Maurizio:

Please excuse me, I didn't know the cross section and the fuller matters.
Cross section: flat lenticular (almost hexagonal)
Fuller length: 76 cm (5 cms from tip)
Fuller width at base: 14 mm
Fuller depth at base: 3 mm

I have to explain how I made the blade. I started with the fuller 3 mm deep and 14 mm wide, it gives me an excellent guideline for making the profile of the cross section and it's difficult to make it after that.
After that I started at the guard trying to keep a constant angle of 10-12 degrees for the whole length to make the cross section. This naturally gave me a linear distal tapper for this reason the fuller got narrower and became more shallow towards the tip.

The cross is made from the same material as the blade and it's 17 cm long. I considered that a longer guard will be annoying while handling the sword. It's only 7 mms thick, but I considered that's pretty strong material unlike brass or bronze or anything that could be cast. Well it's a real pain in the a.. (neck) drilling holes in spring steel, but I found out that dentists drills and routers works fine.

By the way, I couldn't find anything about authentic historical swords pommel and guard weight. Maybe it can be estimated, knowing that the density of steel is around 7.7 g/cm2....

Vincent:

Maybe it's just beginners luck, but the pivot point (corresponding to the cross) seems to be around 52 cm from the guard as I can see with the naked eye. Maybe I will try the pendulum method too.

I don't think swordsmiths were great mathematicians (I even doubt they were literate) in the dark ages, they have had some simpler practical and secret methods for doing all that.
Today we live in the computer age so why not integrate those formulas in some programs.

Best regards,
Arpad

Well I don't think I can find a real swordsmith nearby and museums won't let me swing their precious artifacts neither. Good replicas are expensive and my wife is not happy with my obsession for blades. I will surely wake up one morning with may bayonet collection in my back if she finds out that I spend the family's budget on such things.
People here still think that swords are just big heavy knives as seen in the movies. Swords you can find on the market here are just cheap fantasy junk that will break apart at the first impact. I have access to some authentic cavalry and infantry sabers, but they are a complete different story. That's the reason I don't know when a sword feel ok in the hand. Blacksmiths are specialized in making horseshoes, so I appreciate every advice from experienced people like you.

I am not an expert, but I can provide the data you ask for.
I set to work, tomorrow or the day after tomorrow I will give you the information you ask for.
Interestingly, comparisons with Vincent.
From handling, I'll see if you can give a POB between 110 and 120 mm. I hope to find the moments of inertia about three principal axes. These may explain Vincent, he is the expert. :p
I make mistakes, but the guard is a little short for the average.
The data will be averaged, then only the experts are good things.
But it can be a starting point. :)
Ciao
Maurizio

Fixing the CoG at 110-120 millimeters without modifying the blade may require a large, over 500 g pommel.

Well, the ancients who discovered the wheel were not less intelligent than those who built the first space shuttle. There are things we learn in childhood and take for granted, like gravity. In the middle ages education wasn't available for the masses just for a few people from higher social classes, or men of the church. It was based more on religion and art.
Today's modern swords are made by CNC machines and are designed with some sort of CAD software. The swords parameters are fixed before the machine starts grinding. I think it's even possible to reverse-engineer the blade, by fixing those parameters like CoG pivot points maybe even harmonic nodes, than building the sword around it.

Ozsváth,
as promised:
1)
weight sword = 1.7410078e+03 GRAMMO (1.74 Kg)
Blade = 913.21587e+00 (0.913 Kg)
Guard = 98.25487e+00 (0.098 Kg)
pommel = 0.618e+00 KG. (0.618 Kg) (around 70 MM.)
if pommel is this:
POB = 110 mm from the guard


principal moments of inertia: (GRAMM * MM^2)
I1 I2 I3 5.7075690e+05 1.3891870e+08 1.3941801e+08


slewing than the main axes
R1 R2 R3 1.8106113e+01 2.8247499e+02 2.8298218e+02 MM

If you make a pommel historical (around) is this:

