Note: to those that have read our earlier report, this report contains some of
the same data, but also additional information and experiments. It was
combined into one report for the ease of reading of those that had not seen
the first report. Also, the formatting on this report was kept to a minimum
to make it easier to e-mail and to understand in e-mail formats. (This is why
equations are listed twice, if you are reading the formatted copy.) This
report includes the data from our earlier experiment, plus adds two additional
experiments.
Third Revision Notes: This is the third revision of this report. We have
now included figures for 4 oz. leather in our data set. We were initially
unable to locate a suitable leather sample, but have finally found some leather
that is really 4 oz. leather.
Objective:
The objective here is to provide some
quantitative data with which
to answer those questions. To do this, we will measure the energy required to
penetrate various armour substances. Then we will measure the amount of
energy delivered by an attacking fencer. These tests were designed with
certain secondary requirements: 1. To control as many variables as possible.
(For example, while the ground in Texas may still be nice and soft, the ground
near Philadelphia in January is rock solid.) 2. That the test and the
results be easily reproducible. 3. That the data returned is quantitative
rather than qualitative.
This test controls several of the variables that have not been addressed in other tests. The surface behind the sample has usually been "carpet" or "ground". By testing the sample without any backing, we have eliminated any variations in the backing. By using the force of gravity (a constant most places on the planet) rather than person-power, we have created a test that can be repeated with the exact same amount of energy applied to the sample.
What follows is the physics details of the test. Feel free to ignore it if so inclined. Note: if you read the earlier report, the physics contained therein were flawed. This did not invalidate the earlier report, as the conclusions were drawn based on the relative numbers. However, the physics has been corrected for these tests, as we are determining an actual energy value.
When a sample is struck, the blade imparts energy to the fabric. If the energy is more than the fabric can absorb, it tears. The equation for kinetic energy is
K=.5mv^2
where K is the kinetic energy (in Joules), m is the mass of the drop-weight (in kilograms) and v is the velocity of the object (in meters/second). Since we know the mass of the weight, we need to know the velocity at the time of impact. Rather than go through a lengthy discourse, we can also observe that the potential energy of an object is
K=mgh
where m is the mass of the object, g is the acceleration of gravity (9.8 meters/second^2) , and h is the height. This potential energy becomes kinetic energy when the object falls. This is a simple, linear equation. If the distance is off by 1%, so will the energy be off by 1%. This should keep things within a reasonable tolerance of error. With this, we can now determine the energy delivered.
Adding in our constant height of 30 cm, (0.3 meters) and g=9.8 yields
K=2.94m
Test blade: broken foil
Drop height: 30 cm
Weight required
Sample to puncture Energy
1 layer trigger 0.5 kg 1.47 Joules
2 layers trigger 1.4 kg 4.12 Joules
3 layers trigger 1.6 kg 4.70 Joules
4 layers trigger 2.2 kg 6.47 Joules
1 layer denim 1.4 kg 4.12 Joules
2 layers denim 2.3 kg 6.76 Joules
Leather #496, front 2.1 kg 6.17 Joules Leather #496, back 2.6 kg 7.64 Joules Leather #496, wet front 1.9 kg 5.59 Joules Leather #496, wet back 1.6 kg 4.70 Joules Leather #523, front 2.7 kg 7.94 Joules Leather #523, back 3.0 kg 8.82 Joules Leather #523, wet front 2.4 kg 7.06 Joules Leather #523, wet back 2.8 kg 8.23 JoulesFrom conversations with other scientists, we had suspected that the leather would require different energy to penetrate the front (smooth side) vs the back (the rough side). Therefore we tested both, as indicated above. We had also been asked to consider if wet leather was different from dry leather (accounting for effects of sweating, etc.). We also wanted to include some leather samples in these tests, but were not able to get some good 4 oz. leather samples. We hope to add this data at a later time. We also wanted to include some leather samples in these tests, but were not able to get some good 4 oz. leather samples. We hope to add this data at a later time.
