Anaysis of adding a fuller of blade performance. This essay focuses on: - Mechanics of structures - Materials Science - Manufacturing processes - Blade performance in Martial Arts applications

1. Mechanics and Materials Science in the making of a Japanese Katana
Bo-Hi

2. Introduction - The Purpose of the Bo-Hi
The most controversial structural element of a Japanese blade is the Bo-Hi. The term
refers to a blood-groove located in the flat of the blade, near the Katana’s spine.
Traditionally, this fuller is added in the construction of a Katana to facilitate shedding
blood off the weapon – hence the graphic name. Let me issue a fair warning here – this
article will go on to talk about the mechanics of a sword cutting tissue. If you would prefer
to avoid that part of this article, skip ahead to the next paragraph.
Figure 1 - Visualisation of a Bo-Hi
Blood that collects on and dries on the blade will interfere with the sword’s smoothness
and create friction. This impedes with clean cuts and in extreme cases could cause a
sword to become caught. Since fractions of a second can mean the difference between life
and death in a swordfight, methods to remove blood from the blade efficiently must be
considered in the construction of a weapon. Wiping the Katana after every cut is not a
viable technique in an unpredictable fighting environment and hence integrating a
cleaning mechanism in the layout of the sword is an attractive solution. This is the
purpose of the Bo-Hi. When a Katana cuts tissue, blood tends to collect not on the smooth
surface leading to the edge of the blade, but in the canal-like fuller. Furthermore, the Bo-
Hi minimises suction – if a blade without such a bloodgroove is buried in tissue, direct
contact between all sides of the blade and the cut tissue may cause suction, making the
blade more difficult to recover. A Bo-Hi creates an artificial channel of air, which
diminishes the strength of this suction, increasing the speed at which the Katana is
returned after a cut.
Lastly, a Bo-Hi confines the blood caught in it. This aids the practitioner – the groove
becomes an effective blood-channel as the swordsman swings the Katana and the blood

3. is guided off the blade. Such a motion is called a bloodshed – the centrifugal force built up
in a swing causes the blood to move outward, and the blood groove confines it, guiding it
outward and off the blade.
1) Increasing Manoeuvrability – Kinematic Consequences of the Bo-Hi
In modern training swords (often made out of Aluminium) a Bo-Hi is added to the blade
to minimise mass. The addition of a fuller may easily reduce the mass of a blade by 11%,
as shown in Table 1. Such a reduction in mass increases the cutting speed of the
practitioner – but a lighter blade has further benefits: since the Bo-Hi effectively removes
a portion of the blade while not affecting the mass of the handle and rear parts of the
sword, the centre of gravity of the sword is moved closer towards the Tsuba (handle).
This diminishes the angular inertia opposing a cut – simply speaking, a smaller force can
lead to higher angular velocities and the sword cuts faster. Furthermore, the diminished
inertia leads to the blade being easier to stop and accelerate again – the blade, colloquially
speaking, is more agile.
Table 1: Comparison of Masses for an example Katana Blade
With Bo Hi Without Bo Hi Difference Percentage
Mass (kg) 1.10 1.23 0.13 -11%
Figure 2 - Comparison of the Centre of Gravity for an Aluminium practice Katana with and without a Bo Hi

4. 2) The impact of a Bo-Hi on Structural Strength and Stiffness
While a Katana which has been equipped with a fuller undoubtedly lends itself to
situations requiring speed and agility, it may lag behind in environments demanding
structural strength. By effectively cutting a circular segment out of the blade’s cross-
section, the Moment of Inertia of the blade (the structural resistance to bending) with
respect to both x and y axes (the nomenclature is entirely a matter of definition, but in
this case they refer to the directions perpendicular to the way the blade points) is
diminished. This means that the blade offers less resistance to being bent, both when
parrying with the flat of the blade and when cutting. This lack of stiffness can be very
detrimental to the function of the blade, especially if it is expected to cut somewhat rigid
armour or padding.
Table 2: Comparison of Moments of Inertia around x and y axes for an example Katana
Moment of Inertia (mm^4) With Bo Hi Without Bo Hi Difference Percentage
Moment of Inertia around x 760 1140 -375 -33%
Moment of Inertia around y 6870 7150 -280 -4%
However, the swordsmith has a say in this compromise between mass and stiffness: if the
same volume of metal is used in making a blade with a Bo-Hi as in one without, the
thickness or width of the Katana increases (the smith can decide which simply by
constructing the blade accordingly). Due to the nature of the structural property, the
sword with a Bo-Hi could have a higher Moment of Inertia than the blade without. This is
because Steiner’s Law states that the Moment of Inertia of a surface at a certain distance
from the base axis (our x or y axis) will be equal to the moment of inertia of the same
surface if it were lying on the base axis, plus the distance from the base axis squared and
multiplied by the area of the surface. Mathematically, this is expressed as
𝐼 𝑥̅ = 𝐼 𝑥 + (𝑦̅𝑠)2
∗ 𝐴,
where 𝐼 𝑥 is the moment of inertia around the base axis, 𝑦̅𝑠 is the centre of gravity in y
direction and 𝐴 the area of the section. This mathematical statement translates into
observable mechanics accordingly: adding an additional 10% of width to the blade
without altering the surface area of the cross section (necessarily by taking away material
somewhere and adding it on the side) can increase the moment of inertia further than
adding 10% more surface area without changing the width of the blade at all.

