Cutting power- cutting ability in swords- a Primer..

[Michael Tinker Pearce]

Let's examine the various factors that influence the cutting ability of swords- just for general education.

The main factors involved in cutting are (in no particular order) Velocity, sectional density, Momentum at the Point of Impact (MPOI,) edge geometry, cross section and sharpness. All of these things inter-relate in a sword's cutting ability.

Energy is important to cutting ability and power. Energy is governed by mass and velocity- with velocity being the most important of these two. Contrary to firearms and impact weapons when attempting to cut through a target you want to transfer as little energy to the target as possible. *The more energy you start with, the more you can afford to expend displacing material as you cut through.* With two swords of the same weight, one would expect the faster sword to have more energy and cut better- right? NO, because there is a lot more to it than that.

Other factors enter into it as well- the ratio of mass to cross section is called sectional density. As an example- if we take a rapier and a viking sword that both weigh 2-1/2 pounds that are both an average of .1 inches thick at the point of impact, the rapiers POI can theoretically be moving faster than the viking sword's as the POI is farther from the point of rotation. However, the rapier will not cut nearly as well- and part of the reason is sectional density. The rapier is the same thickness at the POI, and may even have very nearly identical edge geometry. Being broader at the POI the Viking sword has a much higher sectional density- IOW there is more mass piled up behind the cutting edge, so it has greater momentum (and more energy) at the POI. Even if it transfers energy at the same rate as the rapier it's drawing from a deeper well, so to speak. The rapier cannot be moved enough faster than the viking sword to offset this advantage. Well, not by a human, at any rate...

Swords with a thin cross section at the POI experience less resistance to the cut because they have to displace less material. If they also have good Sectional Density they have a deeper well of energy to displace material. Similarly edge geometery comes into play- a steep angle at the cutting edge means that the sword has to displace material faster which 'bleeds off' energy more quickly as well- so a sword with 'bad' edge geometry will cut less well than a sword with 'good' edge geometry even if all other factors are equal. On the other hand if the edge geometry is too fine, while the sword cuts superbly it is easier to damage the edge. As in all things it's a balancing act- between cutting ability and durability.

So- Katanas are pretty thick at the POI and have pretty good edge geometry but aren't very wide- they have a lower sectional density than Viking style swords too. So why do they often cut just as well? Because of a mistake in our assumptions, actually. If the cross section of a Katana is thicker and it's width when measured straight accross the POI are lower than the broad bladed Norse sword the assuption is correct- but this is not the way that a Katana's sectional density should be measured. True, if you pretend the Katana is a viking sword and use it identically, it won't cut as well. Used properly however, the Katana's edge is drawn through the cut at an angle- the the Katanas cross section should be measured at an angle from the POI. If for example the Katana is drawn through the cut at a 45 degree angle it 'stretches' the width of the Katana. The Kat's Sectional Density should be measured across that 45 degree angle. If the Kat has a nominal width of 1 inch at the POI, measured across the 45 degree angle it has a width closer to 1.4 inches- consequently more mass is involved, and this raises the effective sectional density at the point of impact. Within limits the shallower the angle of impact at the POI, the greater the sword's effective sectional density. Striking with the edge at 90 degrees to the target it loses this- hence cuts less well.

Broad, flat-bladed swords are design for optimal cutting when the blade impacts the target at 90 degrees (roughly.) Katanas are designed to for optimal cutting when the edge is moving at an angle to the point of impact. Both methods work for same reason.

What's left? Right, sharpness. All other things being equal, sharp things cut better than dull things. A dull edge transfers energy to the target faster, resulting in a shallower cut. 'Nuff said.

I hope that you were all paying attention, as there will be a short quiz next period.

[D. Opheim]

Great post Tinker!

In referance to a katana, here is a link that has some pics to help explain (or cheat on the test ). I didn't want to "cut and paste" without permission from the author.

http://home.earthlink.net/~steinrl/niku.htm

[Al Massey]

...many of the Viking grips, like talwar grips, are very close-fitting with large, wide angles and do not allow a lot of wrist rotation. This almost ensures that strikes will almost always come in at a bit of an angle. I can't believe this was totally unintentional.

