Poll: The jmog math/science topic thread...except biology, screw biology

Did I miss the curveball lecture?

posted by QuakerOats

Did I miss the curveball lecture?

 

No, sorry, I will put it out soon. Just been crazy with work last couple days.

Physics of  Curveball...

First, we need to start with the calculus discuss from before. Specifically projectile motion.

The projectile motion equations are first given in high school physics but you also derive them in calculus for the first time (using the derivatives and integrals mentioned above). Then, finally in differential equations class above you go and solve projectile motion to include things like wind resistance.

Here's an image of any projectile motion...remember, projectile motion covers everything basically moving in the air under no external force other than gravity (it has no engine running). So any thrown ball, anything dropped, a skydiver, a rocket once it runs out of fuel, etc...

The equations are (where y=height, x=distants, t=time, theta=angle of intial release)

The only issue with this equation is that the y (height) equation assumes initial release from the ground. To fix this just had an "h" for initial release point (if its 5 feet off the ground then h would be 5).

These equations are, again true for baseballs, golf balls, tennis balls, rockets (once out of fuel), bullets shot from a gun, etc.

Now, these equations eliminate one important factor, which becomes more important the faster the speed/velocity of the projectile...wind resistance.

These equations are the once you first learn because wind resistance makes it more complicated to solve. 

For instance...something that is moving pretty fast in the air, the motion curve could be vastly different if you include air resistance. If it is moving slow then the curve is relatively the same.

A curve for an object moving fast..

Ok, so how does all this relate to a curveball?

Have you EVER heard someone say that a curveball is an illusion, it is physically impossible to throw a ball with enough spin to actually make it curve inside of 60 ft 6 in (distance from pitching rubber to home plate).

These people who say this understand physics of a baseball through high school and first year college physics as well as the differential equations level of math (2 full years of calculus in college). The first couple years you ignore wind resistance. You can't make a ball curve AT ALL without wind resistance.

Secondly, even with wind resistance, the mechanism of why a ball curves (will cover below) would require such HUGE amounts of spin on a sphere that it is humanly impossible to make a sphere curve based on spinning in the air. 

So, let's cover that physics first, how does spinning a ball help a ball curve?

It's called the "Magnus effect". Its a physical phenomenon that a spinning ball in air/water/whatever will cause it to move one direction. 

The friction caused by the rotation actually causes more friction on the side that is spinning into the direction of flight (against the wind resistance) than the side that is rotating away from the direction of flight (with the wind resistance).

This difference in wind resistance on 2 different sides of the same object will create MORE resistance on the left side of the ball in the picture than on the right side of the ball. This will create a high pressure "air" on the left side of the ball and a "low" pressure air on the right side of the ball.

The problem with the math on this is, in order to spin a ball fast enough to make it curve, according to the equations, the spin rate would have to be astronomical (read breaking your wrist/elbow on every successful curve). This is why some people say the curveball "is an illusion".

The problem with this statement is that the equations have to assume that the ball is a sphere, and the equations are "right" that if the ball were a perfect sphere a curveball would be impossible to throw as a human.

However, the stitches on the ball, that have been there since baseball was created, creates EXTRA resistance as it spins. The stitches on a ball are exactly what makes a curve ball possible. 

This is also why good pitchers know how to grab/hold the ball in different positions of the ball to get different "spin rates" which allows the ball to curve more or less even with the same arm motion/velocity.

Along the same lines, the "hair" on a tennis ball and the white "lines" where hair is not is why a tennis ball will curve. The dimples on a golf ball help add distance, but they are also the reason a golf ball will curve (slice or hook).

This same reason is why if you followed the flight of a baseball thrown as a normal fastball or any normal throw from the outfield, etc and tracked it against the projectile motion equations. The flight would look very "flat" meaning it wouldn't curve "down" after a peak like the graph above. You also hear the phrase in baseball about pitchers that throw in the high 90s/low 100s that their fastball looks like it "rises". 

A normal throw/fastball has "backspin" by the way it releases off the fingers. This "backspin" makes the Magnus Effect want to curve the ball upwards. However, gravity wants the ball to curve down. The low 100s fastball doesn't REALLY "rise", but our brain/eyes are so used to seeing the ball start to "fall" near the end of its flight that when it doesn't "fall", we think it is rising. A very hard thrown fastball or ball from the outfield absolutely wants to "rise" by the Magnus Effect, but the Magnus Effect is not quite strong enough to overcome gravity. The ball will "flatten" out and then eventually fall to the ground anyway. 

