# What is Force Dispersion? And how it keeps you safe from swords.

We know that pressure is what makes a sharp sword cut or stab. But it’s also a really important factor in not getting injured with a blunt sword!

This article assumes you already have an understanding about Force vs Pressure, and Impulse/Peak Force. If you don’t, someone might have already written some equally awesome articles on the subject:

This is an article about modern sparring safety, so all impacts describe blunt weapons.

## Without Protective Equipment

Given that we all know about the difference between force and pressure, we can look at one of the ways our equipment keeps us safe, which is by dispersing the impact forces.

First, let’s think of a bone that runs very near the surface, like the radius.

The radius is very near the surface, so we can almost consider impact with a blunt sword as occurring directly on the bone (ignoring any thin layers or skin/muscle/fat in-between).

One of the most important injury criteria is how much pressure a bone is subjected to. Imagine that the sword impact hits with 1000 N of force — an arbitrary magic number.

 Pressure Exerted Hit with flat* 500 psi Hit with feder edge 4,800 psi Hit with sharp edge 1,450,000 psi

(assumptions at bottom of article)

What a surprise. Hitting edge on with a feder generates way more pressure than with the flat*. And using a sharp sword is more dangerous than using a blunt sword! It’s a good thing you have me here to run the math, or you would have never known.

*The flat is also much less stiff than the edge, so the total force would also be smaller. This makes the edge/flat pressure ratio even higher.

## Force Dispersion

Perhaps you aren’t too keen on any of the above scenarios. The answer is clearly to strap a piece of metal to the wrist.

Why exactly would this help? If you didn’t guess that the answer is ‘Force Dispersion’, you are probably skimming a little too fast. When the sword hits the metal, it will pass all the force through to your arm. But rather than keeping it all in one point, it spreads the load out. Look at it this way:

Going back to our pressure calculations, imagine that the 3mm feder edge is now a whole 4 inches wide. This would bring the applied pressure down from 4,800 psi down to 143 psi, reducing the pressure by 33 times!*

But how do we know exactly how much area the force is dispersed over? It’s somewhat complicated to calculate, and it involves:

• How thick the material dispersing the force is.
• How stiff/rigid the material dispersing the force is.
• What the shape of the material dispersing the force is. For example, curved surfaces will gain ‘strength’ by the way their shape can disperse the force through the object internally.

As for exactly how the pressure is distributed through the object, it’s a complicated task that keeps many engineers gainfully employed. Approaches range from simplified models with approximate calculations, to Finite Element Analysis computer software. If you’ve ever seen a ‘sciencey’ picture with a bunch of blue and red shading, it was probably the computation of a pressure distribution.

*This is a terrible way to quantify a number, but also the most colloquial.

## Combining Soft and Hard

We (should) know that just having rigid gear strapped directly onto you doesn’t make impacts all that comfortable. This is because even though you dispersed the force over a wider area, there is still the exact same amount of force coming through to you. While we can’t do anything about the total impulse transferred, we can add some padding to reduce the peak force you experience.

(If you ignored my earlier advice and did not read the article on I’m not to blame if you don’t properly understand this.)

Which brings us to the best way to design gear: a hard outer shell to disperse the pressure, and a soft inner layer to reduce the peak force. Not a surprising conclusion, given that protective gear is already designed this way.

## Cracked Skulls and Brain Injuries – A Tale of Better Masks

Let’s take a look at two common ‘failure modes’ of the head in a blunt sword impact.

 Failure Mode Cause Key Variable Skull Fracture Too much stress placed on cranial bones. Pressure Concussion Excessive acceleration/deceleration of the brain. Force

We have two distinct ways that the sword will ‘mess you up’. And they are both caused by different things.

1. To prevent skull fractures, we want to decrease the pressure exerted on any given point of the skull. We can best do this by having a rigid covering over the skull, which disperses the pressure generated by the sword’s impact.
2. To prevent concussions, we want to decrease the peak forces delivered on the head. This means that we want to arrange the padding/suspension in such a way that we make the force transfer to the head over a longer period of time, rather than all at once.

There is already one important takeaway from this:

If you want to help prevent concussions, focus on the padding/suspension rather than making the mask more armored!

Now, concussions are a complicated topic and they require a lot of thought. But just from this simple example, we can help make sure we are looking in the right direction. So next time you are thinking about how we can make better gear, keep in mind the concepts of pressure and peak force!

## For physics people

I used the following approximations to get my numbers:

 Quantity Value Method Impact cross section of radius bone 10 mm Guess based on looking at my arm Width of a flat sword 29 mm Albion Crecy @~ 300 mm from the tip Width of a blunt edge 3 mm Ensifer Feder edge Sharp sword 10 um Literature values for mediocre sharpening jobs of knives are typically a radius of 5 um. I used this to ballpark a value.