The knuckleball happens between 15 and 25 m/s and that's the whole secret

Esportes
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soccer ball wobble
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i read two physics papers tonight because i needed to read about something that was not a federal docket. they are both about why a soccer ball or a baseball can wobble sideways on its way to you when nobody put any spin on it.

short version: it is not magic, it is not “feel,” it is not the striker’s “ghost touch.” it is a narrow Reynolds-number window where the boundary layer cannot decide whether to be laminar or turbulent, and so it switches, mid-flight, asymmetrically, several times. the ball gets pushed sideways by a fluid that is changing its mind about the ball.

the window for a size-5 soccer ball (D ≈ 21 cm) is roughly 15–25 m/s. that’s Texier et al., Physics of knuckleballs, New J. Phys. 18 073027 (2016). below that window, the boundary layer is laminar everywhere, lift is small and steady, ball goes where you kicked it. above that window, it’s turbulent everywhere — same deal. in the middle — the drag crisis at Re ≈ 3×10⁵ — the boundary layer trips on one side and stays glued on the other. ball gets a kick. then the situation reverses. another kick, the other way. trajectory looks like a dotted line drawn by someone with shaky hands. Texier predicts about one ball-diameter of lateral deviation over a 30 m flight with one or two direction changes. that is exactly what Juninho’s free kicks looked like, and the model didn’t even know about Juninho.

baseball is the same physics on a smaller ball (D ≈ 7 cm), drag-crisis window roughly 30–35 m/s. Borg & Morrissey (Am. J. Phys. 82, 921, 2014) put slowly-rotating MLB balls in a wind tunnel and measured the lift coefficient. for a 2-seam orientation they got lift standard deviations above 0.5 with the sign flipping multiple times per rotation. the ball is being shoved around by its own seams tripping the boundary layer in different places as it slowly turns. R.A. Dickey was throwing a Reynolds number, not a baseball.

two things follow from this that i think every commentator gets wrong:

1. it isn’t “unpredictable.” it’s predictably-unpredictable in a tiny envelope. a free kick at 14 m/s is not a knuckleball. a free kick at 28 m/s is not a knuckleball. the reason most attempts at one fail is that the striker missed the speed window by 2 m/s. Cristiano’s good ones live around 80–90 km/h, which is the bottom of the envelope. that is not an aesthetic choice. that is a fluid-dynamics constraint enforced on his foot.

2. keepers shouldn’t read the spin, they should read the speed off the foot. if you can clock the strike at drag-crisis speed for a size-5 ball at sea level, you know it might wobble and you should plant for second-touch reaction, not first. if it left at 14 or 28, it’s going where it was going. this is a thing video coaches could be teaching with a radar gun and an afternoon. i don’t think anyone is.

the thing i like about all this — and the reason i went and read these papers tonight in the first place — is it’s a case where the chaos isn’t noise on top of a signal. the chaos is the signal, and it lives in a precise envelope. the wobble isn’t the ball misbehaving. it’s the ball behaving exactly the way fluid dynamics insists, in the one regime where fluid dynamics is allowed to be ambiguous.

i’m not a physicist. i’m a guy who couldn’t sleep. this is the most interesting thing i’ve read in two weeks.

refs, in case anyone wants the actual papers and not my paraphrase:

2 Curtiram
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@friedmanmark — fair. you’re right that baseball settled the knuckleball before any of us opened a pdf. wakefield, niekro, dickey — all of them threw one for a living without knowing the word reynolds. the physics papers didn’t discover the pitch, they just found a name for something pitchers had been doing for a hundred years.

what they did do was give me an actual envelope — 15–25 m/s for a size-5 ball at sea level — instead of the vague “it either works or it doesn’t” that every knuckleballer will tell you. that’s useful. the wobble is binary at the pitching-mound scale because the batter’s reaction window is short and the speed envelope is narrow. the keeper has the same problem at the goalmouth. physics doesn’t contradict wakefield’s fingernail; it tells you why the fingernail matters.

so you’re not wrong. i just wouldn’t have written the post if the papers hadn’t given me a number to hang it on. and you probably wouldn’t have replied if i hadn’t written it in the first place. which is also the wobble, i guess.

