Digital Experimental Archaeology:

Hero of Alexandria and His Automata in

CAD

Duncan Keenan-Jones

Classics, University of Glasgow

Digital Classicist Seminar, Berlin

15th November 2016

Overview

Introduction Hero & his automata

Project aims Hero and his predecessors

Libation mechanism

Methods Computer-aided design (CAD)

Mathematical simulation

Hydraulic simulation

Conclusion

Hero of Alexandria

First century AD

Large number of surviving

treatises

: (On the making of the) Automata

Woodcroft 1851

(wikimedia commons)

Schmidt 1899 (wikimedia commons)

.so that whoever chooses to arrange differently will be able

to do it

(Hero, Automata 1.1, trans. Grillo)

Heros mobile automaton

, ,

shrines or altars of suitable size, capable of moving forward under their own power and stopping at certain defined locations; and each of the little figures inside them moves by itself in accordance with either the set purpose or the appropriate story (Hero, Automata 1.1, trans. Grillo)

Drive Mechanism

Programmable 6.1 , . , . (2.)

. .

, [] , . (3.)

, .

6.1 When the cord has been wound to a certain extent around the cylinder, let it be looped around the

knob and wound around the cylinder in the direction opposite to the preceding one. So again, the

fall of the counterweight will unroll the first winding, and the case will move. (2.) Then, after the cord

detaches from the peg, it will turn the wheels in the opposite direction. This is how the case will come back .

However, if we want the case, once it has travelled, to stand still we will wind the cord and put it around

the peg without winding it the other way around immediately. Instead, we will form

Rossi & Pagano 2011 J. Mech. Design

a little bundle, glue it onto the cylinder, wind the cord again contrariwise

and attach it to the counterweight, and what has been said before will

happen.(3.) If we also want the case to move forward and backward many

times, we will make alternate windings more frequently and the intervals

between them the size we choose; we will also make the timings of the

deities whatever period of time we choose by means of loops of slack.

Libations

13(1) After the sacrifice, milk must spurt from the

thyrsus, and wine from the cup. (2) So, this occurs as

follows: a pipe is attached under Dionysos feet, with

two holes near one another on its surface; from these,

small pipes extend up into the inner part of Dionysos,

one leading to the thyrsus, the other to the cup. (3) Let

be the base of Dionysos, the pipe connected to

it, and the holes in the pipe, and and the

small pipes stretching from these: to the thyrsus,

to the cup. Let be a knob () placed on top of the shrine. Inside this let be a container with

a partition in the middle. From the container let

a pipe lead to a certain other pipe , fitted

tightly () to the pipe and attached from below to the surface on which the shrine

rests.

(trans. Grillo)

(pipe)

(knob)

(container)

Experimental Strand

Aims

Technical competence presupposed of the reader

How much must be filled in?

Practical rather than theoretical?

How feasible?

Had Hero built these automata himself?

Libation mechanism

Could it be constructed?

How impressive in practice?

Hero and his predecessors 1.8 ,

1.8 Therefore, in this book I will write on mobile automata and set forth a complex configuration of my own

5.1 , . 5.2 , .

5.1 So, our ancestors have handed down to us a way of achieving forward and backward motion along a single line, though troublesome and involving danger; for success is rarely achieved by following the methods they have written down, as is clear to those who have tried them. (2.) I will show that forward and backward motion along a straight line can be performed both easily and without danger.

20.1 , .

20.1 for I have recorded methods which are feasible, riskless and innovative compared to those described by our ancestors, as is clear to anyone who has tested the earlier devices.

(Hero, On the making of the Automata, translation F. Grillo)

Methods

Quantitative

Reproducible

Documented, available

3D CAD Model (SolidWorks)

Design

Simulation

Full scale physical model

Performance testing

3D CAD Model (SolidWorks)

8 different configurations composed

of 29 sub-assemblies

185 parts

joined by 249 mates

more than 500 sketches made

the housing or plinthion: 512 features

(35 seconds to rebuild)

Tap

( & , kleis & epitonion)

1) close reading of Greek text

in concert with textual strand

(13.5)

, ,

, ,

,

.

(13.5) So, to keep the liquids in

beforehand, let be a key, which, as

stated, shuts the liquids off by means of

a stop-cock ; let a loop of cord be

put around this, with some slack to it

and attached to the counterweight, so

that when it has been pulled taut at the

appropriate time, it will turn the

stopcock and the liquids will be

conveyed.

(Trans. Grillo)

&

Bar, key

tap (Hero Pneum. 1.24-5, 2.2, 22, 24)

Handle with a shaft that rotates?

Tuning peg (LSJ)

Inner cylinder of a tap: here and Vitr. 9.8.11 :ita uti minus tympanum quemadmodum epitonium in maiore circumagendo arte leniterque versetur

Tap (P. Harr. 1.49.9)

Epitonium: tap (CIL 8.23991; AE 1986.25; 1999.169, Dig. 19.1.17.8, Seneca Epistulae Morales ad Lucilium 86.7.1, Varro, Res Rusticae 3.5.16)

2) Ancient

technologies

research

to find culturally appropriate design solutions

Context as close as possible to Heros (time and space)

Nemi tap: best preserved

Kretzschmer 1960

http://rarehistoricalphotos.com/caligula-nemi-ships-1932/

3) 3-D CAD

modelling

Kretzschmer 1960

, ,

3) 3-D CAD modelling Location within 3D space reveals

omissions and inconsistencies

Location of the tap not specified

(13.5)

, ,

, ,

,

.

