Tag: Helmholtz

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With this ring…

vortices in coffee
Vortices behind a spoon dragged through coffee.

How many vortices do you see in your coffee? We finally arrive at the last in this series about the contributions of Helmholtz to the physics of a cup of coffee and the one that was to be the link with the (postponed) Coffee & Science evening at Amoret Coffee: vortices. But, beyond those that form behind a spoon, where do you see vortices in coffee and how can we connect them to dolphins?

Each morning as I prepare a pour over, I wait as each drop of coffee falls into the coffee bath below it. Some bounce up, some stay on the surface for some moments, many more pass straight through and get absorbed into the brew. I will admit that on most mornings, I am not thinking about the fact that I am watching one of the most beautiful pieces of physics unfold in front of my eyes and yet, this is how the processes occurring in the V60 were described by Lord Kelvin:

“[Helmholtz’s] admirable theory of vortex rings is one of the most beautiful of all beautiful pieces of mathematical work hitherto done in the dynamics of incompressible fluids.”

One of the most beautiful of all beautiful pieces of mathematical work? In my morning V60? How can we see these vortices as they fall? Sadly, it is perhaps easier to swap the coffee for plain water and drop food colouring into into it if we actually want to see these vortex rings form. As each coloured drop hits and goes through the surface, it forms a ring that curls up on itself and, if you are lucky, splits into many smaller rings, cascading to the bottom of the pot. You can see a film of the effect here or try it for yourself.

Vortex ring cascade, food colouring into plain water, V60 vortex
Dripping food colouring into a V60 of plain water: visualising the vortex rings that form every morning as you brew your coffee.

Each drop of coffee dripping from the filter into your coffee pot in the morning does this even if you can’t usually see it.

And though these rings must have been seen before Helmholtz’s paper in 1858, and even dolphins play with them in the sea, no one had attempted a mathematical model until Helmholtz. Helmholtz founded his mathematics on several theorems including the fact that a vortex cannot terminate within the fluid. It either has to terminate at the boundary of the fluid (like the vortex formed behind a spoon being dragged through coffee) or it has to close on itself (it forms a vortex ring) (more info here, opens as pdf).

Helmholtz seems to have come to vortices via an interest in organ pipes. He noticed that vortex sheets form at the inner surface of the pipe that can contribute significantly to the internal friction of the air flow through the pipe*. This means that, at the boundary between the moving air and the stationary air at the pipe edge there is a region of turbulent flow which leads to the formation of vortices. For Helmholtz, this had immediate consequences for measuring the speed of sound using pipes. Because where as previously the length of the organ pipe had been taken to be the distance between the maximum vibration (anti-node) and minimum vibration (node) of the sound wave, Helmholtz noticed that the presence of vortex sheets at the surface of the pipe would lead to an apparent lengthening of the resonator. If you used the length of the pipe to calculate the speed of sound, you would be very slightly wrong*.

As he investigated further, he found that these same surface-vortex effects explained a feature of organ design that had been known empirically but never explained. Why is it that in order for the character of the sound to be similar for each note, notes played through short, fat pipes must be accompanied by notes played through tall thin ones? Again it is to do with the air flow past the surfaces of the organ pipe.

vortices, turbulence, coffee cup physics, coffee cup science
Another cool consequence of boundary layers: Vortices created at the walls of a mug when the whole cup of coffee is placed on a rotating object (such as a record player).

In fact, these vortex sheets that appear at the boundaries between fluids appear so often, you can start to see them everywhere! They are in a cup of coffee if you put it on a record player (as with the picture of ink in a takeaway cup here) and they are in clouds that show a Kelvin-Helmholtz instability. Appearing like a series of waves on a cloud in the sky, Kelvin-Helmholtz instabilities occur when a layer of cold dry air flows fast past a layer of hot and humid air. At the boundary of the two layers, a vortex structure forms and because the hot humid air encounters the cold dry air within that vortex, clouds can form at the boundary which reveal the vortices driving them. Although the conditions to create them must occur quite frequently, they last only a very short amount of time (less than a minute is typical) and so are considered quite rare. Look out for them next time you can see that the weather is changing and the clouds are fairly high in the sky.