2)

weight sword = 1.41100e+03 GRAMMO (1.41 Kg)
Blade = 913.21587e+00 (0.913 Kg)
Guard = 98.25487e+00 (0.098 Kg)
pommel = 0.3308e+00 KG. (around 53 MM.)
if pommel is this:
POB = 158 mm from the guard (Vincent you are a great)
But, type Oakeshott Albion that you make, have a POB = 110 mm

principal moments of inertia: (GRAMM * MM^2)
I1 I2 I3 4.3436621e+05 1.1714930e+08 1.1754266e+08
(the handling is in relation to these numbers, Vincent can better explain the value of these numbers, if I do it myself with my English to risk no understood.)

Now, using the mathematical proportions, you can change these values as best you want.
nodes harmonics, and the elasticity of the blade, serves:
Heat treatment, hardness obtained, coefficient of elasticity of the material that uses, energy in Joules (understood as a constant). The point of impact better, I find myself.
To do this, it takes a little 'time, is not exactly easy, but possible.
I use these programs for my work, if you stick to these shares you get exactly those results.
But, you want to replicate a type Oakeshott Albion? I think it's a bit more difficult, they feel the blade, beyond the numbers.
I hope to have you help.
Here a drawing.
Ciao
Maurizio

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 Attachment: 60.23 KB

This is the design of 1 solution

Thanks a lot for helping me!

It's not looking good...
I realize that I know very little about swords and I have much to learn especially on good old physics that I was so happy to forget. As Bruno said, I have to put my blade to a strict diet and grind, grind carefully not to end up with a rapier. I'd be happy with a blade under 800 gram,s a pommel around 300 ending up around 1200 grams. I have to cheat on the distal tapper to bring the CoG under 150 mm. It's still won't be a lightweight one.
I don't fully understand those moment of inertia and those axes . It has to do something with mass resisting acceleration and has direct relation with handling and impact forces. It's a good idea to get those values close to swords with known good handling characteristics.
Maurizio, I don't want to replicate the Albion Oakeshott, I said it just to give YOU an idea about the shape of the blade. They are really good experts and I can't get even close to the quality of the worst sword they ever made. Don't worry about your English, mine isn't so great as well :) I see you have some sort of software to calculate these values. Is there something on the web I can download? I can write one myself if I can find or figure out some formulas, well after taking a good rest on this weekend. I had a difficult week at work and I feel that my IQ have dropped dramatically, under human values :p

Arpad

Hi everybody,

Yes, good old physics can have practical uses among which understanding swords :)

Moment of inertia is a measure of how hard it is to accelerate the object in rotation about an axis. Much like mass is a measure of how hard it is to accelerate the object in translation (conveniently mass does not depend on the direction you want to give to the object, but moment of inertia does depend on the axis of rotation). The classical example for moment of inertia is to take a bar with two weights attached. If the weight are at the ends, the bar will be a lot harder to rotate than if they are at the middle. Yet, the mass and center of gravity are the same in both cases.

Swords are used essentially in rotation and very little in translation, so the moment of inertia is an important property to understand. The thing to remember is that it's the square of the distance from the mass to the axis of rotation that matters.

The moment of inertia of a sword about the axis of the blade is very small, and the moment of inertia about the axis that allow to strike with the edge or with the flat are much bigger and almost equal. That is because the sword is a thin, long object. This is seen on the numbers given by Maurizio:

I1 I2 I3 5.7075690e+05 1.3891870e+08 1.3941801e+08

The interpretation of this line is that the moment of inertia is:
5.7e5 g.mm^2 about I1, which is the axis of the blade
1.39e8 g.mm^2 about I2 and I3, the other two axis.
It's that last figure that is significant. The other moment of inertia can be safely neglected.

These can be computed as Maurizio did, thanks to a CAD program that knows very precisely the geometry of the object, or they can be measured thanks to the pivot points, which is what you did on your blade.

Now what can I do with that?

