Sword Dynamics

Gotas, Mark Jason G. BSME 3A

Evaluating the Effectiveness of Hand-Held Impact Weapons: Swords

Knights of the Medieval Age, Gladiators of Ancient Rome, Samurais of the Edo period, Norsemen of the Viking Age, Classical Antiquity, Myths, and Epics, these were just some of the tales where combat thrived, and conquering was absolute; Such great eras in which melee weapons were a heavy feat in winning. The most iconic weapon of choice a warrior of the ancient times would wield was the sword. From slaying beasts, slashing limbs, stabbing hearts, to slitting throats, warriors need not to fear the terrors of their enemies for the way of the sword would be their saving grace. Throughout history, the sword, or as many called it, the “Queen of weapons”, have been used by cultures all over the world for close range combat. It is a weapon consisting of a long blade and a hilt attached on top of the blade for the bearer to hold and thus had been developed mainly for inflicting wounds by slashing or thrusting. The sword was first considered to have appeared around 2000 BC known as the Bronze Age. During this time, the sword was predominantly a stabbing weapon with a very small leaf shaped hilt. During the Iron Age, which was around the 13th century BC, iron working skills brought forth the iron sword. And although it is mostly inferior to the well-made bronze sword, it was an easier weapon to make and could be produced in mass quantities. But by adding a small amount of carbon during the smelting process of iron, steel could be made, thus producing steel swords which are far stronger and durable than the iron swords. Around 11th to 13th century AD, the sword was redesigned. Metal bars or sheets

were placed between the blade and the hilt perpendicular to the sword known as the quillion or cross guard. It was used not only to counter enemy attacks, but also get a better grip on the sword. During the Late Middle Ages, armor made advances in its ability to protect and so swords also have made advances in its ability to thwart these defenses. In the Modern Era, the major game changer in sword fighting was the invention of the basket-hilted swords. These types of swords have basket shaped-guards that are attached to the hilt to protect the hand of the one who wields the sword. Advances in metal workings also created swords that were lighter and quicker yet stronger. Across the world and over the course of thousands of years, swords have evolved very differently due to available manufacturing methods, materials, and cultural differences. But, regardless of the evolution, swords have managed to keep the same general morphology of a metal blade attached to a hilt. The sword is silent as it leaves its scabbard but as deadly when it is in the hands of a master swordsman. In the instance where two warriors draw blades, exchange blows, and face off in a fight to the death, surely the man with the better sword and the more skillful would survive, a cruel fate for the inferiors during ancient times. Therefore, in sword fighting, two key features would mean life or death to a warrior in a battle: Sword and Skill. The sword which indicates honor, strength, power, and courage is said to be an extension of the mind and body. The bladesmith made the blade by forging, a process where a metal or a combination of metal is heated in a forge then is hammered into shape. Following the forging is annealing, a process in which after shaped, the sword is heated and then allowed to cool very slowly to make the sword soft and easy to grind. Next is grinding, in which the smith uses a grinder to work out the edge and point of the sword and is engraved. But because the sword is still soft, it undergoes through a process called hardening, wherein the sword is heated again to a very high temperature and then cooled quickly in a quenching tank. Repeating this process again but in a much lower temperature in called tempering, it allows the blade to be strong but not brittle.

Finally, the sword goes through the completion process in which the additional parts are added such as the hilt, the guard, and the scabbard. Every wielder has their own preference of sword whether it may be thick, thin, long, short, ragged, or smooth, a warrior always picks or makes a sword whose balance would fit their grip perfectly. Just like any other weapon, there are many factors that affect a sword’s effectiveness, Like how a heavier sword is much more difficult to accelerate or decelerate in thrusting; or how the location of the sword’s center of mass when the distance is multiplied by the sword’s mass would result to the moment of force required for the wielders hand to counter accelerations perpendicular to the blade, including gravity; Or perhaps how the moment of inertia, which is the rotational equivalent of mass, measures how hard it is to rotate a sword and is identified by how mass is distributed throughout the body and the axis about which the sword is rotated. If the moment of inertia of one’s sword is large, then it won’t point well, the sword will feel clumsy and will take a great deal of torque from your hands to move the tip around. A sword with a small moment of inertia would be described as quick, agile, light maneuverable, and fast. If a warrior picks up a sword with a high moment of inertia, it will feel fine until they try to rotate the blade. The sensation would be described as if the sword is dead, it will move slowly, and will be maneuvered poorly. Unless the warrior is strong enough to reach equilibrium with the sword’s moment of force it would have been a problem for the wielder if the weapon was unbalanced. According to Newtons Law of acceleration F=ma, when a single force is applied to an object, the center of mass of the object accelerates. A popular misconception rises when a force is applied perpendicularly to and object. One often hears that force causes the object to rotate around its’ center of mass, which is somewhat true, but really, when force is applied perpendicularly to an object, the object will always rotate around its center of mass in the absence of any applied force, but not really in the presence of an applied force. And when a force is applied far from the center of mass, perpendicular to the sword, the sword rotates away from impact so

easily that very little force gets applied, and less force means less acceleration of the center of mass much like applying a force to a light object. Since we are dealing with rotation, we are trying to find the angular acceleration instead of just linear acceleration. The angular acceleration is given by the formula