Of course, it is not just on Earth and in coffee that we see these vortex structures. We see them in the weather patterns of other planets, in the solar wind and in jets leaving supernovae. And it is not just in fluids that Helmholtz’s mathematics of vortices proved useful. In Helmholtz’s equations the fluid velocity associated with a vorticity described (exactly analogously) the magnetic force produced by an electric current distribution*.

Kelvin Helmholtz instability in clouds over the M3 in January 2020
A Kelvin-Helmholtz instability in clouds over the M3 in January 2020.

Far more could be said about Helmholtz’s work on vortices and its links to both coffee and the weather on Saturn, but that will have to wait until the next Coffee & Science evening at Amoret. Until then, enjoy watching these astonishing structures in your coffee and let me know if you observe anything interesting with them.

This is the last in a series of articles on the contributions of Helmholtz to our understanding of coffee. You can read an introduction here, his work on vision and colour here, the sounds of coffee here and the energy of coffee here. Next time, we’ll be back to experimenting with coffee, please do let me know (on Twitter, FB or in the comments) of any experiments you have been doing at this time, what have you seen in your brew?

*”Worlds of Flow”, Olivier Darrigol, Oxford University Press, 2005

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Making coffee work

Cogs, Wimbledon Common, Windmill, Contact S2b, instant coffee and washing soda developer
Cogs on Wimbledon Common, taken using a film based camera and developed using (instant) coffee. A way to make coffee ‘work’ but not the one linked to Helmholtz.

Search online and you can find videos of machines that lift cogs or turn wheels that are powered by the steam rising off a coffee. You can see an example here and find instructions for how to build your own here (a “stay at home” hobby project perhaps?).

Although such machines are very much for the hobbyist, the principle of the steam engine drove the industrial revolution. And, even now, much of our power network relies on somehow heating water which then drives a turbine that generates electricity. Underlying this is the principle that energy can be transformed from one type to another but is, ultimately, always conserved.

The concept is easiest to visualise with a pendulum or a swing. At its height, the pendulum has a maximum of potential energy but is not moving (so its kinetic energy is zero). As it passes through its minimum height point, the speed of the swing (or pendulum) is maximum and the potential energy at a minimum. Indeed, the amount of potential energy lost by the pendulum is equal* to the amount of kinetic energy gained. The same can be extended to “work” which, in the language of physics is always energy. If a certain amount of energy is put in, a certain amount of work can be produced. In a closed system and without loss, the amount of energy you put in is the amount of energy you get out. In any real system, some of that energy is lost to heat or other methods of loss.

Press Room coffee Twickenham
Whether you make your coffee as a pour over or an espresso, the principle of conservation of energy is always the same. The energy you put in will equal the energy you get out (with some lost as heat as the coffee cools). Pour over at the Press Room, Twickenham.

To use a more coffee related example, in an espresso machine, work is done to put the water under high pressure (and separately to heat it). This pressurised water is then allowed to escape through the coffee puck where the work originally done pressurising it gets transformed into the kinetic energy (speed) of the water going through the group head. Changing the pressure changes the speed at which the water goes through the puck in an analogous way to how changing the height of the pendulum drop affects the speed as it goes through its central point. Of course you won’t always see this because changing things like the grind size in the espresso puck will also affect the route that the water takes as it travels through the puck and so the actual speed at which you see the coffee-infused water leaving the espresso basket will be affected by that too. The real world is never quite so easy as the ideal.

A pour over works in a different way. Here, the energy is stored in the water ‘bath’ in the filter as gravitational potential energy. As the water falls, it gains kinetic energy at the expense of this gravitational energy (or height). As the espresso machine also works with gravity, the conclusion would be that the water will move much faster through the espresso puck than the pour over bed. That this often doesn’t seem to be so is again because of the effects of the resistance of the coffee bed or espresso puck, on the espresso and the pour over.

This concept of the conservation of energy has been engrained into us from an early age. And so it may be surprising that it is a fairly recent principle in physics. For although versions of this principle had been considered for many years, it had not been recognised until the 1840s (by James Joule and Robert Mayer in 1843 and 1842 respectively) that work and heat were interchangeable. And it wasn’t until 1847 that Helmholtz recognised that all energy was conserved. Although at that time he was using the word ‘force’ for what we now call ‘energy’, and what we now call kinetic energy was thought of as a ‘living’ energy. He wrote:

“… the loss in the quantity of potential force is always equal to the gain in living force, and the gain of the first is the loss of the second. Thus, the sum of the existing living and potential forces is always constant.”**

So, among the many contributions to physics that he made, Helmholtz also has a claim to being among those who developed the field of thermodynamics which remains crucial both for physics and for our industrial and technological progress.

