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Thank God I'm a Clemson fan...  

Saturday was an awful day for me watching the Raiders fall to the Texans; but Monday was a different story.  My Clemson Tigers won the College Football Playoff Championship with a thrilling victory over Alabama.  It was one of the most exciting games I have ever watched and was definitely well worth staying up till almost 1 on a Monday night.  Although I could talk about the physics of Deshaun Watson holding up the National Championship Trophy, that would be a little too similar to my last embarrassment of a blog post.  Instead I want to talk about the rotational velocity of Deshaun Watson during one especially big hit put on him during the game Monday.  As I was watching the game and I saw Watson helicopter through the air, my first thought wasn't: "Is he ok???" It was more: "Hey! what a great idea for a blog post!"  So here I am, about to calculate the rotational velocity of Deshaun Watson.  

As you can see by watching the video of the hit below, Deshaun was sent into the air and from hit to re-contact with the turf, his flight took approximately one second.  He rotated almost exactly 1.5 times and therefore, using rotational kinematics, we can find that he was rotating at over 9 radians per second.  Converted to rpms and that would equal 90 almost exactly.  Now most people cant put 90 rpms into context, so here's another way to look at it: Deshaun Watson is 6'3", which means layed straight out, he forms the diameter of a circle that is 75" long.  When calculated, the circumference of that circle is 235.7 inches, and knowing that his head and feet traveled 1.5 circumferences, we can calculate that his body parts on the outer edge of the circle whipped around at 19.9 feet per second.  Converted to mph, thats 13.4 miles per hour! That may not seem like alot but just imagine sprinting at someone and colliding helmet to helmet  at over 13 mph.  That wouldn't feel too good!

 This is exactly what could have happened to Deshaun's head but with the additional force of that other person- running at speeds of up to 20 mph- exerted on his head.  Although I know the math is far from perfect, thinking about football through physics like this makes one appreciate how these athletes put themselves on the line for the games they love.



Today at 4:30 Eastern Time something magical will happen.  THE Oakland Raiders will take the field in a NFL Playoff game for the first time in 12 years.  There are a lot of questions surrounding the Raiders and their chances of even making out of the wildcard round.  Their chances are pretty good as long as they can overcome the Texan's defense, who is 1st in the league in the overall category.  Being the overconfident Raiders fan I am, I predict the Raiders are going to play not one, but two games in Houston before the end of February.  (Houston is hosting the Super Bowl this year).  The only question I have is a big one about rookie Connor Cook.  Obviously to be in the NFL you must be strong, but as a rookie, it is common that players haven't yet developed into their full physical potential.  This being said, the Vince Lombardi Trophy is 7 pounds in weight (3.2kg).  This means after playing the game(s) of his life, Cook will have to hold 32 Newtons of force at bay while hoisting the Lombardi Trophy victoriously into the air.  Depending on conditions, he may also have to deal with a slight torque force if the wind is significant.  As we know, the farther away a torque is from its axis, the harder it is to control if that axis is your shoulders.  Based on these numbers, I believe Cook will have no problem lifting the trophy and winning the Super Bowl for the Silver and Black.

I apologize for my- what some may call- overconfidence and I ask that in the likely case the Raiders lose today you don't make fun of me too much for this.  Thanks!


This Christmas I was lucky enough to get my 4th wood bat from my parents. (Sorry dad for breaking the last 3)  As I was holding it in my hand I noticed it felt lighter than my previous bat, but what confused me was the fact that both had the same length and weight.  Using my ever-expanding knowledge of physics, I got to thinking about it and a few minutes later it dawned on me that its really not that confusing at all.  Despite how un-exact of a science you may expect making wooden bats may be, (after all they are still made by using a lathe and cutting tools) there are exact model types of wood bats that tailor to different types of hitters.  For example, the 271, the most popular model in the MLB features a medium barrel, handle and tapered knob to balance out the weight along the whole length of the bat.  This gives the batter a more balanced feel and is ideal for guys looking for a good balance between contact and power, push and pull hits, etc.  This was the model of my new bat, and to compare, my old wood bat was a 243.  This model is less popular because it appeals to only one kind of hitter.  Anybody looking to drive the ball out of the park, and who doesn't mind a few bad misses, would love the 243.  When held compared to the 271, it feels a good amount heavier because it features a large, long barrel and a skinny handle.  Using the equation for torque, one can easily see how with more of the weight located farther away from the point of rotation (in this case, my hands), the bat barrel will exert more force towards the ground and therefore feel heavier.

This same idea translates into hitting the baseball.  With the 271, considerable power is lost because the handle, which has very low energy during the swing due to where it is positioned in relation to the point of rotation.  There is alot of mass in that part of the bat, mass that is not allowed to contribute to the kinetic energy of the end of the bat, which is the part that collides with the ball and sends it flying.  With the 243, although the added torque makes it harder to control, the mass added to the barrel of the bat pay the hitter back in dividends when the ball is propelled with an energy far greater than the 271 just due to the added mass in the barrel.

It seems like a no- brainer to use the 243, but hitting a 95 mph fastball with something that, when compared to the more balanced 271, feels like a sledgehammer is something that only the strongest and most coordinated hitters- and most of those players sacrifice dearly in the average department for a few extra home runs.  Knowing this about wood bats, I will definitely be more picky about what I swing in the future- all thanks to physics.


I know this blog is all about baseball but sometimes special moments must be capitalized upon... and this is one of those moments.  In light of the great ball game my Raiders had today (hey Justin :)) I thought I would do a blog post on the best defensive end in the league: Khalil Mack.  His tipped pass in the 4th quarter and strip sack later on pretty much sealed the game for Oakland and in particular I want to focus on the tipped pass.  Believe it or not, the physics behind this play are pretty interesting and I had a lot of fun thinking about this play.  It all starts when Mack used speed to his advantage to run around the outside of the offensive lineman.  By doing this, he was able to keep most of the force from the 300+ pound lineman from impeding his velocity and momentum.  Because of his speed built from accelerating into the pocket, he could then take a looping path to Tyrod Taylor and still have time to have an effect on the pass.  Using his incredible strength coupled with speed he fought off both the lineman and the centrifugal force resulting from the circular path and got a had on the ball and Taylor's arm.  At the point of release, other than gravity, the ball had 2 fources acting on it.  It was being propelled forward by Taylor's hand and then the frictional force from Mack's hand was both restricting forward movement and causing end-over-end rotational movement.  This combination in forces put unwanted torque and other outside forces on the ball that resulted in a week, wobbling pass that was picked off by safety Nate Allen inside the Red Zone.  

Basically all of this physics talk is just a long way of saying one thing: Khalil Mack is a beast.  Good game Buffalo.

Here's a link to the video of the play.

And for your additional viewing pleasure, here's a video of my favorite player right now, Marquette King and yet another stupid way to get a penalty in the NFL...



This long weekend, my family took a vacation up at my cottage near Watertown NY.  My father, brother and I all hunt and have been doing so since a young age and every fall we take time to spend some time in the woods with each other hunting for big game.  This time of year, bow hunting is the open season, and sitting in my tree-stand this past weekend, I thought back to a time when my brother and I were first learning about hunting and archery.  My brother, who was 11 at the time was enjoying his fancy brand new bow with sights and everything.  He had sighted the bow in so he could aim directly at the target from 10 yards out and the bow would be oriented at just the right angle so the arrow would arc and hit the target right in the middle.  Now, thinking he was Robinhood, Chad took it upon himself to get into the treestand we had set up to practice with and declare to the world his amazing archery skills.  The next 5 minutes were easily the most frustrating of his life as he proceeded to miss the target on every shot he took, getting closer to tears every time he had to get off the stand and retrieve his arrows after a full round of misses.  Obviously, 11 year old Chad did not understand simple trig and physics because when one looks at the situation closely, it is easy to see why he missed.  The treestand was 15 feet off the ground and against a tree, which formed a right angle with the ground. This right angle meant that the direct path from bow to target was a hypotenuse of a right triangle, therefore meaning the path was farther than 10 yards.  With his bow sighted in at exactly 10 yards, it is obvious that without compensating, the arrow would miss low.  In addition, with Chad being young and not very strong, the bow had to be reduced in power for him to be able to pull back and shoot accurately.  This lack in power meant a lower velocity of the arrow and therefore more time in the air.  Through kinematics, this means there is more time for gravity to accelerate the arrow downward, increasing the amount of error in his shot.  

