July 2021 – Bean Thinking

Press Room coffee Twickenham — A smaller V60. For one cup you would use less coffee, but the errors on the measurement will always be there.

Preparing a good V60 requires 30g of coffee (for 500 ml of water)*. This can be measured using a set of kitchen scales, but a first estimate can also be obtained, if you are using whole coffee beans, by timing the passage of the grind through the grinder. Using an Ascaso burr grinder, my coffee used to come through at an approximate rate of 1g/s, so that, after 30 seconds, I’d have the perfect amount of coffee. Recently however this has changed, depending on the bean, sometimes 30g is 40 seconds, sometimes just less than 30 seconds.

Clearly there is an error on my estimate of the rate of coffee grinds going through the grinder. This may be influenced by factors such as the hardness of the bean (itself influenced by the degree of roast), the temperature of the kitchen, the cleanliness of the grinder and, the small detail that the ‘seconds’ measured here refers to my counting to 30 in my head. Nonetheless, the error is significant enough that I need to confirm the measurement with the kitchen scales. But are the scales free of error?

Clearly in asking the question, we know the answer will be ‘no’. Errors could be introduced by improper zero-ing of the scales (which is correct-able), or differences in the day to day temperature of the kitchen (not so correct-able). The scales will also have a tolerance on them meaning that the measured mass is, for example, only correct to +/- 5 % Depending on your scales, they may also only display the mass to the nearest gramme. This means that 29.6g of coffee would be the same, according to the scales, as 30.4g of coffee. Which in turn means that we should be using 493 – 507 ml of water rather than our expected 500 ml (the measurement of which also contains an intrinsic error of course).

A Turkish coffee provides a brilliant illustration of the type of particle distribution with depth that Jean Perrin used to measure Avogadro’s constant. For more information see here.

The point of all of this is that errors are an inescapable aspect of experimental science. They can also be an incredibly helpful part. Back in 1910, Jean Perrin used a phenomenon that you can see in your coffee cup in order to measure Avogadro’s constant (the number of molecules in a mole of material). Although he used varnish suspended in water rather than coffee, he was able to experimentally verify a theory that liquids were made up of molecules, by the fact that his value for Avogadro’s constant was, within error, the same as that found by other, independent, techniques. Errors also give us an indication of how confident we can be in our determination of a value. For example, if the mass of my coffee is 30 +/- 0.4 g, I am more confident that the value is approximately 30 g than if the error was +/- 10 g. In the latter case, I would get new scales.

But errors can also help us in more subtle ways. Experimental results can be fairly easily faked, but it turns out that the random error on that data is far harder to invent. A simple example of this was seen in the case of Jan Hendrik Schön and the scientific fraud that was discovered in 2002. Schön had shown fantastic experimental results in the field of organic electronics (electronic devices made of carbon based materials). The problem came when it was shown that some these results, despite being on different materials, were the same right down to the “random” noise on the data. Two data sets were identical even to the point of the errors on them, despite their being measurements of two different things.

A more recent case is a little more subtle but crucial for our understanding of how to treat Covid-19. A large study of Covid-19 patients apparently showed that the drug “Ivermectin” reduced mortality rates enormously and improved patient outcomes. Recently it has been shown that there are serious problems with some of the data in the paper, including the fact that some of the patient records have been duplicated and the paper has now been withdrawn due to “ethical considerations”. A good summary of the problems can be found in this Guardian article. However, some of the more worrying problems were a little deeper in the maths behind the data. There were sets of data where supposedly random variables were identical across several patients which suggested “that ranges of cells or even entire rows of data have been copied and pasted“. There were also cases where 82% of a supposedly random variable ended in the digits 2-5. The likelihood of this occurring for random variables can be calculated (it is not very high). Indeed, analysis of the paper showed that it was likely that these values too were either copy and pasted or “invented” because humans are not terribly good at generating properly random numbers.

