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Leonardo
Leonardo da Vinci and Perpetual Motion Author(s): Allan A. Mills Source: Leonardo, Vol. 41, No. 1 (2008), pp. 39-42Published by: The MIT PressStable URL: http://www.jstor.org/stable/20206515Accessed: 18-08-2014 11:20 UTC
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Leonardo da Vinci and Perpetual Motion
Allan A. Mills
3
ABSTRACT
Leonardo da Vinci illustrated several traditional forms of
"perpetual-motion machine" in small pocket books now known as the Codex Forster. He was well aware that these designs, based on waterwheel/pump combinations, mechanical
overbalancing hammers or
rolling balls, would not?and could not?work.
JL. JLumankind has always sought to reduce the
need for its own manual labor. Draught animals were one
solution, but much more beguiling was the concept of ma
chines that would work "by themselves," with no obvious prime mover [1]. Even in ancient times, it appears that at least two
categories had been proposed: the self-pumping water wheel
and the mechanical overbalancing wheel. None of course
worked, and as science and technology progressed it became
apparent that any such device was theoretically impossible. However, before this understanding was fully achieved and
became well known, many technologists and hopeful inven
tors [2] felt obliged to devote time to this hoary problem. Among the former was Leonardo da Vinci. Well aware of the
futility of all suggestions for achieving "perpetual motion," he
simply recorded?and refuted?ideas that were prevalent in
his time.
the same wheel, then the machine
might turn "forever."
A number of empirical attempts to achieve such a hydraulic chimera
perhaps were made but went un
recorded because they never worked.
Drawings and plans of self-pumping wheels persisted into the 18th cen
tury and even into modern times
as amusing artifacts of linear per
spective [3]. Progress in the under
standing of efficiency, friction and
the conservation of energy gradu
ally vindicated the practical knowl
edge that, no matter how ingenious, such devices simply could not work.
The Self-Pumping Waterwheel Wheels turned by flowing water were well known in the an
cient and medieval world and were sometimes used to drive
bucket wheels to raise water for irrigation. The Archimedean
screw was another form of pump. It must therefore have oc
curred to many speculators that, if only the two could be com
bined, with the waterwheel driving a pump to supply water to
Leonardo's Contribution The papers of Leonardo da Vinci bear witness to the semi
quantitative understanding of machines that was emerging in
the late 15th century. Perhaps the least known of his extant
works are three tiny notebooks collectively referred to as the
Codex Forster, now in the Victoria and Albert Museum in Lon
don. They are believed to have been compiled between 1495
and 1497. A facsimile edition has been published, accompa nied by a transcription of Leonardo's mirror-image text in its
archaic Italian [4]. (The facsimile drawings are in their origi
Fig. 1. Leonardo's pump/waterwheel combination in Codex Forster I, folio 42v.
(Giunti facsimile)
i-i?-.-.-. ,.. r f.4i
???Hbi*?*??*,
i
Fig. 2. The "overbalancing wheel" of Villard de Honnecourt (13th century).
Allan A. Mills (retired university physics lecturer), 31 Thatch Meadow Drive, Market Harborough, Leicestershire LE16 7XH, U.K. E-mail: .
?2008ISAST LEONARDO, Vol. 41, No. 1, pp. 39-42,2008 39
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3 T
Fig. 3. Overbalancing hammer wheel shown in Codex Forster n, folio 90v.
(Giunti facsimile)
nal mirror-image form.) Unfortunately, no complete English translation of this
difficult material is available, although ex
cerpts and discussions have appeared in
various works on Leonardo.
Codex Forster /, folio 42v, contains the
drawing reproduced here as Fig. 1. The
accompanying text says that "Screw A lifts
water to screw B, and screw B with the
same water moves screw A." Leonardo
emphasizes that this is impossible in still ("dead") water and heaps scorn on the
designers of such machines. The best that
can be said in defense of the latter is that
the arrangement would demonstrably work for a while if a holding tank were in
corporated at the top of the pump [5]. All that it would require would be to elim
inate friction and improve the efficiency of the machine to 100%!
The Overbalancing Wheel The first recorded representation of
the popular "overbalancing wheel" ap
pears in the sketchbook of Villard de Honnecourt, an enigmatic figure who
traveled extensively in Europe in the
13th century [6]. In Fig. 2, it can be seen
that he is struggling to depict a wheel mounted upon an axle turning within a
stoutly braced frame. Around the cir
cumference of the wheel are pivoted an
odd number (here seven) of mallets hang
ing from their rigid wooden handles. The
lowermost mallets hang vertically, but the
upper ones rest against the rim of the
wheel. The implication is that the four
mallets on the left of a vertical through the center of the wheel will always over
balance the three on the right, causing the wheel to perpetually turn in a coun
terclockwise direction. It must have been
thought that the blows of the descending mallets would assist this motion.