[Michael Simmons]

Very educational, sir!

As I have used my swords, I have noticed that they cut differently depending on how they were used... now I know why.

The funny thing is, most of what you have said is fairly common sense, in retrospect.

--Michael Simmons

[bill tsafa]

this and ophims post are very good. thanks

[bill tsafa]

I had never concedered the effact of drag that a wider balde would have through a cut.

My norman sword has a blade very similar to a viking only longer. 33 inch blade, 2 inches wide , qurter inch fuller running the whole lenth of the blade. single hand with wheel pomel.

I was wondering what effect a wide fuller would have on reducing drag. Such a design would seem like an ideal way to maintain in enough width in the blade to give it energy to fuel a deep, while the wide fuller reducing the surface area. If this is so, then we have stummbled opon another advantage of a fuller, other the reducing weight, that is not commonly known.

[Jim Mearkle]

A lot of people seem to underestimate the cutting capability of a rapier. Some friends of mine experimented with a beef roast and a cheap MRL rapier. Like many, they thought a tip cut would just be an annoying scratch. Imagine their surprise when they found a wrist flick had cut six inches into the roast!

A rapier cut may not sever bones, but anything in front of the bone would be neatly dissected. Things like biceps, pectorals, trachea, etc.

[bill tsafa]

yes i think the rapier is somewhat underestimated. Even if you don't put a sharp edge on a blade, if you strike fast enough it will cut into soft flesh.

I think the rapier can be extremly effective against any other sword because of its reach and speed. But you looses its effectiveness on a battlefield when even light leather armor is worn. No sword could easily break it but the user may break it or bend it himlself if you smashes it against a hard sheild. It is also hard to deflect heavier weapons like pikes, maces and axes.

In a civilian setting, it may be one of the most efficeint swords to use.

[Jim Mearkle]

The farther you hit from the blade's center of percussion, the more energy is wasted by vibration and kickback.

I was planning on looking in my old college physics textbook to see if the term mass/length pops up. If it does, that would help confirm the "sectional density" theory.

[bill tsafa]

Let me clarify my question. About two thirds down the blade the width is 1 inch. Towards the hilt the width is two inches. If i hit at the point that it is 1 inche wide...Will the effect be as if the whole sword was 1 inche wide??? Or does the sword being 2 inches wide further back towards he hilt give it some additiional cutting ability?

[Angus Trim]

Originally posted by bill tsafa
Let me clarify my question. About two thirds down the blade the width is 1 inch. Towards the hilt the width is two inches. If i hit at the point that it is 1 inche wide...Will the effect be as if the whole sword was 1 inche wide??? Or does the sword being 2 inches wide further back towards he hilt give it some additiional cutting ability?

Hi Bill

Too many variables to give you an answer on this.

[Michael Tinker Pearce]

OK- several things. First- Sectional Density isn't really a theory- it's the reason that Main Battle Tanks shoot long-rod penetraters these days. It's why thin, broad-bladed machetes cut certain targets so well. It's pretty well understood.

As to the Black Prince- The increasing width of the sword has an effect on cutting power- if everything else is right it decreases the Polar Moment of the sword, increasing accelleration making it more likely that the sword will achieve maximum velocity prior to impact. Also- maximum cutting power depends on other factors as well. Since this sword tapers pretty radically (do you have a pic you can post, BTW?) the decreasing width towards the point may reduce the sectional density enough to cause cutting power to fall off towards the tip. The tip also may become too flexible to deliver optimum cutting depending on the cross section- having not examined the sword I couldn't really say.

Performance will also vary depending on the target media- many swords will achieve maximum cutting power just behind the tip against soft targets simply because the point is moving fast enough to have more total energy than the COP. If the sword is properly configured (profile and distal taper, polar moment, edge geometry, sectional density etc.) this would be expected. However when we shift to a hard target we can begin to overcome the limits of the sword at the tip- it flexes too much for optimum power delivery even if you don't feel it 'kick back.' At this point the tip has more total energy, but the COP has a better ability to deliver energy. In such a case though the total energy is less the strike at the COP delivers more of the available energy to the target, thus cutting better. Of course there are a huge number of variables at work here- without a hands-on examination of a given sword it's impossible to perfectly predict it's cutting dynamics. Even with a sword in-hand we've occasionally been wrong...