Ί=Iα which is just the rotational version of F=ma where I

moment of inertia and

α=

𝐹𝑑 𝐼

is the object’s

Ί is the applied moment which is M=Fd. Therefore, angular acceleration

. Integrating the angular acceleration, which is the change in angular velocity with respect ϖ

t 𝐹𝑑

to time, we could obtain the angular velocity ϖ = ∫ϖo 𝑑ϖ = ∫0

𝐼

𝑑𝑡 =

𝐹𝑑𝑡 𝐼

, since F, d, and I are

given and are constants. And then integrating the angular velocity, which is just the angular ϴ

t 𝐹𝑑𝑡

position with respect to time will yield the angular position ϴ = ∫ϴo 𝑑ϴ = ∫0

𝐼

𝑑𝑡 =

𝐹𝑑 2𝐼

t2.

When two forces are applied to the sword, much like what the warrior’s forearm does to the handle a simple case of two equal and opposite forces separated by some distance are created, these forces form what’s called a couple. The couple applies a moment of force to the weapon, and that moment tries to rotate the weapon about its center of mass. Note that couples are equal and opposite. If we try to analyze a free-body diagram of a couple with a summation of their forces either horizontally or vertically,

∑ 𝐹𝑥 = 0 ,

then F1 – F2 = 0 since both their

magnitudes are equal. Since they present no unbalanced force to the object, the object’s center of gravity can’t be accelerated, since with no applied force, the equation F = ma gives no acceleration. It is essential that one must understand the inner workings of a sword to draw out their full potential in a swordplay. Too heavy a sword means the cuts / thrusts will be slow and the wielder will tire very quickly. Too light a blade is as if the wielder would move like lightning, but the blade can’t transmit the full force of his strike. The center of mass in most well-balanced blades is a few

inches / centimeters in front of the cross guard. If the center of mass were too far back, within the hilt, it would make the blade feel very heavy and hard to move and it would strike poorly, as more mass at the back of the sword means a lot of your energy would stay there, rather than being in the blade end. If the center of mass were too far forward, it would make the sword feel heavier on the tip. With the weight being out on the end of the blade, it would take a lot of strength to get the sword moving, and particularly to change its direction if in motion. Distinct swords defined the ethnicity of the wielder. The romans developed Etruscan technology, bringing forth blades that characterized the roman military machine: The Gladius. This was a short sword was used for stabbing and was the weapon of the legionary. For the Anglo-Saxons, the Bamburgh sword. It was a weapon from Northumberland and was about 76 centimeters long and was made from six strands of iron, pattern-welded together, which was passed down through the centuries. The iconic Katana of the Japanese, made from a metal called tamahagane, defined a samurai soldier who operated with a strict and noble code of ethics, and wielded weapons that are believed to be as honorable and trustworthy as they were. These were just some the many types of swords different cultures use in battle which aren’t hardly recognized in the modern era because of the rapid advancement of technology. With the rise of the age of massed armies, swordsmiths had to forge simpler, easier-to- make blades. The design of the swords continued to evolve through the following centuries, to suit the fighting styles of the men carrying them. Blade styles also changed as armour improved, making it harder to cut through with a sword’s edge. As a result, the point of the sword became more important, being sharpened and hardened so that it could punch a hole through an enemy’s armour As different swords came in to play, different styles of fighting also rose to the occasion. Stance, grip, and the cut bring as much effectiveness in sword fighting as the quality of sword does. Mastering the skill would bring about the deadliest warrior when paired with his weapon. In a sword fight, cuts and thrusts are the fundamentals of striking; thrusts are directed forward motions taking into consideration the direction of his aim and simultaneously trying to put out the

enemy’s defense whilst maintaining your own. Cuts, when using a sword, focuses mainly on the swing of the sword, slashing your opponent with the swiftest and as little energy applied in the process whilst fatally damaging the enemy. One thing to notice on most swings is that the sword is placed under intense angular acceleration, and centrifugal acceleration, by the arc of the hand’s travel. To put it simply, the hands angular acceleration is determined by the weights and inertias of the sword and arm. Also, the distance from the arm’s axis of rotation to the sword’s axis of rotation determine the centrifugal acceleration that determines the sword’s period of oscillation. The sword, if displaced from a direct line leading from the arms axis of rotation, will act like a pendulum under the influence of the centrifugal acceleration instead of gravity. The centrifugal acceleration, given by the formula

