Saturday, August 14, 2010

Galileo In The Kop

Anfield. Tuesday, 1st May, 2007.

The Champions’ League semi-final, second leg, between Liverpool and Chelsea had just ended 1-1, after extra time. This all-important tie was to be settled by a nerve-wracking penalty shoot-out. A toss of a coin determined the end at which the match would be settled. Liverpool won the toss. The finale would, therefore, take place at their famous ‘Kop’ end, where thousands of their noisiest supporters were congregated.

The fans knew this would be advantageous. When one of their own players stepped up to take a kick, they would be absolutely still and respectfully quiet, so as not to distract him. Conversely, when a Chelsea player did the same, they would move wildly about and create the most raucous din possible. Why? Because they have learned that vocal intimidation affects opponents’ concentration.

Chelsea scored only one of their five penalties. Liverpool converted three and won the match.

As tense as the spectacle was, it was nothing new to the Anfield faithful. After a similarly thrilling European match in the early 1990s, a previous manager, Graeme Souness, equated the Kop’s deafening roar to an extra player. Few disputed his logic. Put simply, crowd noise counts.

Allow me, now, to open up a parallel thread, as it were. It pertains to the equally heady world of pure mathematics. There is a particular type of algebraic curve called a parabola. Physical manifestations of this curve, such as the Sydney Harbour Bridge (Figure 6.1) or a jet of water from a fountain, are thus said to be parabolic. (This shape is important in mathematics, physics and structural engineering. It applies, also, to projectiles. For example, the path of a football kicked into the air will be parabolic. Every time. How hard it is kicked and the angle at which it leaves the ground are immaterial. The same is true of a golf ball, a javelin or a ballistic missile. If a moving object is subject only to gravity, then its trajectory will necessarily be parabolic.)

Figure 6.1: The parabolic bridge spanning Sydney Harbour

Copyright 2010 Paul Spradbery

One of its mathematical properties is of great consequence. Every parabola has a so-called focus. If, for example, a light source is placed at the focus of a parabolic mirror, then, no matter where on its inner surface the light rays contact, they will be reflected in a parallel beam (Figure 6.2). This is the principle of a searchlight.

Figure 6.2: All waves, of either light or sound, emerge in parallel

Now, back to football. In 2003, Liverpool were granted planning permission to build a new stadium at nearby Stanley Park. The proposed new Kop Stand will be - ingeniously - a three-dimensional parabola. The crowd will be seated at and around the focus. As sound waves behave exactly like light rays, the noise generated, tremendous as it is, will be reflected from all over the inside surface of the stand to form a parallel ‘beam’. In other words, only a bare minimum of sound will dissipate. Almost all of it will be channelled, like a searchlight, towards the pitch. The net effect will, of course, be substantial amplification of vocal support for the home team.

There are already some famous behind-the-goal stands in English football. Manchester United’s Stretford End, for instance, was designed for 12,000. The present Kop at Anfield holds slightly more, 12,390, and Aston Villa’s Holte End caters for a whopping 13,472. The new Kop has a provisional capacity of 18,500, which would blow away all today’s competition. Moreover, taking into account its ingenious ‘parabolic reflection’ facility, an amplification boost of, say, 30% would create the equivalent noise of 25,000. This would be double the intensity of noise generated by today’s Kop.

When the new stadium is built, as well as having the combined passion of thousands more fans, Liverpool will also be able to summon the combined expertise of Menaechmus, Apollonius, Galileo, James Gregory and Sir Isaac Newton (Figure 6.3).

More penalties will be missed, for sure.

Figure 6.3: Can the application of mathematics skew the playing field in Liverpool's favour?

Copyright 2010 Paul Spradbery

Copyright 2010 Paul Spradbery

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