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.

 The Data!

First, let's look at a graph showing all of the data (including the one rapier I've measured):

All trainers measured up to 1 April 2014, ordered by effective bending stiffness. Error bars are estimated absolute error due to measurement error. Orange are arming swords, blue are longswords, purple are 'other' and green are the FIE weapons ranges.

Some notes about the data:

• For the second Darkwood Armory Scrimatore, I note 'shifted?' because the difference between the first and second seems within my measurement error. Thus, I attribute the difference in the stiffness to the weapon shifting during measurement (possibly either the bench it was clamped to, or the weapon itself). But for this comparison, both are still pretty reasonable.
• The Knightshop Rawling's Synthetic Longsword I grabbed was pretty beat up (noticeable kinking in blade), and appeared to possibly plastically (if only slightly) deform under the ~310 g-f load I placed on the point.  I label it with an asterisk because it is possible it would be an outlier if I had more samples of that trainer type.
• The error bars get larger as you go up in stiffness because of the smaller displacement measurement. In short, if your measurement is close to the error size, the more any variations can impact its accuracy.

Now let's talk observations. We continue to see a trend in the effective bending stiffness with weapon type: with a couple of outliers (the Hanwei Gen IV practical arming sword and the Rawlings Synthetic Longsword), the longswords tend to have higher bending stiffnesses than the arming swords. If you recall my previous post on this topic, I discussed how this is not surprising, as the deflection increases with length if you keep the bending stiffness and applied load the same. Really, it's the buckling loads (and the strain energy associated with the buckling) that are important but they are dependent on the bending stiffness. So let's see what happens when we look at the critical buckling loads, assuming we've got pinned-pinned boundary conditions (for more on why I chose this for the comparison, see the thrusts and columns post). Note that the data in the following graph is now sorted by the magnitude of the pinned-pinned buckling load (\(P_{cr}^{p-p}\)) - the order is indeed different from the bending stiffness data above.

Pinned-pinned critical buckling loads. Orange are arming swords, blue are longswords, purple are 'other' and green are the FIE weapons ranges.

For myself, having been hit by a thrust from all of these at some time or another, this last graph is quite interesting. Based on the Subjective Index of Sparky Skewering Efficacy, or SISS-E, the above data tells me that there's a break point around 400 N: for weapons with \(P_{cr}^{p-p}\) greater than 400 N, these are all weapons I prefer for armored combat, or to not use at all for fencing unless with people who I trust to have a good deal of control (the Swordcrafts being nearly rigid in the thrust and having a very thick blade making certain binds strange, I prefer to not even use for drilling). Below 400 N, but above 300 N, fall my preferred general-use trainers for both arming swords and longswords. It's also worth noting how much higher that force is than the FIE ranges, something that will get discussed more in a later post.

By comparison to the effective bending stiffness plot, we see that the buckling load range includes essentially 2 ranges of bending stiffness: one for longswords and one for arming swords. This is due to the dependence on length in both the bending stiffness and the buckling load. My SISS-E preferred range of longsword bending stiffnesses for general fencing apparently falls between about 10-15 \(N*m^2\), while for arming swords for general fencing it falls between about 8-10 \(N*m^2\). Of course, this is all just my personal preference but having now looked at a wider range of weapons it is interesting to see the trends I'd anticipated supported. It would still be interesting to look at popularity by purchase number and reported preference. And I've yet to come close to the broad number of trainers in use in HES today. So send in yer measurements! Well, that or send me swords.