Fuller

Theory

The use of a fuller running down the blade has been seen in swords dating back to the early Dark Ages and in some cases before that time. Simply by dismissing them as a way to allow air and blood from the body is a rather naive thought. The maths and physics involved of the use of a fuller in a blade is far more complex than most people realize. Please read the following explanation of the phsyics involved in solving the problem of blade stiffness and lightness. I think the following paragraphs about the physics involved (from Fullers and Blade Stiffness by E. Steenput) will be quite illuminating for some people.

The stiffness of a beam is determined by two physical properties: the modulus of elasticity E of the material, and the moment of inertia I of its cross-section. Fullers will influence the stiffness of a blade by changing I.

To determine I, we have to draw a pair of axes in the centre of gravity of the cross-section.
The I matrix is then determined by the following integrals over the area A of the cross-section:

There will exist a pair of axes, called the neutral axes, for which the component Ixy is zero. This means that a force applied in the direction of one neutral axis will cause the beam to bend exactly in the direction of the axis. That way the stiffness along the two axes can be decoupled and studied separately. If the cross-section has any symmetry, usually the neutral axes are the same as the symmetry axes. In the following we assume to be working with neutral axes. Note: The term "force" is used here instead of the more correct "bending moment" for simplicity.

Diamond cross-section with neutral axes.

Illustration of neutral axes: a sideways force (along the neutral axis) will cause the blade to bend sideways, but a force along another axis will cause bending at an angle.

The stiffness in one of the main directions (let's say sideways) is the integral of the section's area times the square of its distance from the neutral axis perpendicular to this direction. So the more area is farther from the axis, the greater the moment of inertia, and the stiffer the shape.

For simplicity, we will limit ourselves to cross-sections consisting of rectangles. The integral then becomes a simple sum:

For a rectangle of height a and width b, it is easily obtained that

As an example consider the following I beam:

The weight (total area) of this beam is 30. If a force comes from above, bending will be determined by the moment of inertia around the horizontal x-axis:

Because there are two large pieces of cross-section a good distance away from the x-axis, the beam is very stiff along this direction, even though there is only one 'spine'. If the force is applied sideways, the moment of inertia around the vertical y-axis will determine the amount of bending:

There are two 'spines' in this direction. However, the momentum of inertia is smaller, because most of the area is closer to the y-axis. The I beam is far less stiff in this direction. (If you don't believe this, look at any ugly building and check how the I beams are oriented). However, the I beam is less stiff than a solid beam with the same size, for which

and the weight is 120.

But it is a lot still stiffer than a solid beam of the same weight, because the available material is placed further away from the axes. Let's say the beam is 10 by 3 (weight =30). This gives:

Comparison Chart:

Conclusion: If we substitute a sword blade for the I-beam, we can conclude that a fuller will lighten a sword, and a sword with a fuller will be stiffer than a solid sword of the same weight, but cutting a fuller in a sword will *not* make that sword stiffer. It will make it lighter while maintaining most of its stiffness.

However, due to the reduced weight, the fullered blade may "feel" stiffer if you wiggle it, because the force of inertia acting on the blade will be smaller. Another factor to consider is the difference between a forged fuller and a cut fuller. According to certain bladesmiths, a skilfully forged fuller will strengthen the blade.

Another interesting observation is that a fullered blade will be stiffer edgeways as well as sideways. The wider the fuller (or the greater the distance between the "spines") the stiffer the blade will be, edgeways.