## 10 August 2012

### Queen of 10 m!

China's Chen Ruolin is simply unbeatable once she steps on a platform that sits 10 m (33 feet) above an Olympic pool.  Be it synchronized diving or individual diving at 10 m, Chen Ruolin has had gold medals around her neck in both the 2008 and 2012 Summer Olympics.  She essentially ended the 10-m platform final yesterday with an 85.50 on her first dive.  The next closest score was 78.00.  With four more dives to perform, Chen's competition faced an uphill climb that was simply too steep.  Chen's last dive was a back 2 1/2 somersault with 1 1/2 twists.  She needed only 30.61 points for gold.  She probably could have belly-flopped and earned gold!  Instead, she earned 86.40 points, which matched her third dive's score.  Not bad for someone who won't be 20 years old until the end of the year!

I wrote an earlier post about how angular momentum conservation plays a crucial role in diving (click here for that post).  Here, I'll consider what happens to Chen after she enters the water.  On her last dive, I calculate that she left the platform with initial speed 3.34 m/s (12.0 km/hr or 7.47 mph) at 78 degrees from the horizontal.  Her time of flight was about 1.8 s.  She hit the water moving at about 14.4 m/s (51.8 km/hr or 32.2 mph).

Now consider how fast she would hit the pool bottom in the pernicious scenario that the pool water magically disappears after she dives.  The pool is about 5 m (16 feet) deep.  Her impact speed on the pool bottom would be 17.5 m/s (62.9 km/hr or 39.1 mph).  I obviously never want to see that dive!  The point here is that a diver is moving quite fast when hitting the water, and would be moving even faster if the water wasn't there.  Even though diving is an "aquatics" event, most of the scoring happens above the water.  Except for the entry and splash, the pool serves no purpose other than to slow the diver down.

I've written about drag before, but mostly in the context of projectiles moving through air.  Water is about 800 times more dense than air.  Consequently, water is capable of much larger drag forces.  Divers sometimes angle themselves in such a way that they curve through the water after entry.  Other times, they may go straight down until they just make contact with the pool bottom.

Besides drag, another important force on a diver while slowing down in the water is the buoyant force.  The density of the human body is roughly 1.062 times that of water.  That means that while completely submerged, Chen feels an upward buoyant force on her that is about 94% of her weight.  With a mass of just 47 kg (corresponding to a weight of 104 pounds), the upward buoyant force on Chen is approximately 434 N (97.5 pounds) while she is completely underwater.

As fast as divers enter the water, it's a good thing there is plenty of upward force from drag and buoyancy to slow them down over a relatively short distance.  Without the pool water, a diver would never make it to the medal stand!  That's surely obvious, but it's nice to think about exactly why and how the pool water functions in the sport of diving.

Will Chen Ruolin make it three in a row when the Summer Olympics hits Rio de Janeiro in four years?  I won't bet against her!