Weight required Sample to puncture Energy 4 layers trigger 2.4 kg 7.06 Joules
Weight required Sample to puncture Energy 4 layers trigger 2.0 kg 5.88 Joules
Weight required Sample to puncture Energy 4 layers trigger 2.9 kg (that's a lotta nuts) 8.53 Joules
1. The epee did not penetrate significantly better than the foil.
2. The accepted premise that 2 layers of trigger is about equivalent to one layer of denim seems valid.
3. The factory schlager required about 10-18% less drop weight to penetrate the four layer sample than the foil or epee. This supports the concept that the untipped factory schlager is more likely to penetrate than a broken foil or epee.
4. The weight required to penetrate the sample by flattened schlager was almost 50% more than the factory schlager. This indicates that the untipped weapon can be made much safer by flattening the tip.
5. The weight required to penetrate the sample by the flattened schlager was 20% more than the epee and 33% more than the foil. This suggests that if we feel that four layers of trigger is acceptable protection while using foils and epees, it is also acceptable protection from untipped flattened schlagers.
6. While we did not directly test a broken schlager, we believe that the broken schlager would require more weight to penetrate, since the broken weapon has a greater surface area, and bend is not a factor in these tests.
7. The suede side of the leather does seem to be significantly more resistant to puncture when dry.
8. Note that the supposedly heavier leather failed more easily than the lighter sample.
9. Wet leather does appear to fail at about 10% less weight.
10. The rapid failure of sample #496 back when wet may be an anomaly of the leather.
11. The puncture resistance of leather varies widely, not just between pieces but even on the same piece. We cannot estimate exactly how wide this variance is given our relatively limited sample. A full statistical analysis would be way beyond our Junior Scientist budget.
12. A Free Sample Prodigy diskette placed at the bottom of the sample can prevents repeated punctures of the bottom of the can, and possibly your carpet. While one can postulate that puncture-proof armour can be made from such disks, further testing is needed.
Test blade: flattened schlager
Drop Height: 30 cm
Sample Weight Reaction 4 layers trigger over 2.9 kg "OUCH!!! That's more than I ever Cadet Esteban's thigh (8.53 J) want to be hit with in a bout." Even though Esteban complained, the blade did not punch through any layers of the trigger. This was a really really painful thing, but not damaging to the sample or Esteban. (It did leave a bruise.)
Sample Weight Reaction 4 layers trigger over 0.75 kg "OUCH!!! That hurts a lot, but just Cadet Esteban's thigh (1.8 J) just barely less than the last one." The weight was the weight of the complete weapon. This drop also produced no damage to the sample or Esteban. (A little bruise.)
This demonstrates that the energy required to penetrate a backed sample is
much different than to penetrate an unbacked sample. This then necessitates
an experiment to determine the energy to penetrate a backed sample.
Test blade: broken foil
Drop height: 30 cm
Weight required Energy for Sample to puncture Energy unbacked sample 1 layer trigger 1.6 kg 4.7 Joules 1.47 Joules 2 layers trigger 2.1 kg 6.2 Joules 4.12 Joules 3 layers trigger 2.5 kg 7.4 Joules 4.70 Joules 4 layers trigger 3.0 kg 8.8 Joules 6.47 Joules 5 layers trigger resisted 3.4 kg (10 Joules) Notes: on 1 layer, the puncture went through the fabric and clear through the lamb. On 4 layers, the blade broke the skin, but did not penetrate any of the fabric. Since we were more interested in the condition of the backing than the condition of the armour, we considered this as a "penetration".
Weight required Sample to puncture Energy 4 layers trigger 3.1 kg 9.1 Joules
Weight required Sample to puncture Energy 4 layers trigger 2.8 kg 8.2 Joules
Weight required Sample to puncture Energy 4 layers trigger 3.2 kg 15.0 Joules
1. The results from this experiment largely support the conclusions from Experiment 1.
2. Esteban is a wimp.
3. Some people might be led to conclude that a Leg o' Lamb is a very expensive and wasteful way to perform these tests. We conclude that no price is too high to pay in the name of science. We conducted a further experiment on the lamb, wherein we cooked it up and ate it, and we therefore conclude that it was a damn tasty treat.
4. This test points out even more dramatically that a schlager can be made a great deal safer by flattening the tip. This is a very simple thing to do, and there is no reason we shouldn't require it.
