(Ed. This is part of a 5 part series. Comments that indicate a failure to read previous entries shall be mocked and, possible, moderated with extreme prejudice. The author took the time to do the research, you can take the time to read it)
Knowing how much force is required to cause a concussion doesn’t tell us much if we don’t know how hard we are hitting. Fortunately Master Llwyd Aldrydd has created a machine for measuring the force generated by thrusts and has used it to acquire several hundred data points including blows from single-handed rapiers, two-handed swords, and rapier spears. The data he collected is available here for download as an excel document. The analyses presented here were carried out using the data from Pennsic 43 (.xlsx file download) combined with the “second” data collection.
Methods:
A total of 78 fighters delivered a total of 1275 blows using a variety of weapon and blow combinations. Specifically, fighters delivered as many as 3 blows of each of the following types:
- Single-handed strike with a rapier
- Single-handed strike with a two-handed sword
- Two-handed strike with a two-handed sword
- “Harpooning” strike with a two-handed sword
- “Fixed hands” strike with an Alchem rapier spear
- “Pool cue” strike with an Alchem rapier spear
- “Controlled combat” strike with an Alchem rapier spear
However, not all fighters completed all of the different types of blows. The weapons used varied between individuals. For our purposes here, we will focus on only the single-handed strikes with a rapier. A total of 73 individuals delivered 3 strikes with the rapier, for a total of 219 measured impacts.
Results:
Descriptive Statistics of single-handed Rapier strikes |
||||
Blow 1 | Blow 2 | Blow 3 | Total | |
# Strikes |
73 |
73 | 73 |
219 |
Mean(lbs) |
21.93151 |
20.81507 | 20.09589 |
20.94749 |
Std Dev (lbs) |
7.48949 |
7.058046 | 7.888396 |
7.490252 |
Median |
22 |
20 | 19 |
20 |
Mode |
20 |
15 | 19 |
20 |
Min |
8 |
9 | 5 |
5 |
Max |
40 | 37 | 39 |
40 |
The first step in determining what a “typical” blow is like is to explore measures of centrality. In most cases it is sufficient to look at the mean amount of force, which we can see is about 21 lbs. However, median and mode are other measures of centrality that should be considered when trying to figure out what is “typical.” It is frequently the case in statistics that we assume that data follows a “normal” or “gaussian” distribution, in which case, mean, median, and mode should have the same value. If we look at the data above, we can see that both the median and mode are 20 lbs, which is pretty similar to 21 lbs. I have also chosen to show the descriptive statistics for each of the 3 blows separately because it helps to demonstrate that the “total” is, on its face, representative of the three separate blows.
The next step is to look at how much variance is present in the data. For instance, it is possible that one fighter (or group of fighters) were hitting with 5 lbs while another fighter (or group of fighters) was hitting with 35 lbs of force. Or, alternatively, everybody could be hitting with 20-21 lbs of force. These two situations are very different from each other, and so we need to determine how “wide” our expected window of force should be. A simple method for inferring this is to look at the range. We can see above that blow force ranged from 5 – 40 lbs. This value doesn’t really help us to determine whether 5 lb or 40 lb blow were common nor does it help us to determine whether most fighters were hitting with around 20 lbs of force, so instead we need to use a different measurement such as standard deviation. What standard deviation tells us is how much of a difference from the average to expect. The standard deviation in the sample shown above is around 7.5 lbs, which means that we would expect most blows to land in the range of 13.5 lbs – 28.5 lbs.
The standard deviation is, however, still a rather blunt instrument because it does not take into account the shape of the data. A good way to see the shape of our data is to make a histogram that shows the frequency of each quantity of blow force (Figure left). From this graph, we can see that most of the blows did occur within the 13.5 lb – 28.5 lb range centered around the average, as we might have expected.
As noted above, it is typical to assume that data fits a normal distribution for the purposes of modelling, but that isn’t always true. In fact, if we overlay our “Observed” data with what would be “Expected” from a normal distribution, we can see that it looks similar (Figure center), but that it doesn’t fit perfectly (Figure 1 middle). Now, we don’t expect that observed data will ever be perfect, so rather than just looking to see if they visually match, we can also do a statistical test called a chi squared goodness of fit test. If we do so, we find that X2(6) = 15.26,p < 0.05, which means it is statistically unlikely that our observed data follows the normal distribution.
I have also generated a third chart (Figure right) that shows how frequently a blow occurs at or below a given force level. From this we can see that 80% of blows fell over the range of 10-30 lbs and that 60% of blows fell in the range of 15-25 lbs, which helps to illustrate precisely how much more frequently blows were to land near the mean than they are at the extremes.
What does this all mean?
For starters, the data demonstrate that typical single-handed blows fall within a range of around 15-30 lbs, which is significantly lower than the force that we calculated to be required to cause a concussion in our previous article. However, we know that concussions do occur as a result of single-handed rapier blows and so we must conclude that 1) fencers hit harder during actual sparring than they do when delivering blows against the machine and/or 2) other factors lead to concussions in SCA fencing.
