## 01 July 2015

### Physics of a Jump Spin Reverse Crescent Kick

My last blog post came a fortnight ago.  It focused on a flying side kick.  For this post, I wish to look at one of my instructor's jump spin reverse crescent kicks.  This particular kick is challenging for sure, but I love for it for all the physics goodies I can examine.  Below is a video of Cody Davis of Super Kicks in Forest, Virginia showing how it's done.
Part of what makes this kick challenging is that one must jump from a guard position.  Mr Davis began in a left-side guard and kicked with his right leg.  There is no run up or step in to get a little extra "hop" before launching off the mat.  As you'll note in the video, Mr Davis is able to kick higher than the padded target.  The proof is in the image below (click on the image for a larger view).
The video below shows the same kick (on a different day), but this time filmed from behind.
It is on the back view that I wish to focus.  Mr Davis launched himself off the mat with a speed of about 2.8 m/s (6.3 mph).  His center of mass elevated 0.4 m (1.3 ft) at maximum height; he was off the mat for a time of 0.55 s.  My goal now is to take you through that five-ninths of a second and show you just how much technique is involved in the kick.

The image below shows Mr Davis in a left-side guard, preparing to execute the jump spin reverse crescent kick (click on the image for a larger view).
From that position, he must "jump" and "spin."  His back leg, i.e. his right leg, will deliver the blow.  Because the imagined target will be hit with the outside of his right foot, we say that the "reverse" part of the foot, opposite the "crescent" side, is what hits the target.  In the above image, what is about to do damage is farthest on Mr Davis' body from the target.  The image below comes almost 0.4 s later (click on the image for a larger view).
Mr Davis has dropped his center of mass about 12 cm (4.7 in) in an effort to temporarily store energy.  His body is now like a coiled spring.  Energy is stored in his outstretched arms, bent legs, and bent back.  That stored energy is needed to generate the necessary kinetic energy that's required to execute the kick.  Just 0.28 s later, Mr Davis is in the configuration shown below (click on the image for a larger view).
More great physics here!  Note how his arms are extended from his body.  That is very important for what is about to happen.  Think about an ice skater about to enter her final spin.  Her arms, and mostly one leg, are extended fully before going into the spin.  Look at the image below, 0.25 s later (click on the image for a larger view).
He has pulled his arms in closer to his body!  That maneuver lowered his moment of inertia, and because he was up in the air with very little external torque, angular momentum conservation means that he spins faster than he did at the launch.  His rotational speed in the above image is about 95 rpm, or about one-fifth that of a helicopter blade!  Note, too, that his right leg is bent at about 90 degrees.  Bad form on this type of kick is swinging a straight leg.  The bent leg not only maintains a proper fold, it keeps moment of inertia down while large rotational speed is needed.  Just 0.12 s later, we come to the money shot (click on the image for a larger view).
A jump spin reverse crescent kick is really a front kick at heart.  Master that at the beginner's level and you're well on your way to being able to jazz it up.  In the above image, Mr Davis has kicked his right leg forward and it makes contact with the imaged target with the outer part of his foot.  By fully extending his right leg, moving his arms slightly outward, and having his left leg slightly off center, Mr Davis has lowered his moment of inertia considerably, which dropped his spin rate by more than half.  The kick has been delivered and now Mr Davis must rotate another 90 degrees (click on the image for a larger view).
The above image is 0.13 s after the previous image.  Note that Mr Davis has nearly refolded his right leg.  That proper technique reduces moment of inertia, which gets him to turn faster.  Think angular momentum conservation again!  The "fold" and "refold" parts of a kick are not something karate instructors insist on for pedantic reasons.  There is practical physics behind those exhortations!  Now fast-forward 0.38 s to the image below (click on the image for a larger view).
Mr Davis has now landed and returned to his left-side guard.  Compare that to the first one in this series and you'll see that Mr Davis turned 360 degrees.

It's certainly an impressive kick and one that takes years of practice to perfect.  Buried inside the kick is a much simpler front kick.  Master that first, then move on to the spin, and think about the physics!