# The Mathematics of a Perfect Cup of Coffee

Coffee has been part of human culture for a long time. (Image: pixabay / CC0 1.0)

Researchers are a step closer to understanding how to prepare a perfect cup of coffee with the help of mathematics. Coffee is one of the most widely consumed drinks in the world, with estimates of more than a couple of billion cups consumed each day worldwide. Brewers have developed a wide range of methods to make the perfect cup of coffee, but few have ever posed the question mathematically.

In order to better understand the advanced mathematics involved, a group of researchers, led by Dr. Kevin Moroney at the University of Limerick in Ireland, and Dr. William Lee at the University of Portsmouth in the U.K. put forward a brand new model of coffee extraction from drip filter machines.

The researchers looked at the effect of grain size on the way that coffee comes out of a drip filter machine. (Image: Nicholas Lundgaard via flickr / CC BY-SA 2.0)

Drip filter coffee is made by pouring hot water over a bed of ground coffee beans, otherwise known as grains, housed in a filter. Gravity pulls water through the filter, dissolving the coffee into the liquid on its way through.

## Grain size does matter

The researchers looked at the effect of grain size on the way that coffee comes out of a drip filter machine. They found that coffee is extracted from the grains in a two-step process.

The first step involves the rapid extraction of coffee from the surface of the grain. The second step is slower, and involves the extraction of coffee from the center of the grain.

It had previously been known that grinding coffee beans too finely could result in a cup of coffee that is strong and bitter. On the other hand, not grinding them enough can make the end result watery and bland. The research took that observation and made it quantitative by explaining why grain size plays such an important role in determining the taste of coffee, but also quantifies that relationship through formulas.

The research discovered that other factors also come into play when making great cup of coffee, including the shape of the coffee bed in the filter and the flow pattern of water. (Image: Sam Howzit via flickr / CC BY 2.0 )

Their research noted a trade-off between water flowing over the surface and through the interior of the grains. When the grains are large, the overall surface area is less. The water also flows more quickly through large grains, and because the water’s spending less time in contact with the coffee, the amount of extraction is less.

On the other hand, fine grains increase the amount of surface area. Also, when the grains are small, the flow of water is slowed, increasing the amount of coffee extraction.

## Shape and flow also contribute to taste

The research discovered that other factors also come into play when making a great cup of coffee, including the shape of the coffee bed in the filter and the flow pattern of water.

The shape of the coffee bed in the filter is deformed as the coffee is brewed. When first starting to brew, the coffee grains are sitting flat at the bottom of the filter, but at the end of the brewing cycle, they are coating the walls of the filter, which can affect the taste of the coffee.

The research could allow users to fine-tuning a machine for a particular grain size and flow pattern of water, resulting in a perfect cup of coffee every time! (Image: pixabay / CC0 1.0)

The flow pattern of water into the filter also can affect taste. A single jet of water down the center, like water coming out of a tap or a broad pattern like a showerhead, has different effects on the shape of the coffee bed in the filter, and thus its taste.

The research is of great interest to manufacturers of drip filter coffee machines, as it could allow users to fine-tune a machine for a particular grain size or flow pattern of water, resulting in a perfect cup of coffee every time!