The Classical Waterwheel Problem
An Operative Case
The following is a great example that demonstrates that modern science is extremely overrated as a form of applicable knowledge. The case I present here of the waterwheel problem shows that, in terms of the power of modern science to solve engineering problems, its high degree of specialization and lack of operative discipline are the fundamental obstacles to solve concrete real-life problems.
Waterwheels can be considered as classical machines because they were extremely present already millennia ago in China, Greece, India, Rome, etc. to the point that one can even tell about the core values of a culture by mere observation of how the energy of water is technically transferred into mechanical work. Depending on the materials employed and the dimensioning of their parts, waterwheels can enormously vary their efficiency when transferring the potential energy of a given flow of water into mechanical work. So the problem essentially consists in the following: Given a set of building materials with their specific properties: Which is the specific architecture required in the waterwheel so that the efficiency of capturing the energy can be maximized?...
In the 1930s, my grandfather –on the part of my mother- engineered the first hydroelectric station for providing electricity to an area of Galicia (Spain) called Bergantiños. He never attended any engineering school –in the most academic sense of the word “school”- because at the age of 13 he started working in Cuba in the field of electro-mechanical crafts, similarly as how my other grandfather –on the part of my father- was initiated into blacksmithing at about that same age. Therefore, his work was mostly operative and didn´t require necessarily the assistance of the type of theoretical/mathematical science that is mostly taught today. However, if one carefully studies today the power station he constructed in the 1930s one is obliged to affirm that it´s “perfect”, in the sense that the specific technical configuration of the station maximized the capturing of energy present in the water flow. Even though the turbines that are available today in the industry have much better performances than those employed by my grandfather, I´ve often seen them very badly chosen and erroneously installed in many places around the region I live. So, in spite of the cult of high-tech devices that characterizes our time, it’s fair to say that -in architectural terms- the work of my grandfather still stands as much superior to most power systems that are constructed today. What´s more, even though today we have available superb materials like carbon fiber, etc. there isn´t any guarantee whatsoever that the construction of a classical waterwheel –based on the simplest model represented below- with such materials shall attain the architecture of maximum efficiency.
Though it seems apparently simple, the classical waterwheel problem isn´t taught today in any engineering faculties in the world because of its highly multidisciplinary character; the first approach to its solution involves Newtonian mechanics, fluid mechanics, thermodynamics and stress materials, and generally only about 1 in 30 aeronautical or industrial engineers master all these fields at the same time. Though challenging, these analytical approaches provide a first physical modeling of the processes involved, but then the next challenge is that the calculation of the rotation dynamics of a waterwheel don´t provide analytical/formal results, or in other words, that given a specific architectural configuration of the waterwheel, calculating the time it takes for the wheel to rotate a specific angle requires computation (due to the presence of elliptic integrals in the physical models of this type of rotating process…). Hence, simulating the dynamics of a machine as apparently simple as a waterwheel requires massive processing power!! We don´t have to delve into quantum physics to discover that the waterwheel problem would´ve even challenged the minds of Albert Einstein, Werner Heisenberg or Richard Feynman!
Even by supposing that we succeed in attaining this phase of the waterwheel problem by combining the features of software like Matlab, Phyton or Wolfram Mathematica, the most efficient solutions that the computer simulations shall provide us might not be efficient in terms of the selfsame construction of the machine, that is to say, it often happens that the optimal architecture provided to us by the computer might be too costly or even unfeasible to produce with the means we have at reach. This is a quite similar problem as when purchasing high-performance wheels for one´s racing bike… In this regard, it´s worth pointing out that the concern with efficiency and performance that characterizes today´s engineering, sport and economic practices isn´t what defines the form of traditional architectures like the waterwheel but that durability weighs much more, or in other words, what really matter in these architectures is that they maximize the total amount of energy extracted from nature during their useful life. Efficiency is only part of the process, similarly as how in athletics the urge for efficiency very often has inefficient results in the long term. Ultimately, it´s the case of the tortoise and hare in Aesop´s famous fable…
At this level of the waterwheel problem there is no single scientific approach available that can assist us due to the existence of countless chaotic variables that transcend the computer modeling domain. And yet there´s no doubt that such perfect architectures were effectively built during the past and still stand today, even without any computing technology, without any so-called “A.I.” and without having available the type of physics we have available today.
In my work as an industrial engineer, I´ve had to model into scientific language the most diverse physical processes before increasing their performance, yet in the case of the waterwheel problem this approach is insufficient, and the increase in computing processing power is affected by abrupt diminishing returns. However, in nature the capacity of living beings to solve this energetic problem occurs without thinking…
Beyond the limits of scientific reductionism, the waterwheel problem can easily carry our minds and work to the true center of the physical world. The polar character of this problem very much resembles the polar character of the sun or the Aristotelian “unmoved mover”. The old lineage of the Operative Freemasons made use of other many symbols (the plumb/level and the chisel/hammer which are also linked to the construction of the Egyptian pyramids - See Operative Traditions III) but at this moment in time the waterwheel constitutes the most evocative symbol of operative knowledge, mainly due to the fact that, after the 2019 global non-renewable energy production maximum human societies are now obliged to capture renewable energies in the most durable way.
If we look closely at the physics of a waterwheel we can soon discover that it perfectly symbolizes the mechanisms by how all beings also aspire to transfer the flows and currents of life into durable forms.
Why not consider traditional waterwheels as fossilized forms of living beings?...
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Miguel A. Fernandez is an industrial engineer with a work background that ranges along the fields of chain supply logistics, renewable energy, process modeling and project managing. He has written 7 essays and 2 novels. More information is available here.