5. Consequentially, a sword made of a given amount of steel with a Bo-Hi can be stiffer than
a blade made out of the same amount of material without a fuller, as demonstrated in
Table 3.
Table 3: Comparison of Moments of Inertia around x and y axes for an example Katana, with area of
the cross section being kept constant
Moment of Inertia (mm^4) With Bo Hi Without Bo Hi Difference Percentage
Moment of Inertia around x 760 819 -74.1 -9%
Moment of Inertia around y 6870 6400 445 7%
Lastly, the addition of a Bo-Hi comes with the addition of further variables in the
calculation of the Moment of inertia for the cross-section of the sword – the x and y
coordinates of the centre of the circle and the radius thereof. This allows the smith to
effectively control the moment of inertia by altering the variables pertaining to the Bo-Hi.
Since the moment of inertia inversely influences the degree to which the blade is bent
upon impact, controlling the location and size of the groove is a method of controlling the
reaction of the sword to an impact. An example of this added variability is shown in Table
3 – the addition of the Bo-Hi increases the Moment of Inertia around the y-axis and hence
increases the structural stiffness of the sword to impacts on its edge. As a Katana
experiences larger forces when cutting with its edge than it does when parrying,
diminishing the Moment of Inertia around the x-axis is order to increase the Moment of
Inertia around the y-axis can increase the overall performance of the sword.
3) Mechanics, Materials Science, Swords and Stress
While talking about the cross-section of the blade, a further impact of the Bo-Hi needs to
be mentioned. Since by adding a blood groove, the smith effectively removes two circle
segments from the cross-section – these circle segments lie in the rear section of the blade
– the centre of gravity in the x-direction is shifted toward the edge of the sword. Despite
this shift being comparably small, as seen in Table 4, the mechanical and material-related
consequences are significant.
Table 4: Comparison of Centres of Gravity of the cross-section of an example Katana
Centre of Gravity (mm) With Bo-Hi Without Bo-Hi Difference Percentage
Centre of Gravity in x 16.1 16.5 -0.420 -2.54%

6. If a Katana (or any sort of mechanical beam) is subjected only to a load perpendicular to
it – this means that the sword is only being bent, not compressed or pulled apart overall
– the stress distribution through any cross-section of the blade can be approximated to a
linear relationship. The minimal negative stress lies in the region of the sword that is
being compressed most while being bent and the maximal positive stress in the region of
the sword that is being pulled apart most significantly, colloquially speaking.
Figure 3 - Simulation of deformations incurred in a Katana subjected to a load
Figure 4 - Stress distribution along the x-axis throughout the cross section of a Katana
If the force bending the beam is acting along the x-axis, as would be the case if the sword
struck a target and experienced a certain resisting force, the maximal compressive stress
would lie at the spine of the blade, as represented in Figure 5. The maximal tensile stress
conversely would lie at the edge of the blade. With the stress distribution being
𝜎 𝑚𝑎𝑥
𝜎 𝑚𝑖𝑛

7. represented in a linear equation, one region of the cross section necessarily experiences
a stress of exactly zero. This region lies at the centre of gravity of the cross section –
consequentially, the zone of the cross section lying between the edge of the blade and the
centre of gravity experiences a positive, tensile stress. By shifting the centre of gravity
toward the edge of the blade, the size of this region is diminished, as Figure 6
demonstrates.
Figure 5 - Stress distribution throughout the cross section of a Katana with a Bo-Hi and a Katana without a Bo-Hi
At this point, material science takes over from mechanics. Compression and tension may
be expressed in the same units and both be defined as force over unit area, but they do
not have an equal impact on the performance of a material. Steel subjected to forces
pulling it apart will be increasingly vulnerable to the onset of fatigue cracks – this is
because once such a fatigue crack has formed, the external force continually pulls apart
the two sides of the crack. An identical steel that is subjected to compressive rather than
tensile stress will experience a diminished impact of fatigue – fatigue cracks are
effectively pressed together, and the strength of the material does not wane over time. It
is therefore in the best interest of the swordsmith to minimise the area of the sword’s
cross-section that is subjected to tensile stresses, as such stresses promote the weakening
of the blade through fatigue.
Furthermore, the maximal stress throughout a cross-section – as one may deduce by
observing the linear stress-distribution graph carefully – acts at the point furthest from
the centre of gravity. Since an extreme positive tensile stress is more likely to lead to
material failure than a negative stress would, minimising the maximally incurred positive

