Physics of a Flying Side Kick

Cody Davis is one of 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 below.

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!

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.

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!