The simplest model soon proves that, as depicted, the uppermost mallet falls
over too soon: a manually started wheel
rapidly comes to rest in equilibrium. To
day, we understand that the turning ef
fect ("moment") of any mallet is given by the product of its mass times the distance
of its center from a vertical through the
center of the wheel. The wheel comes to
rest with the sum of the moments on the
left equal to those on the right, and no
external work can be done. It makes no
difference if there are an odd or an even
number of mallets.
Da Vinci's Hammer Wheels Codex Forster IL measuring only 9.5 x 7.0
cm, depicts on folio 90v the overbalanc
ing hammer wheel shown in Fig. 3. The
circumference of the wheel bears ratchet
Fig. 4. A more complex hammer wheel shown in Codex Madrid I, folio 145. Leonardo's drawing has been digitally contrast-enhanced and rectified.
t *
^??jVisi iift>A >^?Ua^? W*** &T*v?v* y^HW^W^y^^ii^
l^MU -??Aft .Ci(?M^'OP%' ^?P^pHhA^ft?v**j(l?A? SI?
r^i^m^j %tr*nr?M^ ******
f^*f* T f^^ffV ^cuW- *?> v?^r>?^*t*
Vs
s
Fig. 5. A model of the "overbalancing hammer wheel." (? Allan A Mills)
teeth, and a pawl permits counterclock
wise rotation only. The pivoted hammers
have therefore been positioned around
an inner disc, where coarser teeth sur
rounding the pivots prevent the rigid handles from hanging vertically except toward the bottom right-hand side. Ca
sual inspection of the drawing might im
ply that the wheel will continuously rotate
counterclockwise, but Leonardo is well
aware that it will, in fact, soon assume a
stable, stationary equilibrium just like de
Honnecourt's mallet wheel.
Another drawing in Codex Forster II (fo lio 90r) is of a hammer wheel with addi
tional arcs upon its face. This particular
drawing is cramped and unclear but is re
peated in Codex Madrid /, folios 144 and 145. (Dated to 1490-1496, this work is now available in facsimile with an ac
companying commentary by Ladislao
Re ti [7].) The second drawing has been
rectified and is copied here as Fig. 4. The
arcs upon the face may represent initial
attempts to construct the loci of the cen
ters of gravity of hanging weights as the
wheel turns, but they neither are sym metrical nor serve to position the ham
mers around the rim of the wheel rather
than hanging vertically?as shown once
they leave the lowest point. Simple peg like stops are the simplest way of ensur
ing this, as shown in the model illustrated
in Fig. 5. The most significant part of Fig. 4 is the way in which Leonardo has com
pounded the moments in mobile-like [8] chains to prove that, as drawn, the wheel
is resting in equilibrium about an imagi
nary vertical line through its axis. Many
examples of this diagrammatic construc
tion are to be found in this codex, which
has an emphasis on mechanics.
A Model Hammer-Wheel For this model (Fig. 5), I fastened 12 brass
weights to phenolic-fiber arms. The as
semblies pivoted at equal intervals around
a 20-cm-diameter disk. Protruding pegs were positioned near each arm so as to
limit its swing. The resulting wheel was
supported by a low-friction axle through its center and could be rotated manually in both clockwise and counterclockwise
directions. Either way, it soon came to
rest in equilibrium. As the weights were
equal, it was expected?and confirmed?
that the sum of the distances of the cen
ters of the five weights on the left from a
central vertical was equal to the sum of
the corresponding distances of the seven
weights on the right.
3
Fig. 6. Leonardo, rolling ball wheel of Codex Forster II, folio 91r.
(Giunti facsimile)
7 *, f
Fig. 7. Leonardo, rolling ball wheel of Codex Forster II, folio 91 v.
(Giunti facsimile)
?
Mills, Leonardo and Perpetual Motion 41
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3
Fig. 8. A model based on Fig. 7. (? Allan A. Mills)
Rolling-Ball Wheels Leonardo also illustrates in the Codex
Forster II (91 r and 91 v) two wheels based on balls rolling around guides posi tioned within the disc (Figs 6 and 7).
The second is perhaps the most aes
thetically pleasing: 12 compartments based on arcs of diameter equal to the ra
dius of the main wheel give a pinwheel
appearance. Balls confined within the
closed compartments will tend to roll
to the lowest points, which (as shown) fall upon the locus of a circle. Again it
may appear to casual visual examination
that a greater number of balls on the
right will cause the wheel to overbal
ance and turn clockwise, but a model
(Fig. 8) confirms that moments rather
than mere numbers of balls on either side are
the operative factors. It soon takes up a
stationary equilibrium position where
the moments about the axis on the right are balanced by the greater distances
involved on the left. The J-shaped chan
nels sketched in Fig. 6 are equally un
successful.
