In today’s World Cup match between Brazil and Chile, it came down to penalty kicks. If neither team is ahead after two extra 15 minute time period, each team gets 5 penalty kicks. The team that scores the most of these 5 wins the match. Brazil won. Oh, was that a spoiler? No, it can’t be. Surely you know the score by now.
It seems pretty tough to stop one of these penalty kicks. How about a quick analysis?
How Fast is a Kick?
Of course, there isn’t a perfect side angle view of these penalty kicks. This means that it would be difficult to get a trajectory of the ball. However, I don’t really need that. I only need an estimate of the speed. Since I know the ball starts 12 yards from the goal, I can find the velocity by measuring the time of flight. Yes, these things go pretty fast. I find it’s easiest to use Tracker Video Analysis just to get the start and end time of the kick.
Using this method, I get the following speeds. Note that this is just an estimate because if the ball is kicked at an angle it actually goes farther to goal line than just 12 yards.
- Kick 1: 24.94 m/s
- Kick 2: 39.18 m/s
- Kick 3: 17.9 m/s
- Kick 4: 30.47 m/s
- Kick 5: 39.18 m/s
- Kick 6: 30.47 m/s
- Kick 7: 34.28 m/s
- Kick 8: 24.42 m/s
- Kick 9: 24.93 m/s
- Kick 10: 30.47 m/s
This gives an average kick speed of about 30 m/s. Really, the video I used was mostly on the crappy side so that these numbers cold be off.
Reaction of a Keeper
Really, not the reaction. I am thinking of the acceleration of a keeper (goalie). Here is a plot of the position of a keeper during a kick. In this case, he starts his move 0.2 seconds before the ball is actually kicked.
He seems to have a fairly constant acceleration of about 5.26 m/s2. So, if he starts in the center of the goal, how long will it take him to reach one side of the goal? A goal is 7.32 meters wide so this means he must travel 3.66 meters. Since he starts from a speed of zero, I can jsut use one of the kinematic equations.
With a final x position of 3.66 meters and an acceleration of 5.26 m/s2, I get a time of 1.18 seconds.
If I used a distance of 12 yards for a ball with the lowest speed of 17.9 m/s, that gives a time of travel at just 0.61 seconds.
How to Block a Kick
Now for the important point. How do you stop these kicks? The answer is simple: guess. Guess which way the ball is going to be kicked and move that way after the kicker has already determined his kick direction. It’s just that simple.
Oh, but what if the keeper had a greater acceleration? Let’s double it and make it 10.52 m/s2. This would still give a time of 0.83 seconds to get to the side of the goal. Not good enough.
But maybe guessing would work. According to this site, 85% of the penalty kicks are successful goals. So, if you guess and get just one block you could consider yourself (as a keeper) successful.
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