(13.5) So, to keep the liquids in

beforehand, let be a key, which, as

stated, shuts the liquids off by means of

a stop-cock ; let a loop of cord be

put around this, with some slack to it

and attached to the counterweight, so

that when it has been pulled taut at the

appropriate time, it will turn the

stopcock and the liquids will be

conveyed.

(Trans. Grillo)

3) 3-D CAD modelling Peleg 1996:34

Casa del Torello, Pompeii (Leander Touati 2011 Opuscula)

3) 3-D CAD modelling

Not stated that the cord runs

through the columns (Hero

not always consistent)

13.7 ,

,

.

The pipes and must run through one of

the shrines little columns which is hollow under

the shrines base, in order to be invisible. (trans.

Grillo)

Cod. Marcianus gr. 516, XIII c.

codex Guelferbitanus Gudianus gr. 19, XVI c.

MS

Diagrams Differences?

3) 3-D CAD modelling

Other pulleys are mentioned: Bacchants (16.3)

pulleys for cords to turn Dionysos and Nike (13.7-8)

No mention of extra pulleys at bottom

Cords for screws

17.2

.

17.2the cords from below

will be brought upwards into

section and attached to

the counterweight inside

section by means of a

pulley; for all the cords which

are brought up from below

will thus be out of sight.

(Trans. Grillo)

(3b 3D Printing)

Testing

4) explanatory 2-D

drawings For construction

3.1 , , , . , , , . , . (2.) , . . , . (3.) . , . . (4.) . .

3.1 Let there be a base approximately one cubit long, about four palms wide and nearly three palms high, with a small wavy moulding running around both its upper and lower part. Four little columns, roughly eight palms high and two palms wide, stand on the corners, with little base-mouldings placed at the bottom and capitals in line with them placed on the top. On the capitals lies a kind of entablature running all around and one-eighth the height of the entire column, approximately five fingers. (2.) On the entablature are laid small boards covering its upper surface, and a small moulding runs all around. On the covering stands prominently, in the middle, a circular little shrine with six pillars. On this stands a little cone-shaped dome with a projecting surface , as stated. (3.) On the peak stands a Nike with spread wings and holding a wreath in her right hand. In the middle of the shrine stands a figure of Dionysos holding a thyrsus in his left hand and a cup in his right. A little panther sits by Dionysos side at his feet. (4.) In the spaces before Dionysos and behind him, on the surface, is an altar with shavings made from working the boards, dry enough to burn easily. Outside Dionysos shrine, at each column, stands a Bacchante arrayed in whatever way one chooses.

(4.4) . .

(4.4) I employed the mentioned dimensions out of necessity; for the sight, were they any larger, would arouse suspicion as though someone was contriving these movements from the inside.

Performance insights from modelling Standing rather than reclining

Trade-off between counterweight fall and visibility

Modelling Insights

Poor visibility for lower observers

Theatrum tectum (covered theatre, Pompeii)

Simulation

Dimensions

+ Vitruvian orders

All mechanisms

In SolidWorks

Provide data for simulation

Pipe size

13.7 ,

, .

The pipes and must run through one of the shrines little columns which is

hollow under the shrines base, in order to be invisible. (trans. Grillo)

14.5 mm

(ext. dia.,

Williams

1893 Quart.

Musical Rev.)

(Pompeii,

www.gettyimages.co.uk/detail/illust

ration/italy-naples-museo-

archeologico-nazionale-sistrums-

organ-stock-graphic/148352858 )

Spouts with 5mm orifices

(Pompeii Herculaneum)

Lead regularly beaten into

sheets of 2-3 mm

(Dessales 2013, 1901, 197-9)

Wright 2007 Interdisciplin. Sci. Rev.

1 mm

thick Smallest ancient pipes?

Pipes cant be bigger, or plausibly smaller

Hydraulic simulation of adequate tank size

1. Bernoullis equation: obtain hL(friction head losses) by assuming v2 < v2 without friction loss p1/ + z1 + v1

2/2g hL = p2/ + z2 + v2

2/2g

P: pressure, z: elevation, g: gravity,, : specific weight

2. Calculate initial f (friction factor) using Swamee and Jain correlation (assumes turbulent but close)

3. Darcy-Weisbach equation + minor losses (K): recalculate v hL = (K + fL/D)v

2/2g

D (pipe dia), L (pipe length)

Hydraulic simulation of adequate tank size

1. Darcy-Weisbach equation + minor losses (K): recalculate v hL = (K + fL/D)v

2/2g

D (pipe dia), L (pipe length)

2. Recalculate f: f = 64/Re (laminar flow), others for turbulent (Colebrook 1939 J. Inst. Civ. Eng.)

3. Repeat from 2 with recalculated f, v until convergence

4. Calculate time to empty tank from Q = vA

1.73 m/s

1.22 x 10-5 m3/s

4.19 s to empty

~ 2.1 s per

performance

Hydraulic simulation of adequate tank size

Ancient hL greater?

Nemi tap: smooth

Physical testing

How big could a

be?

Nut, (olive) stone,

grain, gem (LSJ)

Round head of a

probe

1.30 m/s

9.12 x 10-6 m3/s

5.56 s to empty

~ 2.78 s per

performance

codex Guelferbitanus Gudianus gr. 19, XVI c.

MS

Diagrams

Schmidt

Conclusions

3D Modelling reveals silences in Heros text

Lack of pulleys in basis for rectangular motion notable

Had Hero built the rectangular motion?

Data from Heros text modelled in 3D CAD are sufficient for a constrained hydraulic simulation of the libation mechanism of Heros mobile automaton

Suggests larger tank than could probably fit in the puren

Further testing in physical model

The End