Physical Principles of Sword Design

In contrast to our design philosophy, this page serves as a living document describing some of the math and physics underlying our approaches to sword design. What we've found is that while plenty of information is available about historical fencing techniques, details on the physics and engineering of swords are hard to find, often confusing, and sometimes inaccurate. Here we explain some of these principles so you can understand how and why we make our choices.

If you have any questions or comments, feel free to reach out to jeremy@eskerforge.com. I can't promise I'll have time to reply, but I will read your message.

Heavier swords do not grant an advantage in longsword fencing.

This is a common misconception that sometimes comes from thinking about frictionless swords in a vacuum without gravity. It's easy (for a physicist with too much paper on their hands) to think about two rods hitting each other and the heavy one pushing the lighter one out of the way. However, this is so detached from the way longsword fencing works as to be useless. Namely, your sword is attached firmly to two hands, and you probably weigh more than your sword. In one-handed combat, mass can indeed matter at the start of a strike, or a "beat". After initial contact, when two swords are together and being pushed ("the bind"), mass in and of itself hardly matters.

Stiffness does matter. This misconception is reinforced by lighter swords often being floppy (which is a disadvantage). Material is needed to give a longsword things like length, stiffness, and strength, but the added weight is not a benefit to the sword. For lethal combat, increased mass helps deal more damage to an opponent through deeper cuts or blunt force, but this is explicitly not our goal when fencing.

We strive to make our swords as light as possible by putting the mass where it is needed.

There are actually two kinds of stiffness. You can have a sword that is really strong in a bind and hard to deflect, but is also incredibly safe when thrust.

The "gravity sag" of your sword can be measured as the distance the tip of the sword sags downwards under its own weight when held out horizontally. We have found this to correlate strongly with people saying a sword has good Presence in the Bind. A large gravity sag means a sword is "floppy", where the tip of the sword may take time to catch up to the base especially during quick movements. The gravity sag itself is technically not a stiffness, because it's a distance and not a force, but is similar to the SCA Flex Test. Gravity sag is a bit more useful because it tells you how much the sword deflects due to the sword's mass itself, instead of an arbitrary mass attached to the tip. We do not recommend using the SCA Flex Test as a measure of safety.

The "axial thrust" stiffness, or what people care about when they talk about safety and "flexibility", is measured by pushing the sword into a scale and recording the force. High axial thrust flexibility is needed to reduce the impact of thrusts on your opponent. To measure sword flex, we recommend the "Sword Buckling Load Test Procedure". This gives a higher value than flexing using the pommel, but is more consistent and also more reflective of the true force from a thrust while fencing. We do not recommend flexing from the pommel for this measurement. We also recommend testing the flex in both "directions" and taking the higher value, as imperfections in sword geometry can favour flexing to one side.

We strive always to produce swords that are strong in the bind, safe in the thrust.

This seems obvious at face value - something lighter of course won't hit as hard. What's not obvious is that even when you put the same energy into the strike, meaning the lighter sword swings faster, a lighter sword will still hit softer than a heavier sword.

For the physics-minded among you, this is because "how hard it hits" is given by momentum, while "how hard it is to swing" is given by energy. Energy is proportional to the "square" of the speed, which just means that if something has four times as much energy, it only has two times as much speed. It is also "linearly" proportional to the mass, meaning something moving at the same speed with twice as much mass has twice as much energy. Momentum is linearly proportional to the mass, but it's also linearly proportional to speed.

Let's say you get some really bad feders, and one is four times as heavy as the other. If you swing them with the same energy, because of the "square" dependence the lighter feder will move only twice as fast as the heavy one. The heavy one has a factor of 4 increase to its momentum from its mass, while the lighter one only has a factor of 2 increase to its momentum from its speed. So the lighter one will hit half as hard.

To be clear, "heavy" here doesn't just mean mass, it also matters where that mass is. Reducing mass in the late sections of the blade is crucial for bringing down the rotational inertia of a sword, and lowering impact force. We design our swords to minimize impact by reducing inertia, reducing traumatic injury to your opponent.

When you transition your sword between point-forward guards, there will naturally be one spot on the blade that doesn't move. This is called the "forward centre of percussion" of the sword.  For a two-handed fechtschwert used in blossfechten (unarmored fencing), this is always at or near the tip of the sword. This means when you move your sword guided by your forward hand, the sword will naturally stay pointed at your opponent.

