Denjoy–Carleman–Ahlfors theorem

Main information about ancient artillery comes from the five surviving Greek and Roman sources: two treatises by Heron of Alexandria, Belopoeika and Cheiroballistra, and from the books by Biton of Pergamon, Philo of Byzantium and Vitruvius Ancient artillery consisted of elasticity-driven devices for shooting projectiles (arrows, bolts, stones etc.) which evolved from the composite bow.

The earilest artillery pieces, like gasrtaphetes were driven by a composite bow. According to Marsden's analysis of ancient sources, they were invented in Syracuse in 399 BC, when tyrant Dionysius I gathered there an assembly of expert craftsmen to conduct a research on new armament. XVI.41.1-3. . Diodorus says that these were the first catapults, and describes the impression new weapons made during the siege of Motya by Dionisius. These catapults were arrow shooting and it is conjectured that they were powered by a composite bow.

More powerful pieces were driven by torsion of a spring made of an appropriate organic material, usually sinew or hair, human or horse. Torsion-powered pieces were probably invented in Macedonia, shortly before the times of Alexander III. According to Philo, Ctesibius experimented with metal springs and pneumatically-powered machines, but there is no record of their actual use. The reason is that metal springs were not sufficiently resilent at that time. In the Middle Age metal springs were successively used in crossbows.

The stone-throwing machines were torsion-powered, and their first recorded use is in the siege of Tyre by Aexander.

Torsion artillery reached its highest development in the Hellenistic period, probably at the time of Demetrius Polyorcetes. No improvement, except in details, were ever made upon the catapults of Demetrius. The Romans obtained their knowledge from the Greeks, and employed the Greek specialists. Torsion artillery was used until after the spread of gunpowder.

Nomenclature

The names of the artillery pieces changed with time. Though all inventions in the field of artillery were made by the Greeks, the best known are the Latin names, ballista and catapulta. Catapulta (καταπελτης οξνβελης) originally meant an arrow- or bolt- throwing engine. A ballista (καταπελτης λιτοβολος or πετροβολος) was a more powerful machine primarily designed for throwing stones. Sometimes ballistae were used to fire extraordinary projectiles, like pots with snakes, or even parts of dead bodies, with the purpose of terrifying the enemy. For example, the Romans catapulted to the camp of Hannibal the head of his brother Hasdrubal. Artillery was also used as flame carriers. During the last night of Demetrius attack on Rhodes the Rhodians fired 800 cylinders with some incendiary substance; the cylinders being subsequently collected and counted; they managed to set fire on Demetrius' armored tower.

At some time between 100 CE and 300 CE a change occurred in the nomenclature. Thus in the 4th century CE catapulta indicates a one-armed stone-throwing engine, also known as onager, while ballista means a two-armed piece which shoots bolts only.

The authors of Greek treatises classified artillery pieces into two categories: euthytones and palintones. Hero writes that eutitones were arrow-throwing, while palintones usually stone throwing, but sometimes could also shoot arrows or both. The precise meaning of these terms is disputed. According to Schramm, Marden and their followers, this distinction reflects the difference in the shape of the detail of the frame which is called "hole carrier". According to the so-called "French school", the arms of an eurhytone extended outside the frame, while the arms of a palintone moved inside the frame. The problem arises because the ancient descriptions that we have do not contain original pictures, and the meaning of certain technical terms is unclear.

Dimensions, materials and performance

Much research was done by Hellenistic Greek scientists and craftsmen on the design of artillery pieces. The main parameter that determines the sizes of all parts of the machine is the weight of the projectile or the length of the bolt (arrow). The fundamental size characteristic is called the hole diameter; it is the same as the diameter of the spring (which is a bunch of sinew rope). Vitruvius gives the following formulas for the hole diameter: it is the length of the bolt divided by 9 for the bolt-throwing machines, or

$1.1(100W{)}^{1/3},$

for the stone-throwing machines, where W is the weight of the projectile in Attic minas (1 mina=436.6 g), and the hole diameter is measured in dactyls (1 dactyl=19.3 mm). Then the dimensions of all parts are defined as fixed multiples of the hole diameter, for example the length of the arm is 7 hole diameters.

Most of the frame detail were made in the Hellenistic period of wood. Hero of Alexandria proposed metal frame and metal cylinders to enclose the springs. Depictions on Trajan's column and archelogical evidence indicate that these metal artillery pieces were widely used by the Romans.

An important detail, washer used in the stretching of the spring was always made of metal, and these washers are the only pieces of Hellenistic artillery, besides the stone balls and arrowheads which are found by archeologists.

The preferred material for the springs was sinew and human hair. Horse hair was considered an inferior substitute. In 250 BC, Rhodes sent to Sinope for her war with Mitridates about 3/4 of a ton of women's hair. In 225 BC Seleucus gave Rhodes a present of hair weighting 1000 talents. This gift was a part of international relief program after a catastrophic earthquake. This shows that a large trade in human hair existed in Hellenistic period.

A typical ballista could throw a stone weighting 1 talent (60 minae = 26.2 kg) at the distance of 400 yards. There existed heavy ballistae able to throw stones weighting 3 talents and more.

Much longer ranges were claimed by Athenaeus Mechanicus ...a three-span catapult shot 700 yards (three and half stades); its springs weighted twelve minae. A four-cubit palintone engine shot 800 yards (four stades).

