BONK! - Analysis of Blunt Impact Forces

This article is the first in a very long time (apparently like 2 years), owing mainly to life happening.

Not too long ago, a friend approached me with a question: “How much of a force multiplier is a sword?”, in the context of getting hit by blunt swords during training.

It’d been a while since I did much mechanics, so I set down to answering that question.

24 Sept 2017: Edit to clarify Kinetic Energy/Momentum relationship
11 Nov 2017: Finally fixed the inaccurate statement regarding inelastic collisions, and re-explained a bit. Hopefully this is a bit more accurate.

To Straighten Or Not to Straighten: That is the question!

I was at an event this summer that included an armored deed of arms (read: dudes in full armor fighting as dudes in full armor). As sometimes happens during such events (and really any fencing), a sword bent enough to permanently deform it. A marshal was about to straighten it when a participant called from the sidelines to replace the weapon because after bending it back, it may be more likely to break the next time.

Replacing the bent weapon was a safe call for many reasons, and in my opinion the right call at the time. But how about that breaking part? Let's talk a bit about that and a mode of failure called fatigue.

For the impatient: yes, bending the weapon back does indeed increase the likelihood of failure, especially if it is loaded the same way repeatedly (it likely will be) or has been bent back multiple times. How much it increases the likelihood depends on many factors, but it is a safe play to remove the weapon from use until it can be repaired properly (if it can be at all, which also depends on many factors). Flexible trainers of all types will tend to have a lifetime due to the cyclic loading and and a failure process called fatigue, but that lifetime will generally be fairly long (like years) if they are properly made, used and maintained. However, notches and other surface damage, and plastic deformation of the blade can dramatically lower this lifetime. And the main danger of fatigue failure is that it can occur with little to no warning during the use of the item, unlike most acute failure modes like fracture.

For the patient: read on.

Use of Thrust Study: Protective Equipment Standards Revisited (Part 1)

In a series of earlier posts, I talked a bit about equipment safety standards and how the homologation rules used by the FIE could be useful in constructing a set of HES-specific equipment safety guidelines. However, much of that was very high level as I had no data to back up some of my claims and could not work through some comparisons with the FIE standards. In my posts on effective bending stiffness and blade buckling, I used FIE weapons rules to provide some comparisons with HES trainers but did not discuss their relevance to safety equipment in much detail.

So now that we have some data on thrusts, and that is the major focus of FIE homologation, let's use the data to see what we can learn! In this part, I'll focus on neck injuries and some mask constraints based on the thrust data.

Droppin' Stuff!

Now that the International Congress on Medieval Studies in Kalamazoo, MI has come and gone, I can talk about some tests I did for a good friend's paper at the conference: penetration testing on a reconstruction of the Lubbek Wappenrock. This marks the first real outing of Da Towa, and so this post will also discuss some of the changes I have made and will make in the future.

The post-drop carnage.

What's That Sound?

Since I'm chugging away on a rather detailed follow-on post to the thrust & buckling post, I figured it was time for a fun one… and this time it's one that I'd been thinking about for a while.

Ever heard that metallic ping when heating a metal pan on a stove, or letting one cool? I'm willing to bet most people have.

Ever wonder where it came from?

Effective Bending Stiffness & Buckling Load Update!

Last year, I wrote a post about the effective bending stiffness of flexible trainers and had measurements of trainers I was able to get my hands on at the time. Well, thanks to my good friends at the Chicago Swordplay Guild, CSG North, the CSG 'Southern Expeditionary Force', the Rocky Mountain Swordplay Guild, and the Susquehanna Valley Swordplay Guild, I was able to get a pile more during a recent trip to Chicago.

So let's get down to details, then into the data:

• The measurement process was the same as outlined in the previous post
• I only added arming sword and longsword measurements. Sorry rapieristi and other later-period types: I'll give you all some love once I put together a portable method to deal with all them crazy hilt fittings.
• I decided to calculate the absolute error in the effective bending stiffness, \(EI\), based on the estimated accuracy of my measurement methods. These will be included on the graphs given here. For the FIE ranges, since these were back-calculated, I've assumed the error to be zero (no measurements, no error).
• I also updated the buckling load list, and will include those as well to help put things in perspective.
• I decided to interpret the data based my own personal experience with the weapons based on the Subjective Index of Sparky Skewering Efficacy, or SISS-E, since I found some of the trends interesting.

Bathroom Scale Apparatus Gets An Upgrade!

In a previous post I talked about some unholy things (and by unholy, I mean awesome) I did to a digital bathroom scale so I could make a force measurement setup. Well, I finally arrived at a setup that I was able to use, so I wanted to take some time to document the equipment. The equipment discussed here is the same equipment used to collect the force data in the thrusts and column buckling post.

Here's the DAQ system and a single load cell being tested.

Update 4 March 2014: fixed a typo in the force resolution. It should have been 6 N, not 0.6 N.

Thrusts, Columns and You!

In an earlier post, I talked about determining the effective bending stiffness for sword trainers. Towards the end of that post I mentioned that this quantity, the product of the elastic modulus and the relevant area moment of inertia (\(EI\)), is useful when looking at what occurs when a blade just begins to flex. This sort of analysis can be used to look at how the effective bending stiffness of a trainer can be translated into an equipment safety design rule.