Rag&Bone, Rag & bone, coffee Victoria, coffee Westminster
Rag & Bone Coffee in front of St Matthew’s Church. Much of our understanding is based on our assumptions about how the world works. The challenge for us is to identify those assumptions that underlie our thinking.

There is perhaps a cautionary note here for any who are tempted to think that science and religion are always somehow in opposition. For the British scientists who contributed to the development of the idea of conservation of energy (such as Joule and William Thomson (Lord Kelvin)), the concept was founded on the idea of a Creator God: as only God could create or destroy, so it followed that energy of itself, could never be either created nor destroyed, it could only be transformed from one form to another. The idea of a God was, for them, implicit in the idea of the conservation of energy**.

Helmholtz had a philosophical disagreement here. For him, the principle was founded on a Kantian understanding of philosophy***. Certainly certain things had to be assumed at the beginning (such as the principle of causality and the existence of matter outside of our perception of it). But once these assumptions had been made, the principle of conservation of energy followed in a deterministic manner.

Does this matter? In our everyday experience of engines and the way things work, conservation of energy certainly seems to be crucial. We no longer question the principle but assume that one form of energy is transformed into another and is continuously conserved even as it is dissipated into the universe as heat as our coffee cools. But nonetheless, Helmholtz’s understanding was founded on certain assumptions, beliefs, just as Joule and Kelvin’s. It helps to be aware of the philosophical underpinning of our science so as to ensure we don’t have over confidence in what we can, and cannot, know.

So Helmholtz can teach us something else as we gaze into our coffee. Our world is multifaceted, and what we believe about what the world is, influences and informs our understanding of how the world works. Our challenge is to look into ourselves as we sip our coffee and to start to see what we believe we know and what we can actually know. And if we were to really do that, what conflicts would we find?

*With the usual caveats of no energy being lost to friction etc.

**”Helmholtz and the British Scientific Elite: from force conservation to energy conservation”, David Cahan, Notes Rec. R. Soc (2012), 66, 55-68

***”Helmholtz: from enlightenment to neuroscience”, M Meulders, MIT press, 2010

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Listening to coffee

coffee tasting notes
Do we pay attention long enough to discern tasting notes such as those in the cup profile here? My current coffee, from Amoret – where you can currently buy this coffee and see if you can ‘hear’ these tasting notes.

Do we taste and appreciate coffee in a similar way to the manner in which we would appreciate a complex piece of music?

Perhaps the idea seems fanciful, maybe even non-sensical. How could it be that the way that we appreciate flavour is similar to how we listen (and how is this related to physics)? Coming from someone who is a clear amateur in both appreciating coffee and appreciating music, you would be forgiven for being a little dismissive (though I’d hope that you would trust me on the fact that there will be a link with physics). But, by being an amateur in taste, I think it is possible to see a first connection: it is in how much attention and learning (training or practise) we give to our perception of our sensation.

A great nineteenth century physicist, Hermann von Helmholtz, was also a medical doctor (and a keen amateur musician). In thinking about how we listen to sounds, Helmholtz suggested that “sensation” was physiological – the effect of the note on our ear or the chemical on our taste buds – but “perception” was psychological – how we hear the notes together or discern the flavour notes of a particular coffee.

Think about how you recognise a type of coffee that you love, or distinguish between a washed and a natural? Or how you know that the instrument that you can hear through the speakers is a violin. With the latter, it is because the fundamental note played is accompanied by a set of harmonics that are distinctive to that instrument. A flute or a piano will have a different set of harmonics and so a different sound. It has been through listening to different instruments that we have learned to identify them, but it is through training and practise (or experimental physics) that we can start to discern the various harmonics.

