汤姆·布雷迪的“不完美”螺旋球
这是汤姆·布雷迪。他是美国橄榄球史上最伟大的四分卫。
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This is Tom Brady. He's the greatest American football quarterback of all time.
Derek: 你能听到它从你身边飞过吗?
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Can you hear it go by you?
Tom Brady: (笑)是的,这很吓人。
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(laughing) Yeah, it's scary.
他赢得了七次超级碗,并创造了历史上最多的达阵传球记录。
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He's won seven Super Bowls and has thrown the most touchdown passes in history.
Henry: 噢。
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Ooh.
Derek: 噢,那个击中了胸部,我听到了。
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Ooh, that one hurt the chest, I heard that.
Tom Brady: 正中胸口。
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Right in the chest.
Henry: 我很高兴我没有接到那些球。
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I'm like glad I'm not catching those.
每个四分卫都以他们投出紧密螺旋球(tight spiral: 橄榄球在空中高速旋转,轴线与飞行方向一致的传球方式)的能力而自豪。你投出的螺旋球越紧密,意味着你对橄榄球的控制力越强。
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Every quarterback takes pride in their ability to throw a tight spiral. The tighter the spiral you throw means the more control you have of the football.
我们详细分析了他的投掷。
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We analyzed his throw in detail.
Derek: 有人曾用慢动作拍摄过你的出手和所有细节吗?
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Have people shot you in really slow motion for the release and everything?
Tom Brady: 从未有过。
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Never.
我们发现了一些令人惊讶的事情:即使是汤姆·布雷迪也无法投出一个完美的螺旋球。不信你看。
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And discovered something surprising. Even Tom Brady can't throw a perfect spiral. Just look.
Tom Brady: 喊“hut”。
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Said hut.
在他的长传中,无论他多么努力地让球围绕其长轴干净地旋转,如果你仔细观察,你会发现这种轻微的晃动。不仅如此,球还会轻微地偏离方向,这意味着即使是汤姆·布雷迪也无法投出直线球。实际上,他所有长传都会向右弯曲。
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On his deep passes, no matter how hard he tries to spin the ball cleanly around its long axis, if you look closely enough, you'll notice this little wobble. Not only that, there's a slight drift to the ball, which means even Tom Brady can't throw straight. Virtually all his long passes curve to the right.
但这并非失误,它们实际上是准确投掷橄榄球物理学的基础。为了找出原因,我们进行了全面的计算流体动力学分析,在风洞中测试了旋转球,甚至在真实的橄榄球中嵌入了传感器。
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But these aren't mistakes, they're actually fundamental to the physics of throwing a football accurately. To find out why, we ran a full computational fluid dynamics analysis, tested spinning balls in a wind tunnel, and even embedded sensors in real footballs.
Tom Brady: 这太疯狂了。
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That's crazy.
现在,平心而论,我们有什么资格向汤姆·布雷迪讲解橄榄球呢?
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Now, admittedly, who are we to tell Tom Brady anything about football?
Derek: (德里克哼着)我从来没怎么踢过橄榄球。我在加拿大长大。我更喜欢打冰球。为什么我根本投不好呢?这太糟糕了。
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(Derek grunting) I've never really played much football. I grew up in Canada. I'd be much happier to be playing hockey. Like why can't I throw at all? That is so rough.
Tom Brady: 好的,他会指导你的,我现在就不费劲去做了(笑)。
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Okay, well, he'll walk you through it, I'm not gonna bother doing it (laughing) right now.
Derek: 是的,是的,是的,是的。
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Yeah, yeah, yeah, yeah.
Tom Brady: 试着这样做,过度倾斜。所以不要站直——
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Try to do this, over-exaggerate the tilt. So instead of standing straight up-
Derek: 是的,向前倾?
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Yeah, lean forward?
Tom Brady: 倾斜得就像你几乎是一个游击手,对吧,就像你要摔倒一样,然后你就这样,像那样。
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lean like you're almost like a shortstop, right, and like you're falling over, and then you're just here, like that.
Derek: (德里克哼着并笑着)
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(Derek grunting and laughing)
Tom Brady: 接得好。
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Good catch.
所以稍微倾斜一点。
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So lean over a little bit.
Derek: 我感觉我还没准备好。
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I feel like I'm like not ready for it.
Tom Brady: 所以像游击手一样蹲下。
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So get down like a shortstop.
Derek: 是的,是的,像这样?
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Yeah, yeah, like this?
Tom Brady: 还要更多。
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Even more.
Derek: 还要更多?
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Even more?
Tom Brady: 是的。现在侧手投掷。
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Yeah. Now throw it sidearm.
Derek: 是吗?我觉得这很奇怪。看,那是一个更好的投掷。
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Yeah? I feel like this is weird. There you go, that was a better throw.
Tom Brady: 那是一个更好的投掷。
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That is a better throw.
Henry: 真的很棒。
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It was really good.
Derek: 投出非常紧密的螺旋球的关键是什么?
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What's the key to throwing like a really tight spiral?
Tom Brady: 对我来说,关键首先是,你必须对橄榄球施加非常轻的握力。我经过一段时间才明白,我必须让我的动作非常高效。我必须将所有能量都直接导向目标,并保持非常放松的姿势。然后,这是一个非常流畅、高效的投掷动作。
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The key to me is, first of all, you gotta have very light grip pressure on the football. I learned over a period of time that I had to be really efficient with my mechanics. I had to have all my energy going right toward the target with a very relaxed posture. And then it's a really smooth, efficient throwing motion.
Derek: 那么你是如何真正赋予球旋转的呢?
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And then how are you actually imparting the spin to the ball?
Tom Brady: 所以你实际上是在最后手腕猛地一抖。我甚至可以非常慢地做,只是在最后猛地一抖手腕。即使是这一点点手腕的抖动,也会在球从我的指尖释放时产生一点点“啪”的声音,并赋予球旋转。亨利,你不能把这么简单的球都掉了。
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So you're really popping your wrist at the end. So I can even go really slow and just pop my wrist at the end. And even that little bit of wrist pop will create a little snap on the ball as it releases from my fingertips. Henry, you can't drop the easy one.
这种“啪”的声音和它产生的旋转是布雷迪破纪录投掷的关键。但最大的问题是为什么?我的意思是,旋转对橄榄球到底有什么作用?
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That snap and the spin it creates is the key to Brady's record-breaking throw. But the big question is why? I mean, what does the spin actually do to the football?
这似乎是一个简单的问题,但其物理原理比我最初想象的要复杂得多。事实上,研究这个问题的物理学家直到五年前才接近真正的答案。所以让我们从头开始分析。
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It seems like such a simple question, but the physics turned out to be much more complicated than I initially thought. In fact, physicists studying the problem didn't get close to the real answer until just five years ago. So let's break it down from the start.
问汤姆一个问题,他能不让球旋转就投出去吗?
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A question for Tom is, can he throw the ball without spinning it.
Tom Brady: 像指关节球(knuckleball: 一种几乎不旋转的投掷方式,导致球体轨迹难以预测)那样吗?
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Like a knuckleball?
Derek: 是的,你能投出橄榄球的指关节球吗?
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Yeah, can you knuckleball a football?
Tom Brady: 是的,我可以试试。我能下手投吗?
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Yeah, I could try. Can I throw it underhand?
Derek: 是的,是的,是的。
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Yeah, yeah, yeah.
Tom Brady: 是的,你想怎么扔就怎么扔。
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Yeah, however you wanna toss it.
Derek: 即使是上手投,也没有办法不让它旋转,否则它会让你很麻烦吗?
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Even overhand, there's no way to do it without getting a spin on it or it's just gonna mess with you?
Tom Brady: 我的意思是,你几乎得把它横着扔。
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I mean, you'd have to almost throw it sideways.
Derek: 是的,是的。
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Yeah, yeah.
Tom Brady: 哦,那个有点旋转。
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Oh, that spun a little bit.
旋转:稳定飞行的关键
当你投掷一个不旋转的球,并且它与运动方向完美对齐时,空气流过球体似乎是完全对称的。但这并不稳定。任何轻微的扰动,比如一点点风,都会导致更多的空气撞击球体的一侧而不是另一侧,这开始改变球体的方向。现在,那一侧有更多的面积暴露在迎面而来的气流中,所以它偏转得更多。
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When you launch a ball without spin, perfectly aligned with the direction of motion, it seems like the air flowing over the ball will be totally symmetric. But this is unstable. Any slight disturbance, like a tiny bit of wind, will cause more air to hit one side than the other, and that starts to change the ball's orientation. And now more area on that side is exposed to the oncoming air, so it deflects even more.
因此,球的阻力增加,它被推离航线,并可能开始翻滚。球上的总阻力与暴露在气流中的面积和阻力系数(drag coefficient: 衡量物体在流体中受到的空气阻力大小的系数)成正比。阻力系数只是衡量物体流线型程度的指标。
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So drag on the ball increases, it's pushed off course, and it can begin to tumble. The total drag force on the ball is proportional to the area presented to the airflow and the drag coefficient. That's just a measure of how streamlined an object is.
当橄榄球笔直地指向运动方向时,它相当流线型,阻力系数仅为0.14。这比子弹还要好。但如果它侧着飞行,阻力系数为0.85,这比一头牛还要差。
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Pointed straight in the direction of motion, a football is pretty streamlined, with a drag coefficient of just 0.14. That's better than a bullet. But on its side, the drag coefficient is 0.85, which is worse than a cow.
Tom Brady: 天哪,我今天学到了很多。我将用这个来和所有四分卫说:“伙计,你的阻力系数太差了。”(笑)“我们在做什么?我们需要0.14。0.85,不行。”
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Man, I'm learning a lot today. That's what I'm gonna use with all the quarterbacks, going, "Man, your drag coefficient sucks." (laughing) "What are we doing? We need .14. .85, no good.
更糟糕的是,当橄榄球侧着飞行时,它暴露在迎面气流中的面积增加了近70%。再加上更高的阻力系数,这意味着阻力是橄榄球与投掷方向对齐时的10倍。所以一个不旋转的球最终可能会侧着飞行,这意味着它的减速速度会快10倍。此外,当它翻滚时,空气会从不同方向推动它,使其运动变得不可预测。
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To make matters worse, when a football is going sideways, it exposes nearly 70% more area to the oncoming air. And combined with the higher drag coefficient, this means that the drag force is 10 times greater than when the football is aligned with the throw. So an un-spinning ball can end up going sideways, meaning it decelerates up to 10 times faster. Plus, as it tumbles, the air pushes on it in different directions, making it move unpredictably.
在某些情况下,你确实希望这样。比如在将球踢回给对方球队时,弃踢手有时会故意让球翻滚,使其不规则地被推来推去。这使得对方球队更难预测球的去向并接到它。但当你传球给自己的球队时,你希望球的轨迹是可预测的,并且尽可能快和远。为此,你需要旋转。
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Now, in some cases, you actually want this. Like when kicking the ball back to the other team, punters sometimes intentionally kick the ball end over end so that it gets pushed around erratically. That makes it far harder for the opposing team to predict where the ball's gonna go and get under it. But when you're passing to your own team, you want the ball to be predictable and go as fast and as far as possible. And for that, you need spin.
旋转的好处在19世纪中期克里米亚战争期间变得非常明显。那时,士兵们装备的是发射圆形铅弹的滑膛枪(musket: 一种早期火器,枪管内没有膛线)。为了在战场上更快地重新装弹,这些滑膛枪的子弹做得比枪管小得多。但当火药被点燃时,一些膨胀的气体就会从子弹周围逸出,使得子弹的枪口初速(muzzle velocity: 弹丸离开枪口时的速度)不可预测。
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The benefits of spin really became clear in the mid 1800s during the Crimean War. Back then, soldiers were armed with muskets that fired round lead balls. And to make reloading faster on the battlefield, these musket balls were made significantly smaller than the barrel. But when the gunpowder was ignited, some of the expanding gases would then escape around the bullet, making the bullet's exit velocity unpredictable.
这,再加上不一致的制造和圆形弹丸糟糕的空气动力学性能,意味着滑膛枪在某种程度上是不可靠的。
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This, combined with inconsistent manufacturing and the round ball's poor aerodynamics, meant that muskets were somewhat unreliable.
有一位英国陆军的射击教官曾说过一句名言:“我愿意整天站在那里被射击,只要向我射击的滑膛枪手每次都承诺瞄准我。”
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There was a British army musketry instructor who famously said, "I'm willing to stand and be shot at all day long, as long as whoever's shooting at me with the smoothbore musket promises to aim at me every single time."
Henry: (亨利笑着)因为他知道子弹实际上永远不会(笑)射向枪瞄准的地方。
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Because he knew the bullet's never actually gonna go (laughing) where the gun is being aimed.
Derek: 所有这一切在1854年秋天发生了改变。俄罗斯军队蜷缩在塞瓦斯托波尔,被法国和英国军队围困。士兵们看着英国军队在远处山坡上布阵。他们远远超出了标准滑膛枪的射程,所以俄罗斯人并不担心,直到突然间,一扇窗户破碎了。
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All of that changed in the fall of 1854. Russian troops huddled in Sevastopol under siege by French and British forces. The soldiers watched as British troops set up on a distant hillside. They were far out of standard musket range, so the Russians weren't worried, when suddenly a window shatters.
他们正在向塞瓦斯托波尔海军基地俄罗斯兵营的窗户射击,距离900码,他们正在向窗户射击子弹。
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They were shooting through the windows of the Russian barracks at their naval base in Sevastopol, 900 yards away, they're shooting bullets through the windows.
但这些并非普通子弹。八年前,一位富有进取心的法国陆军军官克劳德-艾蒂安·米涅(Claude-Etienne Minie)取得了突破。他开发了一种带有空心底座和铁塞的锥形子弹。因此,当发射时,气体压力将塞子推入底座,使子弹膨胀,紧紧地压在枪管壁上,这样气体就不会逸出。这使得子弹的枪口初速更加可预测。
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But these were no ordinary bullets. Eight years earlier, an enterprising French army officer, Claude-Etienne Minie, made a breakthrough. He developed a conical bullet with a hollow base and an iron plug that would fit into it. So when fired, the gas pressure drove the plug into the base, which expanded the bullet, pressing it firmly against the barrel walls so no gas could escape. This made the bullet's muzzle velocity much more predictable.
但它也促成了另一件事。膨胀的子弹可以抓住刻在枪管内部的螺旋形凹槽,这被称为膛线(rifling: 枪管内壁的螺旋形凹槽,用于使子弹旋转以提高精度)。这使得子弹在射出时旋转。这是关键,因为所有旋转的物体都具有一个可以保持的基本物理量,即角动量(angular momentum: 描述物体旋转运动的物理量,使其抵抗方向变化)。这有助于它们抵抗方向的变化。就像旋转的陀螺一样。
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But it also enabled something else. The expanded bullet could grip spiral grooves carved into the inside of the barrel, called rifling. This imparted spinned the bullet as it shot out. And this is key because all spinning objects have a fundamental quantity they can serve, angular momentum. This helps them resist changes in their orientation. It's just like the spinning top.
现在,如果没有旋转,陀螺就会像你预期的那样倒下。但如果我们加上一点旋转,我们就可以看到它抵抗方向的变化。所以如果我轻轻一碰,它就会重新调整方向,朝着其角动量的方向。
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Now, without spin, the top just falls over like you'd expect. But if we add a little bit of spin, we can see that it resists changes in its orientation. So if I give it a little touch, it reorients itself in the direction of its angular momentum.
Derek: 旋转的子弹也会发生类似的情况。它的角动量抵抗其旋转轴的变化。因此,即使风对子弹施加了不平衡的力,它也能保持其方向。这减少了阻力,有助于弹丸飞得更远、更快、更准确。当汤姆·布雷迪投出紧密螺旋球时,发生的情况也完全相同。
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A similar thing happens with a spinning bullet. Its angular momentum resists changes to its axis of rotation. So even if wind applies an unbalanced force to the bullet, it maintains its orientation. This reduces drag and helps the projectile fly further, faster and more accurately. The exact same thing is going on when Tom Brady throws a tight spiral.
Tom Brady: 螺旋球的重要部分是你感觉到风吹向我们。如果球有任何晃动,它就会在风中遇到很大的阻力,这会大大降低球的速度和准确性。螺旋球越紧密,旋转越多,它就越能穿过空气,风对球的影响就越小。所以对于任何优秀的四分卫来说,在有风的条件下投出紧密螺旋球非常重要。
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The important part of a spiral is you feel the wind blown at us. If the ball wobbles at all, it's gonna catch a lot of resistance in the wind, and it's gonna slow the velocity of the ball down a lot and the accuracy. The tighter the spiral and the more it spins, the more it can just rotate through the air and the wind will have a less effect on the ball. So for any good quarterback, the ability to throw a tight spiral is really important when you play in windy conditions.
旋转的球将保持其方向,因此以较小的迎风面积和较低的阻力系数穿过空气。所有这些都说得通,但奇怪的地方来了。如果球保持其方向,那么在一个长距离的“万福玛丽”式传球中,它应该一直保持像这样向上倾斜,就像它被投掷时一样。但事实并非如此。
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A spinning ball will maintain its orientation, and therefore cut through the air with a smaller frontal area and a lower drag coefficient. This all makes sense, but here's where things get weird. If the ball is maintaining its orientation then on a long Hail Mary pass, it should stay pitched up like this the whole time, just like when it was thrown. But that is not what happens.
翻转效应与陀螺进动
橄榄球中存在一种悖论,那就是当你释放球时,它的角度可能是正30度。
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There's kind of a paradox in football, which is, when you release the ball, you're angled say positive 30 degrees.
Derek: 好的。
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Okay.
Tom Brady: 当你的接球手接到球时,它的角度是负30度。
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And when your receiver catches it, it's angled negative 30 degrees.
Derek: 完美,我喜欢这样。
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Perfect, I love that.
Tom Brady: 所以我们刚才说的是,角动量使得球难以转动。
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So what we just said was, angular momentum makes the ball hard to pivot.
Derek: 好的。
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Okay.
Tom Brady: 但我们看到的是它在四秒内从这样翻转到那样。
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But what we saw was it pitches from this to this in four seconds.
Derek: 对,翻转(turnover: 橄榄球在飞行过程中,其尖端逐渐向下倾斜,与抛物线轨迹保持对齐的现象)——
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Right, turnover-
Tom Brady: 是的,没错。
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Yes, exactly.
现在,翻转效应(turnover effect: 橄榄球在飞行过程中,其尖端逐渐向下倾斜,与抛物线轨迹保持对齐的现象)对于一个好的投掷至关重要,因为它意味着在弧线的每一点上,球的方向都与其运动方向紧密对齐。这意味着它始终直接指向气流,从而最大限度地减少阻力。
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is what we would call that. Now, turnover is essential to a good throw because it means at every point along the arc, the ball's orientation stays closely aligned with its direction of motion. That means it stays pointed directly into the airflow, which minimizes drag.
现在,你可能会觉得这没什么大不了的?我的意思是,箭和羽毛球也会沿着弧线路径自行对齐。但这在这些情况下之所以有效,是因为物体是前端加重的。羽毛会捕捉空气并被推到较重的尖端后面,由尖端引导方向。但橄榄球完全不同。它没有羽毛或鳍,而且它的重量沿轴线均匀分布。所以它不能使用相同的机制来对齐自己。
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Now, sure, you might think this isn't that crazy? I mean, arrows and birdies align themselves along the path of the arc as well. But that works in these cases because the objects are front weighted. The feathers catch the air and get pushed behind the heavier tip, which leads the way. But a football's totally different. I mean, it doesn't have feathers or fins, and its weight is evenly distributed along its axis. So it just can't use the same mechanisms to align itself.
因此,在2020年,《美国物理学杂志》(The American Journal of Physics)的主编决定弄清楚这个问题。
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So in 2020, the editor-in-chief of "The American Journal of Physics" decided to figure it out.
我惊讶于有多少容易被驳斥的错误解释被发表出来。当你仔细思考时,这根本说不通,因为空气阻力会把橄榄球的头部向上推,而你却希望橄榄球的头部向下。所以这相当奇怪。
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I was surprised at how many bad explanations that were easy to debunk got published. When you think about it, it doesn't make any sense, because the air resistance would push the nose of the football up, and you want the nose of the football to go down. So it's pretty curious.
Henry: 于是普莱斯建立了一个理论模型来解释橄榄球的翻转效应。今天,我们将通过在风洞中模拟汤姆·布雷迪的投掷来验证他的发现是否成立。
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So Price put together a theoretical model to explain the football's turnover. And today, we're gonna see whether his findings hold up by simulating Tom Brady's own throws in a wind tunnel.
能与我非常尊敬的汤姆·布雷迪有任何关联,不仅因为他的技术,还因为他的职业道德。这简直是超凡脱俗。
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The idea of having anything to do with Tom Brady, whom I greatly respect, not only because of his skill, but because of his work ethic. It's otherworldly.
我们这些球里有传感器。所以我们应该能够从球内部看到球实际飞行的速度。为了确保准确,我正在用老式方法测量这些球的速度,这可能是一个我将来会后悔的决定。
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We have these sensors in these balls. So we should be able to see how fast the balls are actually going from inside the ball. And just to be sure, I'm measuring the speed of these balls the old-fashioned way, a decision I might regret.
Tom Brady: 你想站在假人旁边用枪测量吗?我会把球从你头顶扔过去。
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Do you wanna go right on the side of the dummy with the gun? I'll throw it right over your head.
Derek: (德里克笑着)
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(Derek laughing)
Tom Brady: 我不会打到你,相信我。是的,就在那里,完美。准备好了吗?
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I won't hit you, trust me. Yeah, right there, perfect. Ready?
Henry: 好的。45。
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Yep. 45.
Tom Brady: 也许再往那边挪一点点。完美。
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Maybe scoot just a smidge more that way. Perfect.
Henry: 天哪(哔——)。46。你还要再来一个吗?
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Holy (bleep). 46. You gonna do another one?
Henry: 49。我的天,这太吓人了。那大约是每小时80公里。但你在比赛中真的会用到那个速度吗?
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49. My God, that's scary. That's like 80 kilometers an hour. But would you actually use that speed in a game?
Tom Brady: 那会是一个很好的速度。那是一个正常的传球。
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That'd be a good speed. That's a normal pass.
Henry: 那太吓人了。
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That's like terrifying.
那只是普通投掷的速度。对于他的长传,速度甚至更高,超过每小时60英里,也就是将近每小时100公里。现在,我可不会站在那个“大炮”前面。我天生就不是运动员。
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And that's just for a regular throw. For his long throws, the speed jumps even higher, over 60 miles per hour, that's almost 100 kilometers per hour. Now, I'm not about to step in front of that cannon. I was not built for being an athlete.
Tom Brady: 你是为分析而生的。(笑)
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You're built for analyzing the. (laughing)
Derek: 没错,我是来获取数据的。这就是为什么我让亨利在这里。
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That's right, I'm here for the data. And that's why I've got Henry here.
Henry: 噢。
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Ooh.
Derek: 噢,那个击中了胸部。我听到了。
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Ooh, that one hurt the chest. I heard that.
Tom Brady: 确定你不想换德里克来吗?(笑)
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Sure you don't wanna swap in, Derek? (laughing)
Derek: 你做得很好。当汤姆·布雷迪投掷时,你必须快速反应。但这种压力并不仅限于橄榄球场。
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You're doing great. When Tom Brady is throwing, you gotta react fast. But that kind of pressure isn't limited to the football field.
现在,互联网就像橄榄球一样。当你在网上时,威胁从四面八方袭来。现在,你有黑客,你有追踪器,你有你甚至从未谷歌过的东西的广告。
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Now, the internet's a lot like football. When you're online, threats are coming at you from all sides. Now, you got hackers, you got trackers, you got ads for things you never even googled.
你甚至不需要靠近某人就能惹麻烦。
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And you don't even have to be near someone to mess with them.
(笑)那很接近了。(笑)有了今天的赞助商NordVPN,就像你拥有自己的进攻锋线一样。
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(laughing) That was close. (laughing) With today's sponsor, NordVPN, it's like having your own offensive line.
Henry: (亨利猛地呼气)NordVPN为你提供真正的保护。它隐藏你的IP,伪装你的位置,并加密你所有的互联网流量,这样就没有人能看到你在网上做什么。威胁防护可以阻止恶意软件,停止追踪器,甚至保护你免受那些烦人的广告侵扰。即使你没有连接到VPN,它也能工作。
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NordVPN gives you real protection. It hides your IP, masks your location, and encrypts all your internet traffic so no one sees what you're doing online. Threat protection blocks malware, stops trackers, and even protects you from those annoying ads. It even works when you're not connected to a VPN.
此外,NordVPN有严格的无日志政策,所以他们从不追踪、收集或分享你的私人数据。你可以在多达10台设备上使用一个账户,无论是台式机、平板电脑,甚至是你的手机。所以即使你在球场上,你也能受到保护。当你在网上时,不要只是站在那里毫无保护,建立你自己的进攻锋线。
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Plus, NordVPN has a strict no-logs policy, so they never track, collect or share your private data. You can use it on up to 10 devices with one account, desktop, tablet, or even your phone. So you're protected even when you're on the field. When you're online, don't just stand there unprotected, set up your own offensive line.
需要明确的是,NordVPN不附带五名300磅的进攻线员,但它确实像其中一名线员一样保护你的连接。Nord通过我的链接为你提供独家折扣。所以当你注册时,请务必访问nordvpn.com/veritasium,或者扫描这个方便的二维码。通过这个优惠,你将获得两年计划的折扣,外加额外四个月的免费使用。如果你仍然不完全相信,Nord提供30天退款保证,所以你可以完全无风险地试用。只需访问nordvpn.com/veritasium查看。我要感谢NordVPN赞助本视频。现在,回到汤姆·布雷迪。
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To be clear, NordVPN does not come with five 300-pound linemen, but it does protect your connection like one of them. Nord is giving you an exclusive discount through my link. So when you sign up, make sure to go to nordvpn.com/veritasium, or just scan this handy QR code. And with this deal, you'll get a discount on a two-year plan, plus an extra four months free. And if you're still not totally convinced, Nord has a 30-day money-back guarantee, so you can try it out completely risk-free. Just check it out at nordvpn.com/veritasium. I'd like to thank NordVPN for sponsoring this video. And now, back to Tom Brady.
Derek: 有人曾用慢动作拍摄过你的出手和所有细节吗?你有没有回看过那些?
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Have people shot you in really slow motion for the release and everything? Did you ever watch that back?
Tom Brady: 从未有过。
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Never.
Derek: 你们准备好了吗?
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You guys ready?
Henry: 我准备好了。
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I'm ready.
Ricky: 三、二、一。
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Three, two, one.
Henry: 我的天。你没事吧?你没事吧,瑞奇?
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Oh my God. Are you good? You good, Ricky?
Ricky: 是的,是的,我没事,我没事。
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Yeah, yeah, I'm good, I'm good.
Henry: 那是有机玻璃还是真玻璃?
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Is that plexy or is that real glass?
Derek: 那是有机玻璃。
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That's plexiglass.
Henry: 太不可思议了。
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That's incredible.
Tom Brady: 你只有一次机会做这些事。
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You get one shot at these things.
Henry: 哦(哔——),好吧,我会尽力而为。我们再试一次好吗,即使摄像机坏了?
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Oh (bleep), all right, I'd have given it my best. Should we try one more, even if the camera breaks?
Henry和Derek: (笑)
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(Henry and Derek laughing)
Ricky: 我没看到裂缝——
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I don't see the cracks-
Henry: 哇。
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Wow.
Ricky: 所以我们可以再来一次。
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so we can go again.
Henry: 我们再试一次。
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Let's try one more.
Tom Brady: 你开玩笑吗?
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Are you kidding?
Henry: 让我再用力一点。
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Let me just throw a little harder.
Tom Brady: 好的,我们再来一次。
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All right, let's go again.
Henry: 我要再用力一点。
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I'm gonna throw a little harder.
Ricky: 噢。
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Aw.
Tom Brady: 现在我们坏了。
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Now we're broke down.
Henry: 那个就在那里。我们能回放投掷吗?
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That went right there. Are we able to watch the throw back?
Tom Brady: 好的螺旋球。(笑)哦,那太酷了。
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Good spiral. (laughing) Oh, that's so cool.
传感器显示布雷迪当天最大旋转速率为每分钟628转。所以有了这些数据,让我们在风洞中分析布雷迪的投掷。
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The sensors show Brady's maximum spin rate on this day was 628 revolutions per minute. So armed with this data, let's analyze Brady's throws in a wind tunnel.
Derek: 你通常能获得多少数据?
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How much data are you used to getting?
Tom Brady: 零。
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Zero.
Derek: 真的吗?
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Really?
Tom Brady: 我打球的时候?
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When I played?
Derek: 是的。
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Yeah.
Tom Brady: 都没有。
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None of it was available.
Phillip: 所以这是大学里的低速风洞。这个风洞设施可以达到大约0.2马赫,也就是声速的20%。
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So this is the low-speed wind tunnel here at the university. This wind tunnel facility can get up to about Mach .2, so 20% of the speed of sound.
Derek: 通常这个风洞用于开发用于创新可持续飞机设计的先进机翼几何形状。但今天,它被用于橄榄球。
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Typically this wind tunnel is used in the development of advanced wing geometries for innovative sustainable aircraft design. But today, it's being used for football.
Phillip: 我们有一个安装在转盘上的支杆。我们这里实际上有一个六分量测力计(six-component load cell: 一种能够同时测量物体在三个方向上的力和三个方向上的扭矩的传感器)。有了这个六分量测力计,我们可以测量所有三个方向的力和扭矩。然后我们有一个电动机,对吧,我们可以旋转它来模拟螺旋球。
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We have just a sting mount mounted to a turntable. We actually have a six-component load cell here. And with this six-component load cell, we can measure all three components of force and torque. We then have an electric motor, right, that we can spin to basically simulate the spiral.
Derek: 首先,我们将模拟布雷迪的一次投掷,球以他经典的螺旋球方式直接进入气流。一切都如我们所料,没有产生显著的力或扭矩。但在比赛中,球不会这样直线飞行。在任何投掷中,它的质心都遵循大致的抛物线轨迹(parabolic trajectory: 物体在重力作用下沿抛物线路径运动的轨迹)。
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First, we're gonna simulate one of Brady's throws where the ball travels straight into the airflow with his classic spiral. And everything proceeds as we expect, no significant forces or torques develop. But during a game, a ball doesn't travel like this in a straight line. During any throw, its center of mass follows a roughly parabolic trajectory.
所以假设你在投掷时将球完美地与这条抛物线对齐。那么,从球的角度来看,仅仅片刻之后,这条抛物线开始向下弯曲,远离球体,这意味着更多的空气会撞击球的底部而不是顶部。现在,你可能会认为这会使球向后倾斜,但这只有在球不旋转的情况下才会发生。如果它正在旋转,那么情况就大不相同了,你可以通过这个惊人的演示看到这一点。想象一下这个高尔夫球环就像橄榄球的横截面。
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So let's say you align the ball perfectly with this parabola when you launch it. Well, then, from the ball's perspective, just a moment later, this parabola starts to curve down away from the ball, which means more air will be hitting the underside of the ball than on top. Now, you would expect this would tilt the ball back, but that's only what happens if the ball is not spinning. If it is spinning, then the situation is very different, which you can see with this amazing demo. Imagine this ring of golf balls is like a cross-sectional slice of the football.
这就是当我试图用这个吹叶机把它推回去时发生的情况。我的意思是,它像你预期的那样向后倾斜。但如果我做完全相同的事情,但这次让轮子旋转,它就会向右倾斜。如果我们放慢速度,你就能明白为什么。所以当环经过吹叶机时,力就施加在那里。但每个球仍然有旋转方向的动量。所以它实际上在施加力的地方再向前90度达到峰值,这被称为陀螺进动(gyroscopic precession: 旋转物体在受到外力矩作用时,其旋转轴会垂直于力矩方向发生缓慢旋转的现象)。
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Here's what happens when I try and push it back with this leaf blower. I mean, it tilts back just like you'd expect. But if I do the exact same thing, but this time, get the wheel spinning, tilts out to the right. And you can see why if we slow it down. So as the ring passes the leaf bar, that's where the force is applied. But each ball still has momentum in the direction of rotation. So it actually reaches its peak 90 degrees further along from where the force is applied, and this is known as gyroscopic procession.
Tom Brady: 所以如果风吹到它,它就会保持尖端向上。
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So if the wind was hitting it, it's gonna keep the point up.
Derek: 所以你会认为它只会把它推回去。
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So you'd think that it would just push it back.
Tom Brady: 对吗?
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Right?
Derek: 但因为它在旋转,当你向上推时,它实际上会向右倾斜。
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But because it's spinning, when you push up, it actually tilts to the right.
Tom Brady: 哦,有意思。
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Oh, interesting.
Derek: 但这还不止。当球向右倾斜时,它会使那一侧暴露更多的面积。所以现在,由于陀螺进动,球会向下倾斜。当更多的空气撞击球的顶部时,它就会向左偏转。而这又会使球向上偏转。现在我们回到了起点。所以这个循环会重复,但由于这是持续发生的,球的尖端会围绕气流方向描绘出一个圆。所以我们得到了一个缓慢的晃动。
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But it doesn't stop there. As the ball tilts right, it exposes more area on that side. So now, because of gyroscopic procession, the ball pitches downward. And with more air hitting the top of the ball, well, it's going to deflect to the left. And that is going to make the ball deflect back up. And now we're back to where we started. So this cycle is going to repeat, but since this is happening continuously, the nose traces out a circle around the direction of airflow. So we get a slow wobble.
Tom Brady: 我们以前开玩笑说,每当你没有投出紧密螺旋球时,你就会称之为“紧密晃动球”。那是布雷特·法弗(Brett Favre)创造的短语。他让球出去时有点晃动,他就会说:“哦,紧密晃动球。”
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We used to joke, whenever you would not throw a tight spiral, you would call it a tight wobbler. That was a Brett Favre-coined phrase. He let it go and have a little wobble to it, and he'd go, "Oh, tight wobbler."
Henry: (亨利笑着)
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(Henry laughing)
Derek: 现在,如果球只是直线飞行,这就是全部的故事。但请记住,球的路径是抛物线,这意味着从球的角度来看,迎面而来的空气不断向下倾斜,远离球体。所以球试图围绕气流方向进动,但那个方向却在不断变化。
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Now, if the ball were just traveling straight, this would be the whole story. But remember from before, the ball's path is a parabola, meaning that from the ball's perspective, the oncoming air is constantly dipping down away from it. So the ball is trying to process around the airflow direction, but that direction is constantly changing.
例如,当球到达进动的底部时,气流也向下移动了。这意味着球不会像你预期的那样向左倾斜那么多。所以当它向上进动时,它不会回到它开始时那么高。随着时间的推移,正是这一点逐渐使橄榄球的尖端向下倾斜,使其与抛物线路径保持对齐。
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For example, by the time the ball has reached the bottom of the procession, the airflow has moved down too. And what that means is the ball is not gonna tilt out to the left as much as you'd expect. So when it processes back up, it doesn't go as high as where it started. And over time, it is this that gradually pitches the nose of the football down, keeping it aligned with its parabolic path.
Tom Brady: 我能把所有这些都可视化,你那些花哨的科学词汇。
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I can visualize it all, your fancy science words.
Derek: 好的,好的。
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Okay, okay.
Tom Brady: 我回到了我的高中时代。我是一个非常普通的理科生,所以。但你教了我很多。
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I'm going all the way back to my high school days. I was a very average science student, so. But you're teaching me a lot.
Derek: 当球穿过空气时,球的底部会比顶部受到更多的空气阻力。
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As the ball goes through the air, there's gonna be more air resistance on the bottom of the ball than on the top.
Tom Brady: 球的前部,而不是后部,因为它首先撞击风。
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The front of the ball, not the back, 'cause that's hitting the wind first.
Derek: 球的前底部。
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The front bottom of the ball.
Tom Brady: 所以这意味着,它会产生这种进动效应,将其向外推,向下推,向右推。无论你做什么,它都会产生晃动。
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And so what that means is, it creates this processive effect that pushes it out, pushes it down, pushes it right. It creates a wobble no matter what you do.
Derek: 非常酷。
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Very cool.
Tom Brady: 所以晃动实际上不仅无法避免,而且对于确保球沿着你希望它遵循的路径飞行至关重要。
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So wobble is actually not only impossible to avoid, but it's essential to make sure that the ball follows the path that you want it to follow.
Derek: 你可以在风洞中看到这一点。我们把球向上倾斜了三度,它可以向任何方向转动。
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You can see this in the wind tunnel. We've tilted the ball up by three degrees and it's free to pivot in any direction.
是的,你确实看到了倾斜。哦,那太棒了。我们看到的是,它开始时自身对齐大约偏离三度。你知道,因为我们就是这样让它旋转起来的。但随着气流开始,它会指向最小化阻力的方向。那太酷了。我的意思是,这正是我们所期望的,但亲眼看到它仍然令人难以置信。
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Yeah, you're definitely seeing a pitch. Oh, that's awesome. What we're seeing is, it's starting out aligning itself about three degrees off. You know, 'cause that's how we spin it up. But as the airflow starts, it's pointing itself in the direction that minimizes drag. That's so cool. I mean, that's exactly what we were expecting, but it's still incredible to see it in person.
传球的微妙偏转与环境影响
Derek: 如果你观察真实的橄榄球飞行,你会发现右撇子投掷时,球会更多时间稍微向右倾斜。正是这种倾斜产生了力,通过进动,逐渐使球的尖端向下倾斜。它产生了汤姆·布雷迪所说的翻转效应。
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If you look at a real football flight, you'll notice that it spends more time angled slightly to the right when thrown by a right hander. That is what creates the force, which, through procession, gradually pitches the nose downward. It creates the turnover effect that Tom Brady was talking about.
Tom Brady: 我只是想把晃动重新定义为不一定是坏事。
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Just wanna reframe the wobble as not necessarily a bad thing.
Derek: 好的,很好。
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Okay, good.
Tom Brady: (笑)是的。佩顿·曼宁(Peyton Manning)的球也有很好的晃动,但他通过这种方式完成了许多达阵。
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(laughing) Yeah. Peyton Manning had a good wobble on the balls, but he found a way to complete a lot of touchdowns that way.
Derek: 但球向右倾斜也产生了意想不到的副作用。我们听说右撇子投掷的球会向右偏转,而左撇子投掷的球会向左偏转。你认为这是真的吗,或者你注意到这一点了吗?
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But the right-ward lean of the ball also has an unintended side effect. Something we've heard is that for right-handed throwers, the ball will drift right, and for left-handed throwers, the ball will drift left. Do you think that's true or is that something you notice?
Tom Brady: 所以我不一定会同意这一点。
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So I wouldn't necessarily agree with that.
Derek: 所以我们让汤姆沿着场地的一条线笔直投掷。无人机设置好了吗?那是一个相当直的投掷。
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So we got Tom to throw straight down one of the lines on the field. Is the drone set? That's a pretty straight throw.
Tom Brady: 亨利,别动,你让它看起来很糟糕。
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Henry, don't move, you're making it look bad.
Derek: (德里克笑着)
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(Derek laughing)
Tom Brady: 我会站稳。你越不动,我的投掷看起来就越好。就像一个捕手,当你为投球做准备时。
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I'll stay planted. The more still you go, the better it looks for my throw. It's like a catcher. when you frame the pitch.
Henry: 我会准备好的,我会准备好的。(笑)
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I'll frame it, I'll frame it. (laughing)
从地面上看,他的传球惊人地笔直。但从无人机上看,如果你仔细观察,就在传球的最后,球确实向右偏离了。这是因为直到现在,我们一直忽略了一个非常重要的空气动力学效应,那就是升力(lift: 垂直于流体流动方向的力,由物体与流体相互作用产生)。当球向右倾斜时,它会向那个方向产生升力。倾斜越大,这个力就越大。向右倾斜是让球在其抛物线路径中翻转所必需的。但这确实意味着右撇子的投掷倾向于向右偏转。
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From ground level, his passes looked amazingly straight. But from the drone, if you watch closely, just at the end of the pass, the ball does drift off to the right. This is because up until now, we've been ignoring a very important aerodynamic effect, which is lift. When the ball is tilted to the right, it generates lift out in that direction. The more it's tilted, the larger this force is. The rightward tilt is required to get the ball to turn over during its parabolic path. But it does mean that right-handed throws tend to drift, right?
这种效应很微妙,但有些球员凭直觉就能注意到。1991年秋天,杰里·赖斯(Jerry Rice),通常被认为是史上最伟大的外接手,更换了四分卫。他不再接到右撇子乔·蒙塔纳(Joe Montana)的传球,而是接到左撇子史蒂夫·扬(Steve Young)的传球。对赖斯来说,有些不对劲。他不确定具体原因,但他表示传球总是差一点。当然,实际发生的情况是球偏离了他预期的地方。乔·蒙塔纳的右撇子传球向右偏转,而史蒂夫·扬的传球向左偏转。这是一种微妙的效应,但它是进动的一部分,它能最大限度地减少球的阻力,让球飞得更远、更快、更准确。
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The effect is subtle, but some players notice it intuitively. In the fall of 1991, Jerry Rice, generally considered the greatest wide receiver of all time, changed quarterbacks. In place of the right-handed Joe Montana, he was now catching passes from the left-handed Steve Young. And for Rice, something felt off. He wasn't sure exactly why, but he said the throws were coming up short. Of course, what was actually happening was that the ball was drifting away from where he expected it to be. Joe Montana's right-handed throws drifted to the right, whereas Steve Young's drifted left. It's a subtle effect, but it's all part of the procession that minimizes drag on the ball and lets it fly farther, faster and more accurately.
Tom Brady: 所以这不是因为你是一个糟糕的四分卫,投掷时有晃动,而是因为风,你知道吗?
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So it's not because you're a bad quarterback throwing it with a wobble, it's because wind, you know?
Derek: 好的,那么如果你在一个穹顶体育场,没有风呢?
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Okay, so what if you're in a dome and there's no wind?
Tom Brady: 看,那是一个很好的问题。所以我只是说这是空气阻力。所以即使在穹顶体育场,同样的事情也会发生。
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See, that's a great question. So I'm just saying this is just air resistance. So even in a dome, the same thing would happen.
无论是在室外体育场还是封闭式穹顶体育场,球都会一直晃动。但室外体育场的投掷难度要大得多,因为有风。当球以每小时50到60英里的速度投掷时,大部分流过球的空气是由于其自身的运动,但在阵风超过每小时15英里的情况下,天气开始发挥主要作用。
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Whether in an outdoor stadium or a closed-top dome, the ball will always wobble. But outdoor stadiums are significantly harder to throw in because of the wind. With the ball being thrown at 50 to 60 miles per hour, most of the airflow over the ball is due to its own motion, but in winds gusting over 15 miles per hour, the weather starts to play a major role.
我们委托NFL数据团队对室外体育场和室内穹顶体育场的传球成功率进行了分析。他们发现,无论距离如何,室内体育场的传球始终更准确。所以也许布雷迪在新英格兰的福克斯伯勒体育场受到了不公平的对待。你更喜欢在没有风的比赛中投掷吗?你喜欢风、雨、雪吗?这重要吗?
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We commissioned the NFL data team to do an analysis of completion percentage in outdoor stadiums versus indoor domes. And they found that throws in indoor stadiums are consistently more accurate, no matter the distance. So maybe Brady was hard done by Foxborough, New England's stadium. Do you prefer to throw in a game when it's no wind? Do you prefer wind, rain, snow? Does it matter?
Tom Brady: 我更喜欢室外,70华氏度,潮湿,微风,只是为了让你保持凉爽。
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I preferred outdoor, 70 degrees, humid, tiny little breeze, just to keep you cool.
Derek: 对,但你为什么喜欢在室外而不是在穹顶体育场呢?
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Right, but why did you like being outdoors as opposed to being in a dome?
Tom Brady: 我觉得我在室外的深度感知更好一点。我喜欢自然空气的自然感觉。穹顶体育场总是感觉像一个真空。
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I felt like my depth perception was a little better outside. I liked just the natural feel of the natural air. The dome always felt like a vacuum.
Derek: 如果天气不好,你认为你比其他四分卫有优势吗?
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Do you think you had an edge if the weather was bad compared to other quarterbacks?
Tom Brady: 我会说是的。原因是我可以说我一直在这种天气下练习。我认为习惯这些条件,熟悉风、湿度、雨、雪,你知道,草地、人造草皮,我确切知道在每种条件下穿什么。我打了23个赛季,每年100到120次练习。
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I would say yes. And the reason why is I'd say I practiced in it all the time. And I think getting used to the conditions and the familiarity of the wind, of the humidity, of the rain, of the snow, you know, grass field, turf field, I knew exactly what to wear for every single condition. I played 23 seasons, 100 to 120 practices a year.
Derek: 你经历了一切。
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You saw everything.
Tom Brady: 所以那是2000多次练习。你知道你想要袖子的厚度,你会说:“好的,温度是多少?50华氏度。好的,这是我在50华氏度时穿的衬衫。哦,35华氏度,这是我在35华氏度时穿的两件衬衫。你知道,这是我戴的暖手筒。你知道,这是我放多少热包在暖手筒里,以便在30华氏度而不是50华氏度时保持手暖和。”
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So that's over 2,000 plus practices. You know the thickness you want your sleeves, you go, okay, "What's the temperature? It's 50 degrees. Okay, this is the shirt I wear when it's 50 degrees. Oh, it's 35 degrees, this is the two shirts I wear when it's 35 degrees. You know, this is the muff that I wear. You know, this is how many heat packs I put in the muff to keep my hand warm when it's 30 degrees versus 50 degrees."
Derek: 你把一切都调整好了。
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You had it all dialed in.
Tom Brady: 你必须这样做,我的意思是,你只是随着时间的推移观察,然后你,你知道,变得越来越好。这很像F1赛车。你知道,一切都只是为了让你感觉最舒服而做的一小部分事情。
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You just have to, I mean, you just observe over time, and you, you know, get better and better. It's a lot like an F1 car. You know, everything is just fractions of, you know, things to do to make yourself feel the most comfortable.
汤姆·布雷迪的直觉式掌握
所以也许布雷迪比他自己承认的更具科学性。在他的383场职业比赛中,超过7700次传球成功,以及数万小时的球场经验,布雷迪直觉地理解了我们刚刚分析的所有物理学原理。此外,他知道如何利用这些效应,在短短几秒钟内将球传到他想去的地方。在一场不可能完美的比赛中,他内化了所有复杂的物理学、运动学、空气动力学,但他仍然让它看起来很简单。
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So maybe Brady is a bit more scientific than he gives himself credit for. Over 383 career games, more than 7,700 completed passes and tens of thousands of hours on the field, Brady intuitively understands all the physics we've just analyzed. Plus he knows how to harness these effects to get the ball where he wants it to go with just a few seconds to throw it. In a game where perfection is impossible, he's internalized all the complex physics, the kinematics, the aerodynamics, and he still makes it look simple.
Tom Brady: 是的,我不用动。(笑)所以我们实际上和汤姆·布雷迪一起制作了一个视频,教我们如何投掷橄榄球。如果你想了解更多,可以在这里查看。
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Yeah, I don't have to move. (laughing) So we actually made a video together with Tom Brady teaching us how to throw a football. And if you wanna learn more about that, you can check it out right here.
现在我们为你准备了一些你以前从未投掷过的球。
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Now what we got for you are some balls that you've never thrown before.
Tom Brady: 哦天哪,你们又搞了什么花样?
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Oh God, what have you guys got cooked up?
但我们还没完。
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But we're not done yet.
搞什么鬼?在其他运动中,表面都被精确设计到最小的细节来控制气流。但橄榄球几十年来几乎没有改变。所以我们测试了橄榄球的设计是否真的最佳。为了找出答案,我们让汤姆·布雷迪投掷了一系列定制球,包括一个旨在完全消除他旋转的球。
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What the heck? In other sports, surfaces are engineered down to the smallest detail to control airflow. But footballs, they've hardly changed in decades. So we tested whether a football's design is really optimal. And to find out, we had Tom Brady through a series of custom balls, including one built to eliminate his spin entirely.
Tom Brady: 我甚至不知道你怎么能投出那样的球。
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I don't even know how you could throw that.
在调查过程中,我们实际上发现了一种秘密技术,球队正在用它来改造他们的球,并给他们的球员带来优势。但我们会在未来的视频中讨论这个问题。所以请务必订阅并保持关注,我们到时候再见。
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Now, in investigating this, we actually uncovered a secret technique that teams are using to modify their balls and give their players an advantage. But we'll get to that in a future video. So make sure to subscribe and stay notified, and we'll see you then.
Tom Brady: 那太疯狂了。
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That's insane.
Henry: (亨利笑着)
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(Henry laughing)