A popular term used to describe a sword someone likes is “Presence In The Bind”. But what does that mean? Like any good question it means we are going to have to learn some physics before we have an answer.
Refresher Course: MoI
If you’ve read any SwordSTEM articles about blades you have probably heard me harp on “Moment of Inertia” before. In fact “Center of Percussion? Vibration Node? Balance Point? What does it all mean?” was the first article I ever published, back in 2018. Simply put the Point of Balance (aka Center of Gravity) is the point at which the sword balances. The Moment of Inertia is the resistance to rotational acceleration, be it how hard it is to get up to speed or how hard it is to stop.
The Point of Balance is a popular statistic to advertise for swords, but not a very useful measurement. The Moment of Inertia (MoI) is never advertised, and is a very useful measurement. Why is that? Because the MoI is much more difficult to measure, take it from my experience. (An Alternative Method for MoI Determination)
The reason for the difficulty is that the Point of Balance is a static property and the MoI is a dynamic property.
Static vs Dynamic Properties
Static properties can be measured without moving something, and dynamic properties can only be measured by something in motion. Which is why the Moment of Inertia is so tricky to measure, you have to get the sword moving and get a precise measurement of just how it is moving.
The Point of Balance, on the other hand, can be measured from a static position.
Fun fact: The fact that we have static properties at all is due to the earth’s gravitational force. We can measure things like mass because we can see the effect of gravity on them. If you were floating in space and wanted to determine the mass of your new feder it would be just as tricky as measuring the Moment of Inertia.
1 + 1 = 3
The two types of properties are each applicable to different types of physics problems, named equilibrium and non-equilibrium problems.
If you are posing in an exaggerated guard position out of measure you are in an equilibrium situation. There is force going through your legs to support your body, but we can simply look at the external forces and internal forces to come up with a solution.
If your opponent sees this farcical position and launches an explosive attack they are now in a non-equilibrium situation. Simply put if you record the exact moment the foot lands and do a force balance you no longer have a complete picture of the situation. Because even though we can do a force balance between the bodyweight and the floor there is still the horizontal motion to consider.
To figure out how the motion will develop we must take into account the inertia, velocity, and force balance. It is a much trickier proposition. But we also have a 3rd classification, quasi-equilibrium.
Quasi-equilibrium is when things are moving, therefore not in equilibrium, but we just treat it like an equilibrium problem anyways. If you are slowly changing guards the sword has inertia, but this inertia is a trivial amount and can probably be ignored. If you change guards quickly then the inertia is large enough that it can not be ignored, least of all the inertia you are generating in your body segments which are also moving quickly. Which is why training movements at low speeds, which generates unrealistically low amounts of inertia to counteract, is not as useful as people think it is. (Slow is slow and fast is fast. And don’t let anyone tell you otherwise)
What Is “Presence In The Bind”?
If Presence in the Bind was a real physics term I would have led with the definition. But sadly it wasn’t something I was introduced to in my education.
First we have to figure out if this elusive quantity is a static or dynamic property.
The Search, Episode 1: Equilibrium
Considering the equilibrium case is fairly straightforward, and similar to the question “what weighs more, a pound of feathers or a pound of rocks?”. This is a trick question in that people will instinctively think of the rocks as heavier, however we are explicitly told they are the same weight.
An equilibrium — or more specifically quasi-equilibrium — blade interaction will work the same way. What has a stronger bind, a messer or a rapier? Let the picture explain:
Remember that this assumes that the length from the hand to contact is equal. If you are actually sparring a messer vs a rapier you will probably find that the blade contact is frequently closer to the hilt of the messer than it is to the hilt of the rapier, hence why the messer feels ‘better’ in the bind. But it is not a property of the weapon, only of the crossing point between the two weapons. If you were able to stop time at the moment the blades have stuck, replace a messer or rapier, and restart you would find the bind performance the same.
Because the swords don’t have a lot of momentum the only relevant parameters are the force of the blades on each other and the forces of the hand on the hilt. The actual blade design and weight distribution will not change any of this.
Aside: The other possibility is that the sword does not actually perform appreciably differently in a quasi-equilibrium condition, but offers a superior feeling to the user. The property which we did not examine is blade stiffness, and it is possible that Presence in the Bind is used as a proxy for stiffness. Which would be interesting, as stiffness is a measurement which is directly measurable and already a selling point of swords.
Now, not all blade contact is equilibrium. We also need to consider the other case.
The Search, Episode 2: Non-Equilibrium
A non-equilibrium example of blade contact is what happens during the active parrying phase, or when a sword is doing a dynamic movement at high speed. So could Presence in the Bind be a non-equilibrium parameter?
First of all we are going to have to decide what the “bind” is. If you define the initial impact as part of the bind, and that the Presence in the Bind is the ability to get an advantageous displacement, we already have a term for that. The Moment of Inertia is the sword’s resistance to rotational acceleration, or in this case the harder it is for the opponent to stop your sword.
I’m rather unconvinced that Moment of Inertia is actually Presence in the Bind for two reasons:
- While there is no universally agreed upon definition of the bind, by most measures the relatively low blade energy (i.e. after a swing has completed) is a defining feature.
- The Moment of Inertia is a quality that affects every sword motion, and you will notice it’s effect far more in dry handling than you ever will in sword contact.
Presence in the Bind is considered a good thing, and pumping up the Moment of Inertia to accomplish this would lead to swords which are harder to accelerate and hit a lot harder.
Episode III? Non-bind equilibrium
There is one other possible conclusion, which doesn’t fit into the two categories I outlined. If you are a regular SwordSTEM reader you have probably heard me complaining about Point of Balance as a sword measurement on several occasions. It won’t affect the actual bind dynamics appreciably, as the weight of the sword is negligible compared to the forces you are putting on it. And it doesn’t directly equate to how hard the sword hits, that’s what the Moment of Inertia is for. But what it does effect is how the sword feels in your hand(s) as it sits out in front of you fully extended.
If you have two swords that have the same mass and Moment of Inertia they will feel the same when you swing them around. But the higher Point of Balance sword will probably feel like it can add some more ‘omph’ when pressing on another blade, even if that isn’t true. And that is about the closest real physical quantity that could be associated with people’s assessment of Presence in the Bind.
Based on my analysis I think there are only two reasonable conclusions for what Presence in the Bind means:
- It is a way for sword makers to advertise swords which hit really hard using different words to escape negative attention. Be it through stiff or high MoI products.
- It is a term to refer to swords that have a high Point of Balance in relation to their Moment of Inertia. This means that it is not actually indicative of improved bind performance.
- It is a term made up by sword makers to sell more swords, and embraced by sword buyers to make themselves feel better about their sword of choice.
In order to determine if #2 is a real thing, there would need to be a way to quantify Presence in the Bind, and then correlate it with the sword’s Point of Balance. Getting it quantified seems like it could be rather difficult, and my gut feeling is that the endeavor would be a wild goose chase. And the end result would essentially be the same as #3: it is not a meaningful property to assess a sword with.
And if I am voting, lot is cast on #3, and my hypothesis is that Presence in the Bind is a meaningless marketing term. Hot take, you heard it here first. Now go and drive social media engagement with your vocal complaints.