The way that we hear the different harmonics concerns the way that their waveforms add together. This is underpinned mathematically by Fourier analysis, which describes how any wave form can be made up of a summation of sinusoidal waves. Incidentally Joseph Fourier was also the scientist who proposed the idea of a greenhouse effect back in 1824 (which you can read more about here, or in relation to coffee here). Where you may have experienced these wave combinations is in tuning a guitar (or similar instrument). When you play two notes that are nearly exactly the same, but not quite, the waves of each will add together as they make their way from the plucked string to your ear. As they travel, at some points the two waves will combine to form a large amplitude wave and at other points the two waves will exactly cancel out. We would hear it as a type of “beating” (on-off-on-off) that you can hear as you attempt to tune the two strings together to play the same note. When the two plucked strings play the same note, the two waves will only add together to be louder, they will not cancel each other out and you should hear one, continuous and smooth tone.

Guitar, coffee
From resonances to the way we sense the world around us, there are a number of connections between coffee and music.

You can be an amateur musician and still appreciate the physics that is underlying this aspect of your ability to play (tuneful) music. But Helmholtz had noted a bit more than this. Owing to the way that waves combine, and which in the simplest case gives the ‘beats’ that you notice as you tune the guitar, when you play two notes together, if you listen carefully you will not only hear the two notes, but a third, a so-called combination tone. Discovered by the organist Georg Andreas Sorge in 1740 (you can hear one of his compositions here), this third note has the frequency of the first minus the second note. So, for example, if you were listening to C4 and G4 (at 264 and 396 Hz respectively), you would additionally hear a note at 132 Hz (C3). It is incredibly difficult to be able to discern such a combination tone which maybe part of the reason that it took so long to discover them. To learn to hear the note would take a lot of practise and no less attention when listening to a piece of music. How often do we truly listen to a piece of music to be able to do this?

Where Helmholtz came into this was that, not only did he explain the origin of this combination tone (in terms of the way the waves combined), he invented a device that allowed us mere amateurs to be able to hear it. One end of a tube was designed to fit snugly into the listener’s ear, with the other end open to the sound. The size of the tube determined which frequency of sound would reach the ear. Using these devices Helmholtz showed that, not only was the combination tone a real phenomenon, it had a mathematical basis in physics. And of course there was more. If you could hear the note of the subtraction of the two sound frequencies, you should be able to hear the note of the sum of these two frequencies too. In the example above, you should hear a note at 660 Hz. This combination tone had never been heard before, it came as a prediction of Helmholtz’s theory of how sounds added, itself sparked by a profound attention that he paid to listening to music.

Using a similar resonator to that used for distinguishing the combination tone based on difference, Helmholtz showed that this note too was audible. It was a prediction of what we should be able to hear based on the physics of what was going on. It extended our ability to perceive music.

The beat of a drum or the resonance on our coffee – the links between music and coffee go further than this.

In what way is this linked to tasting coffee? It is in how we learn to distinguish our taste. Just as a musician can, with time and attention, learn to discern at least a difference combination tone so, with practise, we can train our palette to discern intensities of sweet, of sour and subtleties of acids. We amateurs can hone our skills using the SCAA coffee flavour wheel, tasting each coffee we prepare to detect the sweet, roasted or floral notes that we read about on the packs of coffee we buy. To actually describe these coffees requires skill and a large amount of practise in cupping coffee. But to develop those skills to the point of being Q-grader requires an attention to detail that is quite incredible (you can read about the training needed to become a Q-grader here). Just as with music, for some of us, even a lot of practise will only ever allow us to appreciate the work of others rather than produce it ourselves.

Of course, training our palettes requires drinking a lot of coffee, but it also means making mixtures of salty or sweet liquids and thinking about how they taste. Cupping hundreds, thousands, of coffees and paying attention to the complete flavour profile of them. Is there a flavour equivalent to Helmholtz’s summation combination tone that is waiting to be discovered? It will need someone skilled in matters of coffee appreciation and experimental science. Someone who has demonstrated the attention required to carefully listen to the taste of our coffee but who can also work on the theory of how those flavours are perceived. There are many people working on the physics, chemistry and physiology of taste and smell. Could you be one of them?

This is the third in a series of the contributions of Hermann von Helmholtz to our appreciation of the physics in coffee – it goes far beyond the vortices he may be famous for. The introduction is here while the contribution of Helmholtz to our understanding of colour and vision is here. Future posts will consider hot coffee and of course, what happens as we stir it. Much of the material for this post has been found as a result of reading Michel Meulder’s excellent biography of Helmholtz: “Helmholtz: from enlightenment to neuroscience” (2001).