A gratuitous image of some interesting physics in a V60. If anyone would like to hire a physicist for a cafe, in a 21st century (physics) recreation of de Moivre’s antics at Old Slaughters, you know how to contact me…

Interestingly, a further problem both for the Ivermectin study and for the Schön data comes when you look at the standard deviation of the data. Standard deviation is a measure of how variable is the measured outcome (e.g. duration of time a patient spent in hospital). For the ivermectin study, analysis of the standard deviations quoted on the patient data indicated a peculiar distribution of the length of hospital stay, which, in itself would probably just be a puzzle but in combination with the other problems in the paper becomes a suggestion of scientific fraud. In Schön’s data on the other hand, it was calculated that the precision given in the papers would have required thousands of measurements. In the field in which Schön worked this would have been a physical impossibility and so again, suggestive of fraud. In both cases, it is by looking at the smaller errors that we find a bigger error.

This last detail would have been appreciated by Abraham de Moivre, (1667-1754). As a mathematician, de Moivre was known for his work with probability distribution, which is the mathematics behind the standard deviation of a data set. He was also a well known regular (the ‘resident’ mathematician) at Old Slaughters Coffee House on St Martin’s Lane in London^[1]. It is recorded that between 1750 and 1754, de Moivre earned “a pittance” at Old Slaughters providing solutions to games of chance to people who came along for the coffee. I wonder if there are any opportunities in contemporary London cafes for a resident physicist? I may be able to recommend one.

*You can find recipes suggesting this dosage here or here. Some recipes recommend a slightly stronger coffee amount, personally, I prefer a slightly weaker dosage. You will need to experiment to find your preferred value.

[1] “London Coffee Houses”, Bryant Lillywhite, 1963

Up in the air with a Pure Over Brewer

The diffuser sitting on top of the Pure Over coffee brewer. The holes are to ensure that the water falls evenly and slowly onto the grounds below.

The Pure Over is a new type of coffee brewer that is designed to brew filter coffee without the need for disposable paper filters. The brewer, which is completely made of glass, is a perfect size for brewing one cup of coffee and, as promised, makes a lovely cup without the need for wasteful paper filters. Generally, for 1-cup filter coffees, the Pure Over has become my go-to brewing method, although it does have a few idiosyncrasies to it that are helpful to be aware of while brewing.

An advantage of this brewing device is that it provides a large number of opportunities for physics-watching, including a peculiar effect that connects brewing coffee to an air balloon crash into the garden of a London Coffee House. It concerns a feature of the Pure Over that is specific to this particular brewing device: the ‘diffuser’ that sits on top of it.

The glass diffuser has five small holes at the bottom of it which are designed to reduce the flow of the water onto the coffee bed so that it is slower and more gentle. In order to avoid the paper filters, the Pure Over features a filter made of holes in the glass at its base. This filter does surprisingly well at keeping the coffee grounds out of the final brew, but it works best if the coffee bed just above it is not continuously agitated. The idea of the diffuser is that the coffee grounds are more evenly exposed to the water, with the grounds closest to the filter being least disturbed and so the coffee is extracted properly.

As water is poured from a kettle through the diffuser, the water builds up in the diffuser forming a pool that slowly trickles through the holes. Initially this process proceeds steadily, the water is poured from the kettle into the diffuser and then gently flows through and lands on the coffee. At one point however, the pressure of the steam within the main body of the brewer builds until it is enough to push the glass diffuser up a bit, the steam escapes and the diffuser ‘clunks’ back onto its base on top of the pure over. Then, this happens again, and again, until there is a continuous rattle as the steam pressure builds, escapes and builds once more.

The ideal gas laws, such as that found by Jacques Charles, relate the volume and pressure of a gas to its temperature. The application of the laws helped to improve the design of steam engines such as this Aveling and Porter Steam Roller that has been preserved in central Kuala Lumpur, Malaysia.

