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My aim with this project was to test the effectiveness of Kevlar in dissipating energy to prevent blunt force trauma. I found the energies of the projectile and the force on impact, but these numbers don’t really tell me what kind of injuries a person would sustain. I wanted to analyze my data to see how much blunt force the projectile would actually cause to a person. However, there is no magic number of newtons or joules that is the threshold because it depends a lot on the size of the person and where they were hit.

 

After some research I found a paper published in 1976 by some scientists and engineers doing research for the Department of Justice on blunt trauma and body armor at the Edgewood Arsenal.[1] These scientists shot large blunt projectiles at goats and noticed a connection between several factors and were able to derive an equation that predicted the level of injury from an impact. The model assumed a direct hit over the liver, as the liver is very large and a likely organ to be damaged by blunt trauma. If the model value is less than 414 then the person has a 0% chance of serious injury. If the value is between 414 and 1451 then the person has a 50% chance of serious injury. If the value is greater then 1451 then the person has a close to 100% chance of serious injury. In the case of the liver, serious injury can range anywhere from a bruised liver to a bleeding liver, both of which are bad.

 

The year before (1975) another scientist also working for the Departments of Justice at Edgewood Arsenal showed that seven layers of Kevlar 29 would stop a .38 caliber round.[2] I will do my tests with a 380 auto round, which has an equal diameter and very similar power to the .38 round used in those tests. I will also be doing my tests using eight and twelve layers of Kevlar, which should be plenty to stop the rounds.

Formulas

KE = ¹/₂ mV²

·      m = mass of projectile in kilograms

·      V = velocity of projectile in m/s

 

 Tr = trauma = MV²/WD

·      M = mass of projectile in grams

·      D = diameter of projectile in cm.

·      W = weight of target in kg

 

Tr = 2 * 1000 * KE /WD

·      Tr  < 414 = 0% chance of serious injury         

·      414 < Tr < 1451 = 50% chance of serious injury

·      Tr > 1451 = 100% chance of serious injury

Results

First I calculated the trauma that would be produced by a projectile just fast enough to break the eggs without the Kevlar. I used W = 77 kg which is about the mass of an average-sized male. (See Table 9.) For comparison, I also computed the trauma for an average-sized female using W = 55kg.  (See Table 10.)

Both male and female have near 0% chance of serious injury if hit by a projectile with enough energy to break the egg at 5cm, without Kevlar.  However, the female is much closer to the border of the 50% likelihood region. At 10cm the male is pretty close to the center of the 50% region. However, the female is right at the border of the two regions, which means that there is a very high probability of serious injury. This shows how a projectile can injure one person much more than another because the trauma it produces depends on the person’s weight.

 

Next, I calculated the blunt trauma caused when shooting projectiles fast enough to break the egg under various layers of Kevlar. (See Table 11.) To do this, I first considered the minimum energies required to break an egg with different layers of Kevlar (See Tables 6, 7, and 8). I calculated how much energy was hitting the Kevlar and how much damage this would cause to a person if the Kevlar did not dissipate any of the energy. I only did the egg at 5cm because I could not generate fast enough velocities with the slingshot to break the egg at 10cm behind Kevlar.

What this shows is that these projectiles would cause serious harm to a person if the Kevlar were not dissipating their energies, but since these are the lowest energies that break the egg, we know only about 27J (KE_R)[3] is actually getting through the Kevlar to the ballistics gel, and 27 J was not enough to cause serious injury (See Tables 12). So the Kevlar is preventing serious injury.

I wanted to compare my results to the scientists who claimed that Kevlar would stop a .38 bullet. I wondered how much trauma would be caused by a .38 bullet impacting layers of Kevlar.

 

One consideration was that the trauma model depends on the diameter of the projectile, but since the Kevlar is dissipating the energy over a larger area, the diameter that is striking the ballistics gel is much bigger than the projectile. In the original goat paper, the scientists did a first test with clay behind the Kevlar and measured the crater created, and used that as the diameter when they shot the armored goats.

 

In the previous tests with the slingshot and egg I found the amount that varying layers of Kevlar dissipated energy on impact. Since I cannot test the dissipated diameter on impact the way the scientists did, I will have to instead use the original diameter of the projectile and the dissipated kinetic energy. Both of these methods should work equally well because according to the formula, doubling the diameter or halving the kinetic energy should do the exact same thing.

This top (Table 13) is what we got based on dissipated energies using the diameter of the projectile. The bottom (Table 14) is theirs using the increased in diameter.

There is a very significant difference between the two sets of data, but this is probably just because our dissipated energies were not completely accurate. I think the problem is due to the increased mass, and therefor increased momentum, of the steel ball we fired from the slingshot. This most likely cause the projectile to push far enough into the ballistics gel to physically crush the egg, instead of breaking the egg with the pressure wave. This would cause the dissipation values to be too low and therefor our blunt trauma to be too high.

Conclusion

These results tell us quite a few things. They show that injury from blunt trauma is very dependent on the weight of the person getting hit. They also show how good Kevlar is at taking otherwise potentially lethal impacts and making them far less damaging. But most importantly they show how our tests with 5cm and 10cm gel blocks compare to actual impacts on people. The truth is, they aren’t perfect; the 5cm block egg is too easy to break, and the 10cm egg is too hard to break. The ideal depth for these tests would probably be somewhere around 7cm, but due to the limited power of out slingshot, we have no way to test this. Our best bet for testing with a .38 caliber bullet is to use the 5cm block with 8 and 12 layers of Kevlar. If my hypothesis is correct, the 8 layer test should break the egg, but the 12 layer test might protect it.

[1] United States. National Institute of Law Enforcement and Criminal Justice. Department of Justice. Body Armor: Blunt Trauma Data. By Victor R. Clare, James H. Lewis, Alexander P. Mickiewicz, and Larry M. Sturdivan. 1976. Print

[2] United States. National Technical Information Service. Department of Commerce. A Method for Soft Body Armor Evaluation: Medical Assessment. By Michael A. Goldfarb. 1975. Print. 

[3] KE_R = KE * (1 -  fraction dissipated by Kevlar layers)

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