# Punches Hit Harder Than Cuts?

I was watching someone have some fun punching a pell before gearing down, and I noticed something very interesting. The base of the pell was rocking considerably more than when the same pell is hit by a sword! How can this make sense? Don’t we use swords because they can do more damage?

## Peak Impact Force

When a sword hits, the impact is quick. This means a rapid deceleration, as the sword is moving fast and is stopped in a very short period of time. And, as we know from Newton’s First Law of Motion, the way we get a deceleration is by exerting a force against a moving object – in this case a contact force between the sword and the target at the point of impact. The sword strike generates a lot of force when it hits, but the important part of this paragraph was right at the start: this impact is quick. The force between the target and sword doesn’t exist for a lot of time.

A punch, on the other hand, has a much lower peak force than a sword strike. However the impact will last longer, as the momentum of the puncher’s body is transferred into the target. Illustrated this looks like:

On first glance you will say, “Duh, the sword hits harder. That’s why swords beat fists in real life.” Nothing shocking here. This peak impact force is what is going to do things like break bones in a sparring environment.

## Sharp Impact

I’ve been talking about peak force but what really breaks bones is peak stress. We remember from previous SwordSTEM articles that Stress = Force / Area. A blunt sword edge already has a much smaller area than a fist. This means that in addition to producing a higher peak force we also get an even higher peak stress, due to the even smaller contact area of the blunt sword edge. And if you reduce the sword’s surface area even more by, say, making it sharp, the stress goes through the roof. So high that the flesh and bone can’t withstand it at all, and the sword just moves right through.

## Momentum Transfer

Thus far I’ve established that:

1. Swords have higher peak force than punches.
2. Blunt swords are more likely to break bones than punches.
3. Sharp swords are more likely to cut through people than punches.

All very profound conclusions. But another important quality is the amount of impulse the impact delivers. Impulse is a fancy word for a change in momentum. If you have a high impulse impact there is a lot of momentum transferred.

The momentum transfer is equal to the peak force multiplied by the time a force is applied. If you have a constant force the math is easy, but for a more realistic force-time curve it is not so simple. Fortunately we have the magic of calculus to help. Below is the same graph of peak force vs time that I showed earlier. To the right is the same impact, but the amount of momentum transfer is plotted instead.

You will see that the sword impact imparts very little momentum, a quick blip and then nothing. The punch, on the other hand, has a much longer impact time. Which allows it to transfer a significantly higher amount of momentum. Or we can think of it another way: if you want to give someone a boost on the swings, do you give them a push or a punch in the back? The punch is a poor choice even without considering the social ramifications; the boost in swing height will be marginal. A more steady push will deliver a lot more momentum.

## Injury Mechanisms

An impact can injure in two ways, and quite possibly both at the same time.

• Peak Force
• Momentum Transfer

Most of our HEMA protective equipment is designed to protect us from the peak force. A high peak force will fracture your skull, an injury which I can’t think of a single case off the top of my head. Transferring momentum to the head, on the other hand, will lead to a concussion. Something I can think of too many examples off the top of my head*. (This is also why making the mask shell harder won’t prevent concussions, but if we had a fractured skull issue that would be the solution.)

*Both my editor and I agree there has to be some sort of joke connection in a paragraph that mentions skull trauma, concussions, and the phrase “off the top of my head”, but neither of us has managed to put one together.

This, for the most part, makes sense. A sword is optimized for cutting rather than bludgeoning; if you want to bludgeon there are much better choices in the medieval weapons arsenal. Coincidentally these are also ones you don’t see high intensity sparring with, as our equipment isn’t designed to deal with these kinds of impacts.

You will also be imparting a different level of impulse depending on where you hit on the blade. When you strike near the tip the blade is moving very quickly and can generate a very high peak force on contact. But the impulse is low, as you don’t have to stop the whole sword dead. The protective equipment disperses the peak force, and the wrists buckle to some degree allowing a lot of the sword’s momentum to not go into the target.

If you strike closer to the cross, and center of mass, the sword will slow itself much more when it hits the target, rather than trying to follow through. And this impulse must, naturally, go into the target. In the article Swords in Space: The First (?) Frontier I compared swinging at a pell with, and without, releasing the sword right before impact. When I released the sword you can see it still follows through without slowing down too much. If I repeated the same swing while striking close to the cross the sword would basically stop when it hits the pell. (I did do this for curiosity’s sake, but the video didn’t have a place in the article and has since been lost.)

This is why strikes that hit close to the cross are more likely to do things like cave in a mask. When a strike hits the mesh, the force is dispersed from the strike area into the mesh all around it. Typically this is enough to repel the force of the impact, and our mesh is undamaged. However if we strike on the strong, the sword can’t ‘pass by’ the mask, the mask is now tasked with stopping the whole thing. And thus this large area of mesh that is dispersing the force still isn’t enough, and the whole thing must deform.

Side Note: Both cases assume full arm extension, which increases the center of rotation and the angular momentum of the blade. If you pull your arms in you both strike closer to the tip, and decrease the angular momentum of the strike. I have an article on arm extension in cutting, so I won’t get into it here.

## Thrust

A thrust is a little bit different, because it doesn’t have an angular momentum component and always strikes with the point rather than somewhere along the blade. (I’ve been trying to popularize “false edge thrust” as a term for pommel strike, but I don’t know if it’s catching on yet.) But what we can affect is the apparent momentum of the sword.

When a thrust lands it can have:

• The momentum of the sword
• The momentum of the sword + arms
• The momentum of the sword + arms + body

It should not be shocking to you that as we add more mass we are going to get more momentum. And hence more impulse is required to stop it.

This isn’t unmitigatable. If you allow your arms to bend by relaxing (breaking your structure) your arms create a kind of “crumple zone”, disconnecting the momentum of your body from the sword, and allowing you to stop yourself with your feet rather than their face. This is basically the same as throwing the sword at them, rather than driving the thrust with your body.

Fun Fact: If you thrust someone hard enough to knock them off their feet, a more flexible sword doesn’t make that momentum transfer go away. It just spreads it out over a longer period of time and allows people to regain their balance/stop their momentum as the impulse is being transferred.

## Wrapping It Up

Our HEMA gear is pretty good at force dispersion, but where it is weak is in dealing with a ton of impulse. Which is okay! We have to make some sacrifices for mobility, and all in all this is a good one. There is no avoiding the fact that we are trying to swing our swords as fast as possible, and when you swing that fast there is a lot of energy in the blade. Which is why we have gear and not “control” (The Myth of Control). But needing gear to mitigate impact peak forces is different from having to gear against someone throwing their whole body weight into a blow.

That is also why the baseball bat swings that brutalize the hell out of our ribs work poorly when used against cutting targets. There is a ton of momentum in the strike, leading to a ton of impulse in the impact. But that is a blunt impact, and not a sharp one. It’s not even more “martial”, as increasing the effectiveness of a sharp blade is dictated by controlling the cutting plane. It’s just an increase in partner wear and tear for no reason.

TL;DR:

• Swing your sword like a sword and it will be safer in sparring. Use good cutting mechanics rather than good clubbing mechanics.
• Relax your arms and grip before impact to lessen the connection between your body and your sword.
• Adding more armor to a mask doesn’t prevent concussion. It prevents skull fractures. You need padding/suspension to prevent concussion.

(caveat emptor: “don’t swing the sword so hard/fast” is also used by people to justify their poor structure. It’s funny that it is said by both people who understand cutting very well, and people who understand cutting extremely poorly.)