And because you are probably so surprised I havent talked about baseball at all, here's a picture of one of the game's best pitchers Madison Bumgarner who is an avid hunter.  

Image result for madison bumgarner hunting







The Crowhop

Keeping with my outfield theme, Crowhops are critical to the outfield position.  A crowhop is a shuffle-step like movement that allows a fielder to throw the ball with greater initial velocity and therefore more distance.  Although I've been around the game for over a decade, the physics behind the crowhop never really seemed interesting until you take a deeper look.  Standing still, a player can still throw a ball with tremendous speed.  All of this velocity is coming from the muscles in the arm and torso as the body is whipped through the throwing motion.  When a player crowhops, they are simply adding initial velocity by moving their body towards their target and now, with the same force as before throw the ball substantially harder.  One thing you may see players do is fall down or somersault after a crowhop throw in an effort to achieve as much follow through as possible.  The follow through is critical because the longer you keep your hands on the baseball, the longer your force will be imparted on it and therefor the larger the velocity the throw will have.

Enjoy these impressive outfield throws made possible by using a crowhop!



Tonight, the 2016 Gold Glove Awards were presented.  For those of you who dont know, the Gold Glove Award is given to two MLB players for each defensive position that had exceptional seasons playing defense (making athletic plays, committing few errors and so on).  The award is given to two players per position because a winner is chosen from the two main leagues under the MLB: the National and American Leagues.  One particularly fascinating position from a physics standpoint is the position of outfield.  To the innocent bystander, a strong defensive outfielder looks to have the easiest job on the field.  They have the longest time to field the ball and almost never have to quickly throw it to beat a fast runner.  They just jog around catching balls that the batters lob up in the air.  What most people dont realize, is that outfield is really HUGE, and the longer time it takes for the ball to get to the fielders means just more time for physics to play with the ball in extreme ways.   Lets take the outfield of the World Champion Chicago Cubs for example... the total area of grass in the outfield is roughly 90000 square feet.  This means on any given play, a major league outfielder can be expected to be in charge of give or take 30000 square feet of turf!  To cover this insane amount of ground, elite outfielders can get up to over 20mph while hustling for the ball, and all the while they are tracking data such as launch angle, apex height, projected landing and initial exit velocity.  All of this is estimated mentally and happens within a few seconds of the contact of the bat.  Another huge factor in tracking a fly ball is the spin, which leads to the Magnus Effect.  With balls leaving MLB bats at anywhere from 90-105 mph, the rpms on the ball can be even greater than what was put on it by the pitcher.  This Effect can move a ball several inches from the mound to home (which is 60.5 feet away) so just picture how many tens of feet the ball can move because of the Magnus Effect when it is driven distances exceeding 300 feet.  Using all of this, outfielders need to calculate one thing before they even move: projected landing spot.  In the video below, Reds outfielders Tyler Holt and Billy Hamilton both make amazing plays in the ninth inning to help keep a four run lead over the Phillies.  Notice, when the STATCAST metrics come up, how fast their first step was and how efficiently they ran their route.  These stats are amazing because in less than half a second, both fielders knew exactly where to run to get to their projected landing spot.... and they ran to that spot with over 93% accuracy.  Nobody but a baseball player could project the landing spot of a ball spinning over 1000 rpm and travelling at over 85 mph within a 93% accuracy in under .5 seconds.  When you think about outfielders like this, you gain a whole new appreciation for the players and the true brainpower and athleticism that goes into a seemingly easy position.

So that leads me to believe: maybe people dont play right field when they are young because they are seen as bad, its just because they have a very promising future as a physicist...