What we're trying to do in this thread is lay out the basic factors that cause a sword to cut well or less well. Note the use of the word basic. All of the variables interact with each other, so the only way to achieve easy answers is to take the sword in question and go out and cut things with it and observe the results. Then we have to try and figure out how the variables are interacting to have an understanding of what's going on... Then we can move on to the next sword seeking to improve it based on what we learned from the first sword... Of course you also have to look at what the sword is made to do, and try to figure out how to work with the different variables to achieve the desired goal... If we swordmakers actually thought about all this stuff every time we made a sword we'd probably go nuts- oh, wait... Explains a lot, doesn't it...

[bill tsafa]

Thanks for the response. This is the sword I am talking about:

http://www.by-the-sword.com/acatalog/images/54073.JPG

The tip is a bit too flexible as you said but of all my swords I find this one the quickest and most agile. It weighs about 5 lbs but i can stop it mid stroke much better then a 2.5 lb irish hand and half sword I tested. I think this is an ideal dueling longsword but I was curious how the cutting theory would apply to a sword of this shape and balance.

[Jim Mearkle]

Originally posted by Michael Tinker Pearce
OK- several things. First- Sectional Density isn't really a theory- it's the reason that Main Battle Tanks shoot long-rod penetraters these days. It's why thin, broad-bladed machetes cut certain targets so well. It's pretty well understood.

Perhaps theory isn't the right word. Let's use the word "model" then, as in a conceptual framework used to explain oberved phenomena.

With projectiles, the rod shape is really the only feasible way to maximize the kinetic energy and concentrate it on a small area. With blades, an edge is used to do that, which adds more complications.

Take for example, cutting with a leaf blade. Say our cutter, who we shall call "Cadet Esteban" for reasons we won't go into here, is standing too close to the target and cuts with the narrow part of the blade. The sectional density model says only the blade section at the point of impact matters. Cadet Esteban could be using a light weight hunting hanger and get the same results.

In reality, all that mass hanging out there past the point of impact would contribute to the cut. Not as much as if Cadet Esteban struck at the COP, but it would contribute some.

So for a true measure of the cutting power of a sword, one really must look at the entire sword, taking into accoutn the moment of inertia of the sword, about its point of rotation (not necessarily the center of mass), and also add in the body mechanics of the person wielding it.

So, I'm not saying "section density" is wrong, just incomplete.

[Michael Tinker Pearce]

Dead right, Jim- sectional density is only one of many factors that all work together to make the sword cut optimally. Edge geometry, cross section, moment of inertia, sharpness, node location etc. - all these things interact together to determine a sword's performance. 'Model' is a much better word than theory also.

The thing is that no single aspect can be taken in isolation- they must all be considered together. Thus are headaches born...

[Matt Galas]

Hi, Guys!

Very interesting thread! A few comments:

What you've written certainly corresponds with what I've found in practice. I've done a fair bit of cutting using lead bars as target. I had an English military backsword (ca. 1900) which had a narrow blade at the center of percussion. Try as I might, I could only cut halfway through the bar of lead (horizontal cut from the left). Then, I tried the same cut with an A-Trim hand-and-a-half sword, which was about half again as wide at the COP. Cut right through the lead bar, with half the effort.

If you haven't read it, you should read the excellent discussion of the cutting ability of swords in Colonel Marey's excellent book from the 1840s. He's got some very interesting observations, based on a lot of practical cutting experience. The book is available in reprint from Ken Trotman books in the UK. The French title was Memoire sur les Armes Blanches, or something similar.

[Tomehr Jochnowitz]

Hi all,

Very interesting thread.

You have established that energy retention is important, and that transfer of energy to the target is inevitable - both at the initial penetration of the edge; and through drag, while the blade is traveling through the target. Different cross sections of similar sectional density will perform differently when cutting different materials, and the density and thickness of the cutting medium are factors, too.

