Making Sport of Physics

Physics of a Flying Side Kick

Cody Davis is of one my talented karate instructors at Super Kicks in Forest, VA.  He has always dazzled me with his kicks, especially his jump kicks.  What I will analyze now is one of his flying side kicks.  A real-time video of his kick may be seen here.

Let’s now look at some of the physics behind such a spectacular kick.  The image below shows Mr Davis just as he has left the mat (click on the image for a larger view).

He ran from right to left and elevated off the mat at a speed of about 4.0 m/s (8.95 mph) and at an angle of approximately 46 degrees from the horizontal.  His center of mass was about 1.9 m (6.2 ft) from the front of the target.  Notice his arms are out.  He will pull them in and rotate them while in the air so that he can get his hip to turn clockwise (as seen from above).  That will ensure maximum power when it’s time to kick.

Check out Mr Davis at the top of his trajectory (click on the image for a larger view).

This image is 0.28 s after Mr Davis left the mat in the first image.  Note how his body has turned; you can see his back more clearly here than in the first image.  Note also how his left arm is extended in a front punch while his right arm is tucked closer to his body.  Further note how his legs are tucked in.  What that does is store potential energy much like a compressed spring.  While at the top of his trajectory, which had his center of mass 1.3 m (4.3 ft) off the mat and 0.42 m (1.4 ft) higher than at launch, Mr Davis had a center-of-mass speed of roughly 3.0 m/s (6.7 mph).  With a weight of 750 N (169 lb), Mr Davis had a kinetic energy at the peak of his trajectory of about 329 J, which is almost the latent heat needed to melt a gram of ice.  Think about that for a moment.  A great karate athlete at the top of a flying side kick has as much kinetic energy as the energy needed to melt just a single gram of ice.  That’s quite a lot of energy needed for such a small amount of ice!

We now come to point of impact, shown below (click on the image for a larger view).

Just 0.12 s from his peak trajectory point in the previous image, Mr Davis made use of that stored energy in his tucked legs.  By extending his kicking leg at the point of impact, he made his foot move faster than his center of mass.  His foot entered the target’s padding at a speed of 7.0 m/s (15.7 mph), more than 2.5 times his center-of-mass speed.  The target weighs 1155 N (260 lb), 92% of which is contained in the black base.  Mr Davis kicked the target 1.2 m (3.9 ft) above the mat with an average force during the first 1/30 s of nearly 1150 N (258.5 lb).  That is essentially the weight of the target!  He continued to drive his foot into the target as he fell and managed to overturn the target.  The target’s heavy base helps keep the target upright, unless a powerful flying side kick comes along!

Watch the video again.  If you think it’s easy to defend against a flying side kick, keep in mind that from launch off the mat to impact with the target took just 0.4 s.  If you saw Mr Davis running before his launch, you would obviously have more time to get out of the way or prepare for some type of defense.  If you were facing the opposite direction and only turned when you heard Mr Davis launch off the mat, that’s another matter entirely.  You will need exceptionally quick reflexes and fast mental processing to defend against that kick in a time of only 0.4 s.

As with most things that people do well, executing a flying side kick like Mr Davis requires years of training and practice.  It’s worth it because that’s an amazing kick!

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A Thrilling Win for Vandy!

After seeing my beloved Vanderbilt Commodores fall behind Cal State Fullerton 3-0 after nearly six innings yesterday before rain suspended the game, I thought we were sure to lose today when the game resumed.  Losing the first game in the College World Series puts a team on a tough track to win it all.  But what’s great about sports is the totally unexpected.

We got a run to finish off the bottom of the sixth inning.  We got to the bottom of the ninth down two runs.  After a couple of doubles got us a run, Jeren Kendall came up with a man on second.  On the second pitch he saw he hit a home run to right center, ending the game and giving Vandy the 4-3 win.  The image below is the screen capture I took while watching the game (click on the image for a larger view).

How sweet it is!  We continue the march to defend our title with TCU up next.

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Women’s World Cup Time!