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Looking at coffee

coffee at Watch House
Observing the colours in our coffee can reveal much more than just the chemistry of the cup.

How do you see your coffee in the morning? Through blurry eyes, a red-ish/brown liquid that you may admit to noticing more for its aroma and taste than for how you look at it? But what is it about that lovely red colour of a fresh filter coffee viewed through sunlight? And what about the way that the glass jar curves towards you and then bends away, how do we perceive distance?

The colour question has historically been more problematic. For Aristotle, the rainbow was composed of a mix of three colours, which fitted with Pythagorean numerology*. Newton thought there were seven, which fitted with the harmonies in music theory. Goethe (who also developed a colour theory) liked to quote “If you show a red rag to a bull it becomes angry, but a philosopher begins to rage as soon as you merely speak of colour”**.

Today, in schools we are taught that there are three primary colours for light: red, green and blue. This is because all colours of light can be observed by careful weightings of these three colours and when the three are combined we see white light. But what does it mean that light has primary colours? Is not light just a vibration, why is it that we see colour at all? It comes down to our physiology and how we sense the world.

It was Thomas Young (who also showed the wave-like properties of light) who first proposed that these three ‘fundamental’ colours were associated with three types of ‘resonator’ in our eyes. The idea was significantly developed by Hermann Helmholtz during the 1850s. Each type of receptor responded to light at all frequencies but responded most sensitively in a smaller range. Generally humans have three types of frequency sensitive (and so colour sensitive) receptors, though those with colour blindness have fewer and there are even some of us with four. Most of us though, have three types of receptors sensitive in the red, blue and green regions of the spectrum. Hence we perceive the light as white if these three types of receptor are stimulated equally, that is, if we combine blue, red and green light. The red colour seen as you brew a fresh pour over of coffee in front of a window through which sun is streaming at dawn, is red because of these activated red-sensitive cone receptors in your eye.

Sun-dog, Sun dog
A ‘rainbow’ of colour as seen in a ‘sun dog’ observed in central London. But what is colour really?

But Helmholtz went further than this. Have you ever been staring at a bright object and then turned away towards a dark wall and had the experience of seeing the same bright object ‘projected’ on the wall but in a different colour? Both Goethe and Helmholtz observed themselves as they ‘saw’ these phantom images and watched the images as they changed colour before eventually fading. While Goethe incorporated his observations into his general colour theory, Helmholtz linked the phenomenon to these same cone receptors in the eye. He realised that if your red-sensitive colour receptors had become saturated by watching a bright red object (such as a red-hot piece of iron for example), they would not respond so quickly when you looked away at a blank bit of wall. So if you, for example, ordinarily perceived the wall as white, because the red-colour receptors had been taken out for a while, your blue and green receptors would dominate while the red would not respond and so cause you to observe a greener phantom image. Would we ever see a green phantom coffee?

Unlike the question of the colour, the question of depth perception has some thoroughly more modern elements. For while many had thought about how we realise that space has depth, the binocular effect of our two eyes was not realised until relatively recently. In fact, that two, 2D images taken from slightly different angles and viewed separately through each eye appeared as if they were a 3D image, was only discovered in 1838. Prior to that, it had been thought that perhaps we knew about depth because of our learned familiarity with the size of objects, much as Fr Ted explained the distant cows to Dougal (which is one of the clips here).

Shadows reveal a lot. From the position of the light source to information we interpret as informing us about how different objects relate to each other. And again, why is it that shadows appear blue on snow?

Apparently between 1855-59, 29% of scientific papers concerning the eyes were about this problem of stereoscopy or binocular vision. Helmholtz’s contribution to the debate was to show how much of our realisation of depth was a learned but unconscious process and also how much relied on the involuntary movement of our eyes to ‘calibrate’ the surroundings after fixing on something. That movement of your eye that is impossible to control but you can watch in others as they concentrate is there for us to check that what we think we are seeing is what we are seeing.

Just how much is revealed to us, about the coffee and ourselves, by our gazing at it? When Feynman discussed colour vision in volume I of his Lectures on Physics, he wrote “We make no apologies for making these excursions into other fields, because the separation of fields… is merely a human convenience, and an unnatural thing. Nature is not interested in our separations, and many of the interesting phenomena bridge the gaps between fields.”*** Our world is intricately connected, we only have to gaze at our coffee to have an intuition as to how much this is true.