8. stress at the cost of amplifying the largest compressive stress is a certainly worth
considering.
4) Consequences of the Forging Process
At the same time, the viability of adding a Bo-Hi is constrained by the method of
craftsmanship. In contrast to a plain blade, a Katana with a fuller cannot be forged without
subtractive methods (removing material from the blade during manufacture) or the
utilisation of significant impact. Either of these methods are prone to leaving macroscopic
irregularities in the surface of the material being forged. These jagged surfaces shape an
angle of attack for fatigue, providing the unsmoothened angles which promote the
formation of cracks.
Furthermore, both methods of crafting, if not rigorously conducted, are prone to not
result in a uniform depth and width of the Bo-Hi. This may leave areas of the blade with
a diminished Moment of Inertia and hence a diminished resistance to bending. But aside
from causing a mere loss of structural stability, a reduced Moment of Inertia magnifies
the stress incurred in a given section of the Katana, as is easily seen in the relevant
formulas. The tensile stress throughout a cross-section of the blade is given by
𝜎𝑥 =
𝑀(𝑧)
𝐼 𝑦
𝑥,
where 𝑀(𝑧) is the Moment due to the Force acting on the blade, 𝐼 𝑦 is the Moment of
Inertia against bending around the y axis, and 𝑥 refers to the x-coordinate relative to the
centre of gravity of the cross section. Since the incurred stress 𝜎𝑥 is inversely proportional
to the Moment of Inertia, a diminished Moment of Inertia will lead to an amplification of
the experienced stress. An amateurish, or simply careless crafting of a Bo-Hi, which may
cause irregularity in the Moment of Inertia, will therefore lead to increased localised
stress. This type of miscalculation in construction is one of the most common cases of
structural failure. In the case of a Katana, an irregular Bo-Hi would have the most
impactful effect on a Damascus steel sword - if a region incurring amplified stress through
a diminished Moment of Inertia coincides with a region more prone to damage due to an
improper binding between two layers of steel, the regional strength of the Katana is
reduced dramatically.

9. 5) Auditory impacts of the Bo-Hi
If constructed appropriately, a fuller must not be a liability – even though shedding blood
off a weapon is hardly necessary in the practice of modern sword arts, Bo-Hi’s have
become more rather than less popular in the modern era. Part of the reason for this
seemingly counterintuitive phenomenon may or may not have been intended by the
unnamed inventor of the ingenious cleaning mechanism. The Bo-Hi is a curved, elongated
groove along the side of a Katana. An expertly executed cut guides air through this canal,
which acts as a resonance body – much like the body of a violin or acoustic guitar. The
Katana’s motion causes a vibration in the surrounded air molecules, and the fixed length
of the groove only allows for vibrations of fixed wavelengths (the 1st-nth harmonics).
With wavelengths corresponding to a certain pitch of sound, each Katana that is equipped
with a Bo-Hi has its own array of wavelengths and hence its own distinct sound to it.

10. Summary of Findings
Advantages Disadvantages
 Facilitates removing blood from the
blade
 Facilitates removing Katana from
tissue by diminishing suction
 Reduces mass of blade and hence
increases velocity
 Shifts centre of gravity closer to
handle and hence facilitates handling
of blade by diminishing angular
inertia
 Enables the smith to alter the moment
of inertia in accordance to the
required deformation in reaction to
impact force without altering the
mass of the blade
 Shifts centre of gravity of the cross-
section of the blade toward the edge
of the blade, reducing the areas of the
blade which incur positive tensile
stresses  prevents cracking of the
sword and reduces fatigue
 Shifts centre of gravity of the cross-
section of the blade towards the edge
of the blade, which reduces the
maximal tensile stress
 Causes cuts with the sword to create
distinct sound
 Reduces structural strength and
resistance to bending by diminishing
the moment of inertia of the blade
 Augmenting the blade with a Bo-Hi
significantly increases the risk of
unsmoothened angles being formed,
which serve as a starting point for
fatigue cracks
 If improperly forged, the Bo-Hi
creates sections of the blade which
incur extreme stresses, which
facilitates damage to the sword