Mechanics

Introduction

Techné (tecnh), whence ‘techn-’ words, means any art, craft, technique, set of skills, or body of knowledge; Ingenium (Latin) whence ‘engin-’ words, means ingenious, very clever, or complex; Méchané (mhcanh) whence ‘machin-’ words, means any man-made device to achieve something.

The Greeks and Romans were very creative and innovative in the area we now call mechanics. The Greeks inherited some simple machines, and put them together in novel ways to make complex machines, from the compound pulley to the Antikythera mechanism. The Romans inherited a lot of machines from the Greeks and others, and developed some of them further to make bigger or better or new machines for their world with its own set of priorities, from the water-powered water wheel to the as-yet not understood mechanisms for flooding and draining the Colosseum.

An obvious point is often overlooked: for men (however strong) to be able to lift or move a stone, they need to be able to get a grip on it. The size or shape of the stone sets limits on how many men can get round it. Therefore, it doesn’t matter how many slaves were available; only so many would be able to work on the problem directly. If more force is needed than that number of men can provide, then machine(s) must have been used to move it.

Some technical terms

Mechanical work = the product of (i) the force exerted on a body, and (ii) the distance it moves in the direction of that force. Work = Force x distance, joules. The capacity of a body to do work is its energy. Potential energy = capacity of doing work by virtue of its position (e.g. height). Kinetic energy = capacity of doing work by virtue of its motion (e.g. falling)

Power

is the rate at which work is performed, in joules per second (= 1 watt). 1 horsepower = 746 W. The average real horse (as opposed to this abstract figure) can only sustain this for about 3 hours; for an 8-hour day 570 W is more normal. Force is defined as the product of the mass multiplied by the acceleration; the force required to accelerate 1 kg by 1 metre in 1 second = 1 N (N for Newton). 1 Newton = very conveniently approximately the weight of an apple!

Tensile strength

Any material can be broken if it is pulled apart in opposite directions hard enough. Tensile strength refers to the point at which a specimen breaks when pulled; less than that is what force something can withstand. For homogeneous materials, the tensile strength is effectively independent of the size of the specimen. The tensile strength of ancient plant rope was perhaps c. 16 MPa (mega[=million]pascals; 1 Pa = 1 N/m2); Cotterell & Kamminga (1992) 225

Elasticity

If stress is applied to a solid, it will deform. Up to a point, it will return to its original size and shape. Different materials have different points at which this no longer happens. Movement back to the original is called elasticity.

Resilience

Work performed in deforming an elastic solid is stored in the solid and recovered when it is unloaded, e.g. drawing a bow; release the string and the energy in the bow is transferred to the arrow. The maximum elastic strain energy a material can store is called its resilience.

Mechanical properties of some materials commonly used in antiquity

 Material Density (kg/m3) Tensile strength (MPa) Resilience per unit mass (J/kg) Wrought iron 7800 150 3 Bronze 8700 120 3 Pine 460 90 900 Ash 600 120 1000 Oak 610 90 900 Sinew 1300 100 3200 Horn 1300 120 2000

Source: Cotterell & Kamminga (1992) 68

Animal power

 Animal Power (W) Ratio to horse Horse 570 1.0 Bullock 340 0.6 Camel 960 1.7 Mule 290 0.5 Ass 140 0.3

Source: Cotterell & Kamminga (1992) 38

The bullock has a lower power figure than a horse because it is being measured in Watts, and that involves the time element; a bullock is stronger than a horse but takes longer to do the same amount of work.

Like people, animals had multiple roles in antiquity. Horses were good for speed, but relatively expensive to keep, difficult to harness efficiently, and much of Greece and Italy is unsuitable for keeping horses. Oxen are slower but stronger, relatively cheap to keep, easy to harness, better than horses on rough ground (especially muddy), and could be eaten (Greeks and Romans did not generally eat horsemeat). Hence the preference for oxen over horses for draught; we even find an ox-powered ship! (De rebus bellicis, C4 AD)

Human power

Over a full day 5 men can perform about the same work as one horse.

 Mode of exerting force Force (N) Pushing horizontally with one hand 130 Pulling horizontally with one hand 100 Pushing vertically upwards with 1 hand 150 Pulling vertically downwards with 1 hand 250 Pushing with both hands horizontally against wall using a foothold 700 Pushing with shoulder against wall using a foothold 860

Source: Cotterell & Kamminga (1992) 24

Water powered machines

Water power has limitations. All types of water wheel need a constant supply. An undershot water wheel is easier and cheaper to construct than an overshot; it uses kinetic energy of flowing water. An overshot wheel needs water to be brought to the top of the wheel, needs boxes of right size for the flow, and has a minimum working speed. It uses the potential energy of falling water. But bringing water to the top might be very expensive and laborious. The overshot is much more efficient than the undershot, and can generate at least twice as much power (3kW or more).

