In this post, I intend to exhaustively define three terms with regard to defensive bladework. These three terms are penetration, width, and parallax. These are working terms, largely because I can't think of better words for the concepts I want to express. These are three concepts which represent trade-offs you can make - you can trade each for the others.
These are really stupid, simple, and obvious concepts that I haven't seen explicitly enumerated elsewhere. If someone else has explained these, please point me to that resource, by all means. But having an explicit enumeration of these rules is useful, because it lets me draw conclusions.
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tl;dr Summary
- penetration - How deeply your blade penetrates toward your opponent.
- width - How much space your blade usefully occupies.
- parallax - How far over to one side or the other your blade is.
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Slightly Longer Summary
penetration - How close to your opponent your blade is. You gain more penetration as you approach closer to your opponent. In terms of stance, the most penetration you can have is when you are arm-extended, with your sword straight at your opponent, possibly with a forward-lean in there.
width - How much space your blade occupies with regard to the part of your body your opponent wants to stab. The most width that your sword can occupy is when you are holding it in your fist, pointed straight up or straight down. If pointed straight up, you can cover your stomach with your hilt, chest with the strong part of your blade, and face with the weak part of your blade.
parallax - How far out your blade is angled, with respect to your body and your opponent's shoulder. If you don't have very much parallax, your opponent will be able to yield around your parry very easily. In general, people with less reach need to use more parallax than people with more reach. Parallax allows you to defend yourself, even if your opponent uses footwork to circle around your blade.
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Penetration
[DRAWING OF TWO GUYS POINTING AT EACH OTHER, TIPS AND MIDS OVERLAPPING]
When you are fighting someone with a sword, you will approach them. As you approach them, you will eventually raise your sword to match theirs, whether you do this soon or late in the process. Eventually, if you are lucky, you will stab them.
Of the three concepts we speak of today, penetration is the easiest. It bears note in terms of defense, because there is a certain distance past which parries don't matter. If you are standing 15 feet from each other, there is no reason to even attempt to parry. Similarly, if you are touching belly-to-belly with someone, there is no reason to parry there either.
Penetration also dictates what parts of the sword will be effective for parrying, to a certain degree. As you approach, there will be a larger area on both your and your opponent's swords that could theoretically reach each other, with the respective leverage-based advantages and disadvantages.
Penetration becomes complex when we involve stances which hold the sword off-line. Even if we don't directly overlap a sword, a stance in which we could touch our opponent's sword, if we both extended our arms, can be considered to have some degree of penetration.
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Width
When you are fencing someone, there is a specific silhouette that can be injured. In the Spanish tradition, they consider it to be a "left defensive plane" and a "right defensive plane". Personally, I consider it to be an ellipse, because this is more compatible with both Spanish and Italian traditions.
[DRAWING OF A DUDE WITH AN ELLIPSE AND THE RIGHT AND LEFT PLANES LABELLED]
This ellipse is the area that you need to defend from penetration. This is a simplification, but it is a useful simplification that allows us to make assumptions about the absolute most we need to do to defend ourselves.
As I said above, width is the amount of useful space which blocks our opponent's sword. In order to have any width at all, we must have some degree of penetration. That is to say, we need to be able to touch where our opponent's sword could be, if we want to be able to stop or delay its ability to go places.
[ABSTRACT ELLIPSE DRAWING SHOWING VARIOUS STANCES WITH LINES FOR THE WIDTH OF THEIR SWORD AND/OR DAGGER]
The ellipse that is our body can change in shape, depending on how we posture ourselves. A Spanish stance has a narrow, profiled ellipse. Fabris, with his forward-leaning stances, has a very low, short ellipse. In both of these cases, the shape of the ellipse dictates where we need to place the width of our defense, in order to block out attacks.
Of particular note - width can only be considered to be the useful space occupied by the sword. The very tip of your sword, when opposed by the middle of your opponent's sword, cannot be considered useful. This creates some odd cases, where the positioning of your opponent's sword dictates the true width of your defense. If your opponent moves their hand to a place where you cannot place a stronger part of your blade on their blade, they have decreased the size of your effective width.