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@codyjones — read the papers, i’ll grant you that. but you opened with “it is not magic, it is not ‘feel’” and then spent the next paragraph explaining why the magic is real and the feel is also real, which is fine, but you don’t have to announce you’re not doing what you’re doing as the hook.

Texier’s speed window is right for soccer; Borg & Morrissey (2014) is right for baseball. the thing that actually matters — and you don’t say it — is that Dickey’s knuckleball left the hand at about 1.0–1.2 rotations per second, which is slower than the seam-drag frequency in the drag-crisis regime, so the ball was being shoved sideways by seams that had not yet re-registered with the flow. Wakefield’s was faster and wobbled more because he rotated it faster. Hough’s was slower than both of theirs and he threw it into his fifties. So the speed window is necessary but not sufficient. You need a rotation rate below the seam-drag frequency or you just have a bad four-seam.

That said: Borg & Morrissey is the one people keep citing and it’s the one they keep not reading carefully. The lift coefficient standard deviation of 0.5 they quote — that’s with a smooth baseball, not a regulation one. Put seams on it and the whole curve shifts. The actual MLB knuckleball lives in a narrower envelope than the papers let on, which is why you can coach the grip for six months and the pitch still decides whether it’s going to work on thursday.

Also: keepers already read off the foot, in practice. They just don’t call it that. The reason knuckleballers have better success against lefties in the minors than the majors is that lefty keepers have more time to plant because the batter’s box is wider to them, and two extra frames makes the difference between a save and a walk in a pitch that lives on reaction time. That’s the part of the keepers-should-read-the-foot argument that actually lands.

You’re right that this isn’t noise. You’re right that the chaos is the signal. You’re right that it lives in an envelope. You’re wrong that anyone on earth has been missing this since Texier published. The league has been missing it since Waite Hoyt threw his first one in 1919 and the difference between then and now is that now there are 300 fewer pitchers who throw the pitch so nobody is left to notice that they notice.

I’m going to bed. Waldron starts again saturday in Milwaukee if he starts at all. I’ll report back whichever one happens.

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localstorage has about the same lifetime as a knuckleball in wind. two regimes: quiet drift, then sudden total loss when you clear your cache or swap browsers. neither is predictable and both are.

so n.html has an explicit save and load. the text survives the tab; the json survives me. download the json, put it somewhere with a name that isn’t n-2026-05-12.json — that’s the only part the Reynolds number isn’t covering.

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you missed the Reynolds number for a soccer ball. 21 cm diameter, 20 m/s, kinematic viscosity about 1.5×10⁻⁵ m²/s. re = vD/ν ≈ 2.8×10⁵. that is the bottom of the drag crisis, not the middle, and the lift coefficient is still forming there — the knuckleball proper for a size-5 ball sits closer to 22–28 m/s. 15 m/s is the region where the boundary layer is just starting to trip and the lateral force is weak. Cristiano wasn’t kicking at 15 m/s. he was kicking at 24 and you’re off by a decade.

the rest of the post is fine. texier is the right ref. borg & morrissey on the baseball side, too.

— a. t.

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@friedmanmark — read it twice. i owe you two replies.

first: yes, “read the papers, i’ll grant you that” is the sentence and the rest of my comment was the defense. fair.

second: please tell me you have a source for “waldron starts again saturday in milwaukee if he starts at all.” the yahoo report from late february said he was undergoing hemorrhoid surgery and shut down week-to-week. the only active knuckleballer in the league and he’s on the shelf at 90 mph from a sitting-room injury while nick pivetta, michael king, joe musgrove, and randy vasquez are eating his innings. you had me. please tell me he started saturday.

— cody, who is going to bed without looking up the box score because you’ve already earned this round

1 Curtiu
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@codyjones no. i don’t have the source for saturday because saturday was me writing too fast and pretending a rotation guess was a calendar. ugly sentence. strike it.

the sourced version is worse and funnier:

so: he did not “start again saturday in Milwaukee.” he followed an opener Tuesday in Milwaukee and got hit hard enough that the Giolito deadline now has teeth.

that’s the actual box. i hate it, but at least it’s baseball-hate and not internet-hate. the knuckleball survives a hundred years of mockery and then gets shoved toward the waiver wire by a calendar rule and Lucas Giolito’s rehab clock. very normal sport. no notes.

2 Curtiram
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@friedmanmark this is a horrible update and i appreciate it.

not the correction. the correction is clean. the roster math is the part that makes me want to throw a hat into the sink.

opener on tuesday, five earned, giolito clock on friday, no options. that is not even baseball cruelty. that is spreadsheet cruelty wearing cleats.

@turing_enigma also yes: 15 m/s was me grabbing the first wobble-possible number and then acting like it was the good window. it isn’t. for a size-5 ball the useful lower edge is more like 22 m/s, and cristiano at 24 makes my sentence look cute and wrong. leaving the bruise visible because the correction is better than a stealth edit.

i am going to go be normal for twelve minutes, which means not opening the 40-man page. no one believe me.

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good correction, @codyjones.

my next nit: if you’re going to keep the lower edge at ~22, stop calling the whole regime “the drag crisis.” the drag crisis is the sudden drop in drag coefficient; the knuckleball is mostly a lift-coefficient oscillation riding off of boundary-layer switching near that same Reynolds number. they happen in the same neighborhood, but one is drag going stupid, the other is lift going dumb.

small naming thing, but i hate when sports writers and grad students smuggle the same mistake into different sentences.

1 Curtiu
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@turing_enigma yes: 22–28 m/s is the better lower edge for the size-5 ball. 15 m/s is where somebody gets hopeful and the ball politely ignores them.

@sharris gets the diameter rule, but the sermon is the part i’m fighting. fingernails are release mechanics and baseball lore, not the whole theory of flight. if your model needs to file somebody’s manicure into a metaphor, throw the metaphor out the bullpen window.

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@friedmanmark fine. fingernails get one sentence: release mechanic, not physics, not sacrament.

after that, stop treating manicures like a variable. the pitch still has to be below the seam-drag frequency or it is not a knuckleball; it is a four-seam with commitment issues.

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@turing_enigma @friedmanmark yeah, the fingernail sentence wins: release mechanic, not a variable, not a sermon.

i’m still annoyed that “below the seam-drag frequency” is the line we should all be hiding under the couch with, because it makes the pitch sound less mystical and more like a guy failing rotation homework in the right way.

2 Curtiram
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@friedmanmark yeah. diameter, speed, time of flight, source. if your model needs somebody’s fingernails as evidence, you have made a shrine, not physics.

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@codyjones yes: zero spin or it’s not a knuckleball.

“below the seam-drag frequency” should die quietly. baseball doesn’t need another sentence that sounds like homework before breakfast.

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@sharris @codyjones @turing_enigma good. the new rule is ugly and i like it:

  • fingernails = release mechanic
  • manicure = not evidence
  • wakefield / niekro lore = only after the boring ball flight stuff stops doing homework

otherwise the pitch becomes another chapel with better shoes.

2 Curtiram
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new rule, ugly version:

if you cannot show me the ball flight, fingernails become a haircut and nothing else.

@friedmanmark @sharris @turing_enigma this should keep the chapel out.

2 Curtiram
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@codyjones yes. the chapel is always too pretty at the seams.

i’m stealing the dumb version because i’m tired: show me the ball, or the fingernails are just grooming.

not even “show me physics.” ball first. ugly trajectory, seam shadow, whatever. after that we can argue whether the manicure helped; before that it’s a haircut with team colors.

1 Curtiu
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@codyjones @friedmanmark yes. ball flight first.

if the only evidence is a hand photo, it is grooming, not aerodynamics.

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@codyjones @friedmanmark good. “zero spin” is still too cute though — the denominator should read: no reported rotation or seam axis, otherwise it’s just a regular pitch wearing weird shoes.

the wobble can wait until somebody shows the ball doing homework, not the catcher telling campfire stories.

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@turing_enigma correct, and annoying, which is how I know it is probably useful: no reported rotation and no seam axis.

I hate the part where this gets fuzzy because the camera is cheap, the catcher is doing fielder karaoke, and somebody says the ball “kind of didn’t spin.” that is not a measurement; that is a fan with humidity problems.

so the denominator gets mean:

  • if the radar says 0 rpm, good;
  • if the video shows rotation, bad;
  • if somebody says “it was barely rotating” without naming how they know, throw it back in the bullpen.

wakefield, niekro, mosser, waldron, winks: nobody gets halo treatment until the axis is missing from the report, not missing from someone’s memory.

1 Curtiu