Simple machines

The lever

Evidently was a machine in operation from very early times, e.g. lever press for olives from c. 1500 BC. [Aristotle] Mechanical Problems (C3 BC) is largely about levers and their applications. The law of the lever was expressed by Archimedes (C2 BC): In equilibrium, the weights are proportional to their distance from the fulcrum.

The wedge

Works by dynamic action – movement. [Aristotle] Mechanical Problems 19 (C3 BC) asks why an axe placed on wood and heavily weighted does not split it, but an axe striking it, even without the weight, splits it. Cf. modern safety adverts about a back seat passenger in a 30mph collision weighing the same as an elephant: weight x velocity x duration. An axe delivers huge force briefly on small area.

The winch/capstan

Certainly in use by C5 BC; probably from much earlier times. The winch/ capstan essentially = a drum; the winch has a horizontal axis, the capstan a vertical. Both were usually operated by handspikes in antiquity. There is some debate over the nature and use of the crank in antiquity; its only real advantage is relative speed over handspikes, but the operator must be able to resist the reverse thrust applied by the load at weakest positions, i.e. 4 and 10 o’clock positions, or a ratchet must be fitted.

The pulley

Earliest known is C8 BC, Assyrian. It probably originated from a rope thrown over a tree. The pulley allows a person to pull down instead of haul up (compare push-pull force statistics). It is most useful in combination, in a block, which = the compound pulley. The compound pulley was traditionally invented by Archimedes, C3 BC, but is described in [Aristotle] Mech. Prob. 18, so is earlier.

The screw

Screws were perhaps in existence from turn of C4. The water-screw (endless screw enclosed in a cylinder) was traditionally invented by Archimedes (C3 BC), and there is no earlier literary or archaeological evidence refuting that. A machine for cutting the internal (female) thread in the nut is described by Hero (C1 AD). The efficiency of ancient wood screws is estimated at c. 30%. Known uses are in presses, orthopaedics, and precision instruments.

Inclined plane

Basically = a ramp, up which loads can be dragged, instead of trying to lift them. Much used by the Egyptians; little used by Greeks and Romans.

The wheel and roller

Solid wheels from 3rd millenium, N. Mesopotamia. The spoked wheel appeared in Mesopotamia and China during the 2nd millenium BC. Spokes offered lightness and resilience. The mechanical efficiency of large wheels is discussed by [Aristotle] in Mech. Probs. Mechanical efficiency = the ratio between the input and the output of work. The roller is a log, preferably round and true, preferably used on a well-made wooden track; 6-7 men needed per tonne load in experiments. 1st literary evidence for use = Herodotos, used for transporting boats over the Isthmus of Korinth.

Gear wheel

Allows the user to change the direction of power from vertical to horizontal and vice versa. They were also used in precision instruments, including with teeth meshing in same plane. There is little literary or archaeological evidence for the use of gear wheels in antiquity, but the Antikythera mechanism (C1 BC) demonstrates a level of sophistication far ahead of what is described in the surviving literature.

Machines in the early C3 BC

[Aristotle] Mechanics was perhaps written by Straton or a contemporary (he was scholarch of the Lyceum c. 287-268 BC). It mentions (in alphabetical order): Axe, balance, compound pulley, forceps (for tooth extraction), lever, oar, potter’s wheel, pulley, roller, sling, steelyard (= balance with unequal arms; mass to be weighed goes on short arm, moveable weight goes on long arm; long arm marked in units), tongs, toothed wheels (i.e. gears), wedge, wheel, winch (= windlass).

How the compound pulley works

The reduction ratio is the number of ‘apparent’ ropes between the weight and the lifting post; the force applied to lift obtained is 1 for ‘each’ rope (i.e. each vertical section of what is really 1 rope). The rope from top pulley to man doesn’t count. So a rope tied to the bottom of the top pulley block, run down to the load, round pulley, back up to the top block, and over to man, has a reduction ratio of 2 (the load is held by 2 ‘ropes’). Pull such a rope by 12 inches and the load will rise by (12/2) 6 inches. Add another pulley at the top, tie the rope at the top of the bottom block (attached to load), pull the rope 12 inches and the load will rise by 4 inches.

Using a compound pulley the rope as well as the man can lift more than it is otherwise able to. E.g. a rope with a tensile strength of 20kg could be used to lift a 60kg weight if 3 pulleys were used. In practice, odd numbers of pulleys work best, because the rope terminates at the top of the bottom block, which is more convenient for tying/untying. Efficiency decreases as the number of ropes increases, since the tension increases in each successive rope drop (and thick ropes are less efficient too, because stiff). The trispastos (3-pulley) and pentaspastos (5-pulley) were common; if more lift is needed, Vitruvius recommends the use of two or more 3- or 5-pulley sets, with different gangs working each, rather than increasing the number of pulleys within each block. He also suggests using a winch as well if necessary. He advises his Roman readers not to employ the method of a single lifting post restrained by three ropes from the top worked by three gangs; although this method allows the load to be swung around to the side, as well as lifted, he observes that it needs great skill and experience to do properly and safely, and that it's best left to the Greeks.