An incredibly busy academic year, followed by preparations for leaving the country for my upcoming sabbatical year, have cut my blog writing significantly.  But a World Cup in the beautiful game is too enticing to stay away from writing.  The 2015 FIFA Women’s World Cup begins this Saturday (6 June) in Canada.  FIFA isn’t exactly anyone’s favorite organization right now, and I doubt many people are sad to see Sepp Blatter leave his position as president of FIFA.  I sympathize with the female athletes who will have to compete in Canada on artificial turf.  It seems next to impossible to imagine male athletes being made to play their sport’s biggest competition on artificial turf.  Oh well, we have to accept what’s coming and try to enjoy soccer played at its pinnacle in the women’s game.

For all the controversy associated with playing surfaces, I doubt there will be much controversy over the match ball.  The Adidas Context15 is a textured ball that behaves much like the Brazuca used in last year’s Men’s World Cup in Brazil.  My research colleagues at the University of Tsukuba in Japan, Takeshi Asai and Sungchan Hong, sent me wind-tunnel data for the new Context15.  With their permission, I show a comparison of the drag coefficients for Brazuca and Context15 in the graph below (click on the image for a larger view).

Keep in mind that 10 m/s is the same as 36 kph and a bit more than 22 mph.  The precipitous drop in the drag coefficient is the so-called “drag crisis,” which is where the air flow around the ball changes from laminar to turbulent as the speed increases.  The takeaway from the above plot is that Context15 should behave similar to Brazuca.  Having the drag crises in roughly the same speed range is key to the comparison, as is the high-speed value of the drag coefficient.

A great month of soccer is coming.  The day before the Women’s World Cup ends will see this year’s Tour de France begin.  Two months of great sports ahead!

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Having More Fun Examining Stephen Curry’s Shot

I wrote a blog post (click here) at the end of last year on Stephen Curry.  Another news organization asked me to look at Curry again.  That guy can flat-out shoot!  He’s got a great release with little wasted motion.  What a joy to study!  Click here for the latest article I contributed to on Curry’s shooting.

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What if you have a gun to your head?

No, I’m not being figurative with my blog post’s title’s question.  I mean it literally:  what if someone has a gun pointing at your head?  Check out the photo below (click on the image for a larger view).

What you see above is your humble blog writer pointing a practice handgun at the head of his karate and Krav Maga instructor, Clifton Abercrombie of Super Kicks (webFacebook) in Forest, Virginia.  My instructor is about to demonstrate a Krav Maga technique for defending oneself against an assailant who points a gun right at the head of a would-be crime victim.  Krav Maga means “contact combat” in Hebrew and is an Israeli martial arts system that is essentially an amalgam of the best techniques from various other martial arts systems.

Does what you see above look a bit scary?  I’m certainly not crazy about seeing a gun pointed at anyone’s head.  Using practice weapons in a safe environment, I train with several others in Krav Maga, and part of our training involves escaping the frightening situation mimicked in the photo above.  I frankly have no idea how well I would do if ever unfortunate enough to find myself with a loaded gun pointed at my head.  I hope that training will give me an automatic response so that I’ll at least be able to fight back.

What I wish to focus on here is the physics behind what Mr Abercrombie is about to do next.  His main goal is to get the gun’s barrel out of line with his head – and do it quickly!  What about moving his entire body to the side?  Too much mass!  It will take too long.  He will move his arms, which are much less massive than his whole body.  The best athletes have been measured to have a reaction time of not less than about 0.2 s.  During those measurements, however, athletes knew what was coming and how they were to react.  For most us in a car, we have a reaction time of at least a full second.  The study of human reaction time involves neurophysiology, biomechanics, and a host of other goodies.  First the eye (or some other sense organ) detects something, then the brain processes a signal, and then the brain tells the body to do something.  That’s obviously highly simplistic, but if an attacker with a gun isn’t expecting resistance, assuming the attacker’s reaction time to be a full second isn’t likely to be that far off.  Note that I use reaction time to mean the time between Mr Abercrombie initiating his defense, which may be imperceptible to me if I’m staring at his face and perhaps yelling at him, to the time when I fire the gun in response to my brain finally processing that he is fighting back and getting a signal to my hand to fire.