Last night, in Cleveland, two landmark events happened in a city mostly considered the laughingstock of sports.  In one night, the Indians won game one of the World Series against the Cubs and the Cleveland Cavaliers hoisted their Championship banner on opening night of the NBA regular season.  With these stadiums right across the street from each other, it got me to think: with Cleveland fans so starved of sports success, they took full advantage of this opportunity to be loud and support their beloved Cavs and Indians.  With the sheer volume coming from each stadium last night, I also wondered what kind of noise would disperse into the surrounding city.  With these thoughts, I went ahead and made a visual representation of the sound waves coming out of each stadium and the possible sites of constructive and destructive interference.  Although the possibility of me going back in time and going to Cleveland and actually seeing if there is detectable interference is slim to none (most likely none) its still cool to wonder what a passerby in Cleveland would hear if they are going in-between the two stadiums who were louder than they had been in years last night. 

cleveland capture.PNG


Checking Your Swing

The feat of checking a baseball swing is truly one that requires much physical power.  The majority of people compliment the batter's keen eyesight when he stops his bat mid swing, when in reality they should be complimenting his strength.  Thinking about it from a physics perspective, it is simple to see how much strength is required to stop a swing.  250 milliseconds after the ball is released, the batter starts his swing, generating all the force he can out of muscles in his arms, legs, hips, shoulders and abdomen.  If he were to commit to it, the next 150 milliseconds would be spent taking a complete swing at the ball.  If he changes his mind, he must do so within 50 milliseconds of the start of his swing for a very important reason: he must slow the bat back down to rest using the muscles in only his upper body, taking his hips and legs out of the equation.  Compared to the arms and shoulders, the lower body generates a force considerably larger.  This means, if applied to kinematics, the roughly 50 milliseconds of full force, full body swing, could only be stopped with roughly 100 milliseconds of full force from the batters upper body in the exact opposite direction.  With MLB swings clocking in at over 80 mph, it is a true physical marvel that these players can stop their swing in such a short period of time.

To take this a step further, we can even estimate the force a batter needs to apply to the bat to get it to stop within that 100 ms time frame.  Given that the swing is 80 mph and the batter has exactly 100 ms to stop his bat, we can use  gif.latex?a%3D%5Cfrac%7Bv_%7Bi%7D-v_%7Bf%7D%7D%7Bt%7D    to determine the the acceleration of the bat when the opposing force from the arms is applied.  By plugging in the values converted to m/s and s, we can find that:  gif.latex?a%3D%5Cfrac%7B-35.7%20%5Cfrac%7Bm%7D%7Bs%7D%7D%7B.1s%7D%3D-357%5Cfrac%7Bm%7D%7Bs%5E%7B2%7D%7D . This means that using his upper body, the batter is decelerating his bat at -357 meters per second squared.  Plug this into the force equation  gif.latex?F%3Dma and assume the league- standard 32 oz (.91kg) bat is being used and you get:  gif.latex?F%3Dma%3D%20%28.91kg%29%28-357%5Cfrac%7Bm%7D%7Bs%5E%7B2%7D%7D%29%3D-324.87N .  Here we can roughly estimate that an average MLB player applies a 325 Newton force to his bat when he checks his swing.  This is just as impressing as it is eye opening... just because they only run 90 ft at a time doesn't mean pro ball players aren't very powerful athletes!

Also, enjoy this video of Yasiel Puig, one of the strongest guys in the league actually break his bat because of how fast he decelerated his hands.  Enjoy!



Playoff Physics

In the short period of time I got to watch the Dodgers/ Cubs game before I started working on my physics, I noticed a strange game plan that the Dodger base runners were employing against Cubs lefty pitcher Jon Lester.  After a four pitch walk to lead off the bottom of the first, Dodgers player Enrique Hernandez started to bounce back and forth and side to side as he was taking his lead from first, trying to distract Jon Lester from his task of pitching.  To people who aren't familiar with the game, a left handed pitcher is oriented on the mound so his body faces first base.  This means whenever he is looking forward, he always will see the base runner.  Usually, a base runner keeps a low, explosive stance to aid him in reacting in a moments notice to anything that my happen on the field.  In Lester's case, the runners tonight moved in every direction possible to distract Lester.  The runners knew that he is a pitcher who doesn't like to try and pick people off so they took advantage of that by getting huge leads and trying to get into his head.  Personally, I do not think this strategy is beneficial for one main reason.  If Lester decides to pick off at the right moment, he can catch the base runner with all of his momentum heading away from the base, the runner will have to apply a huge force to totally reverse his motion and dive back to the bag.  This split second of decelerating, stopping, accelerating and then even decelerating again due to the friction of the dirt as he slides into the bag, gives Lester ample time to deliver even a mediocre throw that will nail the runner.  This chance is a huge one to take, especially for a team up against one of the best pitchers on the best team in baseball.  If LA wants to win tonight and take a 3-2 lead in the series, they will have to be smarter on the bases.  


Sports Authority Field at Mile High doesn't have that name for just any reason.  Home to the Denver Broncos, it is exactly one mile above sea level and is surrounded by the thinnest air in the NFL.  As far as football goes, thin air really benefits the home team in many more ways than expected.  Other than the obvious facts that kicks and passes go farther, daily practice at that elevation can make a football team extremely effective when it comes to the physical side of the game.  When the Broncos are away, the thicker, more oxygen-rich air they play in only makes them a better, more effective team that is seemingly better conditioned than their opponents. These conditions work well for football, but not so much for the very different game of baseball.  

Coors Field, also in Denver is home to the Colorado Rockies, who unlike the Broncos, are not known for their league- dominating defense.  In fact, despite larger fences and a deeper outfield, Coors Field is known as a hitter- friendly park, or in other words, a park that makes it easy to hit home runs.  Now one may say that occurrence is due to the simple fact that less air means less drag and therefore farther flight, but those people are mistaken.  This truth has to do with everything that happens before the batter hits the ball, and even before the stadium itself was constructed.  The architects who designed Coors Field were very much aware of the fact that balls would carry farther in the thin air of Denver.  To combat this, they pushed the outfield fences back well past the average distances to left, center and right fields.  Because of this move, the designers created the largest outfield in the MLB, and with it, the most area for outfielders to cover.  This creates many prime landing spots for balls hit by opposing teams.  Its also worth mentioning that the longer fences weren't really long enough, and since its first game,  Coors Field has had a very strong "hitter- friendly" reputation.  

Now architecture is all well and good, but some may still ask: what does this all have to do with physics??  The answer lies in what happens to the baseball in this high elevation and large outfield.  Before the game is even started, a shipment of official MLB balls are received and stored in a room separate from both teams (and safe from any Boston players with air pumps from their favorite NFL team) until the umpires and stadium officials take balls as needed for the game that day.  Sitting untouched at such a high altitude actually dries out the balls and makes them denser than normal (because of the low humidity at high elevation).  This denser version of the ball is prime material for hitters, as it is more responsive to the force sustained from the bat and will travel much farther than a more moist ball.  Humidity aside, from the second the ball is released from the pitcher's hand, the defense is put at yet another disadvantage.  As I've covered before in a previous post, airflow over a baseball and the Magnus Effect dictate the direction and severity of the "break" (curve/ movement) in a baseball.  With less actual air in the space around the ball, there will be less interacting with the seams, meaning less overall movement of the pitch and therefore a much easier pitch for a hitter to drive over the fence.  Then of course, when the ball is in the air, less air density will offer less resistance to the flight of the ball and through all of these factors, baseballs fly out of Coors at a very high rate.  

Since the construction of Coors Field, many studies have been done on the effects thin air on baseball and as a result, humidifiers have been added to baseball storage rooms at Coors.  This has actually helped reduce the amount of home runs but this thin air, coupled with the so-so skill of most Colorado players (sorry Rockies fans) makes a very unfortunate combo that calls into question the true meaning of "home field advantage".   


The beauty of baseball is the fact that any single detail of the game to can be analyzed way more than most people want to know.  Everything from the moisture of the grass to how a player catches a ball can play huge roles in a game.  Even in something as small as catching a ball, physics can be found in not only the method of catching but in the actual construction of the baseball glove.  During a professional baseball game, players routinely throw the ball at speeds approaching 100 mph and can hit the ball even harder than that.  Some of the power hitters in the league can produce batted ball speeds of 120 mph.  This is an impressive feat in itself not even considering the fact that there are men trying to pluck that ball out of the air and make a play to get that batter out.  The glove plays a huge role in allowing the fielders to handle such a force.  The pocket of the glove rests between the thumb and index finger and serves as a place for the ball to decelerate in a place that isn't directly over the hand and wont hurt the player.  Anybody who has caught an object with their bare hand knows that if traveling fast enough, it can deliver a pretty punishing blow.  The leather webbing pocket on a glove gives the ball a larger surface area to distribute its force upon and even expands to give the ball more time/ space to decelerate.  Following Newton's second law, if the ball is caught with the pocket of the glove, it is given more time to decelerate and therefore will have a smaller final acceleration.  With this smaller acceleration, the glove, and therefore the player, will have to deal with less force with a glove than without one.