This is my theory, using a Dao and Wakizashi with comparable sectional density as my hypothetical subjects:

1) The Dao, with it's thin, flat cross section, will favor well at the initial penetration but drag due to it's wide blade. The Wakizashi, due to it's niku, will have to struggle to wedge through the cutting medium as the ji penetrates.

2) The denser the target (assuming it does not break) the better the thin cross section of the Dao will fare, since it's spine will travel more easily through the path paved by the main bevel. The tough material would hardly peel away from the Wakizashi's shinogi, and would wedge the blade.

3) The larger the diameter of the target the better the Wakizashi would fare, as the aerodynamic boat-tail shape of the mune will allow the target to close in behind the spine. The falchion would suffer of friction along the large surface area of it's sides.

Please forgive me if I carried on excessively or off topic - just glad to join the conversation

[Dane Hendricksen]

Target cutting with a sword is like perfecting your golf game in many ways.

[Sam Anderson]

I like the fuller concept... how about a wide, deep fuller, which decreases weight, increases width and maybe slightly stiffens the length of the blade, while moving some serious surface area out of the cutting path? Does the decreased area make up for the mass-reduction? Or maybe just pound in the fuller, leaving weight and mass similar, but getting everything but the edge out of the way.

[Michael Tinker Pearce]

This is pretty much what was done with Viking style Type X swords- the mass at the tip was reduced however- giving the COP a higher terminal velocity off-sets the lost mass and the increased sectional density and reduced resistance more than off-sets the loss of mass.

[Federico Fain]

Michael,
I am not sure I understand why sectional density should increase if I cut at a 45 degree angle versus at a 90 degree angle (as you mention in the katana example).
This if sectional density can be summed up as the ratio of mass behind a unit of edge thickness at least, which is how I interpreted it.
In my view by keeping the sword straight against the target or angling it to 45 degrees you should cause no change in the ratio fo mass behind each unit of edge "real estate". This because the portion of blade that goes from the POI to the tip ("top of the blade" hereafter, for convenience) already weighs down on the POI even if the sword hits at 90 degrees (perhaps even more so in fact). If I angle the sword at 45 degr. against the POI certainly I cause the blade to be virtually "wider" at the POI, and this means more mass backing the edge, but;
a) as mentioned above, this mass would be backing the edge anyhow, even at a 90 degr. cut. In fact, on a relatively rigid sword like a katana all the energy from the top of the blade will be weighing down on the POI at the moment of a cut, not just the section of blade behind the POI (unless the top of the blade breaks away at the moment of impact it has to). Even on a flexy sword this transfer of energy should be 80% or more.
b) even more interestingly, leverage comes into play and multiplies the weight of the top of the blade at the moment of strike. Part of this will be transferred to the POI.
Let's take the tip for example. Assuming I hit with the POI with a large swing the tip will carry big speed and when the sword stops against the target the mass of the tip itself will too have to transfer its energy somewhere, at the square of its speed nonetheless. That somewhere can only be two places; the POI and the grip (everything else is in suspension). Part of the energy carried by the tip then goes to the POI, which means that if I hold my sword at a 90 degree angle to the target I transfer more of this type of energy to the POI, not less, if my phisycs are not flawed here, because my tip will likely carry more speed against the target due to the wider angle it draws.
Notice that, due to their blade geometry, katanas have heavy tips compared to most western swords.
c) width of the POI is not the only factor to consider when analyzing sectional density, if sectional density, again, has to mean the amount of mass bearing down on each surface unit of edge. A wider blade cuts better because (among the other factors) it carries more weight behind the POI (without making for a thicker edge) due to what's behind the POI and AROUND IT.
In fact, the difference in sectional mass between a rapier and a viking sword, as mentioned in your example, become more evident exactly when you take in account what's transferred down on the POI bY the fast moving part of the blade in its entireness, rather than just by the section of blade at the POI.
Assuming the top half (what moves fast in a cut) of a rapier blade weighs 250 grams, and the top half of a similar lenght (1 meter, for semplicity) viking sword weighs 500grams, a 10mm section (the POI) of rapier blade must weigh 5 grams. The same 10mm section of viking sword blade is more like 10 grams. But what makes the viking sword a formidable cutter versus the rapier is not just the weight at the POI, rather the fact that the mass which is relevant to the POI at the moment of impact is at least the entire top half a meter of blade (500 grams versus 250). And it's when you do the square of 500 grams versus the square of 250 that you get the difference between bone chopping energy or just muscle shearing.
And the katana?
She weighs just as much or more per blade meter, only thicker at the back of the blade rather than broad bladed. Yes, this should make for lower sectional density versus a western sword, but;
a) the edge itself on katanas is, as we know, quite sharp, so the initial ratio of energy transferred per portion of edge real estate is the same
b) true, the katana gets much thicker as it goes through the target, but the progressive wedge shape must compensate here (low drag qualities compared to fullered blades or less progressive profiles). But most importantly;
c) the superior rigidity these swords are known for more than compensates in my view (virtyually no energy is lost flexing the blade).
This rigidity element should not be underestimated because it is really the single most important factor in making the katana a good cutter, even if it's an incidental one (i.e. derived, as some say, from the quality of steel available at the time).
A rigid sword will give you total transfer of energy and waste nothing in vibration and wobblying. So..
d) this may also be one of the factors that often allow, as some say, the katana to cut more easily with the upper part of the blade, compared to many western sword which taper more aggressively and sacrifice some blade rigitidy in exchange of good handling. And what does increase as you move the POI up along the blade? Velocity, clearly, as the closer to the tip you get the broader the arc you draw. And, as you correctly pointed out, velocity is the single most important factor in delivering energy in a cut. And if we assume that the katana cuts even just marginally higher in the blade than most western swords of comparable blade lenght (after all Japanese sword arts practicioners hardly know where the COP on their swords is) I am sure that, even in physics, the increased energy delivered via higher velocity must be more than enough to compensate for and push that big wedge (I refer to the katana's blade cross section here) through the cut, especially after its thin edge opened the cut well and with little energy transfer.

