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Calculating the Energy of a Ballistic Impact

Nov 4, 2022 | Ballistic Resistance

When creating a shielded enclosure, there are numerous calculations that need to be done. Read how estimating the energy of a ballistic impact influences the manufacturing of our blast-resistant products.

What does ballistic mean?

The term “ballistic” is used in mathematics and physics to describe an object in flight and the effect the object has upon a surface on impact. A ballistic object is launched and then flies through a medium with a momentum that carries it through a trajectory in space.

Graphic representing what's a ballistic impact and a projectile.
A baseball ball can be a projectile.

Any object launched in space by the exertion of a force is called a “projectile.” While we typically consider a projectile a weapon such as a bullet or an arrow, the term can be applied to a thrown ball, a ballistic missile, or a diver jumping from a diving board.

At TotalShield, we typically focus on projectiles accidentally launched into ballistic flight in an industrial setting. Examples of this could include:

  • A payload accidentally releasing from a high-speed centrifuge
  • A part becoming dislodged during a rotational test
  • A fragment being released during a high-speed drilling operation
  • A fitting, flange, or gauge being expelled during a pressure test
  • A fan blade being thrown from a fan or turbo
  • A piece of shrapnel being projected from an explosion

Ballistic flight and the energies associated with ballistic impact are well understood and among some of the first areas explored in classical physics, in a discipline called “Kinematics”, or the study of moving things.

Understanding Ballistic Impacts

The purpose of this blog post is to explore the energies associated with a ballistic impact. When a projectile hits a second object, the kinetic energy of the projectile is converted into various other forms of energy such as sound, heat, potential energy, etc. We can collectively refer to these energies as impact energy.

The projectile might bounce backward from the barrier; in this case, kinetic energy is transferred back into the projectile. The various types of impact energies associated with the ballistic impact are unimportant for our purposes. What is essential is ensuring that the projectile does not come into contact with a human being.

If, for example, a projectile pierces a polycarbonate shield barrier and continues in flight, only a portion of the kinetic energy has been absorbed by the barrier, and we would say that the shield has failed.

A barrier pierced by a projectile.

This is, of course, something that we do not want to ever happen with a TotalShield blast mitigation product. That is why we spend time understanding the nature of all the ballistic events that may occur during a customer’s industrial or testing process so that we can design a safety enclosure that will not fail under ballistic impact.

In our terminology, a ballistic-resistant barrier is successful in containment if the barrier stops the projectile. If the projectile penetrates the barrier and travels any distance past the barrier surface, then that barrier has failed containment. As we discussed in our blog post about centrifuge safety enclosures, certain situations require two levels of containment: primary containment and secondary containment. In this case, if a projectile pierces both barriers, we would again say that the barrier or safety enclosures have failed containment.

What is More Important: Mass or Velocity?

We will explore the calculations associated with ballistic impact energies shortly. However, one thing we have frequently encountered during discussions with customers is the question of which types of impacts are more damaging: a small, fast projectile or a large, slow projectile? And which is the more critical consideration, the projectile’s weight or its velocity?

Or, to put the question another way, which would cause more damage to a human being, the impact of a 1-pound projectile traveling at 10 miles per hour or a 1-gram object traveling at 100 miles per hour?

The short answer is that a 1-gram object traveling at high speed is much more damaging than a large object traveling at a slow speed. The table below illustrates the differences in kinetic energy between these two objects:

Object MassObject SpeedKinetic Energy
1 lb10 mph4.53 Joules
1 gram100 mph28.32 Joules

It is an interesting result and perhaps non-intuitive for some. The 1 lb object is 453 times more massive than the 1 gram object. However, it is only traveling at 1/10th the speed and therefore has only 16% of the kinetic energy of the smaller object.

This illustrates that velocity is much more important than weight when determining impact energy. When velocity is the same between the less and more massive objects, the more massive object will contain more kinetic energy. However, as the velocity of the less massive objects increases in relation to the larger object, it will quickly surpass the kinetic energy of the more massive object.

Looking at the equation for kinetic energy illustrates why this is true. The equation can be expressed as:

Graphic showing the equation for kinetic energy.