I can compute an equivalent object that has exactly the same dynamic properties as your swords (it will move in the same exact way) but that has a much simpler mass distibution. This allows to compare the mass distribution in a very visual way... I did that with a stick of uniform thickness, with a point mass on it that materializes the concentration of mass you achieve through tapers and addition of hilt components. Several swords are represented like that in the image below:

[ Linked Image ]

The length and thickness of the rectangle represents the mass of the stick in the equivalent object, the bar that sticks out represents the point mass. The more it sticks out the biggest the point mass is relative to the stick. The red line shows the location of the cross on all swords.

I've included several swords I own or have measured for comparison. The Squire is the Albion sword of type XVI. The type XI was made by Angus Trim, and is probably closer to what you want to achieve. The "G. Fabre 2" is a type XV made by a French artisan named Gaël Fabre. "Sword" indicates your sword, Ozsváth, simulated with the 100g cross and a light 120g pommel. "Sword MA 1" and "Sword MA 2" are the swords given by Maurizio.

As you can see the main property of the big hitter types is that they have a big stick part. My conjecture is that a properly balanced sword must have the point mass very near the cross, because it fits neatly into how our brain controls the weapon. I've checked that on many swords from type XI to rapier. As you can see, your blade when mounted with a very light pommel has this property and looks pretty similar to my type XI. But Maurizio's swords have their point masses far into the handle and still have very big sticks. This is the symptom of too much pommel and not enough work on the blade, I think. It makes the sword feel slower than your brains expect from the static feel. The sword by Gaël Fabre is already borderline in my opinion as far as point mass location is concerned (I've heard people around the table say that they felt a bit unresponsive, less lively compared to originals).

If you wanted to have a smaller stick like the type XVI and XV, one way is to have more taper in both blade and tang. But for a sword of this type I think the big stick is appropriate.

I hope this makes some sense,

Thanks Vincent for the highly illustrated explanation. I'm still a bit confused here. As far as I understand one can make the equivalent model for the sword, let's say a thin rod and two weights with adjustable positions to simulate the mass distribution. Concentrating mass farther from the pivot point (ex. a large pommel) will increase moment of inertia. You will end up with a sword that will hit hard but it's difficult to control. It will stick to the trajectory imposed by the laws of physics. Well that's great to display the "power of thy sword" by chopping down innocent trees, but a chainsaw is much better for this purpose. After all a sword is a weapon, not just a tool.
Now I see that the crossguards weight has something to do with mass distribution.
On the other hand a sword with too low moment of inertia will lack on power. It's hard to find a good equilibrium between these characteristics.

I tried to swing the blade couple of times. It's a real wristbreaker. It doesn't feels good for a single handed sword, but if I help a little on the end of the tang with my left hand it handles quite well. This must be the consequence of a sudden violent rotation of the tang when I try to stop the blade. That could be the result of pivoting too close to the guard?

Vincent, if you read George Turner's article (http://www.thearma.org/spotlight/GTA/motions_and_impacts.htm), especially the "swords and pendulums" section, you will notice that those pivot points can be located with ease. All you have to suspend the blade at certain points on the hilt (under the index finger or at the cross for the forward pivot point) to act like a physical pendulum and get the period of oscillations. Now the theory says that the location of the corresponding pivot point will be the length of the string of the simple pendulum (ball on a string) which oscillates with the same period. Simple pendulums period are not affected by mass, only by the length of the string and the gravitational constant.
L = (T^2 * g)/(4*pi^2)
You can find all equations needed here: http://hyperphysics.phy-astr.gsu.edu/HBASE/pend.html#c1
Now you can make an adjustable mass pommel and see how it affects the pendulum's period and by consequence the location of pivot points.
I'd really like to have some spare time to do some experiments but at my age that seems to be a luxury.

Oh I'm fully aware of why the pendulum method works, but I had problems finding a reliable solution to hang the sword at a given point without friction and letting it swing. During the course of my reflections I have become so familiar with the waggle test that I gave up trying to perfect the other method, but I guess the pendulum could indeed add further precision.

Another part of my reasonning is that any difference I'm not able to spot by hand and eye (i.e. the waggle test) is not a significant one, but that might be overly optimistic ;)