I have a question that is more economics related. Not sure if it’s been covered somewhere else. So I had some very smart people convince me that the stimulus check is coming out of your refund for next year and I’ve had some smart people tell me it won’t. Which is it?

posted by geeblock

I have a question that is more economics related. Not sure if it’s been covered somewhere else. So I had some very smart people convince me that the stimulus check is coming out of your refund for next year and I’ve had some smart people tell me it won’t. Which is it?

It's not associated with your refund at all. It won't be taxed as income either. 

posted by Dr Winston O'Boogie

It's not associated with your refund at all. It won't be taxed as income either. 

I have been told it’s an advance on your 2020 refund as is next year if u were due 2k back then you would only get 800 because you already got the 1200 

posted by geeblock

I have a question that is more economics related. Not sure if it’s been covered somewhere else. So I had some very smart people convince me that the stimulus check is coming out of your refund for next year and I’ve had some smart people tell me it won’t. Which is it?

The answer is yes and no...

It won't affect your next year's tax returns in the sense that they will be the same amount now, as they would have been before the stimulus passed.

However, it technically will affect them in the sense that this $1200 is an early disbursement of a new tax credit for next year's returns.

So basically they made up a new credit just for 2020 taxes (filed in 2021) of $1200 that didn't exist a month ago. Instead of getting that $1200 next year at tax time, you are getting it now.

If you were going to get $1000 back next year before the stimulus passed, you will still get $1000 back next year but will have some extra lines to fill out regarding this $1200 tax credit you will be getting in the next couple weeks.

Appreciate the curveball symposium …..will circle back later for Q&A.

Been a really busy and interesting week (see my post on the COVID-19 thread). 
 

I will start this backup. Just need a topic anyone is interested in. I don’t want to bore everyone. 
 

My actual area of expertise is industrial furnace/combustion emissions and really anything to do with furnaces (from special chemical atmospheres in furnaces to surface treat metals, etc). 
 

However, I am not sure surface chemistry of metals in a red hot furnace is an interesting topic or even how the combustion emissions react in the atmosphere (CO2, CO, SOx, NOx, etc) or how they are created, reduced, controlled, etc. 

So, if no one has an idea they want explained, I will come up with another theoretical physics one as I really enjoy the thought provoking physics over the calculation heavy physics. Actually enjoyed the one high level physics class I took where all test questions were answered with essays or short answer words (it was all thought experiment physics). 

Would love to see the knuckleball explained.

Something came up in our house today that I thought might be worth an explanation here (or if not, maybe we'll at least get an answer).

My wife and I have been looking for ways to hide our remotes from our toddler.  We tried velcro, but we learned that they'll sometimes fall after putting them back if they're not on squarely.

So then, we thought about using magnets.  The trouble is, the only place we can put a magnet is on the battery case (because of the shape, that's the only flat spot).

Is there any explanation as to what reaction might occur between a AA battery and a reasonably strong magnet?  If it would react, why?  If not, what prevents it from doing so?

Take your time, of course.  I know you and the family have a lot going on.

posted by O-Trap

Something came up in our house today that I thought might be worth an explanation here (or if not, maybe we'll at least get an answer).

My wife and I have been looking for ways to hide our remotes from our toddler.  We tried velcro, but we learned that they'll sometimes fall after putting them back if they're not on squarely.

So then, we thought about using magnets.  The trouble is, the only place we can put a magnet is on the battery case (because of the shape, that's the only flat spot).

Is there any explanation as to what reaction might occur between a AA battery and a reasonably strong magnet?  If it would react, why?  If not, what prevents it from doing so?

Take your time, of course.  I know you and the family have a lot going on.

Magnets will not affect batteries. 

The only way for a magnet to affect a battery is if the battery somehow gets shorted out, i.e. the + and - side of the battery get "connected" via a conductor/piece of metal. 

So the only way for a magnet to mess with a battery is for the metal part of the magnet to connect both sides of the battery, or if like a paper clip also gets pulled to the magnet and the magnet/paper clip combination touches the + and - side of the battery.

No way for this to happen through the plastic case of the remote controller. 

The biggest concern is that most of the remotes nowadays are programmable, i.e. can be setup for any TV, etc. If it is a remote like this, that you had to program a "code" into the remote specific for your TV. The memory, depending on the type, can be wiped out by magnets just like strong magnets near a hard drive.

Strong magnets can wipe out memory storage devices and if its a programmable controller it may stop controlling your TV or whatever device.

posted by jmog

Magnets will not affect batteries. 

 

The only way for a magnet to affect a battery is if the battery somehow gets shorted out, i.e. the + and - side of the battery get "connected" via a conductor/piece of metal. 

 

So the only way for a magnet to mess with a battery is for the metal part of the magnet to connect both sides of the battery, or if like a paper clip also gets pulled to the magnet and the magnet/paper clip combination touches the + and - side of the battery.

