The+physics+of+weapons

__Weapons and the physics behind them__

__How we know about them__ Accounts of weapons are given in poems and ancient stories such as the Iliad. Also, much of what we know about Greek vessels is given credit to documents of instruction telling how to make them and how much red paint one needed. We know about weapons from many works of art such as pots, murals and statues. The other way we can know how a weapon worked and the effect it had can be determined from wounds on skeletons and mummies.

__Math in weapons__ Almost every weapon in the ancient world require math to invent, and all modern ones do. One of the most math involved weapons were the (in chronological order) Whip, Egyptian battle ax, slinger, peltast, trireme, sambuca and helepolis, which are all innovative and successfully effective weapons.

The trireme

Greek vessel all the way from the early pentekometer in the Trojan War to the late decrees in 0AD relied almost entirely on human oar power. These oarsmen were not slaves as is commonly assumed, but highly trained professionals. They were stacked row by row alternating on top of each other to fit as many of them as possible in a length-wise section of the boat. They then rowed on the oar which fitted through a hole in the side of the boat and extended a far length to the water. The longer the oar was from the side of the boat to and the shorter inwardly the more power they had to use when rowing, but the less large their stroke had to be. This is because the shorter the part of the oar on the side where the force is applied the more the force has to be, the equation being: LP=F and as for the conservation of momentum, the more the force the less the movement. So, if a rower had an oar of which 2 meters where on the inside of the boat, and 4 meters on the other side of the fulcrum (in this instance the side of the boat), when he raised his side of the oar 4 feet, the other side would lower 8. This principal of the lever and the combination of the power of one man and multiplied by the collective effort (anywhere from 50-500 rowers) made a very strong force to power these ships. One of the greatest examples we know of the power of these ships’ strength is at the battle of Salamis where the Greek boats bombarded the Persian transports until the Persians were forced to retreat.

The slinger

The sling was a simple device that consisted of two even straps on the side of a pouch. A stone was put in the pouch and spun around with the straps until one of them was released and the stone flew out. Greek slingers were lightly armored, sometimes even not, as they usually, stayed in the back of the army to bombard the enemy at a distance. They often put messages on their sling as well to identify who they had killed, and to jeer at the enemy. One slingers stone was discovered with this massage inscribed on it: ΔΕΞΑ, meaning “take that!” The sling used concentric force, meaning that as it was spun around, the velocity kept changing tangent to the circle, pushing outwards and forwards. This technique made it very powerful, and could kill with a single blow. Though they were hard to aim for an inexperienced person, for a trained slinger it was easy, because the velocity of the stone (the direction and speed of it) at any given point was tangent to the circle of the slingers circles, perpendicular to the sling. Meaning that if you wanted to hit a certain point, you would have to let go of you strap on the sling the moment it was at a 90 degree angle from the path you wanted the stone to take. Once a slinger had used his sling long enough to determine when the sling was in the position it needed to be in to have the correct velocity he could be extremely accurate and deadly.

The peltast

The peltast, like the slinger, was lightly armored and usually stayed in the back of armies. They were essentially a spearman, with two important differences. One he had a strap on the part of the spear closest to him, which acted as an extension of his arm. The longer his arm was the more power he could have in his through using the same principals as the rowers in the trireme; the longer his arm was the longer his swing could be and the more force he could put into it over time. So, in the most basic terms, the strap enabled him to put more power in to his throw. The second important difference was that the strap was wrapped around the spear, so that when he released the spear it would be spinning. The spinning spear has more inertia than the straight one so it would not only have a straighter course as a football does when spun, but it would also have more force on impact, enabling it to pierce through thing it would not normally be able to.

//A vase painting (black on orange) of a peltast//

__Engines of siege__

The sambuca

The sambuca was a machine used in siege to transport troops to the top of a wall or tower. It was a large crawlway supported by a rolling base and a counter weight on the end to make it easier to lift up. The main counterweight consisted of stones, and weighed around 2.5 tons, but the longer and heavier the main crawlway was, the heavier the counterweight needed to be. This is because the equation for a lever, LP=F being the length of the lever, P being the pressure applied, and F being the total force that comes out. So, if you had a lever that was 4 feet on one side and 2 on the other and you put a weight of 6 pounds on the side of 2 feet you would only need 3 pounds on the side of 4 feet to balance it out. The sambuca was then rolled to the wall of fortress it was to siege and the main frame was raised. By the time it was raised the troops could jump out before the defenders could attack it or push it away. Also, it was reinforced with animal hides and on a wooden frame made it so that the defenders could not easily puncture the sides. The bad thing about animal hides was, however, that the wooden frame could be smashed to pieces with a rock or large heavy item without the animal hides being ripped.

