In order to understand the ability of a building to absorb a projectile hit one must understand momentum and the transfer of energy between the building and the projectile. This transfer of energy is generally called the conservation of momentum. Momentum is a property that relates to mass and velocity of a body (or object).
A body moving at a certain rate requires a certain amount of force to stop it. For example, a train travelling at 2 meters per hour is a lot harder to stop than a bullet travelling at 1000 meters per hour. This is due to the mass of the train being larger than the mass of the bullet. And if you were fixed in space, and you were hit by a train you would be instantly compressed. The only reason people survive being hit by cars and trains is due to a brief contact, in which a car or a train transfers its momentum to the person and the fact that the person is not fixed in space
momentum = mass * velocity
Since velocity is a vector quantity and mass is a scalar quantity, momentum is also a vector quantity. What this means in laymen’s terms is that the direction of the hit relative the building surface is critical in the buildings ability to take the hit. The momentum is a function of sin of the direction of the hit.
Conservation of Momentum
The law of conservation of momentum is used in the computation of collisions between objects. What that law states is that after a collision between two objects the momentum is conserved. It may be transformed, but it will still exist. But, momentum is only conserved if there is no friction in the game world, which would translate to loss. The formula for conservation of momentum is the following:
m1V1 = m2V2
Where, m1 is the mass of the first object, m2 is the mass of the second object and V1 and V2 are the velocities of object 1 and object 2 respectively.To better understand momentum, let’s look at an example.
The momentum of the bullet is
PB = mBVB = (0.00500 kg)(300 m⁄s) = 1.50 kg · m⁄s.
The toughness of a material is its ability to absorb energy in the plastic range. The ability to withstand occasional, stresses above the yield stress without fracturing is particularly desirable in blast rated buildings. One way of looking at toughness is to consider that it is the total area under the stress-strain curve. This area is an indication of the amount of work per unit volume, which can be done, on the material without causing it to rupture. Figure 1 shows the stress-strain curves for high- and low-toughness materials.
The high-carbon spring steel has a higher yield strength and tensile strength than the medium-carbon structural steel. Therefore it would be more resistant to a bullet type impact. However, the structural steel is more ductile and has a greater total elongation.. This illustrates that toughness is a parameter that comprises both strength and ductility. The crosshatched regions in Fig. 1 indicate the modulus of resilience for each steel. Because of its higher yield strength, the spring steel has the greater resilience but would be able to absorb less energy.
It is important to note that these curves are based on a unit volume of affected material therefore the size of the impact object needs to be considered in calculations.