Additionally, the shape of the distribution of blow force supports the idea that fencers are exerting control over the amount of force that they are delivering. Fencers were more likely to deliver a blow that was similar to the mean and less likely to deliver a blow at the extremes than we would expect if the data followed a normal distribution, which suggests an active selection towards the center, which is encouraging. However, we should keep in mind that some of this tendency towards the middle may be due to the limited range of the sample distribution. It was physically impossible to deliver blows with negative amounts of force, for instance, and so, compared with the normal distribution, the probability of low-force blows is lower in our sample.
This dataset may also provide us with another way of measuring an “excessive” blow. Currently the rules define an “excessive” blow as one that causes injury. This is problematic for a number of reasons, but the obvious one is that it is reactive rather than proactive and waits until after an injury has occurred to set a boundary. It also sets us up for having more injuries. As you can see above, the amount of force delivered by a blow is distributed over a range of forces. If we were to increase the mean while keeping the standard deviation the same, we would expect that the number of hard blows would increase. Similarly, if we were to increase the amount of variability (standard deviation), reflecting reduced control, while keeping the mean the same, we would also expect that the number of hard blows will increase and of course, if we both raised the mean force and increased the variability, we would expect an even greater increase in the number of hard blows. By setting the threshold for an “excessive” blow as one that is injurious, we are creating a situation where the marshalate lacks the tools to curb an increase in mean force and/or the variance.
Rather than defining an “excessive” blow as one that causes injury a better method may be to define an excessive blow as one that is atypically hard. I expect that in practice, this is how calibration is handled by most combatants and marshals. This approach has the benefit of actively driving calibration towards the mean, and this practice may be responsible for the shape of the data seen here (specifically the greater tendency towards the mean than in the normal distribution).
If we were to use this approach, the next step is to figure out how to define a shot that is “atypically hard.” We can handle this in a number of ways, however two simple approaches are as follows: First, we can calculate whether a blow is likely to reflect the sample distribution and set a threshold value that dictates that the top x% of blows are considered to be excessive. In statistics, a threshold of 5% is frequently used, which would reflect a blow with approximately 38 lbs of force in the current sample. Second, we can treat the problem as a form of outlier detection. In this case, a solution such as the six-sigma method whereby blows that land 6 standard deviations or more above the mean are considered to be excessive. Using the current sample, this would reflect a blow with 66lbs of force. It would be interesting to devise a method to measure the force of a blow and allow a recipient to experience what these levels of force feels like qualitatively. We may be able to do this with a high-speed camera or, alternatively, we could devise a tool that delivers a known amount of force over a cross-section that is similar to our rapier blunts.
Another possible use for this data is in the evaluation of other types of weapons. Llwyd has collected data from two-handed swords and rapier spears delivering a variety of different kinds of blows and it is possible that we could use this data to determine whether these different weapons strike significantly harder than single-handed rapiers. I intend to do this comparison in the near future as part of a separate discussion.
What about cuts?
Sadly, Llwyd’s machine has not (yet?) been used to measure the force of cutting blows. My personal experience with cuts, having now fought C&T in two SCA kingdoms and having some limited experience fighting with HEMA groups outside the SCA is that in general, cuts are delivered with a level of force that is similar to thrusts and that the hardest cuts I have received (ruling out situations where I was actually punched using the guard) are at the very least similar in their level of force to the thrusts that i have received. The society rules for C&T require that blows be delivered with sufficient control so as not to injure opponents and so we might reasonably assume that blow forces will fall within a similar range to thrusts or, at the very least, that cuts will not typically land harder than the hardest thrusts. We could even provide some extra wiggle room and assume that cuts land in a range that is more typical of thrusts by two-handed swords (mean = 26.6 lbs, sd = 9.6, max = 55lbs). In any case, we should not expect that the range of blow forces delivered by controlled cuts should exceed the minimum level of force required to cause a concussion (~100 lbs).
In summary:
The forces measured from thrusts performed using single-handed rapiers are much lower than the threshold we have established for causing a concussion. While no measurements were taken regarding cuts, it is unlikely that cuts typically land five times harder than thrusts, and so we should not expect that either cuts or thrusts will, during typical use, cause concussions on their own. However, the force of the blow may still be a contributing factor in causing concussions, but we must also look towards other factors in order to understand why concussions happen in SCA fencing. These findings should also be considered with the caveat that the human body is certainly capable of delivering the 100 lbs of force necessary and that it remains a possibility that a fighter acting through either gross negligence or through malice can deliver a cut or thrust with sufficient force to cause a concussion.
Pingback: Concussions in Fencing: Part 1 « The Weekly Warfare
Pingback: Alric
Pingback: Gawin
Pingback: Alric
Pingback: Gawin
Pingback: Sigurd
Pingback: Concussions in Fencing Part 4: Techniques for Avoiding Concussions « The Weekly Warfare
Pingback: Concussions in Fencing 5: Armoring Up « The Weekly Warfare