Let’s now turn to the defense.  Check out the sequence of photos below (click on the image for a larger view).

It took Mr Abercrombie just 0.8 s from the first wiggle his hand made that showed he was initiating a defense to getting his hands on the gun, as shown on the left.  If you think a reaction time of a full second is too large and that a safety factor is needed, cut that reaction time in half.  I would not have distinguished his initial hand movements from normal motion.  The first half of that 0.8 s probably passed before I even noticed that he was trying to defend himself.  So if I’m able to react from that in half a second, he still has his hands on the gun before I can fire.  The photo on the right shows that his head is out of the gun barrel’s firing line.  The time between left photo and right photo is just 0.03 s.  Even if I can get a shot off, it will sail over his head.

Note in the very first photo above that I kept my finger off the trigger and along the side of the gun.  While practicing, that’s very important!  Watch what happens next (click on the image for a larger view).

Mr Abercrombie rotated my hand and gun clockwise (as seen by him) and away from him toward his right.  He kept rotating such that if my finger were on the trigger, he would have used enough torque to have broken it!  That’s part of the technique.  Distract the assailant with something to think about (like pain from a broken finger!) while the tables get turned.  I am officially disarmed in the photo on the left, and that took Mr Abercrombie just 0.16 s after he had the gun’s barrel clear of his head.  The image on the right is 0.1 s after the left image.  Note that Mr Abercrombie not only has control of the gun with the barrel pointed away from him and toward me, he still maintains control of my hand.  That’s important because a real attacker is likely to be fighting back at this point.

Now we get to the end and I, as the dumbfounded faux attacker, have realized that I messed with the wrong man!  Click on the image below for a larger view.

Just 0.16 s after the previous image, Mr Abercrombie released my hand.  He then cleared away and secured the gun to his side.  I’m left with an open hand!  The entire technique from the first image I showed above with Mr Abercrombie beginning to move his hands to the final image on the right took just under 2 s.  That was all the time needed for my Krav Maga instructor to react to having a gun at his head to holding the gun himself while at a safe distance from me.  Not bad, huh?

To see the technique play out in real time, check out the movie here.  There are a couple of seconds of set up time, followed by the disarming technique in action.  Mr Abercrombie makes it look simple, but a LOT of training is required to be that good!

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Celebrate Science and Darwin Today!

Today marks 206 years since the birth of Charles Darwin, which means another Darwin Day is upon us.  I will never cease to be amazed by what Darwin did for science in particular and humanity in general.  Painstaking and meticulous work led to a profound revolution of thought.  That Darwin was able to reach the conclusions he did well before the discovery of DNA and without the hundreds of thousands of fossilized species occupying the world’s museums today simply staggers my mind.   Given that DNA evidence and the fossil record have verified Darwin’s seminal ideas, having a Darwin Day is more than appropriate.

Celebrate Charles Darwin today.  Check out the Darwin Day website here.  Celebrate science, too.  For it’s insatiable curiosity about the natural world that propels scientists to great discoveries.

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A Note of Thanks to Blog Readers

Is everyone getting tired of hearing and reading about deflated footballs?  I certainly am.  Like many football fans, I would prefer having the two-week buildup to the Super Bowl filled with stories about matchups, strategies, and predictions.  Instead, we’ve had deflate-gate dominate the past week’s NFL news.  I think most of us hope that nothing illicit took place with any of the footballs used in the Patriots win over the Colts.  We like to believe the games we watch are on the level.  But I also think most of us believe that if any person (or persons) did anything outside the bounds of the rule book, that person (or persons) should be held accountable.

