A Discussion of Machine Results by Lord Gawin Kappler, mka Joe Schaffer, Ph.D. candidate in Neurobiology at UNC-Chapel Hill.

These numbers show that rapier spears hit about twice as hard as the rapiers that are typically used on the field in both the maximum case and in the average case. However, without context, these numbers aren't particularly instructive. Ultimately, the question we must answer is, do these weapons cause an increased risk for injury on the field? In order to do this, clearly we must define which injuries we are interested in. If we assume that these spears will be used solely for thrusts (i.e. no percussive cuts), the the primary injuries that we must be concerned with are fractures of the ribs and sternum and traumatic brain injuries (concussions).

Rib Fractures

Before going into detail, it is worth noting that the forces required to break a rib vary somewhat considerably with age, sex, and location of impact. Ribs, like all bones, are a composite of mineral material and collagen protein. As we age, collagen is reduced, making bones more brittle. This effect is likely elevated in older women who are at risk for bone density loss on top of age-related collagen loss. In regards to location of impact, the lower ribs are easier to break because they are not connected to the sternum.

The bulk of the literature surrounding the biomechanical tolerances of human body parts (ribs included) comes from the automotive industry. These studies typically involve striking cadavers with a striking surface that has greater surface area than our sword tips. In these studies, rib fractures are largely the result of displacement whereas impact pressure would seem to be the relevant factor for our weapons. For example, this study (http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3242539/) was able to generate reliable rib fractures at 1200 N (~270 lbs), but also broke some ribs at 400N (~90 lbs). These forces were applied over a reference area of 48 square inches producing a pressure of 1.875 to 6.25 psi. Less scholarly sources from the martial arts community present some strikingly different figures. This forum post was supposedly created based on an out of print report by the Society of Automotive Engineers and claims that 300 lbs of force are required to break a rib ( http://www.bullshido.net/forums/showthread.php?t=5903). This figure falls in line with the first study. Likewise, this article ( http://www.livescience.com/6040-brute-force-humans-punch.html) cites a biomechanics researcher who states that 3300 N of force is enough to break a rib 25% of the time. This figure is consistent with the upper range of impacts presented in the first study, suggesting at least three different thresholds for causing rib fracture, none of which factor in the small surface area of our weapons.

At first glance, we can see that the force values recorded during Llwyd's experiment don't really approach these values with the exception of the hardest shot delivered with the rapier spear (87 lbs) which is close to the lowest threshold recorded in the first study. However, the problem still remains to consider how surface area of the impact plays a role. If we calculate the pressure delivered using our weapons by dividing the force by the surface area of a typical 5/8 in. diameter bird blunt tip (0.31 sq in), we find that our weapons are delivering far greater pressure than the instruments used in the first study or would be delivered by a hand or foot used to punch or kick. Shearing stress measurements might be a more appropriate metric to compare against. The shearing stress of bone seems to be about 51.6 MPa (~7500 psi) ( http://en.wikipedia.org/wiki/Bone#Mechanical), and a study that tested resistance to breakage by loading them lengthwise (http://www.academia.edu/1512529/Structural_Analysis_of_Human_Rib_Fracture_and_Implications_for_Forensic_Interpretation) provides roughly the same figures with the lowest pressure required for fracture being 32.7MPa (~4700 psi). Based on these figures, the pressure of even the hardest blows are insufficient to fracture ribs.

Traumatic Brain Injury

Traumatic brain injuries such as concussions occur due to the acceleration of the head, leading to diffuse damage to neurons. The general consensus is that 70 - 75 g's are required to cause a concussion, though it is possible to experience higher acceleration without experiencing a concussion. There are some indications that this threshold may be lower, however as a contrast to our numbers, high school and college level football players regularly experience impacts at 20-40 g's ( http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2707068/), and have experienced >200g's without receiving a concussion.

To compute the accelerations generated by rapier-field weapons, we need only to know the mass of a typical head and mask/helm Typical heads mass about 5kg, masks about 2kg and helms up to about 5kg. If we convert the highest recorded spear force of 90lb to metric we get 400 N. Using Newton's law (F=ma) we get a maximum acceleration for the lowest mass (7kg for head+mask) of 57.1 m/s^2. One gravity (g) is 9.81m/s^2, so that 90 pound strike would accelerate the head/mask at about 6 g's. This is well under even the lowest threshold found in the reference above.

The measurements of our combat weapons here would suggest that even though the rapier spears double the g-forces that are experienced by the head due to the impact of the blow, that this additional acceleration represents a fairly small increase compared to the generally accepted threshold for causing concussions.


Based on Llwyd's impact force data, we can't conclude that the increased force of impact will directly relate to increased risk of rib fracture or concussions. The hardest shots measured with the rapier spears are close to the lowest threshold for rib fracture presented in the literature, but this lower threshold is atypical of biomechanical studies and may not represent a real threshold value. None of the weapon impacts come close to other thresholds presented in the literature, which suggests that increased impact force is unlikely to increase the risk of rib fracture on its own. Likewise, the findings here don't support a particularly large increase in concussion risk due to the difference in weapons. Impact by the rapier spears more than doubled the acceleration of the head, however this acceleration (~6g's) was far short of the 70g threshold set forth by the literature for causing concussions.

