04 April 2012

Coriolis, Kobe Bryant, and Things Unseen

Tornadoes devastated parts of Dallas, Texas yesterday.  After viewing some truly terrible video footage on televisions at the gym this morning, I can only hope that there are no fatalities.  Seeing the tornado footage got me thinking about various forces due to the air.  Air forces play crucial roles in many sports, especially those in which balls are bandied about.  The drag force is usually the dominate component of the air's net force on a ball in flight, though the Magnus force is strong enough to alter trajectories and give us wonderful banana kicks in soccer and curveballs in baseball, just to name two examples.

The forces involved with the motion of air in a tornado are certainly much larger than the force a ball feels from the air.  But what is actually pushing on the air itself to make a tornado?  The physics behind tornado formation is quite complicated and not really what I wish to devote space to here.  Suffice to note that air accelerates when pressure differences exist.  Formation of a tornado is greatly dependent on local weather conditions.  What is not a key player in the formation of tornadoes is the Coriolis effect.

The Coriolis effect is named after the French scientist Gaspard-Gustave de Coriolis (1792-1843).  The effect arises when one tries to apply Newton's laws in a reference frame, called "noninertial," where those laws are not valid.  A good rule of thumb for identifying a noninertial reference frame is to note if the frame is accelerating with respect to some previously defined inertial frame.  If we imagine the stars in the sky as being "fixed" over the time we are doing an experiment, then the distant stars sit in an inertial reference frame (they certainly move, and they accelerate, but over the time of our experiments, we don't see much change!).  Usually the Earth is taken to be an inertial frame in which we apply Newton's laws of motion.  Locally, noninertial effects are not that noticeable.  But take a large mass of air in a hurricane or a cannon shell that travels over tens of kilometers and the fact that the Earth is noninertial comes into play.  The Earth turns on its axis, which means that objects on Earth's surface are constantly accelerating.  Recall that acceleration is the time rate of change of velocity, which is a vector that has both magnitude and direction.  Objects on the surface of a spinning object must be accelerating because velocity vectors are constantly changing directions.

It turns out that tornadoes involve air masses that are much too small to be concerned with the Coriolis effect.  If one wishes to calculate the influence of the Earth's rotation on projected objects, one must solve some rather fun equations.  What pops out of those equations is that objects projected in the northern hemisphere, regardless of velocity direction, are deflected to the right because of the Coriolis effect.  The deflection is to the left in the southern hemisphere.  When one analyzes air flows and pressure differences, the Coriolis effect explains why hurricanes in the northern hemisphere rotate counterclockwise as seen from above.  Hurricanes rotate clockwise as seen from above in the southern hemisphere.  Please note that if tornadoes comprise masses too small for the Coriolis effect to play a noticeable role, toilet water is even less effected.  Don't believe the nonsense about the Coriolis effect causing toilet water to spin a certain way when flushed!

If the Coriolis effect won't bother a tornado, it certainly won't bother most of the sporting events we watch.  Did you see Kobe Bryant's great three-point shot last night?  Click here for video.  I calculate that the rightward deflection of Kobe's shot was about half a millimeter, which is about two hundredths of an inch.  Now, the ball was definitely bouncing around the rim after Kobe shot it.  But I don't think half a millimeter was the difference between going in and staying out.  The Coriolis effect is essentially unseen in the sports world.

There were a couple of things that happened yesterday that had not been seen before.  The first was that Baylor University women's team became the first men's or women's team to go 40-0 as they won their second national title (the first coming in 2005).  Baylor's Brittney Griner was sure fun to watch.  Besides all the hype surrounding her becoming the second woman to dunk in the tournament, she possesses a great inside game that is fun to watch.

The other previously unseen thing that happened in the sports world last night was the great Lionel Messi scoring his 14th goal for Barcelona this year in Champions League competition.  Messi scored on two penalty kicks against AC Milan.  What seems almost unfair is that Barcelona not only has the services of Lionel Messi but Andres Iniesta, too.  Iniesta had a great goal in the 53rd minute of the match.

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