Test Procedure: To measure the energy an attacker delivers, we placed a ball on the end of a narrow pipe so the ball rested one meter off the floor. The attacker then struck the ball at varying subjective levels of "impact". By measuring the distance the ball traveled before it hit the floor, we can determine the energy imparted to the ball. (This may remind you of the rattan calibration test, wherein the fighter strikes a bowling ball off a pipe, and gauges his calibration by how far the ball landed from the pipe. In fact, the concept came from that test, although it is being applied in a quantitative fashion here.)
There are certain factors that will detract from our accuracy. Factors such as air resistance and the friction of the ball leaving the stand will absorb energy. However we believe these factors are small enough to be insignificant in our context, and we will ignore them. Further, when an attack hits the target, there are three places for the energy to go.
1. Back to the attacker to be absorbed (in such things as bending the wrist)
2. Into the compression of the blade (bend)
3. Into the target to be absorbed (absorbed by the target or displacing the
target)
In this test, we will minimize the energy absorbed by the attacker by not
breaking the wrist or elbow. We will also avoid loss of energy by blade
compression, since the target is light enough that it will move rather than
resist the blade sufficiently to bend it. (This also avoids energy going back
to the attacker.) Therefore the majority of the energy will be taken in by
the target and transferred to kinetic energy (i.e. moving the ball). This
should provide us with a concept of the near maximum energy an attacker can
deliver to his target. In the field, we expect more energy to be absorbed
into the bend of the blade and by the attacker. This should be more true with
foils than with schlagers, for example, since the foil will tend to absorb
more of the energy in flex than the schlager will. However, these figures
should be fairly realistic "worst case" numbers.
O
ball start O ---------(-------|\
| | \
| | fencer hits ball
| ---\
| / \
X | / \
|----- d ----|
ball lands. Measure distance d.
What follows is the physics details of the test. Feel free to ignore it if so inclined. Once again, we wish to determine kinetic energy. Consider the equation for Kinetic Energy (K):
K=.5mv^2
where m is the mass of the object and v is the velocity of the object (in our case, the ball). To determine the velocity we can use
v=d/t
where d is the distance traveled and t is the time of travel. We can measure the distance the ball traveled. We can determine the time indirectly, and it will remain a function of the height the ball fell from. Since gravity will pull the ball to the floor at a known rate, we know how long it will be before the ball hits the ground. This time will also represent the time it took the ball to travel its distance from the stand. We know
h=.5at^2
where a is the acceleration of gravity (9.8 m/sec^2) and h is the distance from which the ball fell. Solving for t yields
t=sqrt(2h/a)
And we plug this value of t into our previous equation, getting
v=d/(sqrt(2h/a))
Putting this into our kinetic energy equation gives us a mess,
K=.5md/(sqrt(2h/a))
which we can simplify to
K=.25md^2a/h^2
Now we can add in the value of a and the known value of h which we have chosen of one meter (how convenient!)...
K=2.45md^2
Add the further knowledge that the mass of our ball was .45 kg and we have the useful formula of
K=1.114d^2
which is what will determine our results. Since the energy is a function of the distance squared, we will take care to measure our distances accurately, as any error will be magnified.
Blow: an East Kingdom proper blow (i.e. a touch calibration). Each blow resulted in the tip ending up about one inch past the center of the pipe.
Distance Energy Note 44 cm 0.22 Joules 51 cm 0.29 J 51 cm 0.29 J "Southern region calibration" 36 cm 0.14 J "Carolingian calibration" 47 cm 0.25 J
Distance Energy Note 62 cm 0.43 Joules 56 cm 0.35 J 68 cm 0.52 J
Distance Energy Note 76 cm 0.64 Joules 84 cm 0.79 J 82 cm 0.79 J
Distance Energy Note 145 cm 2.34 Joules These were painful just to watch. 148 cm 2.42 J 153 cm 2.59 J 153 cm 2.59 J 158 cm 2.76 J
Distance Energy Note 198 cm 4.37 Joules 223 cm 5.57 J
Consider that when the attacker attacks, there are two things that make up the velocity of the tip; the speed of motion of the attacker's body, and the speed of the attacker's extension. But when we consider the motion of the target, the speed of the defender's extension is not relevant. We are interested in only the speed of the target's body. So what we have is (velocity of attacker's body) + (velocity of attacker's extension) + (velocity of target's body). If we say that the fencers are moving at the same velocity, then the energy is proportional to (2(velocity of fencer)+(velocity of extension))^2. Solving this equation gives us a mess that is not very illustrative without further guesswork. So let's guess that the speed of the lunge and the speed of the extension are about equal. This means that the moving-target scenario delivers 2.25 times the energy of the stationary-target scenario.