The forward centre of percussion is also the position on the blade where rotations at that forward hand transmit maximum force to their target. If you similarly move the blade but from the pommel, you will find another point much closer to the crossguard where the sword is stationary, called the "aft centre of percussion". With a two-handed grip, you can shift force between your two hands to transmit maximal force to any position between these two centres of percussion.

On some blades, and especially on one-handed swords, this forward centre of percussion is intentionally further down into the blade. Unlike two-handed grips, with a one-handed grip you can only rotate the sword at one hand position, so there is only one spot where your strikes can have maximum force (the "sweet spot"). Because of this, the centre of percussion for a one-handed sword is commonly about a quarter to a third of the blade length away from the tip.

There are also some historical exceptions for two-handed swords which are specifically designed to pivot further down the blade—for example, when facing opponents with shields a closer centre of percussion can help in pivoting the blade around the edge of the shield. But in any combat style that relies heavily on keeping the sword tip trained on an opponent, including any type of unarmored two-handed fencing, the forward centre of percussion should be placed at the tip.

One way people measure the forward centre of percussion is to hold the sword just above the hilt and to wiggle it lightly back and forth, then measure the position where the sword stays still. We find several problems with this approach. First, it is very hard to measure that spot, both because it is hard to identify and because it's hard to hold a sword near the hilt while measuring it near the tip. Second, it's somewhat debatable exactly where you should hold the sword - hand position can vary by user.

Funny enough, if you were to lightly hold your blade at the forward centre of percussion and pivot it back and forth, the spot on your handle where the forward hand goes will stay still - "centre of percussion" goes both ways.

Instead of measuring the forward centre of percussion, what we measure is the tip centre of percussion. This is the position on the handle where if you use it to wiggle the blade, the tip will stay stationary. This can be thought of as the grip position on the handle that the sword is correctly balanced for. In our experience most fencers prefer this roughly 3.5 cm below the crossguard. We have come to this both by inspecting grips and seeing where the hand is anchored, as well as by modifying the balance repeatedly and getting feedback on the quality of the handling from testers.

If the tip centre of percussion is closer to the pommel, then reducing pommel mass will correct it. Similarly, if it is further away from the pommel, increasing pommel mass will balance the sword. In other words, any blade can be balanced by adjusting the pommel. While our pommels currently have a specific mass, we hope to make them adjustable in the future, allowing modifications for individual grip position.

Measuring the tip centre of percussion is challenging, but much easier than a typical wiggle test. You lightly hold the handle above the crossguard, and make small movements side to side, watching the tip. It helps to hold the tip just above something on the floor to give a point of reference. If the tip moves with your hand, then your hand needs to move up. If the tip moves opposite to your hand (a little like a clock pendulum), your hand needs to move down. You keep making adjustments like this until it seems almost like the tip is "rolling" on the floor, where the very tip itself stays still. Then, you measure the distance from where your fingers are holding the grip to the edge of the crossguard.

Let's say you've measured the point of balance and tip centre of percussion. If you draw a rectangle with the long edge from the point of balance to the tip of the sword, and a short edge that's as long as the distance from the tip centre of percussion to the point of balance, the area of that rectangle is the angular inertia per sword mass. So if you take this area and multiply it by the mass of your sword, you get the angular inertia of your sword. In other words, the angular inertia of your sword is (distance from tip CoP to PoB) x (distance from PoB to tip) x (mass of sword). We suggest using distances in metres and mass in grams.

This gives us a way to represent all of the handling properties of a sword and compare it to others. If we draw these points and this rectangle, and then rescale the image based on the sword's mass, the area of the rectangle is directly proportional to the sword's angular inertia.

Bonus question: Why is point of balance often used to describe angular inertia?

If you think about this, let's say you moved the point of balance a bit further away from the crossguard. The long edge of the inertia rectangle would get shorter, and the short edge would get longer by the same amount. But a change of a couple centimetres on a 80-95cm edge is pretty negligible, while a the same change on the ~5-10cm edge is much more impactful. So when the point of balance moves further away from the crossguard, the area of this rectangle gets larger, and the sword has more angular inertia. It's harder to swing.

Be careful though, this area just gives you the inertia per mass. A heavier sword will also have more rotational inertia. For example, adding mass to your pommel will never make your sword lighter!

Generally when measuring sword flex, one wants to get a sense of the maximum force the sword will transfer into an opponent during a thrust. Here are some physical principles relevant to this goal: