Bakelants takes Stage 2!

Jan Bakelants of Belgium won today's Stage 2.  He also slips into the overall leader spot with a mere one-second lead over Great Britain's David Millar.  We were a bit slow with our prediction today.  Below is a comparison of the winning time with our prediction.

• Stage 2:  3h 43' 11" (actual), 3h 51' 28" (prediction), 08' 17" slow (3.71% error)

Given that cyclists were still crossing the finish line 17 minutes after Bakelants, our prediction hit the average cyclist today instead of today's elite cyclist.  An error under 4% isn't bad, but after such a successful first stage, anything worse looks bad by comparison.

Bakelants's average speed is given below.

• Stage 2:  11.65 m/s (41.94 kph or 20.06 mph)

Tomorrow's Stage 3 is another of the medium-mountain variety.  Picking up where Stage 2 left off in Ajaccio, cyclists have 145.5 km (90.4) to bike before arriving in the commune of Calvi.  After seeing the east side of Corsica in the first stage, the middle of the island today, riders will travel north along the island's western edge tomorrow.  A category-4 climb greats riders at the start, followed by two category-3 climbs just before the halfway point.  A category-2 climb awaits the athletes near the stage's end, the other side of which should make for an exciting sprint to the finish line.  Below is our prediction.

• Stage 3:  3h 44' 26" (prediction)

The first two stage winners have been a bit faster than we thought.  I won't be surprised if tomorrow's winner edges our time once again.  Enjoy the last day of the race on Corsica!

Less than 1% off Stage 1!

German Marcel Kittel took this year's first Tour de France stage win, which also happens to be Kittel's first ever stage win in cycling's greatest race.  A big crash marred the end of today's competition, knocking out favorites like the Manx Missle, Mark Cavendish.  A bit of serendipity helped Kittel escape the crash.  Below is the comparison between Kittel's winning time and our prediction.

• Stage 1:  4h 56' 52" (actual), 4h 59' 17" (prediction), 02' 25" slow (0.81% error)

I think we'll take that start for this year's race!  We were glad to see the winner come in under five hours.  About halfway through today's stage, my student, Brian Ramsey, contacted me and informed me of headwinds reaching 10 kph (6.2 mph).  I told him that we might be fast with our prediction if headwinds continued to dominate the action.  Instead, racers found themselves aided by tailwinds at the end of the race.  We were lucky to have the weather average out a bit for us.  We aren't good enough weather forecasters to include wind, rain, fog, and/or massive fluctuations in temperature and humidity in our model.  The inclusion of crashes is obviously something we can't do either.

Kittel's average speed is given below.

• Stage 1:  11.96 m/s (43.05 kph or 26.75 mph)

Tomorrow's Stage 2 picks up in Bastia and finishes 156 km (96.9 mi) away in the French commune of Ajaccio.  The medium-mountain stage takes riders southwest through the heart of Corsica.  Along the way are two category-3 climbs, followed by a category-2 climb to get to the 1163-m (3816-ft) peak at Col de Vizzavona.  A great downhill sprint on the other side of the mountain gets riders thinking about one final category-3 climb before a relatively flat finish.  Below is our prediction.

• Stage 2:  3h 51' 28" (prediction)

I hope the three big climbs don't tire riders out too much.  The best of the best should finish in under four hours.  A great downhill awaits the cyclists and we fans tomorrow!

Tour de France Time!

The 100th Tour de France is set to begin tomorrow (29 June) on the island nation of Corsica.  Instead of a short prologue stage, riders will encounter a full 213-km (132-mi) flat stage.  Beginning in the commune of Porto-Vecchio, Stage 1 takes cyclists north along the eastern edge of Corsica toward the finish at the commune of Bastia.  Testing the competitors early will be a category-4 climb as they reach the 45.5-km (28.3-mi) point.  Most of the rest of the stage is quite flat.

As I've done the past two years, I will post predictions for each stage's winning time.  Working with me again this year is Lynchburg College physics major Brian Ramsey.  Our goal, as always, is to predict the winning time, not the person who will win the stage.  The basic model we employ is described in Chapter 4 of my book (click here or on the image of my book's cover on the right side of the blog).  We have modified our model this year and we are anxious to see how well it does.  If it works well, we'll obviously be thrilled.  If not, we'll have to tweak a little here and there and, hopefully, learn a bit more about how the world works.  That's what's great about doing science -- learning something!

So, without further ado, here is our prediction for stage 1:

• Stage 1:  4h 59' 17" (prediction)

This prediction is a bit of a challenge to the athletes:  finish the first stage in less than five hours!  Will they hold back a little, knowing they've got 20 more stages?  Or will some bold rider set a fast pace?

Force Needed for Child Toss

Since posting a piece on tossing a child in a swimming pool, I've gotten several flattering comments and e-mails from family, friends, and colleagues.  The consensus seems to be that though child tossing will never appear in the Summer Olympics, it is highly recommended as something fun to do in a swimming pool.  A few people asked that I compute the force I needed to propel my younger daughter into the air.  That is the subject of this post.

