If what I just described seems challenging, it is! While practicing the kick last week at Super Kicks, my instructor, Clifton Abercrombie, offered a tip for doing the kick better. As soon as Mr Abercrombie said, "Pull your arms in tight to your body as you do the kick," the physics part of my mind said, "Well, duh!" I had always practiced the jump spin hook kick by trying to increase my hang time and focusing on what my kicking leg was doing. It never dawned on me to employ a basic concept from physics to help increase my rotation speed. My "Well, duh!" moment came because I've taught angular momentum conservation more times than I can count!
Mr Abercrombie was kind enough to allow me to film him executing a spin hook kick and a jump spin hook kick, which happen to be the first two moves in our Universal 8 kata. To illustrate how pulling one's arms in helps with the kicks, Mr Abercrombie performed the kicks first with his arms out, much as I had been doing as a karate novice, and then with his arms in, as a more seasoned martial artist will do. The first video below shows "arms out."
Now look at the improvement as Mr Abercrombie performs the same kicks "arms in."
Mr Abercrombie leaves the mat at a little more than 4 mph and has a hang time of about 0.4 seconds. While in the air, there is essentially zero torque about Mr Abercrombie's center of mass (air resistance provides some torque, but that's a small effect). When there is no net external torque on an object, angular momentum is conserved. This powerful law in physics not only helps us understand karate kicks, we use it when analyzing the interior of nuclei and the swirling of galaxies. It's a powerful law! When you see a figure skater going into her final spin, note that she has her arms and one leg extended far from her body. Her initially slow spin gets faster and faster as she brings her arms in. She reduces her moment of inertia as she pulls her mass closer to her rotation axis. To maintain an essentially constant angular momentum, she has to spin faster as her moment of inertia decreases.
Now think about a jump spin hook kick. A lot must happen in less than half a second! Watch Mr Abercrombie perform the "arms out" kicks again. Then watch the "arms in" again. You should notice that he spins faster with "arms in." Because he is spinning slower in the "arms out" case, he must hurry his kick, which leads to a bit more instability than in the "arms in" case.
To better see what is happening, check out the image below (click on the image for a larger view).
The image on the left shows the moment when Mr Abercrombie's right leg is straightened as if it were a side kick. The image on the right shows the 90-degree bend in his right leg, which is the hook. Note that his arms are out.
Now check out the "arms in" version of the above photos (click on the image for a larger view).
Note where Mr Abercrombie's side kick position is. By pulling his arms in, he has rotated faster, meaning his straightened right leg has rotated farther ahead than in the "arms out" case. Note, too, when he achieves the 90-degree leg bend how much more stable his body is compared to the "arms out" case. By getting around quicker, Mr Abercrombie doesn't have to hurry the kick and risk instability. To get a feeling for just how fast such a kick moves, the time interval between the two images above is just 0.133 seconds. Pulling his lower leg 90 degrees translates to a rational speed in that brief time interval of about 113 rpm. That's about a quarter the rotational speed of helicopter blades! Because he was spinning faster in the "arms in" case compared to the "arms out" case, the "hook" part of his hook kick was about 20% faster. That translates into more pain for the unlucky target!
I'll close with a look at the "arms in" case from the other direction. The image below shows Mr Abercrombie landing after executing the "arms in" jump spin hook kick (click on the image for a larger view).
Many years of training and skill development go into what you see above. Note his eyes are forward on the target he was just imagining hitting. Note that his arms are in, but they are on the way out to help arrest his rotation and return him to a left-side fighting stance. Note his perfectly vertical left leg during the landing, while his right leg is perfectly parallel to the floor. I've got many years of work ahead of me before I could come close to that kind of skill. At least now I've got a great physics tip to help me!