 

No way for this to happen through the plastic case of the remote controller. 

 

The biggest concern is that most of the remotes nowadays are programmable, i.e. can be setup for any TV, etc. If it is a remote like this, that you had to program a "code" into the remote specific for your TV. The memory, depending on the type, can be wiped out by magnets just like strong magnets near a hard drive.

 

Strong magnets can wipe out memory storage devices and if its a programmable controller it may stop controlling your TV or whatever device.

Sure.  I know it's generally a no-no to put any reasonably strong magnet near an electronic device.  I figured the fact that it's only really close enough to the batteries for there to be any felt magnetic pull would be enough to make that a non-factor, but if it's not, we can certainly figure something else out.

posted by O-Trap

Would love to see the knuckleball explained.

Ok...in order to understand the physics of a knuckleball, one HAS to start with an understanding of how a curveball works and why it curves.

See above explanation for that...

Now, remember a few things from the above discussion on curveball:

1. A normal thrown baseball has backspin that counteracts gravity a little. A fastball stays "up" longer than what it should based on projectile motion equations normally. The backspin adds lift force just like the side/top spin adds force on the side/top corner of a ball in a curve ball.

2. If we take this added up/lift force off the ball, the ball will drop much faster than "normal". Even if there are no "external" wind forces on the ball like there is on a curve or even a fastball, a knuckleball will naturally drop much faster than a normal ball thrown at the same speed. Our eyes/brains are used to seeing a "normally" thrown ball, so the knuckball that follows more of a "natural" drop looks like it is "falling off the table" to our eyes/brains when in fact its drop is closer to what equations tell us it should be.

3. All of that doesn't explain the side to side erratic motion of a knuckleball however...here's where the physics around the stitches come back into play.

Remember, the knuckleball is really thrown with the fingertips. There are two absolute keys to get a knuckleball to REALLY dance.

1. Ball rotation speed.

2. Pitch velocity.

Ball rotation speed-

A knuckleballer purposefully uses his fingertips to "push" in the opposite direction that our fingers normally spin the ball. This "opposite" finger push actually takes the normal backspin and almost stops it completely, meaning no spin at all. The key spin "amount" is to have less than 1/2 a rotation between the pitcher and the plate.

If you have more spin, it really turns into just a terrible changeup and you likely just gave up a dinger.  If you have no spin at all the flight doesn't really "zig zag" it just drops faster due to the above discussion. The 0-1/2 rotation between the pitcher and the plate is the key narrow range.

So what physics come into play? Two things, similar forces created in the curve ball, and something called the "drag crisis".

Ok, the whole curveball discussion really resolved around wind drag around the ball, and how the drag is more on one side vs the other due to the spin on the ball. This difference in drag creates a force on one side making the ball curve. This force is constant due to the spin rate being constant, and always in the same direction during the said pitch. So a curveball's flight pattern is a slow constant curve. That's what we came up with above.

When a ball is either flying with no or little spin, the non-perfect sphere parts of the ball (in baseball the stitches) 

So, as the ball slowly rotates, as the stitch comes in contact with the wind resistance/drag, the stiches disrupt the air flow. These are called shredded vortices in physics. Think that the stitch disrupts the air flow like a smooth sphere does not. 

Now, if you google videos of a smooth sphere flowing through air, you will see shredded vortices, but they are all behind the ball/sphere, the stitch, as seen in the picture below, causes larger shredded vortices and starts them out in front of the ball.

Now, the problem for the hitter, but to the chagrin of the pitcher, there is no way to predict where that stitch is located and therefore where the shredded vortices start acting on the ball. The stitch could be on the left side of the ball, the right side of the ball, on top, on bottom, etc. You get the idea. That shredded vortice causes faster moving wind on whatever side of the ball that it is on. The shredded vortice acts as a force on the ball and moves it in the opposite direction (similar to the curve). 

Now here's where the problem lies...That stitch is moving (hopefully, as said above you want some spin, just very little). As that stitch moves, so does the location of the force acting on the ball.

In a wind tunnel, the force was measured based on the angle of the ball/stitches. The force was like a "wave" or a "sine wave" if you remember that back in high school math.

So a curveball has a constant force pushing in the same direction the whole time during the pitch.

The knuckleball has a rotating force, the force direction changes based on the location of the stitches, which is why the speed of the rotation is important. If you have too much rotation then the ball won't knuckle at all, it will be more like a slow curve or changeup. If you have zero rotation this "knuckle/vortice force" will be in a constant spot the whole pitch and therefore drop or curve just like any other sinker or curve. If you can get it between that 0 and 1/2 a rotation you have the sweet spot where the ball literally dances back and forth, left and right due to the force moving with the slowly moving stiches.