The animated GIF below shows the portion of my vacation movie that involves my daughter being pushed upward (click on the image for a larger view).

The red data points show the position of my daughter's left shoulder, which is the same reference I used in my previous post.  My daughter's weight is 37 lbs (165 N), which corresponds to a mass of 1.15 slugs (16.8 kg).  What a terrible name for a mass unit!  Using Newton's second law, I came up with the force plot you see below (click on the image for a larger view).

The force I applied to propel my daughter is on the vertical axis; time is on the horizontal.  During the nearly half second it took to launch my daughter, my maximum force reached about 70 lbs (311 N).  During the strongest part of my push, I shoved my daughter with a force roughly twice her weight.

One must be cautious with force calculations that originate with position/time data, as mine do.  Acceleration requires two time derivatives of position, and those derivatives must be calculated numerically.  That is why you see a large force for the first datum and a nonzero force for the last datum.  If I wasn't trying to propel my daughter, my force should be her weight.  But the graph's first datum shows a force about twice her weight.  The reason is that the first couple of times are left off because they are needed to compute the first force datum shown in the graph.   The force calculations for the data away from the edges in the above plot should be good.

Okay, that's enough about child tossing from me.  With the 100th Tour de France starting on Saturday, I've got plenty of other physics goodies to keep me busy!

The Art of Child Tossing

I stayed up late last night watching the San Antonio Spurs blow a golden opportunity to win the NBA title over the Miami Heat.  Instead of analyzing anything from that game, the most constructive of which would concern coaching, I decided to analyze something much more fun -- child tossing.  No, I'm not about to describe some pernicious activity involving a defenseless and unwilling child.  The child tossing to which I refer is the stupendously fun activity of being asked by one's child to throw him or her into a swimming pool, and then gleefully obliging that child.  Writing this post will keep me from thinking about tonight's College World Series baseball game between my Hoosiers and the Beavers of Oregon State.

During my family's recent Florida vacation, we spent several hours in a swimming pool so as to avoid the oppressive heat.  My younger daughter kept asking me to throw her into the pool, and I couldn't turn her down.  She loved getting into a cannonball position and having me throw her as far as I could while I was standing in the pool.  Using a low-price digital camera's movie mode with a paltry 24 frames per second, my wife filmed me throwing my younger daughter into the water.  My older daughter meant to serve as a height reference, but was too far from the plane of my younger daughter's trajectory to be a good length standard (I ended up using my own head!).  The animated GIF below shows my child toss (click on the image for a larger view).

You can see a red trail connecting the data points (I marked my daughter's left shoulder).  I marked the movie frames using a wonderful free video analysis program from Open Source Physics called Tracker (click here to get it).

So, could I compete in a professional child tosser event?  Well, I launched my daughter at just over 5 mph (8 km/hr) at an angle of about 63 degrees from the horizontal.  After a flight time of nearly 0.6 s, my daughter hit the water at a speed of about 11 mph (18 km/hr).  She landed a horizontal distance of roughly 3.2 ft (0.98 m) from the point where I let go of her.  Her entry into the water was about 75 degrees from the horizontal.

Many more goodies may be gleaned from video analysis.  I could look at the small effect air resistance had on the trajectory.  I could examine the force I needed to exert to get my daughter into flight.  I could look at the splash dynamics.  Lots of wonderful physics toys with which to play!

Professional child tossing probably won't catch on, but it's a lot of fun in a swimming pool with kids who love to fly through the air!  That one may use a base-model digital camera and free software to turn fun in the pool into a first-year physics problem makes it all the more delightful.

A Closer Look at LeBron's Game 2 Block

The Miami Heat now find themselves in a one-game hole to the San Antonio Spurs in the NBA Finals.  Between the second and third games of the series, I examined LeBron James' monster Game 2 block of Tiago Splitter's dunk attempt with 8:21 left in the game.  The Heat had a 19-point lead at the time, so the block wasn't the difference maker.  It did, however, emphatically let the Spurs know that Game 2 would not be theirs.

Check out the photo below (click on the image for a larger view).

I analyzed the block frame by frame of the slow-motion video.  The red diamonds show the path of the ball during the block.  The ball starts on the lower right side of the red trail and traverses the red trail until the image you see.  One can really see the ball coming in, and then getting rejected!

I estimate that James took off from the court at about 9 mph (14.5 km/hr or 4 m/s) and reached the top of his leap in around 0.4 s.  The main part of the block too place in roughly 0.1 s, during which James needed an average force of nearly 14 pounds (62 N) to reject the ball.  Instantaneous forces were larger, but 14 pounds is roughly the average force James used to send Splitter's dunk attempt back.

Put simply, LeBron James had to leap to a height that put his hand above the rim, and at 0.4 s to get there, his timing had to be perfect.  Once there, James had to push laterally with a force comparable to what one has to exert to hold a bowling ball.  Not bad!