That being said, we already know that rib fractures and concussions occur with the usage of heavy rapier blades.

This seems to be at odds with the findings here that maximal blows from the heavy rapier provide far less force than is necessary for rib fracture and only about 4-5% of the necessary acceleration to cause a concussion. This suggests that either the methods used for the collection of this data are not generalizable to SCA rapier combat or that these data are only presenting part of the story, namely the role that blow impact has. There are other components to the overall force experienced during a fight that this apparatus is incapable of measuring, the most obvious of which is any acceleration by the person receiving the blow (e.g. the person who is struck steps into the blow). The additional force of a person moving forward is likely larger by an order of magnitude. If we consider an 80-100 lb person who i simply falling (accelerating at 9.8m/s2), then we will have 784 - 980 N of force, or put another way, 80 - 100 g's of impact (good thing legs cushion that). Compared against the 6 g's experienced from the maximum blow delivered by the rapier spear, we can see that the weapon impact presents a fairly small portion of the forces necessary to cause a concussion when compared against the forces generated by one or both fencers moving forward. While spears double the forces provided by weapon impact, again, this still represents a smaller addition of force than any movement forward of either fencer.

If we apply this same consideration to rib fractures, it might allow for the higher threshold value for rib fractures (1200N) to be used and still account for the existence of rib fractures when using heavy rapiers. If this is the case, then we still expect that rapier spears would increase the number of rib fractures (since a maximal blow is still enough force), but would not expect them to become the norm (average blow would be insufficient). However, the degree to which this would matter is somewhat tempered by whether the addition of force (due to one or both fencers moving forward) can be considered to be truly continuous or whether it occurs in a step-wise fashion. If it is step-wise, if the steps have a greater difference in force than exists between the two weapons, then we ultimately won't see a difference in these types of injuries between heavy rapiers and rapier spears as long as we rule out the maximum blow force that can possibly delivered by the rapier spears.

That being said, it is possible that concussions occur as a result of forces that are not strictly tied to the impact. The primary factor in automotive rib fracture literature is rib displacement, so one possibility is that rib displacement by our blades is the root cause of rib fracture while fencing rather than impact force. If this is the case, then rapier spears would only increase the risk of rib fracture if they result in fencers striking deeper into their opponent rather than harder. Displacement of the head due to one or both fencers moving towards each other, for instance, isn't tied directly to the initial impact, but could represent a large amount of force (due to the total mass involved). Likewise, we might consider that if the recipient is moving forward at the time, that they would not only add force to the impact, but would also experience a greater net change in acceleration.

We could also consider that this device isn't measuring forces that are necessarily relevant to the generation of concussions. There are several types of concussions that can be incurred depending on the particular forces involved (direct impact, coup - contrecoup, etc), however one type involves rotational acceleration around the axis of the middle of the head. If the types of concussions we are seeing on the field already have this etiology, then we might consider that the forehead and/or chin are serving as a lever-arm to cause rotation around this axis (i.e. the head snaps back). If this is the case, then we'd expect a multiplicative effect on the force delivered by a blow to certain parts of the head (most likely to the top of the forehead/mask and rising shots to the chin). This ratio should be relatively fixed as a ratio of the distance between the rotational axis of the head and the chin vs. the rotational axis of the head and the midbrain. In this case, the increased impacts of both a heavy rapier and a rapier spear would be multiplied by this fixed value and rather than representing a 5% addition of force towards meeting the threshold necessary to achieve a concussion, the rapier spears would be instead doubling it. This particular model would seem to be in accordance with the practice in boxing to tuck the chin, take blows straight-on (rather than upwards) to the chin, and to strengthen neck muscles in order to resist this sort of rotational movement ( http://www.livescience.com/6040-brute-force-humans-punch.html).

When comparing these two weapons there are other considerations to consider aside from these two injuries. For starters, it should be stated that these injury thresholds can be met even without a weapon. Typical boxing punches are around 5000N, so it should be obvious that any fencer who is trying to harm their opponent could deliver a punch using their weapon. However, setting aside malicious intent, we must also consider other injuries that are related to impact force. Obviously by increasing impact force, we will see increased pain and bruising. Likewise we might also see more blows that "hit a nerve" hard enough to deliver temporarily incapacitating pain/tingling/numbness.

Overall, we know that these values indicate that rapier spears deliver approximately twice as much force as heavy rapier blades. While the absolute thresholds necessary to cause rib fracture and concussion injuries due to impact aren't as clear as we might hope, it seems unlikely that even after doubling the force, that our weapon impacts will approach these thresholds for biomechanical tolerances. This seems to contradict our experience with heavy rapiers, as rib fractures and concussions, while rare, do occur. These findings can, however, be reconciled if we consider that these injuries occur for other reasons than impact force. In the case of rib fracture, displacement seems to be a likely candidate, and more testing might be necessary to determine whether fencers will strike more deeply using a rapier spear than with a rapier blade. In the case of concussion, the relevant forces may instead be related to rotation of the head on its axis. It remains unclear whether this type of acceleration would be dependent on impact force or whether it is more influenced by displacement. Measuring this form of acceleration will require a more complicated model than the current testing apparatus.