15 October 2019

Sumo Glory in 5.5 Seconds!

Ever since I began researching Chapter 9 of my first book, I have been fascinated by the sport of sumo.  I discussed the great Taihō Kōki in that chapter while discussing lovely physics topics like linear momentum.  Though Taihō died three years after my book was published, I still check in on sumo when I can.  I'm glad I watched the final match of the Autumn Grand Sumo Tournament that took place in Tokyo on 22 September (click here for an article in English).  Several top-ranked rikishi, including two yokozuna, were absent from the final of the top division.  But that didn't stop Mitakeumi Hisashi from attaining sumo glory after defeating Takakeishō Mitsunobu in just 5.5 seconds.

Check out the start of the match (click on image for a larger view).
The ring (dohyō) has a diameter of 4.55 m (14.9 ft).  The rikishi are behind the starting lines (shikiri-sen), which are 70 cm (2.3 ft) apart.  The referee (gyōji) is ready for the start of the action, which happens only by mutual consent of the rikishi.  Mitakeumi with a mass of 177 kg (a weight of 390 lb) is on the left and Takakeishō with a mass of 169 kg (a weight of 373 lb) is on the right.  The two rikishi combined for a mass of 346 kg (a weight of 763 lb), which is the weight of a good-sized grand piano or over a quarter of the weight of my Honda Civic.  A lot of mass was about to collide!

The initial charge (tachi-ai) saw Takakeishō opting to stay low and Mitakeumi looking to defend high (click on image for a larger view).
You can see Mitakeumi's hands are out, preparing to keep Takakeishō from getting too low.  Check out the initial collision (click on image for a larger view).
Even though rikishi seldom are able to get to a speed of more than 2 m/s (4.5 mph) or so due to the short distance they travel prior to collision, the combined kinetic energy can be large.  I calculated a combined kinetic energy at the collision to be about 850 J.  If that amount of energy could be turned into work, I could be lifted about a meter off the ground!  A baseball would have to be moving 108 m/s (242 mph) to have that much kinetic energy!  But the only work that kinetic energy was turned into was the work needed to depress and move fat around.  If ever there was an inelastic collision, it's what you see in the above image.  Most of that kinetic energy was gone after the collision.  Before you think of 850 J as being a huge amount of energy, and nobody wants to be hit by a baseball moving over 100 m/s, consider that 850 J is the same amount of energy as 0.2 Calories.  That's only 10% of a Tic Tac!  The next time you pop a single Tic Tac in your mouth, think about how much chemical energy is stored in food.

Okay, back to the action.  Mitakeumi's opening strategy worked; he kept Takakeishō from staying low (click on image for a larger view).
Note that the center of mass of the two rikishi hasn't moved much from the initial collision.  Because both rikishi were pushing back on the floor with roughly the same force, the floor pushed back on them with the same force (Newton's Third Law).  With those external forces nearly canceling, the system of the two rikishi felt no net, external force.  That meant that the system's linear momentum was conserved during the collision.  That's why the center of mass didn't move much after the initial collision.  But now we come to the key point in the action where Mitakeumi took advantage of physics and made sure the system of the two rikishi had a net, external force (click on image for a larger view).
You can see Mitakeumi on the left driving forward while Takakeishō got caught standing still.  The above image is just 1.3 s after the initial charge.  Because Mitakeumi has a little speed to the right, the system linear momentum isn't zero as it was during the initial hit.  The system linear momentum is to the right, which means the two rikishi will likely move to the right after the next big collision.  A split second later and Takakeishō is still stuck (click on image for a larger view).
Takakeishō is essentially at rest in the above instant, and Mitakeumi is heading toward victory.  Check out the next collision (click on image for a larger view).
The system linear momentum is to the right!  Mitakeumi is charging and you can see that Takakeishō is reeling by the fact that his left foot has come off the ground.  Mitakeumi's next big step with his left leg drove Takakeishō right where Mitakeumi wanted him (click on image for a larger view).
Takakeishō doesn't have much room to back up, which was Mitakeumi's intended goal.  Mitakeumi then opted for stability and went low (click on image for a larger view).
By keeping low, Mitakeumi avoided Takakeishō getting the advantage by pushing off the raised ring and offsetting Mitakeumi's balance.  In the image below, you see Mitakeumi low and ready to deliver the winning punishment (click on image for a larger view).
When Mitakeumi next drove into Takakeishō, Mitakeumi had his center of mass dropped and his right leg back for added stability (click on image for a larger view).
You can see that Takakeishō had his feet against the raised ring.  That was his last effort to keep from being pushed out of the ring.  Takakeishō tried to sneak out to his right, but the position Mitakeumi had achieved in the above image prevented that from happening (click on image for a larger view).
All that remained of the match was great technique, strength, and using physics in the way it's supposed to be used.  Mitakeumi next helped with leverage by grabbing Takakeishō's mawashi (click on image for a larger view).
You can just spot Mitakeumi's right hand under Takakeishō's mawashi.  And look at the wonderful stance Mitakeumi had!  His wide base with left foot slightly back prevented Takakeishō from driving off the raised ring.  Now comes the lift (click on image for a larger view).
Mitakeumi had Takakeishō's mawashi fulled gripped with both hands, and Mitakeumi was prepared to lift and push (click on image for a larger view).
Mitakeumi had raised himself and Takakeishō up and driven Takakeishō almost out of the ring.  A lot of chanko-nabe has to be consumed to get that massive and strong!  Takakeishō was done for at this point.  A look from behind shows the precarious situation Takakeishō was in (click on image for a larger view).
Takakeishō was out a split second later (click on image for a larger view).
You can see on Takakeishō's face what second place looks like.  The above image is just 5.5 s after the initial charge began.  That's all the time Mitakeumi needed to take full advantage of the laws of physics and secure a tournament win.  He got a pretty nice trophy, too (click on image for a larger view).
He can put a lot of Asahi Super Dry in that thing!

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