The Double Post – literally half a hair’s breadth

It is deep in the Black Months now.  The rain – and the snow, and ice – has arrived.  The trees are bare, the wind blows cold, and, perhaps the worst of all, the pitch down at the old barn on SW 18th and Morrison is empty and silent.

And the damn Sounders are in the Cup Final.

But.star

Let’s not forget that it was only just over a year ago that we all were raised to topgallant delight by our Timbers’, and Cascadia’s, first MLS Championship.  I don’t think any of us who lived through that mad run up to the Final, and that epic Final match, will forget that season and the joy that came with it.

From Chara’s “Assassin’s Creed” header in LA to the madness of the play-in match and 22 rounds of PKs.

From the cold calculation of the scoreless draw here to the clinical beatdown in Vancouver.

From the wild ride on the FC Dallas bull to the 95th minute Melano dagger to the heart of the beast.

From Diego Valeri’s ridiculously improbable 27-second goal to the final whistle that crowned the Timbers the 2015 MLS Champions.

What a long, strange trip it was.

And now, just as we await the end of the 2016 season and begin to think and wonder about 2017 comes a reminder that it was a stranger, more magical, and less probable trip even than it seemed at the time.

Portland State University physics professor Ralf Widenhorn’s 2016 paper Hitting the Goalpost: Calculating the Fine Line Between Winning and Losing a Penalty Shootout details the ridiculously impossible geometry of SKC’s Abdul-Salaam’s now-famous double-post penalty miss.

As if a penalty shootout that goes to 22 rounds wasn’t crazy enough, Professor Widenhorn’s mathematics makes it clear that the Timbers survived that shot by…well, let’s look:

left-post

Professor Widenhorn begins by reminding us of how thin that margin is even before the ball leaves the penalty spot: “In this manuscript we will use a geometrical analysis to develop the equations that describe the conditions for the ball ricocheting off both goalposts. We know intuitively that the penalty missed by a very small margin, but it is not trivial to get a good estimate by how much it was off. Even the smallest change could have made the difference between winning and losing. For example, the video shows that the ball bounces once as it travels from the left to the right goalpost. Unevenness in the ground could have nudged the ball ever so slightly from its straight path.”

Widenhorn goes on to describe the mechanics of the Double Post.  By far the most likely carom off the left post would have been pinging back out to the right.  The second-most likely rebound would have – disastrously for the Timbers – been into the goal; as we know, Adam Kawarsey guessed wrong and went to his left.  Kawarsey wouldn’t have been able to get to the ball in time to prevent the goal.

sequence

A small but significant possibility would have been a bounce off the post to the left.

The probability of the actual trajectory of the carom – flat across the face of goal – was, in fact, miniscule.

post

As Professor Widenhorn says: “The resulting difference, Δ, is slightly less than 40 m. Hence, if the penalty would have been hit this distance further to the right of the left post, the ball would have gone into the net before the goalkeeper would have reached it. For reference, the average width of a human hair is about 80 m”

Stop and think about that for a moment.

Among the many, many times and places where some event might have ended the Cup run the Timbers’ championship literally survived by half the width of a hair on that night in October.

Not just “A hair’s breadth” but HALF a hair’s breadth.

So when we think back on that amazing season, Professor Widenhorn’s work reminds us; the magic really WAS real.

2 Comments The Double Post – literally half a hair’s breadth

  1. D Mellinger

    I want to read this article, because I did the geometric calculation and came up with half a millimeter, or 500 μm. So we disagree by a factor of 10…. Does anyone know where to get a copy of the article? The online one is behind a paywall, and I’m cheap.

    Reply
    1. John Lawes

      The odd thing is that it opens for me at the link embedded in the post. But I must be registered as an educator or something, because you’re the second person who has mentioned the paywall.

      You might be able to get the hardcopy. It’s in a publication called “The Physics Teacher”, v. 54, issue 7. Here’s the link to the parent pub: http://aapt.scitation.org/journal/pte

      Reply

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