We are making a number of assumptions here. In order to try to add some hard evidence to this theory, we wanted to collect data on the energy from extensions only, and from lunges only, and from a combination of the two. Unfortunately, we were unable to make any measurements of this kind that we could have any confidence in. We are therefore left only with the guesswork above.
Blade Flex: It might seem we have apparently chosen to completely ignore the effects of blade flex in all our experiments. You may also believe, quite correctly, that blade flex is a very significant factor in the field, and should not be ignored. However, these tests have not ignored the issue of blade flex, but rather have addressed its importance by controlling it. We all know that the more flexible the blade, the less of an impact it makes on it's target. In terms of these experiments, this translates to "the less energy transmitted to the target." These experiments have been conducted with the worst case in mind. We all have had instances where the blade did not flex, or did not bend the direction it was supposed to, resulting in a much harder hit. Truly if we are looking for a minimum standard of safety, we must account for these scenarios. Therefore, the attack figures indicate the maximum energy a target could receive from an attack. This number represents a maximum threshold, and field conditions will provide their own margin of safety, as things like blade flex and breaking wrists absorb energy that would otherwise reach the target. Further, when we consider the more dangerous situations (a broken blade or untipped schlager) we know the blade will flex less, thereby underscoring the need to look at the worst case of energy delivery.
1. Experiment 3 did not work out anywhere near as well as we hoped.
2. From our experience conducting these tests, it seems that the amount of energy delivered by an attacker will remain fairly constant regardless of blade. However, we know that in the field, the target will resist the blade, and hence more energy will be absorbed in blade flex. So while these numbers offer insight into the energy delivered by an attacker, they are not an absolute gauge of the energy that a target (or his armour) must resist.
3. The huge pan of kitty litter on the floor was a source of some interest to Thomas' cat. Such a pan should not be left unsupervised for any length of time.
4. There are not a great many conclusions to be drawn from this data, but it does add a good deal of perspective for the other tests, and for our overall conclusions.
1. As expected, it takes a great deal more energy to penetrate the backed sample than the unbacked sample. From the data, we can generalize that it takes about 50% more energy to either penetrate the armour or break the skin of the meat. (We should point out that all of us had the screaming heebie-jeebies at the thought of personally getting hit this hard. Something about the meat just made it too easy to put yourself in its place.)
2. The maximum energy we could generate from an attack (in Ex. 3) was 5.57 Joules. It took us 8.8 Joules to "penetrate" 4 layers of trigger over meat with a broken foil, which is 60% more than we could deliver in an attack. It took us 8.2 Joules to "penetrate" with a factory schlager, which is still 50% more energy than the attack.
3. It is interesting to note that in Experiment 2, when using 4 layers of trigger, we never penetrated any of the layers of trigger before we broke the skin of the meat. While the extra layers certainly offered better protection, it seems that human body will probably fail before the armour tears. We also wish to note that just because a blow did not penetrate the skin doesn't mean the target wasn't going to be in a world of hurt. (Cadet Esteban proved that sufficiently us, but watching the blades hit the meat certainly drove the point home.)
4. Dylan and Thomas have way too much time on their hands. Clearly the East need to schedule more tournaments in the winter months. 5. We believe that four layers of trigger is adequate protection from penetration injuries from any of the blades tested. (We would add the caveat that we still feel that flattening the tip on a schlager makes the weapon much safer.) We do not feel we can draw a meaningful conclusion regarding leather beyond the equivalence between 4 layers of trigger, and the leather samples we tested.
6. The penetration resistance of an unbacked sample appears to be well related to the penetration resistance of a backed sample. This means that we could develop a reliable method to test armour without keeping a leg of lamb in your fencing bag. We hope after further testing that we can propose a new standard punch test.
Editor's Note: In accordance with the Society for the Prevention of Cruelty to Cadets, the editors wish it known that no actual cadets were harmed in the collection of this data. Esteban is in fact a fiction created by the authors to cover the fact that they were stupid enough to drop untipped blades on their own legs in the name of science.