 
12.4.2 Dynamic Properties Combined 
 
Graphics to Show it All 

First let's go through the basic parameters that determine your swords dynamical properties:  Its mass
m. This is a single number, easy to obtain and typically between 1 kg
 2 kg. Mass is a clear thing that does not need more words.
 The center of mass. (COM). Once
more a single number
that gives the distance (in cm or mm) to some reference point. It is also a sufficiently clear entity by now. Typically
we want it on the blade but not too far from the hilt.
 The moment of inertiea
I. This is a measure of the distribution of the mass. It is not a single
unambiguous number and it is not all that easy to calculate. Its value (given in kgm^{2}) is always relative to
a rotation axis. It is usually given with respect to a rotation axis through the COM at right angles to the blade and then
designated I_{COM}. If I_{COM} is known, it is then easy to calculate values
for other axes perpendicular to the blade at some arbitrary distance from the COM.
Generally we want a small moment
of inertia since this makes it easier to swing the sword.
 The effecive mass. This is not a number but a curve with a shape that is determined
by the mass and the moment of inertia of the sword. It gives values (in kg) that decrease from a maximum at the COM (with
a value equal to the total mass) to lower values at both ends of the sword.
The value of the effective mass at some
point relates to the impact felt at that point.
 Percussion points. There are always two points! One point is usually chosen as the pivot point
on the hilt close to the cross guard. The corresponding percussion point then is somewhere down on the blade (or even outside;
off the tip). Its distance from the center of mass depends on the mass m, the moment of inertia I_{COM}
relative to the COM, and the distance of the pivot point from the COM. We want the percussion point to be found in the tip
region because hits on the percussion point do not transmit forces to the hand at the pivot point.
 Vibration node points. Typically swordsmen
are concerned about the location of the two nodes of the (low frequency) second order sidetoside vibrations. They are
easy to excite and to see. The two nodes of the (high frequency) second order edgetoedge vibration might be more important,
however. Luckily, they coincide more or less with the first variant. Ideally, we want the lower vibration node to coincide
with the percussion point.
Vibration node positions are not easily calculated.
It is also not easy to change their position substantially. They tend to be  very roughly  around the hilt and about 3/4 down the blade.
 Point of maximum impact. I have not discussed that yet but it is clear that whenever
you hit something you transfer some energy from your sword to the hittee. There must be a point somewhere on the blade that
delivers the most energy and that is the point of maximum impact. I'll discuss that later in detail.



In essence, all these parameters result from the distribution of the materials
defining your sword. In other words: It is the shape or geometry that counts  and details matter! Change something there
and all the parameters above will change. Some more than others. 

What that means is simple. You cannot sit down, consider what you want with respect
to the parameters given above, make a list with the resulting numbers and curves, and order your sword maker to produce
a sword that meets your wishes. All these parameters are simply not independent. 


You must compromise. There is no "ideal" sword for you, only compromises.
Swords may give you satisfaction with regard to some parameters while leaving something to be desired with respect to others. 

Peter Johnsson
has come up with a very attractive way to illustrate the sword properties that result from Vincen
Le Chevalier calculations ^{1)}.
His pictures are mostly published in "The Sword  Form and Thought" ^{2)}
and I use some of them here with the kind permission of Peter, Vincent and the Solingen museum. Here is what it looks
like with some explanations added by me: 
 
 Sword dynamics graphically 

 


The text insets are from me and I used my nomenclature that on occasion is somewhat
different from that of Le Chevalier. Pictures like that are generated by a computer program that is available for everybody
in the Net ^{1)}. You must supply the basic data, of course, and that involves
some precise measurements. Le Chevalier has explained most of the math behind the calculations and, as far as I'm concerned,
it is sound. There is a lot of information in these pictures. Let me go through the pertinent points:
 You see the basic shape of the sword in some detail and you find the
mass.
 The effective mass curve is shown below the sword and the effective mass at some
special points may be given as a number and in percent of the full mass.
 The center of mass is indicated.
 Two pivot points are chosen, always close to the cross guard or to the pommel. The
corresponding percussion points on the blade are calculated and shown. Since the real
pivot point will be somewhere between the two shown, the blade part between the two percussion points is where you want
to hit (with some preference to the front one).
 The two nodes
of the second order sidetoside vibration are shown.
 The sword's response to attempts at translations are shown as an oval centered at
the cross guard pivot point. The smaller the distance from the pivot point to somewhere on the oval, the harder it is to
move the sword in that direction.
For straight thrusts the full mass is used, for movements at 90^{o} to the
blade the (reciprocal) effective mass in that direction is used. For movements in arbitrary directions, a suitable mixture
of the two values is employed. Assumed is that you just apply a force in the specific direction which, except for the straight
thrust, always results in translation plus some small rotation.
 The sword's response to attempts at rotations are shown as two cones centered at
the cross guard pivot point. The larger the cone, the easier it is to rotate the sword around the cross guard pivot point.
The essential parameter for this is the moment of inertia for rotations around the pivot point.
 Some more information, e.g.. effective masses at some special points, might be given as the need arises.


The power of these diagrams (from the Solingen book)
becomes clear when you use them to compare swords. 


The sword on top is described as a handanda half Sword from 1480  1500. It is 105 cm long
with a the blade length of 81.5 cm and weighs only 0.822 kg The sword on the bottom is actually an "Ulfberht" sword. Its length is 83.3 cm, with a 70.2 cm blade. It
weighs in at 0.79 kg, quite low too. The "Solingen Swords" Link provides a lot of pictures like the ones
discussed here plus some data. It includes very light and very heavy swords, long and short ones, and allows a lot of data
extractions like the one below. Here are the two characteristics of these swords: 


 
 Property comparison of a handanda half Sword
from 1480  1500 and a Ulfberht sword from ca. 1000 AD. 


The Ulfberht has a slightly better translational response, simply reflecting its
slightly smaller weight. Its lower percussion point coincides with the vibration node but is a bit far from the tip. The
effective mass at the node point is respectable but practically the same as that of the longer sword. The long sword has
a far better rotation response. That means that you can get it to swing with a larger rotational speed than the Ulfberht.
Its percussion point (also close to the node point) thus moves considerably faster that that one of the Ulberht and thus
delivers far more punch (the power goes with effective mass and the speed squared!). It is just a much better sword  if
wielded by an expert. It needs more room for swinging and that needs practice. 


I doubt very much that the longer sword was intended for "oneandahalf"
hands. There is actually ample space for two hands on the hilt but given its small mass I tend to believe that it is meant
for one hand only. Why then the long hilt? The answer is simple: 
 

 
Optimizing the dynamical properties of
your sword means optimizing: the pommel and the
the blade taper 

 



The long sword obtains its superior properties to a large extent
because its pommel is far away from the center of mass without taking too much mass away from the blade. The blade is actually
thicker then the Ulfberht blade but more slender and cunningly tapered. There are many interesting pictures of people (including
angels) wielding those swords always with just one hand, here is the link. 

Finding the best pommel mass and distance plus a fitting taper Is not easy because
of all the parameter interdependence. There are no simple rules. I'll give you a few examples of what can be done. 

 