ac = ϖ2r

does not act quite like gravity. One might

think that the period could be found by determining the centrifugal acceleration felt by the swords center of mass, but this is not so. The formula would be similar to that of a normal pendulum, but with the acceleration due to gravity replaced by the centrifugal acceleration of the sword’s pivot point, which is the hand. The physical aspects of cutting are itself a matter of efficient kinetics. It's a matter of the elements of footwork, coordination, gripping method, arm motion, aim, focus, and follow through --all of which require practice to perform proficiently. One must consider each factor there is when using the sword. For example, in a fight, grip would be essential; if you pinch too hard and apply torque on your gripping point, it will unsettle the oscillation. That is why the grip must be as light as possible but not too light where drag could disrupt one’s aim when trying to cut. Stance and footwork may also be another variable. To put it simply, footwork is how you move. Forward and back, in a line, in a semi-circle, a pivot. The basic goal of footwork is to give you a balanced center from which you can lunge, advance, retreat, attack, parry, whatever you’re trying to do. And you use perception to select the right footwork, so you can identify how close you need to be to hit him, and how quickly you can retreat if he surprises you with a lunge. Also, when striking, the

motion of your hand should be as horizontal and straight as possible, otherwise the observation of the fixed point becomes very inaccurate. A sword will also tend to flex somewhat upon strong impact and this too minutely increases the drag and distorts the edge alignment. Cutting damage can be increased by the subsequent application of edge pressure after the initial moment of contact. If the motion of your hand is not quick enough, there will be a motionless point on the weapon. It is only when the frequency becomes high that the motionless point converges to the pivot point. An effective sword cut is also not made by just swinging forward the point or by whipping the weapon around in a big arc so that the tip connects against the target, but rather it is made by utilizing the whole body to place maximum impact on the target with a good portion of the edge. A laceration can of course be made by striking on the human body with almost any object. A powerful cut results from the elements of a well-executed motion in where the warrior swings the sword in which the point of the weapon moves in a circular arc, and the hilt moving forward, combined with coordinated footwork, body motion, agility, strength, as well as edge placement, grip, and focus - not just from brute physical force or merely a super sharp edge. Different tactics can be used when in combat. For instance, a push is when the warrior would press his blade against his opponent’s blade, pushing the tip off their sword away from him thus revealing an opening for him to strike. In a glide, the warrior tries to gently slide his sword along his opponent’s blade toward him, hitting the point to his opponent when he closes the distance. Expulsion, like the glide, slides the opponent’s blade towards him but a great force is applied downwards at an angle in which the enemy’s point is violently turned aside leaving them open to attack. A beat is literally hitting the opponent’s blade to either move it off line, or to startle a reaction from the warrior’s opponent which he can then capitalize upon. It needs to be quick and as little movement as possible to warn it’s coming, because if his opponent anticipates it, the enemy will disengage. A disengage is when the warrior uses a quick motion to move the point of his blade around his opponent’s blade, in order to gain a new target, like from his left shoulder guarded by his hilt, to his right shoulder which is open. This is really useful when an opponent

tries to beat his blade. Lastly, a bind is when the warrior slides his blade over his opponent’s blade in a semicircle and trap the opponent’s blade under his guard. In trying to examine how well the sword cuts and stays in your hands when striking, one must consider the Point of Percussion. Ever get that painful shock to your hand/s when striking a stick, metal, or any hand-held objects to another object? Well, physics describes it as the Point of Percussion- the section of the sword which strikes the target – has a relation to the center of percussion. The center of percussion is defined as the point on an object where a perpendicular impact will produce translational and rotational forces which perfectly cancel each other out at some given pivot point, so that the pivot will not be moving momentarily after the impulse. The same point is called the center of oscillation for the object suspended from the pivot as a pendulum. In relation to energy transfer, there are certain areas on a sword which delivers more energy transfer than others, particularly the point of contact of the enemy’s sword and one’s own. There are two main locations in a sword where vibrations are cancelled out known as vibration nodes. The weapon appears to be stiffer when manipulated from these locations. In most swords from the high Medieval period to the Renaissance, the location of the vibration nodes of the hilt and the blade are also nearly corresponding pivot points. This makes the blade node suited for especially powerful blows, creating what they call a “sweet spot” there. Therefore, the effective mass at the blade node gives a good idea of how much mass the sword would hit with. The percussion point is also related to the center of mass, thanks to the laws of physics. The further out on a blade the balance point is, the further out the point of percussion will be. With different swords made to suit the fight styles of the warriors or the fight styles made to suit their swords, numerous combinations of combat techniques were conceived, and two major styles were born, Eastern and Western styles. Using a German longsword (western), striking would be called Zornhau - the actual action of throwing the blow is very similar to casting a fishing line. Done properly, the momentum of sword moving in its arc will pull you forward, and that's when you step forward and to the side, moving you off-line from your opponent's sword. The