This post is one of a series about the contributions of Hermann von Helmholtz to how we understand the world around us. The introduction is here and it will be followed by thinking about what we hear in our coffee, the heat of our coffee and, of course, what happens when we stir it.

*”The Rainbow Bridge: rainbows in art, myth and science” R.L. Lee Jr, A.B. Fraser, Penn State University Press (2001)

**”Helmholtz: from enlightenment to neuroscience” M. Meulders, MIT press, (2010)

***”The Feynman lectures on physics volume I”, Feynman, Leighton and Sands.

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Connectivity

Shades of light and dark. How do we see shadow, colour, depth? How is it linked to the physics of coffee?
Superscript and subscript

The other morning, grinding coffee in order to prepare a V60 (the last of a fantastically complex Natural El Salvador from Amoret coffee), I was hit by the intense aroma of rich, freshly ground beans. It seems at the moment that we are surrounded by more vivid impressions of things that have, in reality, always been there, but that have previously been obscured by other features of our lives. Such things have been revealed by the changes to our lives that have come about as the result of the “lock-downs” needed to reduce the transmission of Covid-19. The birdsong that seems more dramatic and intense than before the traffic subsided. The colours of the trees as the spring light bounces off and filters through the leaves no longer surrounded by a misty haze of pollution (now suggested through its absence). And of course the smell of the coffee hitting our olfactory senses.

Superscript and subscript

Before this period of social distancing and self-isolation, I had been preparing for another in the series of Coffee & Science evenings at Amoret coffee in Notting Hill. The title of the evening had been “Space Coffee” and we were going to explore the connections between what happened in your coffee cup with features that you can see in the atmospheres of planets such as Saturn and Jupiter. Actually the connections are a lot wider than that and can be seen on the Earth too, but the atmospheres of Jupiter and Saturn have some very peculiar structures that you may not immediately think could possibly be linked to your coffee cup. One of the key people who worked on the science behind this was Hermann von Helmholtz (known as H2 to his friendsa). For the Coffee & Science evening, the important work of Helmholtz was on vortices and fluid rotations, but it turns out that he has more links with a coffee cup than that, connections that can even give us some food (drink?) for thought in this time of separation.

which will win, gravity or light
The world has not really been turned upside down, but certainly the way that we view it could be. An opportunity to re-assess our view points?
Superscript and subscript

Helmholtz made many contributions to the understanding of our world including how we see it. In addition to inventing the ophthalmoscope (in ~1850), Helmholtz was interested in the way in which we perceive colour and how we manage to see in 3D. Thinking about the way in which we see things like light and colour and developing on the idea that how we perceive our world is, ultimately, received in each of our own minds via our sense organs, Helmholtz compared the sensations of light and colour to symbols of language: ways in which we interpret the world around us. As Michel Meulders writes in his fascinating biography of Helmholtz (told from the view point of a medical doctor rather than a physicist)b, Helmholtz had

“…stated lyrically that we should thank our senses, which miraculously gave us light and colour as responses to particular vibrations and odour and taste from chemical stimuli. We should thank the symbols by which our senses informed us of the outside world for the spell-binding richness and the living freshness of the sensory world.”

Superscript and subscript

What does it mean that I should thank my senses for the way in which I smell, see and hear the coffee beans as they are ground?

Superscript and subscript

The connections between Hermann von Helmholtz and coffee are more than just the vortices that form, and more than the fact that Michael Faraday once served him cups of it while he was preparing lectures for the Royal Institutionc. We’ll be exploring those links over the next few weeks, from how we see coffee, through how we hear it and eventually to what ties it all together. Please keep checking back but also, do let me know what new sensory symbols you have perceived in this time of opportunity to attention.

Superscript and subscript

a “Worlds of Flow”, Olivier Darrigol, Oxford University Press (2005)

Superscript and subscript

b “Helmholtz: from Englightenment to Neuroscience”, Michel Meulders, MIT press (2010)

Superscript and subscript

c “Helmholtz and the British Scientific Elite: from force conservation to energy conservation”, David Cahan, Notes & Records of the Royal Society, 66, 55-68 (2012) doi:10.1098/rsnr.2011.0044