It would be possible to replace the balls
with globules of mercury, as used in the
14th-century mercury clock of the Libros
del Saber [9]. Such a construction, how
ever, would be no better as a perpetual motion machine!
Oh speculators on perpetual motion, how
many vain projects you have created in
this search. Go and be the companions of the seekers for gold!
?Leonardo da Vinci [10]
Acknowledgments
I am grateful to Pauline Mills for translations of rel evant passages in the Codex Forster.
References and Notes
1. Hele Shaw, "Perpetual Motion," Nature 37 (1888) p. 254; Henry Dircks, Perpetuum Mobile (London, 1861); Stanley W. Angrist, "Perpetual Motion Ma chines," Scientific American 218 (January 1968) pp. 114-122; Arthur WJ.G. Ord-Hume, Perpetual Motion (London: Allen and Unwin, 1977).
2. Charles F. Partington, The Century of Inventions of the Marquis of Worcester (London, 1825); G.K. Tall
madge, "Perpetual Motion Machine of Mark An
thony Zimara," Isis S3 (1941) pp. 8-14.
3. Maurits Escher's Perpetual Waterfall ( 1961 ) is a well known example.
4. Leonardo da Vinci, // Codice Forster, Augusto Mari noni, ed. and transcription (Florence, Italy: Giunti Barbera, 1992). Available for consultation at the Vic toria and Albert Museum, London.
5. Ladislao Reti, "Leonardo da Vinci the Technolo
gist: The Problem of the Prime Mover," International Leonardo Symposium, University of California, 1966.
6. See the web site of Carl F. Barnes at . He dates the work to 1220-1230 A.D.
7. Leonardo da Vinci, The Madrid Codices, Ladislao Reti, ed. (McGraw-Hill, 1974) ; Ladislao Reti, ed., The Unknown Leonardo (London: Hutchinson, 1974).
8. James J. Sweeney, "Alexander Calder (1898-1976)," in Five American Sculptors (New York: Museum of Mod ern Art, 1969).
9. Allan A. Mills, "The Mercury Clock of the Libros del Saber," Annals of Science 45 (1988) pp. 329-344.
10. Leonardo da Vinci, Codex Forster II, folio 92v.
Manuscript received March 2006.
42 Mills, Leonardo and Perpetual Motion
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Article Contentsp. 39p. 40p. 41p. 42
Issue Table of ContentsLeonardo, Vol. 41, No. 1 (2008) pp. 1-102Front MatterEditorial: A Call for New Leonardos [pp. 2-2]Leonardo on the Web [pp. 4-4]Special Section: Art Embodies A-Life: The VIDA Competition[Introduction] [pp. 5-5]Art Embodies A-Life: The VIDA Competition [pp. 6-15, 17-24]
Artist's ArticleFractured Cybertales: Navigating the Feminine [pp. 26-34]
Special Section: "Leonardo" Celebrates Leonardo da VinciIntroduction: "Leonardo" and Leonardo da Vinci [pp. 36-38]Leonardo da Vinci and Perpetual Motion [pp. 39-42]"L'Arte dei "Romori":" Leonardine Devotion in Luigi Russolo's "Oeuvre" [pp. 43-48]Leonardo, Nonlinearity and Integrated Systems [pp. 49-55]The Proportional Consistency and Geometry of Leonardo's "Giant Crossbow" [pp. 56-63]
Special Section: From the Leonardo ArchiveLetterpress Language: Typography as a Medium for the Visual Representation of Language [pp. 66-74]
Leonardo ReviewsBooksReview: untitled [pp. 75-75]Review: untitled [pp. 75-76]Review: untitled [pp. 76-77]Review: untitled [pp. 77-78]Review: untitled [pp. 78-78]Review: untitled [pp. 78-79]Review: untitled [pp. 79-80]Review: untitled [pp. 80-81]Review: untitled [pp. 81-81]Review: untitled [pp. 82-82]Review: untitled [pp. 82-83]Review: untitled [pp. 83-85]Review: untitled [pp. 85-86]Review: untitled [pp. 86-87]
FilmsReview: untitled [pp. 87-87]Review: untitled [pp. 87-88]
Leonardo Reviews On-Line [pp. 88-89]
Special Section: Transactions"Graph Theory": Linking Online Musical Exploration to Concert Hall Performance [pp. 92-93]The Seven Valleys: Capturing the Numinous in a 3D Computer Game Engine [pp. 94-95]Obliterated Bodies: An Installation [pp. 96-97]Picbreeder: Collaborative Interactive Evolution of Images [pp. 98-99]
Leonardo Network News [pp. 100-101]Back Matter
