Volume: 135(6) - June, 2013
It is commonly thought that ancient engineers and designers had a relatively low level of scientific knowledge and that any success they had was achieved through trial and error. If ancient devices are investigated more closely, however, we can see that such a belief is unfounded. What follows are just a few examples that demonstrate how much ancient designers knew. In fact, design rules and concepts were employed extensively by the engineers of ancient times, leading to machine design from machine elements and to the design of a machine as a system.
With regard to the above, it may be interesting to consider the ‘Delian Problem’, a legend (Theon of Smyrna) about a disastrous pestilence on the Isle of Delos. The oracle of the god Apollo declared that the god wanted a cubic marble altar built for him, twice the size of the previous one. The inhabitants built a new cube by doubling the dimensions of the previous altar, but the pestilence continued. This was because, obviously, the new cube was eight times the size (or volume) of the old one, and not twice the size.
The problem was solved by Eratosthenes with the invention of the mesolabium. The word ‘mesolabium’ comes from the ancient Greek words μεσος (middle) and λαμβανω (to take). The mesolabium makes it possible to graphically compute two mean proportional line segments x and y between two given line segments a and b so that a:x = x:y = y:b. This also makes it possible (if b = 2a) to compute the side of a new cube whose volume is twice that of a given cube (Delian Problem) and, even to compute the cubic root.
We know that in ancient times knowledge was often transmitted (at least as far as mathematics and geometry are concerned) to initiates. Behind the above-mentioned legend there was an important concept: if the design of a device ‘works well’, it does not follow that it is possible to obtain a similar device, but smaller or bigger, simply by scaling the dimensions of the previous design; instead, what will be obtained can be a poor device or even a non-working one.
The mesolabium of Eratosthenes and the mesolabium of Durer are brilliant solutions to the computing of the cubic root; the latter was based on the solution to the problem posed by Hippocrates of Chios (≈470-410 B.C.).
An example of the importance of the mesolabius for machine design can be found in the case of throwing machines. These constituted the artillery of the day, throwing big darts (catapults) or stones (ballistae) by means of elastic energy stored in particular springs. Special mathematical and technical skills were necessary to design a throwing machine. The ‘elastic motor’ of these machines was made using a bundle of women’s hair held by two ‘flanges’ called ‘modioli’. The diameter of the modioli (and hence of the hair bundle) was crucial, just like the caliber in a modern artillery. This was recognized by ancient Greek engineers (e.g., Philo of Byzantium, Archimedes of Syracuse and Hero of Alexandria) and reported by the Roman engineer Vitruvius: the diameter of a modiolus in Roman digits (1 digit ≈19.5 millimetres) was 1.1 times the cubic root of one hundred times the mass of the projectile measured in minae (1 mina ≈ 431 grams).
Another crucial step in designing the torsion springs was establishing the ratio between the diameter and length of the cylindrical bundle of elastic cords. For throwing machines with arms fitted externally to the main frame (or ‘eutitonon’), this ratio was 6.5. In a recent investigation it was shown that by using this ratio, the hair fibers reached their yield point precisely as had been computed, a surprising result indeed.
Another very interesting aspect is that once the diameter of the modiolus had been established, all the other main dimensions of the machine were calculated according to this dimension. This clearly shows that ancient engineers had already introduced the concept of modular design; the words ‘module’ and ‘modulus’ derive from the Latin word modiolus.
A surprising ancient machine was the repeating catapult, a futuristic automatic weapon that threw 481 mm–long darts; each dart was taken from a magazine and located in the throwing position by a rotating cylinder. This machine, described by Philon of Byzantium, can be considered to have combined the most advanced mechanical, kinematic and automatic systems of ancient times, many of which show working principles and conceptions that could be considered ‘modern’. The mechanism was operated by turning levers, windlasses or cranks. This invention was attributed to Dionysius of Alexandria around the first century B.C. Some authors who have studied this device concluded that in a first phase of the working cycle, the operators had to turn the windlass in one direction to charge the weapon and at the end of this phase, when the missile was thrown, the operators then had to turn the windlass in the opposite direction to carry the mechanism back to the starting point. This is based on the belief that the transmission of motion in the main mechanism was made by a Galle chain similar to that used in bicycles and motorcycles.
In a more recent investigation, however, a new reconstruction was proposed, based on an accurate translation of the text by Philon of Byzantium (Ta Filonos Belopoika 75, 33–34). In the text by Philon, the chain is described as being made by πλινθια (little bricks), with the teeth of the chain mail called περοναις (fins). The author has shown that one of these fins could have easily operated the entire mechanism with the chain (hence the windlass) running in the same direction all the time. According to this reconstruction, the device can be seen to be really automatic and thus shows a surprising modernity.
Another very interesting example of ancient designs was the automatic water clock by Ctesibius (285–222 B.C.), who was the director of the Library of Alexandria and who is credited with a large number of inventions, several of them automatic. This device treated the duration of one hour as different during the day and during the night (except at the equinoxes) and on any given day and so automatically corrected for this difference. In order to understand why an automatic device was required for a water clock, we must remember that the length of the Roman or Greek hour was not constant because it was defined as 1/12 of the time between sunrise and sunset during the day and 1/12 of the time between sunset and sunrise during the night. The water clock designed by Ctesibius solved this problem by means of a very interesting mechanical design. In this design, a bottom tank was filled by a constant flow of water from a top tank that was continuously kept full. A yarn was connected to the ball clock and to a counter weight and was wrapped in coil around the pointer axle. The bottom tank was drained daily and the cycle started again. In this way, the pointer made a complete revolution in 24 hours at a constant speed. The dial, however, was fitted to a shaft that was off-center of the pointer shaft. Any time the float passed through a certain position (once a day), it moved a rod that pushed one tooth of a gear. This gear had 365 teeth, so that it made one revolution a year. In this way, the dial made a revolution in one year, rotating with respect to an axis that was off-center of the pointer shaft; the mechanism meant that the pointer axis and the dial axis were aligned just twice a year: at the equinoxes.
In the ‘X liber’ of Vitruvius’ treatise, we find another important example of modernity in ancient engineers’ designs: the concept of unification. Practically all devices, from cart wheels and their components to water pipe diameters, were standardized; even the water distribution in houses was set at about 60 kPa across the Roman Empire by means of six-meter-high water tanks. This standardization, probably required because the legions, moving through the Roman Empire, had to be able to find standardized spare parts everywhere, reveals the existence of mass production and an ancient industrial revolution.
Many other ancient devices testify to the modernity of the ancient engineers’ designs, like the automata of Heron of Alexandria, self-propelled siege towers, odometers and thousands of other designs. It is highly probable that the designs we know of are just a very small part of what was invented in ancient times. The reasons why so many ancient designs have been lost is most likely due to: (i) the burning of the Ancient Library of Alexandria, which contained information about most of the ancient scientists’ and engineers’ knowledge, and (ii) difficulty in recognizing ancient devices from archaeological remains if their shape is not familiar to us.
After the fall of the Roman Empire, during the Middle Ages, the Arabs were the first to study and improve on ancient engineering designs; these were later studied and improved in Europe by the engineers of the Italian Renaissance.
Department of Industrial Engineering
University of Naples – ‘Federico II’
Via Claudio, 21, 80122 Napoli, Italy