As the equation shows, the velocity component of the equation is squared, meaning that the object’s kinetic energy increases exponentially as the velocity increases versus only linearly as the mass increases.

As another example of the importance of object velocity in estimating impact energy, we recently had a customer inquire about a shielded enclosure rated for either UL752 Level 3 or UL752 Level 4 impact rating. Many materials are rated with Underwriters Laboratory 752 “Standard for Bullet-Resisting Equipment.” (Find here an extended explanation of polycarbonate impact ratings). While this customer was not using the enclosure for bullets, they were using the rating level as a proxy for their own ballistic objects and assumed that the Level 4 rating was only marginally higher than the Level 3 rating from an impact energy perspective.

We performed the calculation for them and showed that UL752 Level 4 actually involves four times the amount of impact energy as UL752 Level 3. Why? Because even though the projectile used to test Level 4 is less massive than Level 3, it is traveling almost twice as fast. The table below illustrates the impact energies:

UL 752 RatingBullet MassBullet VelocityKinetic Energy
Level 344 Magnum (16g)1485 fps (452.63 m/s)1638.99 J
Level 430-06 (11.66g)2794 fps (851.61 m/s)4228.15 J

Does Size Matter In a Ballistic Impact?

There is a third consideration we must contemplate when analyzing a ballistic impact. The size of the ballistic object also factors into whether containment can be achieved successfully for a given material or ballistic enclosure. Larger objects spread the impact energy over a larger surface area, and smaller objects concentrate the impact energy into a smaller barrier area. Therefore, mass and velocity being equal, a smaller object will have a greater chance of breaching the containment of a ballistic barrier or safety enclosure.

Impact energy over a defined area is known as impact energy density. Higher impact energy densities result in larger forces on a barrier and an associated higher likelihood of containment failure. In our previous example of the 1-pound object versus the 1-gram object, we did not specify the size of the objects. What if they are both 3-inch (7.62 cm) diameter objects but with different densities? In this case, the area of the object impacting the barrier would be:

Graphic showing the equation to get impact energy density.

The impact energy density is a straightforward division of impact energy divided by the area. So in our previous example the relative impact energy densities would be:

Object MassObject VelocityKinetic EnergyObject Diameter & AreaImpact Energy Density
1 lb (453.4g)10 mph (4.47 m/s)4.53 J7.62 cm dia /
23.94 cm2 area
0.1892 J/cm2
1 gram100 mph (44.7 m/s)28.32 J7.62 cm dia /
23.94 cm2 area
1.209 J/cm2

This is what we would expect. The objects are the same size, so the one-gram object with the higher velocity and impact energy has the higher impact energy density. 

However, what if the 1-pound object was significantly smaller? How would this affect the impact energy density? Let’s repeat the calculation above but with a much smaller size for the 1-pound object. Rather than 3 inches, let’s shrink this down to a little under 0.4 inches (1 cm) in diameter. The impact energy density now looks like this:

Object MassObject VelocityKinetic EnergyObject Diameter & AreaImpact Energy Density
1 lb (453.4g)10 mph (4.47 m/s)4.53 J1 cm dia /
3.14 cm2 area
1.443 J/cm2
1 gram100 mph (44.7 m/s)28.32 J7.62 cm dia /
23.94 cm2 area
1.209 J/cm2

We now see that the 1-pound object, when shrunk down to a 1 cm diameter, has a higher impact energy density, meaning it will be more likely to pierce a protective barrier. 

Please note that the impact energy densities of the materials we use in TotalShield polycarbonate barriers are much higher than in this example. These calculations are meant only for illustrative purposes.

This is why our customer analysis of ballistic impact always begins with determining the mass, velocity, and size of every potential ballistic object in the customer’s scenario.

Conclusion

In summary, a ballistic object flies through space with a mass and velocity, and when it strikes a surface, its kinetic energy is transformed into impact energies. The object’s size is used to determine the impact energy density, and this value can be used to estimate the material required to safely and reliably contain the ballistic impact. 
Of course, there are many other considerations for ballistic safety containment beyond impact energy density, so don’t hesitate to contact us so we can help design a solution to keep your people safe.

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