And after the last spattering of materials science related posts, I promised some more classical mechanics. So here we go!

Let's start with a simple and common scenario: a fencer thrusts at a target with a flexible trainer. I'm willing to bet that a lot of the readers of this blog have been on both ends of this scenario.

I won't say which one I am.

From experience, you'll know that the blade begins to flex after contact. Let's look in detail at what happens in that moment.

Update, 4 March 2014: fixed a typo in the force resolution. It should have been 6 N, not 0.6 N.

Update, 14 Feb 2014: I revisited the initial image analysis and found the approximate speed at time of impact to be about 2 m/s (~6.6 ft/s or ~4.5 mph), though this suffers from the same limitations as the other conclusions from the same analysis.

Update, 9 Feb 2014: I went back and repeated the thrust force measurement with my Lichtenauer (same weapon as the test shown), and my Tinker-Hanwei Arming Sword and Longsword. The results for the Lichtenauer were consistent with those shown here. Woot for repeatability. The data from the Tinker-Hanwei swords exhibited similar characteristics as well, but at lower load ranges as expected based on the buckling load work I discuss here. Yay for predictive science! I am still working through the data, but felt this was worth an update.

The 'Temper of Iron'

"He [Fiore Dei Liberi] also longed to learn the temper of iron, of the nature of each weapon and of its aptness for defense and offense." -- Fiore Dei Liberi, Getty MS as translated by Tom Leoni.

In an earlier post we discussed some of the basics of phase diagrams, using the iron-carbon (i.e. steel/cast iron) system as an example. While some talk of heating, heat treatment and quenching came up in the discussion, this is such an interesting and important area I wanted to give it its own space. Besides, Fiore apparently thought it was important too.

Let's first start with the use of hot working in blacksmithing: I am willing to bet that pretty much everyone reading this blog has seen a blacksmithing scene in a movie that goes something like this:

[Dramatic music plays over a dark scene, a Blacksmith, covered in soot with biceps like sacks of melons, forearms like hams, and a beard ZZ Top would be proud of stands before a glowing forge.]
[Blacksmith pumps bellows as flames jump out of the forge]
[Blacksmith grabs glowing hunk of metal from the forge, and begins hammering it madly]
[Blacksmith looks at the piece, and dips it into a vat of water. The water sizzles as steam dramatically rises from the water]
[Blacksmith then plunges the dark metal back into the forge and repeats the process]
[Fade to black, Fade music]

Let's start with why the above process is ridiculous (and not surprisingly, is not done by blacksmiths)

Concept Clarification 3: 'Instantaneous'

I wanted to do something short and fun, and this lets me bring up one of my favorite units of measure... So here we go:

In previous posts, and in many posts that will follow, I'll say things like 'if we assume we did this instantaneously' or 'If we can do this very rapidly' or 'the change happens nearly instantaneously'. On the outside, this seems pretty simple: I'm talking about something happening in a short period of time.

But how short is short? Like so many things I've mentioned: it depends on who you ask.

Alloys, Microstructures and Phase Diagrams

With some of the basics of material crystal structure out of the way, we can move on to a more detailed discussion of alloys and microstructures. Here, I'll focus on the binary iron-carbon system, the most basic components of all steel alloys and cast iron. The solid solution formed is probably the most widely studied system in materials science and one of the most common engineering materials out there. It also makes for an interesting comparison to the common body of knowledge that trades like blacksmithing developed long before the formal background work was done.

It Glows!... Wait. Why is it glowing!?

Everyone probably knows the phrase 'white hot', many people know that steel glows different colors as you heat it up, and a fair few know that some metals don't really glow much even when you melt them, like lead or aluminum. Also, that molten rock (i.e. magma. You know you said that in Dr. Evil's voice) can appear pretty much the same color as hot steel.

Wazupwitdat?

Let's find out.

Effective Bending Stiffness of Flexible Sword Trainers

Right before WMAW 2013, I got to thinking about certain aspects of equipment safety as discussed a bit in an earlier post. Part of this was about starting an on-going investigation into the behavior of flexible sword trainers from an engineering mechanics standpoint. The hope is that it may inform safety requirements for groups and competitions as well as equipment design, and if nothing else be a bit of science-y fun.

This post will focus on the first part of that investigation: the determination of an effective bending stiffness for flexible sword trainers. I'll present data based on weapons I was able to measure myself, and provide the methodology so others may do the same. I'll take any and all data reported to me, cross-verify it where possible and make it freely available here.

Back in October, I made available a pdf of the procedure I'll discuss here, but this post will get into more detail and present more data so should be thought of as the 'real deal'.

Edit, 10 Dec 13: I fixed a sign error in the flexure formula. Signs be crazy, bro.

Introduction to Crystal Structure

I talked a lot about mechanics in my previous posts, but there is another field that is critically important to understanding material behavior. That field is called materials science, and it focuses on the study of the various properties of materials. It's a fascinating field, covering atomic-level structure and bonding to macroscopic behavior such as stress-strain relations and the origins of plasticity. In many ways, the rather general field of materials science owes its origins to the much older field of metallurgy (the study of metals specifically).