Athenaeus mentions a catapulte designed by Archimedes which could throw a three talent stone at the distance of one stade. This catapult was installed on a ship. Polybius (VIII,7,9) writes that catapults used to defend Syracuse during the siege by Marcellus were throwing stones of 10 talents (262 kg). The largest weight of projectiles mentioned in Vitruvius is 460 pounds.

When describing the siege of Jerusalem by Titus, Josephus writes that the stone balls that were being hurled weighted one talent and traveled two or more stades (400 yards).

Philo of Byzantium writes that the stone walls have to be at least 10 cubits (about 3 meters) thick to be unaffected by stone-shot.

According to Schramm, the best arrow-throwing catapults could be trusted to kill a man at 100 yards, so the accuracy was better than of an early 19th century musket.

Use

The main use of artillery was in the siege of fortified places. The heavy stone-throwing pieces were used to destroy the walls, while the lighter arrow-shooting pieces to clear the walls from the enemy defending them

Several attempts to use artillery in the field are recorded but they were mostly unsuccessful, except when the artillery could be deployed in some protected place. For example, in the Battle of Jaxartes Alexander used catapults to clear the further bank of the river.

The artillery pieces were transported in disassembled state, and it took long time to assemble, install and adjust them. In many cases only few essential parts of artillery pieces were transported, the rest could be made on the place of a siege if timber was available.

Artillery was used in naval battles, as mentioned in Diodorus, book XX. Both Alexander and Demetrius mounted catapults on ships for the purpose of attacking fortresses.

Testing modern replicas

Many attempts were made in modern times to reproduce the ancient artillery pieces, following their ancient descriptions, and to test them. The first success was due to German general E. Schramm in collaboration with A. Rehm. They used horse hair for the springs, and achieved the distance of over 300 m with 1 pound lead shot, and using another machine, 370 meters with 1 meter bolt. This bolt penetrated an iron-plated shield 3 cm thick to half of the bolts length.

Nowadays many working replicas of various types exist.

See also

• Ballista

• Catapulta
• Carroballista
• Cheiroballistra
• Hellenistic armies
• Lithobolos
• Polybolos
• Scorpio (weapon)
• Torsion siege engine

External links

• Template:Cite web

• Template:Cite web

I don't usually mention myself. I take pleasure in sharing interesting material with some others. I also choose to examine the online market place because I do think there's so much to see available. When I'm about the online.
|
My name: Molly Cattanach
My age: 25 years old
Country: Great Britain
City: Nebo
Post code: Sy23 2dq
Address: 60 Quay Street
|
I am 36 years old and my name is Molly Cattanach. I life in Nebo (Great Britain).
|
My name is Molly from Nebo doing my final year engineering in American Politics. I did my schooling, secured 91% and hope to find someone with same interests in Origami.
|
My hobby is mainly Origami. Sounds boring? Not!
I try to learn French in my spare time.
|
My name is Molly (41 years old) and my hobbies are Worldbuilding and RC cars.
|
Hello, dear friend! I am Molly. I smile that I could unify to the entire globe. I live in Great Britain, in the south region. I dream to go to the different countries, to obtain acquainted with appealing individuals.
|
I'm Molly (24) from Nebo, Great Britain.
I'm learning French literature at a local high school and I'm just about to graduate.
I have a part time job in a college.
|
Hello!
My name is Molly and I'm a 30 years old girl from Great Britain.
|
Hello! My name is Molly.
It is a little about myself: I live in Great Britain, my city of Nebo.
It's called often Eastern or cultural capital of . I've married 3 years ago.
I have two children - a son (Effie) and the daughter (Boyce). We all like Origami.
|
Hello!
I'm French male ;=).
I really love Origami!
|
Hello from Great Britain. I'm glad to came here. My first name is Molly.
I live in a city called Nebo in western Great Britain.
I was also born in Nebo 37 years ago. Married in December 2009. I'm working at the university.
|
My name's Molly Cattanach but everybody calls me Molly. I'm from Great Britain. I'm studying at the college (final year) and I play the Banjo for 5 years. Usually I choose music from the famous films :).
I have two brothers. I love Kayaking, watching movies and Slot Car Racing.
|
I'm a 45 years old and study at the college (American Politics).
In my free time I teach myself French. I've been twicethere and look forward to go there sometime computer repair store in hoffman estates the future. I love to read, preferably on my beloved Kindle. I like to watch How I Met Your Mother and Doctor Who as well as docus about nature. I like Origami.
|
I'm Molly and I live in Nebo.
I'm interested in American Politics, Origami and French art. I like to travel and reading fantasy.
|
I'm Molly and I live with my husband and our ipad 2 repair hoffman estates children in Nebo, in the south area. My hobbies are Woodworking, Equestrianism and Coin collecting.
|
Hello, I'm Molly, a 27 year old from Nebo, Great Britain.
My hobbies include (but are not limited to) Art collecting, Racquetball and watching Supernatural.
|
Hi there! :) My name is Molly, I'm a student studying American Politics from Nebo, Great Britain.
|
I'm Molly and I live in a seaside city in northern Great Britain, Nebo. I'm 23 and I'm will soon finish my study at American Politics.
|
I am Molly from Nebo. I love to play Banjo. Other hobbies are Origami.
|
I am Molly and was born on 15 December 1979. My hobbies are Creative writing and Audiophilia.
|
My name is Molly and I am studying Nursing and Gender and Women's Studies at Nebo / Great Britain.
}

my webpage; macbook repair hanover park