# When is it easier to score a goal straight from the corner, in summer or in winter? | Science

To score a goal with a direct shot from the corner, it is necessary to give effect to the ball. This effect must ensure that the ball interacts with the air in a way that does not describe a normal parabola but rather makes a curve that initially moves it away from the goal to end up bringing it closer. The ball describes that curve when it rotates and the physical effect that determines how the spin is going to be known popularly as Magnus effect. The Magnus effect it is a physical phenomenon by which the rotation of an object (the ball in this case) affects its trajectory through a fluid (the air in the case of the soccer ball).

To know if it is easier to score a goal with a direct shot from the corner in summer or winter, what we have to do is to analyze if in the Magnus effect It influences whether it's summer or winter. And indeed, it does influence. This physical effect depends above all on the viscosity and density of the air, the speed at which the ball goes and the radius of that ball. If we analyze these variables, we see that both the speed at which it rotates and the speed at which the ball goes are aspects that the player controls, so we do not care whether it is summer or winter. What we have then are the other variables: viscosity and density of the air and radius of the ball. And in them is where is the answer to your question.

Let's first look at the variables that affect the viscosity and density of air that are different in summer and winter because they depend on the characteristics of the atmosphere. Both the viscosity and the density of the air, but above all the density, are greater with a high atmospheric pressure, a low humidity and a low temperature and that occurs in winter. In any case, what most affects the density and viscosity of the air is the temperature which, moreover, is what changes the most between summer and winter days.

Both the viscosity and the density of the air, but above all the density, are greater with a high atmospheric pressure, a low humidity and a low temperature and that occurs in winter

Density and viscosity are lower in the opposite case: low atmospheric pressure, more relative humidity and higher temperature, that is, in summer. So due to the Magnus effect, the ball will twist its trajectory towards the goal with greater difficulty in summer. The difference in force that would push the ball towards the goal can be up to 15% between summer and winter if the variables we evaluate are optimal, ie if pressure, humidity and temperature are ideal to achieve the maximum Magnus effect. In the calculation we have considered a change of temperature between winter and summer of 30 degrees and a change of pressure of 50 hPa (hectopascals) between anticyclone and storm, data that may be characteristic of a city like Madrid. For a city with a less extreme climate, such as Valencia, the difference would be around 10%.

But if you remember, at the beginning I explained that there was another variable that influenced the Magnus effect: the radius of the ball. The measurement of the soccer ball is regulated. The perimeter should be between 68 and 70 centimeters, and that means that the radius can vary between 10.82 to 11.14 centimeters, which is a variation of 3%. A 3% seems little compared to the 10% we talked about when we referred to air conditions but it turns out that in the Magnus effect the radius is super important. The force that pushes the ball towards the goal through the Magnus effect varies as the radius cubed, ie r3. A variation of 3% in the radius corresponds to a variation of 9% in the force. And that makes it possible to compensate for the effect of density and viscosity by changing the radius of the ball within the limits allowed by the rules of football. If the player encounters a small air density, as in summer, and wants to compensate for the Magnus effect more easily, he only has to inflate the ball a little more. But, beware, it can not exceed 1115 hPa (hectopascals), which is the maximum regulation.

Therefore, the answer to the question is that if we only look at the atmosphere, in winter it is easier to score a goal with a direct shot from the corner. However, this difference can be partly compensated by the natural variability of the ball radius within the permitted limits: the greater the radius, the easier it is.

Ana Cros is a professor of Applied Physics at the Institute of Materials Science of the University of Valencia.

Question asked via email Juan Manuel Gálvez Fernández

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