Now, the question now is this, why doesn't the "dancing/zig zag" pattern start right out of the pitchers hand? Why does it happen only part of the way down the flight path toward the plate?

That's where drag crisis comes into play.

Drag crisis is a phenomenon where the drag coefficient of a sphere drops off suddenly (almost zero) at a certain Reynold's number (think velocity). As the Reynold's number increases from 0 the drag coefficient looks like this...

That huge drop off that happens before the coefficient "recovers" is the drag crisis. We KNOW this happens, we can model it, we can test it, we can put equations to it, but basically its just the "perfect" velocity where the wind resistance just nearly disappears for a given object. It is basically the boundary where "flow" changes from laminar (smooth) to turbulent.

The drag crisis for a baseball is between 65-85 mph. The range is due to the face that the Reynold's Number isn't only based on velocity, it is also based on the air density around the ball. The density of air changes based on barometric pressure, temperature, and humidity. 

When the drag crisis happens to a baseball the "normal" drag forces from wind around the ball REALLY drop away or get very small, and the shredded vortice force mentioned above stays the "same". Therefore the shredded vortice force "wins" and really starts to push the baseball.

For this is the reason that ALL knuckleballs that actually "work" are in the 65-85 MPH range. You will never see a 95 MPH knuckleball pitch and why the ball doesn't start to "dance" right out of the pitchers hand. The ball has to fall into that velocity range before it really starts to dance.

If you don't believe a knuckleball dances, watch the slow motion video of Steven Wright's knuckleballs. Specifically watch the one that starts at 0:48. It literally goes left and right a few times, which is EXACTLY the sine wave force graph shown above.

Also, notice that he throws this pitch the same EVERY TIME, and each pitch in the video "curves" in a different way and a different direction. 

THIS is the reason a good knuckleball is impossible to hit. No one, not the batter, not the catcher, and not even the pitcher knows what way the ball is going to curve. It is random based on where the balls stitches are located when the ball reaches the drag crisis velocity mentioned above, and the force moves as the stitches do.

If you look at any youtube video of pitchers throwing knuckleballs they are all between 65-85 MPH, most around 75-77 MPH.

Here are some MLB players quotes on knuckleballs.

Charley Lau "There are two theories on hitting the knuckleball. Unfortunately, neither of them work."

Jason Varitek "You know, catching a knuckleball, it's like trying to catch a fly with a chopstick."

Richie Hebner "Hitting Niekro's knuckleball is like eating soup with a fork."

Willie Stargell "Throwing a knuckleball for a strike is like throwing a butterfly with hiccups across the street into your neighbor's mailbox."

My favorite though, Bob Uecker is not only the Indian's announcer in Major League, but was a MLB Catcher for about 5 years in the majors. Here's what Uecker had to say about catching a knuckleball...

"The way to catch a knuckleball is to wait until it stops rolling around on the ground and then pick it up."

As someone who played OF in collegeball, but always was the backup catcher...so I would have to come into catch on doubleheaders and when our knuckleball pitcher came in...I agree with Uecker, just get in front, knock it down, and pick it up when it stops rolling around.

Watching the video above, as a former part time catcher, I watch the cathers.

These are the best catchers on the planet, in the Majors, and almost every single one of those knuckleballs are AT LEAST not caught in the pocket of the glove initially, and many of them are missed completely. You never see catchers that far "off" on curves, sliders, sinkers, etc.

That brought me so much joy.  As someone who was somewhat forced to learn to throw a knuckleball (for arm preservation), I ended up getting pretty good at it.  My senior year of high school, we had a starting catcher (also a senior) who was great with his glove, but he was lazy with his body work.  On a low-outside pitch, he'd often just be able to short-hop it open-handedly.  Talented enough that he could get away with being lazy most of the time.

That "most of the time" didn't prove to be the case when I was pitching, because I liked knuckleballs.  I got most of my Ks on them, and the contact was usually beaten into the ground for a nice infield grounder.  Early in the season, I requested that our backup catcher, a junior, be the one to catch when I pitched.  He had great footwork, and he knew how to play a knuckleball.  Just get in front, drop to your knees, and cover the gap between your legs.

Starting pitcher overheard that I requested that he not catch for me, and we got into a snit, but I stand by it.  You just can't count on trying to catch it, because none of us know exactly where it's going.

Thank you for the explanation, jmog.

I had a similar story. I started in OF in college but was the backup catcher. 
 

The starter had a much better glove and arm, but I was much better at blocking a ball in the dirt. 
 

So I always caught our knuckleballer.