So let's talk some mat sci (or materials science, if you're not into brevity… man.), specifically: crystal structure and defects in crystalline materials. As an aside, I'm kind of an odd duck for a mechanical engineer when it comes to this stuff: nanoscale mechanics was my bread and butter for almost a decade. I find this stuff as fascinating as continuum mechanics.

Concept Clarification 2: 'Why?'

In this concept clarification post, I wanted to tackle something part pragmatic, part philosophical. Because of this, don't take this as more than my thoughts on this rather detailed topic.

That something is the question 'Why does X happen?'.

Y U No Cite Books!?

If you've been reading along in my posts and wondered at the number of references to online sources instead of actual texts, the reason is simple:
You'll probably follow a link, but I doubt you'll buy or even borrow about a dozen different engineering textbooks. Let alone keep them handy while you're reading this blog.

For many of the topics I'm covering, the Wikipedia articles are well enough written and good enough for the purposes of providing a place to go get a bit more detail. If you want more than that, go read some books.

Here are some of the texts I regularly consult while working on posts, because they are on my shelf (caveat: some of these are not the clearest or best laid out):

• Belytschko, T. et al. Nonlinear Finite Elements for Continua and Structures. 2003. John Wiley & Sons.
• Callister, W.D. Materials Science and Engineering: An Introduction, 5th ed. 2000. John Wiley & Sons.
• Chadwick, P. Continuum Mechanics: Concise Theory and Problems. 1999. Dover.
• Kreyszig, E. Advanced Engineering Mathematics,  8th ed. 1999. John Wiley & Sons.
• Hibbeler, R.C. Mechanics of Materials, 4th ed. 2000. Prentice Hall.
• Incropera, F.P. & Dewit, D.P. Fundamentals of Heat and Mass Transfer, 5th ed. 2001. John Wiley & Sons.  
• Malvern, L.E.. Introduction to the Mechanics of a Continuous Medium, 1969. Prentice-Hall
• Powers, D.L. Boundary Value Problems. 1999. Elsevier.
• Pettifor, D. Bonding and Structure of Molecules and Solids. 2002. Oxford University Press.
• Reddy, J.N. An Introduction to the Finite Element Method. 2nd ed. 1994. McGraw-Hill.
• Shigley, J.E. & Mischke, C.R. Mechanical Engineering Design, 6th ed. 2001. McGraw-Hill.
• Sims, L. The Backyard Blacksmith. 2009. Crestline Books.

As an aside, The Boundary Value Problems text by Powers is one of the few times I was very happy to have a book written by the professor teaching the class. If you are interested in the topic, it's a great book.

I'll add others to this list as I go, but these cover the basics. I'm missing a basic physics book, a statics and a dynamics book because, unfortunately, I sold those as an undergrad. Luckily, those topics are very well covered by a number of internet sources.

Blogger to me: OMNOMNOMNOM, was Mechanics 101, part 5

Well, this post was going to be a really long explanation of the analysis of our deformable tight-rope support, with some derivations and discussions on some of the finer points of strengths of materials. Then Blogger ate it and saved a blank page. Rather than go through the two weeks worth of work again, I'm just going to skip it and move on to other things.

Lessons learned: don't use browser 'undo' functionality while writing blog. Also: write text of long posts elsewhere and copy it in.

So moving on...

Concept Clarification 1: Strength & Stiffness

I realized that in some of my hurry to get to the fun stuff, I may gloss over some things that are a bit confusing, or I plain forgot to include it. Or hell, I may even have just made a mistake.

These Concept Clarification posts will try to help clear some of those issues up in a short and sweet post. This one will focus on the concepts of Strength and Stiffness.

From bathroom scale to scientific test apparatus

It all started with thinking about how I could instrument my drop tower. More to the point: how I could instrument it without resorting to the thousand dollar setups from places like Omega Engineering. During my search, I came across the affordable button load cells sold at RobotShop.com for robotics and hobby electronics. This one in particular caught my eye, with its 1000 kg-f (9800 N) rated limit. Certainly enough for any materials I may want to test, and even high enough to make a thrusting target for measuring thrust loads.

I kept digging, and learned that the 1000 kg-f load cell I'd found was only rated for 100-1000 kg-f, so any low end force data couldn't be measured. I also found some bathroom scales advertising that they used load cells. One advertised being able to measure a load up to 400 lbs-f (1780 N): for less than half the cost of a big button load cell. So, like any good engineer would, I bought the cheap thing and started figuring out how to make it useful.

This scale has no idea what's about to happen to it.

Why a fuller doesn't make a sword stiffer

"Fullers make swords stiffer"

You've all probably heard it at least once, and possibly even said it. If you said it with me around, I probably made sure you never said it again.

For the impatient: No, they don't. Stop saying it. But kudos for not calling it a 'blood-groove'.
For the impatient who call it a blood-grove: Just stop. Please.

For the patient, read on.
For the patient wondering about hammered fullers and other things, read on... and I'll get to that.