Well if my last blog didn't get you interested about baseball hopefully this one will...

Introduced to 3 pilot stadiums in 2014 and now in its 2nd full season of league- wide use, STATCAST is yet another way for baseball (and physics) fans to geek out about anything that goes on in between the chalk lines.  Essentially, STATCAST uses common methods of tracking and, with the help of computer and human input, creates powerful graphics, videos and analysis in a matter of minutes.  This system is a huge step up from the PITCHf/x technology because of the sheer number of variables it can cover.  Now not only pitches can be monitored in depth, but the entire field of play, including every player and baserunner, who can be analyzed for what could be eternity.  Everything from reaction time, top speed or even vertical jump can be extracted from any play and for any purpose.  This amazing tool is made possible by the Doppler effect and the utilization of that property through Doppler radar.  The waves sent out by the sensor rebound off of the object in question (such as a player, bat or ball) and through the conclusion that altered wave lengths reveal how fast and in what direction the object is moving,  the waves coming back can be analyzed and turned into stats with amazing detail and accuracy.  Not only is the Physics really amazing, but the sheer ability and skill of these athletes are now being brought to light. Any fan can now routinely see a player track down a fly ball and notice that he is running almost as fast as a world class runner.  Seemingly small stats like these open up a whole new layer to an already complex game and help fans develop an even deeper appreciation for the athletes that play our national pastime.

Here is a video of STATCAST being put to great use in a game between the St. Louis Cardinals and the Washington Nationals.  Enjoy!



Last week our physics class failed at a single attempt to calculate the horizontal distance traveled by a projectile launched from a projectile launcher.  After one test launch, we were required to calculate the delta x of a ball launched at an angle of -4 degrees.  I think the biggest factor contributing to our failure was the lack of effective communication and teamwork.  When it came time to gather values to calculate the distance, the main form of communication was that of yelling louder than the next person so you could distribute your information.  With better communication, the class as a whole would have more time to work through the problem and possibly not feel the intense time crunch that we did when we were conducting the lab.  The biggest difference between the first and second shots was the fact that the -4 degree angle meant that the ball had an initial velocity in the downwards direction instead of upwards.  Once I got past that and found the y-component of the velocity vector,  I was able to find time in the air and then plug that into the second equation to find delta x.  Looking back on it, our class definitely had the brainpower to get this right the first time, we just cracked under pressure and gave into the confusion just a little bit.  Overall it was still a great lab and a fun challenge for the beginning of the year.



The Curveball

Baseball.  Often dismissed by many because of how "slow" and "boring" it is.  This being said, anybody who knows anything about physics should strongly disagree with these statements.  The truth is, every 15- 20 seconds, a ball flies towards the batter travelling 80+  mph and curving up to a foot in one direction all the while a batter is trying to hit that ball to distances exceeding 400 feet.  The most interesting piece of this intense chain of events is the movement of the ball, which requires years of practice, refinement and sometimes plain luck.  The most common type of moving pitch is the curveball.  This pitch, depending on the pitcher, can be thrown up to 90 mph and break as much as 16 inches.  There are many methods to throwing the curve but the real secret lies in rpms.  One of the best pitchers in baseball, Clayton Kershaw, imparts 1628 rpm of spin on his curveball, which makes it one of the best ever seen.  Recently, the study of rpm has been a widely discussed topic because of the new developments in MLB's PITCHf/x system.  This system, which was phased into all 30 stadiums starting in 2006, uses 2 cameras mounted in the stadium that track location, velocity, launch angle, release point and spin rate.  This state of the art system proves the theory that rpms are the key to curveballs.  The raised seams on a baseball make it easy to generate pressure differential, and curveballs utilize this advantage by creating an area of high pressure above the ball, forcing it down faster than gravity would normally take it.  Higher rpms generate higher pressure and therefore a better pitch that moves more, has more velocity and will fool more batters.  


Here are some great examples of rpms at work..


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