## 17 June 2015

### 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!