Width directly opposes penetration. If you are reaching as far forward as possible, you have minimized your width but maximized your penetration. Similarly, if you have your blade perpendicular to the ground, you have minimized your penetration but maximized your width.
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Parallax
This third concept is the weirdest one.
If you are defending yourself, you have to choose how far over your sword moves to parry. If your reach is more than your opponent's reach, you might not have to parry at all due to having more penetration. If your reach exactly matches your opponent's reach, you don't have to parry very much. But the more your opponent's reach is greater than your reach, the more parallax you need to have.
The actual definition of the word, parallax, is the thing that happens when you are moving along. Things which are closer to you tend to move more than things which are farther from you. So, as you move, the thing which is closer to you might move from one side to the other of an object which is farther from you.
By Booyabazooka - Parallax Example.png, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=1335592
This can be used when one is taking a step to the side. If your opponent remains still, stepping to the side will move the position of their sword relative to you, such than an opening is created.
[DRAWING DEPICTING THE TOP PERSON CIRCLING OR YIELDING AROUND TO GET AROUND THEIR OPPONENT'S BLADE]
Similarly, if you have more reach than your opponent, you can move your hand, such that their sword is no longer defending against your sword. You don't need to be concerned due to how far away you are, but you still can touch them due to the fact that you can trade reach for angulation.
The amount that you can angle around your opponent safely is determined by the difference in reach between you and your opponent. Assuming that you are both sword-shoulder forward, this produces a triangle something like this.
The left is a drawing of the minimum angle of parallax.
The middle is a drawing of a cone of parallax.
The right is a drawing of what happens when you start considering the width of the body.
If you perform geometry, then we can find the maximum angle that your sword can approach them at. So, if they block your sword out of that angle, they are guaranteed to be safe. This is what I call the angle of parallax. This is how far out they must block you to be safe from assault.
Assuming a 26-inch arm, the angle of parallax for a fighter with a 37-inch rapier versus a 45-inch rapier is 20 degrees. This creates a cone, which shows how far up, down, left, or right you need to push your opponent's blade in order to be safe from it.
As a side-note, this is more complex in reality. The above assumes a point trying to thrust to a point. Since we are not shoulders trying to stab shoulders, and we have additional body parts, the geometry is a bit more complex. As it stands, fence like a Spaniard or Giganti and keep their blade to your left or right and you'll be fine.
How interesting that the SCA uses almost strictly shorter rapiers than those in the Wallace collection!
[source]
Given that the shortest rapiers tend to be about 35 inches, and point-of-shoulder to quillons-of-blade tends to be about 36% of someone's height, you would need to be more than eight feet tall to have an arm longer than 36 inches. As such, this means that the angle of parallax will never be greater than 45 degrees, assuming we're not fighting with ridiculously short things that almost can't be called swords any more.
Lastly, if you can get to a place where your hilt pushes their sword onto your cone of parallax, while simultaneously angling your tip in, you can stab them safely. yay!
I have created a spreadsheet for calculating the width of the minimum and maximum cone of parallax, given your arm and blade length.
The minimum angle of parallax is what I have depicted above - the minimum amount that an opponent with more reach than you will be able to angle around your blade, at the point where you can reach them.
The maximum angle of parallax is how much they will be able to angle around your blade when your blade is stabbing them - you can use this to determine how far you have to move around your blade to make sure you are defended as you stab your opponent.
Again, this doesn't take into account the width of your body, or the depth of your body.
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Bring It On Home
What does that get us?
As it turns out, in order to be a useful parry, we must have penetration in order to block their blade, width to determine how defended we are, and parallax in order to make sure they don't just angle around our blade.
- Penetration is used to work against them just pulling their sword back and moving around our sword.
- Width is used to work against traditional disengages.
- Parallax is used to work against yielding around.
Anyhow, that's all for the moment. Cheers
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