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Ancient Weapons

The Physics

Why does it hurt when someone gets hit by a heavy object? Let's start from the beginning....

While in motion objects carry quantities called momentum and energy. These quantities tend to be conserved (ie stay the same as the object moves) unless they are acted on by some force. A force changes momentum in proportion to the magnitude of that force and the amount of time that force is allowed to accelerate the object. A force changes energy in proportion to the magnitude of the force and the distance along which that force acts on the object. Because of these definitions we will sometimes find either momentum or energy more useful in calculations.

The energy contained in an object's motion is called its kinetic energy. The energy contained in an object's capacity for further motion is called potential energy. Consider my plan to drop a brick off a building: At the top of the building it will have potential energy equal to the gravitational weight of the brick times the height of the building. The brick is not in motion, and thus it has no momentum or kinetic energy. Now I drop the brick over the side of the building....

As the brick falls it is acted on by the force of gravity. That force, for the amount of time the brick is falling, accelerates the brick and gives it momentum. Neglecting air friction, the brick will have momentum equal to its gravitational weight multiplied by the amount of time it has fallen. Gravity also gives the brick kinetic energy; more accurately, it changes the brick's potential energy into kinetic energy. Again neglecting air friction, the brick will have kinetic energy equal to the potential energy it has converted. When the brick reaches the ground level it will have kinetic energy equal to the gravitational weight of the brick times the height of the building.

To add a twist to the problem, imagine that someone on the ground wishes to catch that brick. The brick has momentum and kinetic energy associated with its downward motion, which must be taken away if you want it to stop. If you wish to take away the brick's momentum you must exert a force on it for some amount of time: a short time will require a large force and a small force will require a large time. Similarly, taking away the brick's kinetic energy means your force will have to be acted on over the course of a distance: a short distance will require a large force and a small force will require a large distance. Remember: the force that takes away the brick's momentum is the same as the force that takes away its kinetic energy. These quantities are not independent of each other, both being expressions of the brick's motion.

At what point does the person catching the brick get hurt? First, we have to keep in mind that this person has a physical height. The upwards distance over which he can exert any force is limited by how tall he is! Second, there is an upper limit to how much force a person can exert without hurting themselves. If the catcher can't exert enough force to stop the brick over his limited distance (and therefore, his limited time), the brick will have kinetic energy and momentum when it gets to ground level.

The ground is typically made up of hard substances, capable of exerting very strong forces. When the brick hits the ground it will stop over a very short time and distance. If the catcher is caught between the brick and the ground that force will be exerted through him! Damage occurs when the force exerted on the brick is greater than the amount of force the catcher's body can exert. Bone and muscle aren't as strong as concrete!

From another point of view, the kinetic energy of the brick has to be converted into another form (or "used up") before it will stop. A kind of potential energy is contained within physical structures. If too much kinetic energy acts on a structure, ie the structure is asked to exert more force than it is capable of, the moving object will take away that potential energy. Taking away that potential energy will break the structure, causing damage to whatever that structure is a part of.

If the person catching the brick slows down the brick over a long period of time and distance before it stops it will have less kinetic energy and it may not cause structural damage. If the person is unaware of the brick and it hits him without slowing down there will be a great deal of force exerted on the brick by the person over a short time and distance. The birck will stop, but will likely cause structural damage to the person.

What's the point?
Granted, the arsenal of available ancient weapons includes heavy objects dropped from above, but this example tells a lot of what we need to know to understand a great number of ancient and modern weapons. Blunt weapons are objects in motion, given enough kinetic energy and momentum to cause severe damage to physical structures. Describing the physics of these weapons makes use of specific sub-cases of energy and momentum, but in the end most physical weapons are a device that requires a human body to exert more force than it is capable of, causing damage to its structure.

The Classic: Blunt Force Trauma
Blunt weapons are usually a hard, heavy object swung in a circular motion or jabbed in a stabbing motion. The end result is that the blunt object has kinetic energy and momentum, and the human body is forced to absorb the impact. These weapons function very much like the brick, causing soft tissue damage and breaking bones. Attempting to "roll with the impact" of a blunt weapon is analagous to trying to catch the brick over a large distance and time, requiring a reduced force in order to stop the weapon. If the body exerts less force it will absorb less impact.

Bladed Weapons
Taking what we know about blunt weapons, we can extrapolate to explain bladed weapons, which rely on the pressure exerted by the weapon, in addition to the force. Pressure is defined as a force applied over (or divided by, in algebraic terms) an area. A weapon applying a constant amount of force over a reduced amount of area will result in an increased amount of pressure. The amount of force a structure can exert is related to the amount of structure involved; an object can exert a large force over a large area, but can only muster a small force if a small area is involved. Decreasing the surface area of a weapon striking an object will reduce the amount of stopping force the object exerts, allowing the weapon to quickly damage the structure by forcing it to absorb kinetic energy. Sharp weapons have very little surface area, and thus are only stopped by very strong objects that can exert the necesary force over that very small area.

Much of the damage caused by on an object bladed weapons is dependent on what specific structure it strikes. Severing internal structures is very serious for biological targets, but using a sharp weapon to attack a strong solid object may not do any additional damage. If the target object is capable of exerting the necesary force over the surface area of the weapon it will not sustain significant damage, just as the person who slows down a falling object before catching it will experience reduced damage. Further, even if the bladed weapon breaks through the surface of a solid object it won't have the same damaging effects as on a biological target. Solid objects have no internal strucures, don't bleed, and therefore won't take as much damage from a bladed weapon.

Pointed Weapons
Pointed weapons function very exactly like bladed weapons. By making the blade into a point you have reduced the surface area even further. A very small amount of surface area is required to exert a large amount of force in order to stop the weapon. Pointed weapons punch through structures easily, but are subject to the same limitations as bladed weapons. Does punching a hole in an object always cause a great deal of critical damage?