the distal taper on the tang is seen to be slightly rounded in order to prevent the formation of peaks along the bevels under the habaki. Blade polishing should extend to cover all the area under the habaki and the rest of the tang can be finished with a file.
Process for Setting Nakago Geometry
The most efficient sequence for forming the tang is to profile the outline first, then establish the nakago-no-ha (edge of the tang) width from the hamachi back at a constant ~1.5-2mm, and then carry up the bevel angles to create the taper of the nakago-no-mune (spine of the tang). Optionally finish by giving a very slight radius to both edges with a file.
Example
The example below was forged from shear steel and is just beginning the kaji-togi stage, (rough polish) following yaki-ire (hardening). The kamon logo was hot stamped after ara-shiage (rough shaping) and the nakago has not yet been corrected for the slight bulge that ensued. A file will be used to true all the lines of the nakago before polishing progresses.
Read about the blade and kissaki (tip) here: Classical Tanto Geometry: Blade & Kissaki
See more of the forging and the process of mounting and finishing this tanto.