The vortex
Movement in water and air was Leonardo’s greatest preoccupation. As the
most tangible evidence of natural force, spiraling forms and vortices
held a particular fascination. Their forms pervade the entire spectrum
of Leonardo’s work in the realms of hydraulics, anatomy, mechanics and
art.
- Diagramme of Aristotle's four elements
An accidental force
The framework for Leonardo’s
understanding of the vortex was drawn from late medieval natural
philosophy, derived originally from classical sources. The four
elements – earth, water, air and fire were arranged in concentric
circles. Each desired to find its own level in nature. An “accidental
force” was required to move one of them from its assigned position. An
object above its natural level would exercise weight and desire to
descend according to the rule of gravity. One below its natural level,
such as a submerged bubble, would desire to ascend by the shortest
route possible.
In late medieval theory, the quality impressed
in a moving body by force was termed “impetus”. The concept of impetus
differed from the Newtonian law of the conservation of motion in that
impetus “drains” from an object in accordance with the natural rule of
the pyramidal diminution of power, rather than persisting until opposed
by contrary forces. Nonetheless, impetus was just as remorseless as
Newtonian inertia. On encountering an obstruction, a moving object
would necessarily strive to complete its assigned motion, creating
patterns of eddies or vortices in the process.
- Ms F Fol 18v-19r - The nature of water. Photo RMN - © René-Gabriel Ojéda
Water
As a “Master of water”, Leonardo needed to manage
the movement of water and control its destructive, erosive power. He
studied and recorded the movements of water under variable conditions
repeatedly, adopting a scientific approach to the subject, as
illustrated on Ms F Fol18v.
In the upper diagram, Leonardo
illustrates the turbulent flow of water around a rectangular obstacle
labeled “f”, noting that such “envelopings of courses” are caused by
“the impetus of water under other water”. The lower water strikes the
bottom first and immediately rises to the surface. The upper water does
not descend, but when it encounters the rising water it collides with
it and the two waters “unite and turn about together in their contact.”
In the second diagram, water cascades from the gate of a
lock, falling into other water. That which is closest to the middle is
“most oblique” and that which is closest to the extremities “most
upright”.
Leonardo’s visualizations of water in motion in
these drawings are not unlike the spiraling curls of hair. The visual
appearance of natural phenomena was a natural consequence of its
dynamic force. He remarks that “the motion of the surface of water
resembles the behaviour of hair, which has two motions, of which one
depends on the weight of the strands, the other on the line of its
revolving; thus water makes revolving eddies, one part of which depends
upon the impetus of the principle current, and the other depends on the
incident and reflected motions.”
- Notes on the valves of the heart and flow of blood within it, The Royal Collection © 2005, Her Majesty Queen Elizabeth II
The heart
Leonardo’s study of water became particularly
intense around 1508, coinciding with one of the periods of study of
human anatomy. The human body provided the perfect model for the
engineer and vice versa.
Leonardo’s study of the aortic valve, as illustrated in his drawing Notes on the valves of the heart and flow of blood within it,
was unprecedented. Once again, the approach is highly scientific. He
studied the problem just as he did the flow of water, by making models
of the aorta, giving instructions for making wax casts and glass
models. He noted experiments with flowing water and grass seed to track
the flow of blood through the valves.
Leonardo’s studies of
the shape of the valve cusps showed him that the orifice of the open
valve was triangular in shape. By applying his hydrodynamic studies to
the effects of such a shape on the flow of water from a pipe, he noted
that whether horizontal or vertical, the flow was greatest at the
centre where there was least friction with the sides. The shape of the
outflow through the triangular orifice made three distinct eddies
returning back as they percuss the stationary blood already in the
aorta, as illustrated in the lower diagrams on the Notes on the valves of the heart. The weight of the returning eddies then caused the valve to close, ready for the next surge of blood.
Leonardo came to realize that the essence of cardiac action was its
contraction in systole whereby its contained blood was “percussed” and
expelled along the arteries. The central, most powerful part of the
bloodstream ejected through the aortic pressure valve produces the
pressure wave through the aorta and other arteries, which Leonardo
recognised as the palpable pulse.
- Codex Forster Book 1, Fol 44r - Studies of a pump for perpetual motion, detail © V&A Images, Victoria and Albert Museum
Perpetual motion
The age-old dream of perpetual motion, in
which an object moves forever without the expenditure of any limited
internal or external source of energy, became a fashionable quest for
Renaissance inventors.
In the Codex Madrid, Leonardo
recalled “having seen many men and from various countries brought by
their infantile credulity to Venice with the great hope of gain by
making mills in dead water. Being unable, after much expense, to move
such a machine, they were compelled by great fury to escape from this
debacle”. Carefully drawn “wheels which continually revolve” in the
Codex Forster may well be the designs of others encountered in Venice.
Commenting on the failure of each device, Leonardo noted that such
wheels are “sophistical”. Later he exclaimed “speculators on perpetual
motion, how many vain designs you have created in the like quest! Go
and join up with the seekers of gold”. And yet, he was unable to resist
the challenge himself!
In the belief that spirals and screws
might hold a solution, he applied his beloved principle of the vortex
to the problem. The design on the right of Codex Forster Fol
44r is one of a number of solutions or “compound screws” involving
planar spirals, conical spirals and V-shaped configurations of tubes
combined to achieve continuous motion. The water ascends to the centre
of the planar spiral “s p” and then passes to the pyramidal screw “n c”
running from the point at “c” to “p” and acting as an “equidistant
lever” to turn the whole apparatus. As the device revolves, further
“levers” would come into play, though the precise configuration or
operation is far from clear. Ultimately, the quest for perpetual motion
eluded Leonardo, just as it eludes modern physicists today.
- Madonna, Child, St Anne and a Lamb, Photo RMN - © Daniel Arnaudet
- Study of the Star of Bethlehem, The Royal Collection © 2005, Her Majesty Queen Elizabeth II
The paradise of mathematics
Leonardo famously said that
mechanics is the “paradise of mathematics”. Today, few might agree with
him in light of the complexities of the subject! In accordance with
Aristotle’s concept of science as a systematic inventory of the world,
he set out to classify vortices just as a botanist might classify
plants. Ultimately the task defeated him.
During his last years, the natural forces manifest in the gentle curls of the lamb’s coat in the Madonna, Child, St Anne and a Lamb,
and in the beautiful twisting motion of the leaves of the Star of
Bethlehem plant took on a destructive force in Leonardo’s artistic
imagination. In Ms A he wrote of “hollows in which the water, whirling
around in various eddies consumes and excavates and enlarges
chasms…consuming and devouring whatever stands in its path, changing
its course in the midst of the ruin.”
In the late Deluge Drawing
this prophetic vision of the destructive powers of nature is given full
visual expression. The turbulent forces that condition man’s existence
take the form of swirling vortices of air and water which have now
become synonymous with the uncontrollable and unknowable forces of
nature in Leonardo’s mind.