Beer is best served chilled, and it turns out that math can help. Claudio de Castro Pellegrini of the Federal University of São João del Rey in Brazil recently set out to formulate an equation to determine the optimal shape of a beer glass that cools drinks deliciously. In other words, he was looking for a glass. Prevents the liquid inside from absorbing heat.
The simplest approach is to find a container with as little surface area as possible compared to its volume. This is because heat from the surroundings of the glass penetrates the surface of the glass. The smaller this surface is, the less heat can enter and the longer your beer will stay pleasantly cold. Dating back to ancient times, scholars recognized that in two dimensions, a circle provides the smallest ratio of circumference to area. And this finding holds true in three dimensions as well. That is, a sphere has the smallest possible surface area compared to its volume.
However, a spherical beer glass would be difficult to handle. Moreover, Pellegrini was not interested in the static situation of putting beer in a glass and watching the liquid warm. “The process here is very simple: you request a beer, the waiter delivers it, it’s served, and it’s consumed. Repeat.” he wrote in a preprint paper describing the study, published in October Posted on server arXiv.org. This means that the levels inside the glass change and so do the surfaces that are in contact with the environment. (As the glass drains, more of its surface comes into contact with the surrounding air.)
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Pellegrini started by imposing some constraints on the shape of the glass. It must consist of an insulated, flat base large enough to hold the glass upright. Glass also needs to be symmetrical, as it can be represented as a body of revolution, a three-dimensional shape that is rotated 360 degrees around a two-dimensional object. × Axis or something y shaft. To determine the optimal beer glass shape, Pellegrini adjusted the 2D shape that defines the rotating body. In a previous preprint analysis detailed on arXiv.org in February, he described the optimal glass shape for this method, but found that the most feasible container volume is 2 liters or more, and that the largest glass The volume was over 100 liters.
Next, Pellegrini aimed to design a realistic beer glass. But he had to make some simplifications. He thought the base would completely block out the heat. (In practice, the use of thick glass bases and coasters can help, but perfect insulation is not possible.) He also claims that the temperature of the beer is the same everywhere in the liquid, and that the density of the drink is uniform. I assumed that there was. This is mostly true of filtered varieties. Pellegrini dismissed beer foam as a potential insulation layer. And finally, he also ignored the heat transfer from the human hand to the glass and investigated only the effect of ambient temperature. “In the most dangerous scenario, such as a windy day at the beach (38 degrees Celsius), your beer could become undrinkable in just three minutes (again, based on personal experience and thoroughly reiterated). Yes,” Pellegrini said. I wrote.
How to make the perfect beer glass
Based on these assumptions, the researchers created an equation that describes the beer’s temperature change over time. This is a differential equation. That is, the equation contains a derivative. That is, it is a function that describes the rate of change of a variable (in this case, temperature), which in this case is the shape of a beer glass.
here, T is the temperature of the beer, TU is the ambient temperature, cp specific heat capacity (how difficult it is to heat a substance), ρ is the density, V It’s the volume. aAll The exposed surface of the beer (including the sides and top circular surface), hresume is the convective heat transfer coefficient, which represents the ability to conduct heat. Pellegrini used this formula to calculate four tips for cooling beer as slowly as possible.
It is best to enjoy beer in a cool place at best. TU as low as possible.
Using more insulating materials such as ceramics instead of glass reduces thermal conductivity.
In general, Pellegrini noted, thick foam insulates the beer and prevents carbon dioxide from being lost too quickly. Additionally, wind and drafts cause forced convection and should be avoided. Forced convection plays a much larger role in heat transfer than the natural convection considered here.
All of these tips can usually only be implemented by moving to another location. However, if you’re sitting comfortably at a bar, you’re exposed to the conditions at hand, so if your bar had glasses with an optimized shape to minimize heat exchange from the beginning, you’d be better off. Further welcome. Spoiler: This is not true.
beer champagne flute
The shape of the beer glass is included in the quotient aAll⁄V In the above formula. The smaller this number, the smaller the temperature change. That is why Pellegrini aAll⁄V.
In school, mathematicians learn that such optimization tasks can be solved using derivatives. For example, to find the vertices of a parabola, f(×) = ×2 +3× + 2, the function is derived from: × The result is set to zero: 0 = 2× +3. This means that the vertices are located at: × = –1.5.
Pellegrini also derived the quotient using exactly the same method. aAll/Vis set to zero and the properties of the rotating body are used to derive the function for the optimal shape of the beer glass. According to this, the radius is r Perfect beer glass height function h is given by the following formula:
C is a constant, Rb is the radius of the glass base. This formula states that, like many common beer glasses, the mouth opening of the glass should be large and the glass should narrow towards the bottom. However, the radius of real-world glass does not necessarily decrease over time, and it often has a curved S-shape when viewed from the side. This is not the perfect beer glass.
The exact shape of the optimal glass depends on the radius and constant of the glass base. C, This is determined, among other things, by the height of the glass. Pellegrini first calculated the optimal shape for various base radii of the 19 centimeter-high glass. The resulting shape is reminiscent of a champagne flute.
Engineers then adapted the optimal glass parameters for different types of beer glasses, including imperial pints, American pints, and weizen (wheat beer) glasses widely used in Britain. To do this, Pellegrini entered the parameters of each beer glass. Incorporate the radius and height of the base into his formula to calculate the optimal shape.
The general shape is the same for all types, and it is reminiscent of a champagne flute. But there are some benefits to suboptimal glasses, Pellegrini writes in a preprint. Nadir Figueiredo glasses, which are widespread in Brazil, are in some respects perfectly designed for heat transport, although they are far from optimally shaped. Because a glass holds a relatively small amount of beer, people typically drink beer faster than they drink beer. Quite warm.
This article was first published Wissenschaft spectrum Reprinted with permission.