I now wish to hold myself accountable for a lack of clarity when I first commented on deflate-gate.  When I was contacted by NPR early morning last Tuesday (20 January) to talk about deflated footballs, I had only heard about possible under-inflated balls used in the Patriots AFC title game win over the Colts.  I spoke to NPR’s Geoffrey Brumfiel for at least 20 minutes on the phone that Tuesday morning, and then a couple of quotes made it to air and in a story.  I was talking about the science associated with footballs and pressure and noted that quarterback grip could improve with a little less air pressure in the ball.  I then spoke in general terms about how each quarterback could have performed with an under-inflated ball.  Brady outperformed Luck, so “if” both quarterbacks were using balls with the same pressure inside, it certainly didn’t appear to help Luck.  Where I lacked clarity was not including and emphasizing “if” enough in that comment.  I further assumed the “if” when I wrote a blog post early morning this past Wednesday (21 January).

It was a couple hours later while I was teaching when Geoffrey Brumfiel e-mailed me about an ABC news story (click here for that story).  That story noted that 11 of the 12 Patriots footballs were found to be under-inflated.  That was the fist time I learned that there was alleged proof that balls used in the AFC title game were under-inflated, and that the balls that were alleged to be problematic were the ones provided by the Patriots.  I emphasize those last seven words because before I had seen any alleged proof, I was making general comments about under-inflated balls and the associated science.  Had I seen the ABC news story, which posted after 11:00 pm last Tuesday evening, before I wrote my blog post early morning last Wednesday, I wouldn’t have ended on general terms about both quarterbacks using the same balls.

I was certainly aware of Rule 2, Section 2 on how teams supply balls for a game.  But a few readers contacted me about my general comments that concerned both teams.  They had heard and read news before I had that tests of balls supplied by the Patriots had revealed problems.  To those readers:  Thank you so much for you kind comments!  You reminded me how challenging communicating can sometimes be.  As much as I was focused on the science behind how pressure and temperature affect footballs, I wasn’t as focused on being as clear as possible on my general game comments.

When I wrote another blog post last Thursday (22 January), I emphasized science and concluded that I certainly have no way of knowing the environments in which the balls were tested and retested.  When interviewed by Fox News last Friday (click here for the story), my focus was solely on the science.

My goal when talking to media is to communicate the science behind sports.  Honing my craft of communicating clearly is a never-ending process.  I apologize for a lack of clarity and, again, I thank readers for contacting me with kind comments that sought clarification.

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Footballs, Temperature, and Pressure

Have you ever gotten together with friends and family on Thanksgiving Day and gone outside for your annual Turkey Bowl?  You go into a shed and retrieve your football, only to find that it’s not quite as robust as it was in the summer.  You may not have a leak in your football.  Air molecules don’t bounce around as much in the cold as they do in warm weather.  Inside a football, air molecules bounce around and collide with the interior walls of the ball (bladder, really).  The air’s pressure inside a football will go down with temperature.

The deflate-gate controversy has people asking how how a given drop in temperature affects pressure.  Unfortunately, I keep seeing the same mistake over and over again in the various analyses I’ve read.  Using the ideal gas law is just fine.  Assuming the ball’s volume doesn’t change is a great approximation.  If there are no leaks — and no illegal removing of air — the number of air molecules inside the ball remains constant.  The simple result predicted by the ideal gas law with those assumptions is that pressure is proportional to temperature.

Here is where the problem comes.  The pressure that must be used is the total pressure.  The pressure range that’s stated for a legal NFL football is 12.5 psi – 13.5 psi, but those pressures are gauge pressures.  The gauge pressure is what we measure above the normal atmospheric pressure we experience all the time, and never notice.  Atmospheric pressure is about 14.7 psi.  That’s right, we all have the weight of a bowling ball pushing on each square inch of our bodies.  Luckily, we evolved in Earth’s atmosphere and our cells have interior pressures just above 14.7 psi, so we feel equal forces on each side of our skin.  The legal total pressure inside an NFL football is thus 27.2 psi – 28.2 psi.