[Angus Trim]

Thread cleaned of non-sword performance related posts. New thread started in Beginners forum for the tire pell and sword shaped crowbar question.

[KayaHan]

Greetings..

This, being my first post to this forum, is to clarify a statement I found in Richard F. Burton's "The Book of the Sword". On discussing the sections of sword-blades, he comments on the wedge angle (p.131-132) as:

"For soft substances it should range from ten to twenty degrees, as in the common dinner knife. An angle of twenty-five to thirty-five degrees, being the best for wood-working, is found in the carpenter's plane and chisel. For cutting bone the obtuseness rises to forty degrees, and even to ninety; the latter being the fittest for shearing metals, and the former for Sword-blades, which must expect to meet with hard substances."

After all said (and very well said) by Mr. Pearce, can we assume Mr. Burton suggests these angles for the best edge retention, and not for the best cutting performance? Or, is there something like a unique "wedge angle for penetration" for each material on earth (like "density")? Please note, here we are talking about the wedge angle only, regardless of the blade shape, length, weight, or sectional density.

I am just trying to understand Mr. Burton..

[Federico Fain]

Burton refers to edge retention and, most importantly, resistance. Obviously a paper thin blade will not only lose its edge when hitting hardened bone or metal, but the edge also could very likely bend or break. Hence his reference to increasing sectional angles as the hardness of the material (or magnitude of intended shearing impact) increases.
Another factor is the likelyhood an edge will get stuck into a dense target if too thin. For example, assuming your woodworking axe has an edge that is unbreakeable/unbendable and has absolute edge retention, you'll still won't want the axe to be table-knife thin as it'll likely get deep stuck into the wood each time you strike, while causing a minimal opening. A wider angled edge won't go as deep but will chop away a lot more wood and get stuck less often.

[Robert Lyle]

I believe it also involves the mechanical properties of the materials attacked (elastic modulus? Yield strength? Sorry, it has been thirty years since I took Materials Science 305). Essentially the entering angle acts as a wedge, and tension from the sides of the cut spreading apart causes a the base of the cut. to tear apart.

A less acute edge forces the material apart faster, putting more strain on rigid material. Soft material yields to less stress, so a more acute edge is used to reduce drag and make a deeper cut.