How the winch works

The reduction ratio on a winch is the diameter of the axle to the diameter of the handspikes. So an axle of 2" diameter with handspikes 1’ long has a reduction ratio of 6:1. On such a winch, to wind up 1’ of rope the handspikes would need to be turned 6’. But the operator would be able to lift 6 times more than he could without the machine.

Hellenistic machines

Ktesibios (fl 275-260 BC) reputedly invented the cylinder & plunger, the force pump (‘Ktesibian pump’), a water organ, a new type of water clock, and other pneumatic & mechanical machines, including a compressed-air catapult. See Marsden GRA (1969) 41-2, Drachmann The Mechanical Technology of the Greeks and Romans p. 10

Ktesibian (force) pump is described by Vitruv. 10.7.1-3, and Heron Pneu. 27 (HOS 60-1, and 318-22). Applications in primary sources include fire-fighting (most), irrigation (Pliny NH), washing high ceilings (Isidore of Seville), and bilge pump (Paulinus). Applications in archaeological contexts incl. ships (bilge pump), wells (domestic water), mines (for drainage or ‘fire-and-vinegar’ mining technique), bath (emptying?), basement (remove water seepage?), coastal water-tank (emptying? filling? aeration?). Of pumps found by 1984, 8 were made of bronze and 13 of wood (Oleson).

How the force pump works

Water flows through a one-way valve into a cylinder; it is pushed out by a piston through another one-way valve into a delivery pipe. The piston is operated by a lever. Since the lever action is reciprocating, it is natural to have two cylinders, the pistons being moved by connecting rods attached (by hinges) to each end of the lever. Hinges reduce the sideways movement of the piston. Two pistons thus connected are always at opposite stages of the cycle, therefore when both discharge into one collecting chamber and delivery pipe, the flow is even. The major if not total lift is provided by the piston displacing water from the cylinder. Some suction may be achieved, but not much. The machine was placed in water as deep as required to fill the cylinders; water pressure pushes water into the cylinder. Dramont D bronze pump was restored to working condition: Cylinder bore diameter = 4.5cm; cylinder height = 10cm; cylinder displacement = 0.175 litres. Worked at 60 cycles/minute, discharged 10.5 litres/minute; 95% of calculated discharge. A plastic reconstruction of a much bigger wooden pump (Zewen-Oberkirch) worked at 44 cycles/minute, and discharged 100 litres/minute

Other machines

Heron (fl. 62 AD) gives instructions for building lots of pneumatic and hydraulic machines in Pneumatics; he introduces them as ‘some providing useful everyday applications, others quite remarkable effects’. Unfortunately he does not say which machines are which type. The so-called steam engine is here, along with the first coin-operated vending machine, a windmill-powered organ, automatically-opening doors, and lots more; see Humphrey, Oleson and Sherwood pp. 63-9 for some. According to Suetonius Claudius 34, Claudius sometimes held extra sessions in the amphitheatre, at which combats were held between 'stage carpenters and similar members of the theatre staff as a punishment for the failure of any mechanical device to work as it should'. That's quite an incentive to get the machines right! A remarkable machine mentioned in the sources also concerns Claudius; at the opening ceremony of the Fucine Lake drainage tunnel, a mock sea-battle was staged on the lake. The signal to fight was given by 'a mechanical silver Triton, which emerged from the lake and blew a conch' (Suetonius Claudius 21).

Water lifting machines

Water supply and distribution were relatively mechanized, and used daily over wide areas. Water was the commonest dead load that required lifting in antiquity; they were not building temples etc. every day. Water was lifted for drinking, agriculture, recreation & display, drainage, fire-fighting, and sundry other uses. There were 5 basic types of machine: Shadoof, Water screw, Force pump, Compartmented wheel, and Bucket chain/pot garland. See J P Oleson Greek and Roman Mechanical Water-Lifting Devices for a comprehensive study.

Works on the lever principle. Man powered. Exploits the fact that it is easier to pull down than pull up. The worker actually has to lift more weight than s/he would do without the machine, but it is easier with the machine. The shadoof is good for raising small quantities of water a little height. It is cheap and simple to construct.

Water screw

Uses the simple machine the screw. Man powered; tread in antiquity, crank now. It is good for raising large quantities of water a little height. It is relatively expensive and complicated to build. Traditionally invented by Archimedes; no known literary or archaeological evidence refutes that attribution. Photo here.

Force pump (aka siphon)

Uses lever action. Man powered. It is good for producing a jet of water that can be directed. Discussed above.

Compartmented wheel

There are two types: Tympanon = solid sides, wedge-shaped sections. It is good for lifting large quantities of water little height. Polukadia = many buckets on the rim of an open wheel. It is good for lifting small quantities of water a significant height. Both are normally man powered (tread) but could be water-powered if situated in the right river conditions.

Bucket-chain/pot garland

Normally man powered, but can be animal powered using saqiya gear (cog wheels at right angles). It is good for confined spaces, and for lifting small quantities of water a great height. It was often used in wells.

For war machines see Artillery.