Assume that an NFL football is at 13 psi when checked inside a locker room at 70 F (21 C or 294 K).  Now take the ball outside.  Using the ideal gas law, and remembering that temperature must be in Kelvin, the graph below shows what to expect for the ball’s interior gauge pressure.  The horizontal axis shows possible outside temperatures and the vertical axis shows the gauge pressure (click on the graph for a larger view).

I put a red, dashed vertical line to find the temperature at which the interior gauge pressure hits 12.5 psi, the bottom of the legal range.  That temperature is 60.4 F (15.8 C or 289 K).  You can see in the above graph how a ball that’s legal in the warm locker room can lose pressure in the colder outside.

Now, I wish to make it clear that I do not know how and where referees check balls before games.  I don’t know if balls are checked in a warm environment or if they are checked in the outside environment where the game will be played.  I don’t know the manner in which the balls were rechecked when 11 of 12 of the balls in the Pats win over the Colts were found to be under-inflated.  I do know, though, that if balls that were checked before the game were rechecked at the same temperature at some later date, and found to be at lower pressure, then air must be missing from the balls.

In what I calculated above, I did not account for changes in humidity or anything else.  If air does not leave the football, temperature change is likely to be the dominant factor in changing interior pressure.

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More on Deflate-Gate

I was invited by Geoff Brumfiel of NPR‘s All Things Considered to comment on the controversy surrounding under-inflated footballs used in the AFC title game between the New England Patriots and the Indianapolis Colts.  The Pats won in convincing fashion, 45-7, but a dark cloud now palls the game, so much so that the silly “gate” suffix has been used.  After something like 20 minutes conversation with Geoff Brumfiel, a few of my comments made it to air and into the accompanying story.  That story and an audio link may be obtained here.  What I wish to do in this space is elaborate on what appears in the story by repeating some of my comments to Geoff Brumfiel that did not make the final cut.

Bad weather, like the rain and wind in the Pats win over the Colts, will make a quarterback desire a better grip on the ball.  Water on the ball, after all, reduces friction between the ball’s surface and the quarterback’s hand.  Anyone who has ever tried to palm a basketball, but finds one’s hand just a wee bit too small, has noticed that palming the ball becomes easier if the basketball is slightly deflated.  Deflating a football slightly allows for better grip, too.

Losing a little air reduces the ball’s mass.  How much?  Well, a normal football has nearly 98% of its mass in the non-air material that comprises the ball.  Only a little more than 2% of the ball’s mass is from the air.  Of course, the ball’s volume displaces air, leading to a buoyant force that matches the weight of the air displaced.  NFL balls are supposed to be at a gauge pressure of 12.5 psi (pounds per square inch) to 13.5 psi.  Note that gauge pressure is the pressure above atmospheric pressure, which is about 14.7 psi.  An example I described that did not make it to air is to assume that a ball is under-inflated by 2 psi.  Accounting for atmospheric pressure, that amounts to about a 7% loss in pressure.  The ball’s weight loss, however, is less than 0.2%.  A less massive ball decelerates faster than a normal ball, but the mass loss in my example is too small to have much effect.

Referees are supposed to inspect balls used in games.  A referee sets the ball on the field before the start of each play.  As I told Geoff Brumfiel, an under-inflated ball may not have been noticed by a referee hurrying to place a ball on a play or two, but should have been noticed if balls used for most plays were under-inflated.  Nobody wants to think conspiracy when trying to figure out what happened, just like nobody wants to think a referee is incompetent or that a team cheated.  Given that both quarterbacks used the game balls, both should have had the same advantage that would have come from better-to-grip balls that may have been under-inflated.  Andrew Luck, however, had such a terrible game for the Colts that any advantage would have gone to Tom Brady, the quarterback for the Pats.  Luck’s game, however, does not excuse any possible cheating.

We will have to see what comes of all this silliness.

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Talk on Sunday, 18 January

The Holy Trinity Lutheran Church in Lynchburg has invited me to give a talk on my Tour de France and World Cup soccer research.  My general-audience talk will begin in the church at 6:30 pm on Sunday, 18 January 2015.  This will be my first talk inside a church.  I’m looking forward to it!

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