Eastern style uses forward momentum to help generate acceleration. That's a big reason why everything gets moving before the sword does. A German longsword uses levering to generate acceleration, that's why the sword moves first, and everything follows. A sword is more than just an extension to one’s arm - it has a point of balance close to the hilt, and one doesn’t need to swing the hilt around very fast to make the point of contact move with great speed. Thus, both Eastern and Western traditions in this case will get the sword moving at a sufficient speed to drop the opponent. The Eastern swordsmanship way of maneuvering on a cut does not necessarily make a big difference on force in comparison to the Western tradition - this is just because the blade is moving through an arc. To put it into another perspective, in the German tradition it is the flick at the beginning of body movement, and in the Eastern tradition it is the flick at the end of body movement. In a thrust, though, the body moving first has a serious impact on the force calculation. German longsword, however, treats thrusts in a very different way. German longsword is a style originally used for judicial duels, and thrusts tend to be aimed at the head at the end of a bind. The two styles still differ in some aspects but save one thing, Eastern martial arts have survived longer than Western martial arts. And, any martial art changes over time. It has been a very long time since anybody has had to use a longsword or samurai sword in a duel to the death. So, with the lethal purpose no longer present, there is a degree to which the Eastern martial tradition has created certain artifacts and formalities in techniques that may not have existed if lives still depended on using them well. Swordsmanship is just mathematics and physics. With respect to the sword, if you use a lighter tip against the stronger, thicker base of your opponent’s blade, you would have lost to the battle of physics and thus lost the battle itself. The diverse elements of an effective sword cut are why so many different blade shapes, cross-sections, and other designs were tried out by sword makers throughout history. Size and physical strength of a swordsman as well as the mass of the weapon itself all act to produce the necessary impact velocity of a cut. Maximizing velocity in a cut is, in effect, only about movement through space in a given interval of time. The effectivity of

a sword cut will be determined by the resistance of the target material and the target's relative motion whether it is moving toward, away from, or at a tangent to the edge of the sword at the moment of impact. With respect to skill, Timing, Distance, Perception, and Technique are keys to determine the fate of a warrior in battle. Building momentum, velocity and acceleration, striking at strategic areas, and performing with proper execution with utmost precision are the major feats a warrior must train and master to dominate.

Bibliography

[1] Christopher Aberger, The Secret History of the Sword: Adventures in Ancient Martial Arts, Multi Media Books 1999. [Online] http://medieval.stormthecastle.com/essays/history_of_the_sword.html

[2] Knights Edge, History of the swords, 1994 [Online]. https://www.knightsedge.com/t-about.aspx

[3] Laurie Dove, What Sets the Katana Apart From Other Swords, 2017. [Online] https://people.howstuffworks.com/culture-traditions/national-traditions/what-makes-samuraikatana-sword-special.htm

[4] The History of the Sword, 2018. [Online] https://warfarehistorynetwork.com/daily/military-history/the-history-of-the-sword/

[5] Charles Choi, The Science of Swords: The Sound of Approaching Doom, 2012. [Online] https://warfarehistorynetwork.com/daily/military-history/the-history-of-the-sword/

[6] How It Works Team, The Science Behind the Sword, 2018. [Online] https://www.howitworksdaily.com/discover-the-ancient-art-of-forging-a-deadly-weapon/

[7] The Momentum of a Swinging Sword, 2015. [Online] https://physics.stackexchange.com/questions/170407/the-momentum-of-a-swinging-sword

[8] Peter Johnsson and Vincent Le Chevalier, Documenting the Dynamics of swords, 2017. [Online] http://blog.subcaelo.net/ensis/documenting-dynamics-of-swords/

[9] Randy McCall, Why a Sword Feels Right , 2014. [Online] http://www.tameshigiri.ca/2014/05/16/why-a-sword-feels-right/

[10] Swordplay Style Physics Forum, 2012. [Online] http://www.swordforum.com/forums/showthread.php?110556-Swordplay-style-physics

[11] Cutting Power – Cutting Ability in Swords Forum, 2012. [Online] http://www.swordforum.com/vb4/showthread.php?49143-Cutting-power-cutting-ability-inswords-a-Primer

[12] A. Howitt, Swordplay for Fantasy Writers. [Online] https://mythicscribes.com/miscellaneous/swordplay-for-fantasy-writers/

[13] J. Clements, What Makes an Effective Sword Cut. [Online] http://www.thearma.org/essays/howacutworks.htm#.XA_sG3QzaUk

[14] George Turner, Dynamics of Hand-Held Impact Weapons, Association of Renaissance Martial Arts, 2002. [Online] http://www.thearma.org/essays/howacutworks.htm#.XA_sG3QzaUk