The physics of that ‘kickalicious’ kick
empiricalzeal.com
empiricalzeal.com
Here's a follow up question, that I haven't thought much about. Assume that Rugland launches the first ball at 64 degrees and at 14.4 m/s (about 32 mph). 1.5 seconds later, and 1.5 meters ahead, he kicks the second ball. (So far these are the numbers I get from the data). My question is, given the size of a football, how accurate does he need to be in the launch speed and angle of the second ball, in order to be able to strike the first ball?
You might need to assume a reasonable range for the launch speed to work this out.
Assume the distance of the collision is 10m from launch and occurs 1.7 seconds after the second kick. The margin of error on the arrival time is 1/32 / 1.7 = 1.84%. Using your launch speed centered around your value of 38 mph = 16.9875 m/s, that means the possible range was 16.675 to 17.300 m/s. Interestingly, that's a difference of 1.4 miles per hour, which is also roughly the precision of velocity that baseball pitchers can produce on demand.
By the way, there's more variables on the inputs to the second ball. The timing of the kick is important and controllable too, creating a three-dimensional map of inputs. This could be transformed into and visualized as a 3D graph, showing all the combinations of speed/angle/timing that will result in a collision.
Also, the left-to-right angle must be on target too or the balls won't be in the same vertical plane for any collision at all.
All else being equal, the harder you can kick, the easier this gets. The lower the arc of the first ball, the smaller the angle of intersection between the two trajectories, and the easier the hit. You can get a lower arc by giving the ball more horizontal speed, keeping vertical speed the same (just decreasing vertical speed won't help; the first ball would hit the floor before you can hit it with the second ball)
Of course, all else isnt equal; directional errors likely are some function increasing with both distance and ball speed.
I mention this not to cast any doubt on the kicking video, but because there are a lot of good simulation tools nowadays and faking something up by working out the physics first is only going to get easier.
Here's another example of a physics based take-down (by Rhett Allain) of that eagle lifting a baby video that was doing the rounds. http://www.wired.com/wiredscience/2012/12/eagle-picks-up-a-k...
The exception would be doing several difficult moves in a row without fail.
An interesting, and far more skill showing (imo) version of this video would be to show how close they were on each of the tries - If for example he was within a couple of meters of collision each attempt, I would call that very high skill. But if the other attempts were dozens of meters apart, the skill would be much lower.
Complete aside: Mind exploded from unit mismatch. Miles per hour then meters? Gah....
Just please dont use gradians for angle measurement :)
One example can be viewed at http://www.youtube.com/watch?feature=player_detailpage&v...
But, if I were going to fake the video, I'd have my kicker kick the first ball for real and mime kicking the second (or if that looks fake, really kick a second ball but paint it out)- and then use the same video physics package this guy used to predict where the balls should be at time t, painting the second ball (and both balls, after they "collide") in, frame-by-frame, on the path it charts out.
Besides that the problem doesn't begin to approach PhD-level...
You could probably say the same thing of me when I'm running or cycling. But whatever calculations my brain performs, the results are not accessible to myself or to anyone else; and I can't tell my brain what calculations to perform, so I can't tell anyone else what angle to lean at, and if I go to the moon I will have to let it work out for itself that gravity is not a universal constant.
You could also say the same thing when a cat twists in midair to land on its feet, "using" the principles of angular momentum. (Scare quotes because the cat has no idea what angular momentum is.)
Rugland's feat is certainly impressive. (And in a different class to my examples, in that he doesn't get constant feedback; if my balance is wrong I can adjust, if he kicks wrong the ball misses. But you could describe my feedback-integration using complicated physics as well, so I don't think that invalidates my point. I'm pretty sure "knife throwing" and "blindfold juggling" would have been suitable examples, but I don't personally possess those skills.) And I'm certainly not saying he's stupid.
But to call this intelligence, seems to be extending the word far beyond its usual boundaries.
> The main lesson of thirty-five years of AI research is that the hard problems are easy and the easy problems are hard. The mental abilities of a four-year-old that we take for granted – recognizing a face, lifting a pencil, walking across a room, answering a question – in fact solve some of the hardest engineering problems ever conceived. ... the most difficult human skills to reverse engineer are those that are unconscious.
On the other hand a NFL level kicker is roughly 50% for 50+ yard field goals. [1] Therefore the 5 50 yard field goals should be possible for an NFL kicker in something like 2^5/2=16 tries. ( Similar for the 60, 50 etc sequence, using again the stats,
1/3.* (24./47)* (96./141.)* (120./136)* (119/121.) = .1
it should require something like 10 tries. ( Assuming a probability of 1/3. for the 60 yrd.) So I think the video is genuine, but only because I wonder why anyone would spoil an impressive video by just one special effects shot.) To really convince me, one would need to calculate the kick of the second ball, since this is the moment where animation and reality have to match.
[1] e.g. David Ackers 24 - 47 for 50+ http://sports.yahoo.com/nfl/players/4587/career
Hitting the crossbar requires kicking something ~8.5" in diameter at something 5" wide so you've got a 'window' of 22" to aim at. With practice you might be able to do it 3/5 times from 20 yards.
(3/5)^4 =~ 1/8
So 8 tries to do it 4 times in a row.
To get the ball to come back like that each time the 'window' is now about 1" (if that). Outside that window and it bounces down to the ground, or glances the bar and goes behind the goal, or bounces way up in the air and never returns to you. So each kick is now 3/(5x22) and (3/(5x22))^4 = 1 in 1.8 million. Good luck.