The Perfect Goal Kicking Angle - Numberphile

This is based on the sport of Rugby Union. The principles could be applied elsewhere - why not try it?

NUMBERPHILE

Videos by Brady Haran

[omarvelazquez]

"Maths is the art of reasoning from bad drawings" - Numberphile, you have a new T-shirt

[OneTrueBadShoe]

I love Ben's presentation skills. He makes it easy to understand.

That's why he's one of my favorites.

[Henrix]

Surely someone has a database of kicks and it probably lines up quite well with this result

[iansimcox]

The 30 degree launch angle is interesting information too. It means if you wanted to practice launch you put the ball on the 5m line and aim to hit the crossbar

[RFC-]

Another factor is that, even for a professional player, shooting _harder_ (meaning the ball goes further) often implies a loss in _accuracy_ (on top of the reduction of the target's angular size). So, even if they could still clear the crossbar, they might lose so much control over direction and bend that they'd miss the posts. But, of course, to model that you'd need data from specific players.

[johnchessant]

8:28 I love that he organized the presentation so that the listener delivers the key insight.

[Bodyknock]

Regarding the range of kicks, rugby fields are 70 meters wide, so the maximum the distance x could be from the center of the posts is 35 meters. That makes the maximum 45 degree hypotenuse you would kick is about 49.5 m. Professional rubgy players can kick over 50 meters in distance so basically if they're placing the ball right at the sideline and kicking at the 45 degree angle it's doable but probably almost at the edge of what they can do with any consistency.

[timseguine]

As sure as the sun rises in the East, Ben Sparks will have brought a GeoGebra file.

[JustinoElArtista]

This is one of the beautiful things about sports. Athletes aren't necessarily doing equations in their heads, but they definitely are using their kinesthetic intelligence to understand and solve these angles. The best athletes aren't just the strongest or the fastest, but also mathematicians. Proper mathematicians, on the other hand, can give language to the rule of thumb athletes use so that those without great kinesthetic intelligence can understand what's going on.

[EebstertheGreat]

To answer the question about kicking in American football, you do get to kick extra points from the middle of the field (the middle of the 15 yard line in the NFL), but field goals don't work that way. When kicking a field goal, you snap the ball from wherever it was downed to someone who holds it on the field, and the kicker kicks it. However, if the ball is ever downed near the side of the field rather than the middle, it is moved toward the middle anyway to the nearest hash mark. So you never really have to kick from a significant angle. The most extreme possible angle (excluding oddities like dropkicks) would be from the hash mark at the goal line (or, say, half an inch back from the goal line), which is 18'6" from the centerline and 30' from the end line (where the uprights are), which is a 32° angle if you want to get it through the center of the uprights. But nobody actually kicks from the line of scrimmage; they snap it back 7-8 yards so that it doesn't get blocked. That makes the distance to the end line 51'-54' and the angle less than 20° even in this improbable worst case. So angles are not really a problem in the NFL.

BTW, when you take air resistance into account, the optimal angle of elevation for a projectile to maximize distance is always less than 45° anyway. So that's not just about the biomechanics of your leg.

[MisterMajister]

Ben Sparks is such a legend. I hope we get many more videos like this from him!

[grempal]

Love this video. Reminds me of my best conversion ever. It was a very wet game with a couple inches of standing water on the touch line. Wing scored a try at the left touch line. The only dry spot to place the tee was between 5 and 7 meters from the try-line right on the left touch line. I kick with my right foot and have a natural ability to bend my kicks. This ability to bend my kicks let me aim at the far upright or just outside of it and the curvature of the kick increased the effective angle between the posts because the ball will be approaching the uprights more like a central kick. Anyway, I nailed the kick dead center between the uprights and got a compliment from the sir.

[koolguy]

Another note on the "optimal" launch angle of 45 degrees that's often quoted. That value ignores air resistance, and it turns out that when you factor in air resistance the optimal range angle is in the 30s (almost in line with optimal leg power angle)

[SirWilliamKidney]

I love this, we need a giant match with the whole numberphile family!

[geckoman]

I have coached basketball, and it always blew my kids minds when I told them basketball was mostly just geometry. Everything from passing to shooting can be made easier (or harder) based on angles to the defense or the basket.

Similar to the video, shots with arc, the basket looks bigger to the ball than flat shots.

[lordvenusianbroon]

The opposing team are also allowed to try and block the kick....so you also have to take account of how fast another player can get to between the ball and the posts, near the kicking spot, in the time it takes for the kicker to 'approach' the ball ;-)

[davidg]

I had one physics professor that gave us the same problem weekly during the term -- maximize the range in a specific direction of a projectile with certain givens. With each iteration, he introduced another real world factor to up the difficulty. By the end, we had an insane equation covering air resistance, wind, Coriolis effect, and some others.
Long story short: If you're throwing spherical chickens in a vacuum, 45° is ideal. For pretty much all real world scenarios, expect it to be in the 25°-40° range. If you have a wicked backspin on your golf swing, you might even need to go as low as 15° (Magnus effect).
So I'm not surprised that 30°-ish is considered ideal for launching a rugby ball.

[Jivvi]

Fun fact: a try in rugby was originally called a touchdown, and "try" referred to the subsequent attempt at goal. Originally the scoring was very different, and most of points came from the kick. This changed over the years, and when the touchdown eventually became more valuable than the kick, it started being called a try.
American football never changed those terms (an extra point attempt is still officially called a try), but they did remove the requirement to actually touch the ball down.

[iseriver]

The fact that you can pretty much describe anything physical with maths is pretty cool. Even something as benign as walking out and kicking a ball.

[nosy-cat]

"It gets messy, so don't do it unless you're brave" – oops, paused and tried (and cried) just before Ben said that.