The pressure of the steam builds until the force exerted upwards by the rising steam is greater than the weight of gravity pulling the diffuser down. Once enough gas escapes, the pressure is reduced and so the steam no longer keeps the diffuser aloft which consequently drops with a clunk. The motion could take our thoughts to pistons, steam engines and the way that this steam movement was once exploited to drive our industrial revolution. Or you could go one stage earlier, and think about the gas laws that were being developed shortly before. There’s Boyle’s Law which relates the pressure of a gas to its volume (at constant temperature). That would perhaps partially explain the behaviour of the pure over. But then there’s also Jacques Charles and his observation that the volume of a gas is proportional to its temperature (at constant pressure). This too has relevance for the pure over because as we pour more water in from the kettle, we warm the entire pure-over body and so the temperature of the gas inside will increase. Consequently, as the amount of hot water in the pure over increases, the temperature goes up, the volume of that gas would increase but is stopped by the diffuser acting as a lid. This leads to the pressure of the gas increasing (Boyle) until the force upwards is high enough, the diffuser lid rises upwards on the steam which escapes leading the pressure to once again drop and the diffuser top to go clunk and the whole cycle begins again.

Of course, we know that Boyle’s law is appropriate for constant temperature and Charles’s law is appropriate for constant pressure and so the laws are combined together with the Gay-Lussac/Amonton law into the ideal gas laws which explain all manner of things from cooling aerosols to steam engine pistons. And yet, they have another connection, which also links back to our pure over, which is the history of hot air balloons.

Charles discovered his law in around 1787, a few years after the first non-tethered hot air balloon ascent, in Paris, in June of 1783. The hot air balloon is a good example of the physics that we can see in the pure over. Although Charles must have suspected some of the physics of the hot air balloon in June, he initially decided to invent his own, hydrogen filled balloon which he used to ascend 500 m in December of 1783. Hydrogen achieves its lift because hydrogen is less dense than air at the same temperature. However, it is the hydrogen balloon that links back to coffee and coffee in London.

The first balloon flight in England took place using a hydrogen, not a hot-air, balloon in 1785. The balloon was piloted by Vincenzo Lunardi who was accompanied by a cat, a dog and, for a short while, a pigeon (before it decided to fly away). But it was not this successful flight that connects back to coffee, it was his maiden flight on 13 May 1785. On that day, Lunardi took off from the Honourable Artillery Company grounds in Moorgate, flew for about 20 minutes and then crashed, or as they said at the time “fell with his burst balloon, and was but slightly injured”⁽¹⁾ into the gardens of the Adam and Eve Coffee House on the junction of Hampstead Road and, what is now, Euston Road. In the 1780s the Adam and Eve coffee house had a large garden that was the starting point for walks in the country (in the area now known as Somers Town)⁽²⁾. Imagine the scene as, quietly appreciating your tea or coffee, a large flying balloon crashes into the garden behind you.

The Adam and Eve is no longer there, in fact, its original location now seems to be the underpass at that busy junction, and the closest coffee house is a branch of Beany Green. However there is one, last coffee connection and it brings us back to the pure over. The pressure of the steam under the diffuser needs to build until the upwards force of the steam can overcome the gravitational force down of the weight of the glass diffuser. In the same way Lunardi had to have enough lift from the hydrogen balloon to compensate for the weight of the balloon and its passengers. Lunardi had wanted to be accompanied by another human on the day of his successful flight. Unfortunately, the mass of two humans in a balloon was too much for the balloon to accommodate which is why, the human was replaced by the dog, the cat and the pigeon.

Which may go some way to illustrate how far the mind can travel while brewing a cup of coffee, particularly with a brew device as full of physics as the Pure Over.

1 London Coffee Houses, Bryant Lillywhite, George Allen and Unwin publishers, 1963

2 The London Encyclopaedia (3rd edition), Weinreb, Hibbert, Keay and Keay, MacMillan, 2008