The helepolis

The helepolis was a large tower which was rolled up to the wall of the fortress or stronghold it was intended to siege and padded doors on the front of it opened. The specified fortifications were then bombarded with assorted sizes of rocks and metal bolts from gastrphetes, oxybeles and lithobolos, which were all extremely powerful machines that could pierce hoplons (A type of large, round and very strong shield used by hoplites) at a quarter mile range and strip ramparts at point blank. This large construction weighed a lot, due to its size and equipment. One, found at the siege of Rhodes, an island in the northeastern Mediterranean, had a base of 72 square feet and a height of 130-140 feet and a total estimation of 150 tons. Much of its weight was due to the iron protection on three of its sides, which when the math is done can add up to 3442.5 square feet of paneling, which you determine by getting square-root the base getting you the width and length of the tower, which is approximately 8.5. You then multiply the width by the height and the three, as the paneling covers three sides. With the iron and all, propelling a 150 ton object is not easy so the Greeks had to come up with a way of making the burden easier and they succeeded. What they did was spread the work out over time and space, as a pair of pliers of lever would. They made a wheel that could be turned around by mules or human force, that uses the same equation as the lever, LP=F. The only difference is that the length (L) is the distance between the middle of the wheel and the outside edge, so, the farther you are away from the middle of the wheel when pushing, the less force you have to apply each foot of pushing.

Egyptian warfare

The battle ax == The Egyptian battle ax was a very powerful tool in warfare and replaced the Egypt’s most used weapon, the mace. Over sixty mutilated Egyptians were found on a battle field with battle ax cuts in them and the mummy of Seqenenre Ta’o, a Theban king. What makes the battle ax so effective is its use of the property of the conservation of momentum and the law of gravity to create its effectiveness. It uses the conservation of momentum which the equation is: KE = ½ MV2 KE being Kinetic Energy, M being mass, and V being velocity. So, if the velocity of the ax is 19.4444444 (70 kilometers per hour), the weight of the ax is 13.6077711 kg (30 pounds) then the kinetic energy (and momentum would be 12600 KE. And according to the conservation of momentum though, all of the momentum would be transferred to the object the ax would strike. So, if the force is 12600 KE, and the head that the ax strikes is 8 kg (the average weight of a head), then the head would have to travel at 448.998886 meters per second (1 616.3959 Kilometers per hour) or crack, be smashed, break open and/or be sliced into pieces. The blade gets thinner and ends in a point, so all of the momentum is transferred into one spot, the //point//, where the ax strikes, and not the whole head. ==

The whip
== The whip was not generally used in war, but rather for torture and the forced movement of animal (and sometimes even human) work force. To spite popular belief, the pyramids were not built by a bunch of reluctant Egyptian slaves, but recruited workers who greatly wanted the pyramids built. They believed that the pyramids were some sort of machine that would almost “launch” or “catapult” the pharaoh’s soul into heaven, and then he would let them in when they died after him. The whip was used on slaves, which where either prisoners of war or the sons and daughters of them. What made the whip so effective was at the speed it traveled. The whip, when used correctly easily breaks the sound barrier, which is why a whip goes “CRACK!” when flicked fast enough, and was the first human invention to break the sound barrier. The reason it can go so fast is because, as the conservation of momentum explains, if an object with going an lower speed, (the handle) transfers all of its force to an object with a low mass the (end of the whip), the momentum will have to be made up in speed. The equation for momentum being: KE = ½ MV2, KE being Kinetic energy (momentum), M being Mass in kilograms, and V being the Velocity of the object in meters per second. So if the handle weighed 10 k, and you moved in at 4 meters per second, the momentum would be 16. Since momentum is conserved (assuming there is no air resistance), a whip end with the mass of 10 grams would have to be traveling 80 meters per second (900 miles per hour!) to have a KE of 16. ==