Daytona 500 Finish Line Math

I was not able to see yesterday's Daytona 500, in which Denny Hamlin beat Martin Truex, Jr by the smallest time since electronic scoring came into NASCAR back in 1993.  But headlines and stories this morning got my attention.  Most stories I read reported a winning time of 0.010 s, i.e. three digits past the decimal were stated.  I then read that Hamlin "won by inches" in several articles, some of which gave winning distances in the range 4 in - 6 in.  Before I saw the photo finish, the numbers weren't making sense to me.

A NASCAR race car travels about 200 mph, which converts to 3520 in/s.  Winning by 0.010 s means winning by (3520 in/s)(0.010 s) = 35.2 in, which is nearly 3 ft.  That's why the numbers I read didn't make sense to me.  I'm assuming a constant speed here and in what follows, a reasonable approximation for such a short time interval.

I then watched a replay of the final lap.  Speedometers on the lead cars showed they were just over 190 mph in the final turn.  I grabbed a screen capture of the finish (click the image for a larger view).

That winning distance looks larger than 6 in to me.  I checked out one web site (click here) that told me that the Toyota Camry Hamlin was driving is 189.2 in long.  Another web site (click here) told me the tire diameter is 28 in.  Using either of those reference lengths as my calibration distance, Tracker told me that the winning distance was about 20 in.  If Hamlin's tires really have a diameter of 28 in, a 20-in winning distance looks reasonable.  The gap between Truex's car and the finish line looks smaller than a tire diameter, but not by much.

So take the winning distance to be 20 in.  If the winning time really was 0.010 s, that means a speed of 2000 in/s = 114 mph.  That can't be right!  If the cars were going 200 mph and the winning distance was 20 in, the winning time would have been (20 in)/(3520 in/s) = 0.00568 s.   Crank up the speed to 220 mph and the winning time drops to 0.00517 s.  Drop the speed to 180 mph and the winning time increases to 0.00631 s.  All three of those times round to 0.01 s, but the winning time was reported as 0.010 s, i.e. three digits past the decimal.  I actually found a couple of articles that had the winning time as 0.011 s, but that makes what's being reported even worse!

I didn't see the race and thus may have missed commentary about the winning time.  It seems to me that the winning time that was reported was too big by a factor of 1.8 or so.  If there are any NASCAR fans out there who can provide me with a missing detail, I would love to hear from you!

Remembering the Paragon of Bravery

Seventy-two years ago today, a plane crashed in a park near where I'm currently living in Sheffield.  A United States Army Air Force B-17 Flying Fortress named "Mi Amigo" was hit while flying a mission over Denmark.  Returning to England, the plane was headed for a crash in Sheffield's Endcliffe Park.  Sighting children playing in the park, the crew chose not to try for a crash landing on the large, flat, grassy area of the park and instead crashed the plane into a wooded area on a hill in the park.  All ten on board were killed.  Protecting those kids in the park made all ten instant war heroes as much as any of their previous deeds.

My younger daughter and I were in Endcliffe Park yesterday (Sunday, 21 February).  She fed ducks on two ponds and then played for awhile on the playground.  As we were preparing to leave, I saw men and women wearing my country's Air Force uniform.  It dawned on me that this was the Sunday when the annual remembrance of the plane crash would take place.  My daughter and I went to the crash sight and watched the ceremony.  I took the photo below just before the ceremony began (click on the image for a larger view).

It was a beautiful day in the park; the sun was out and wind sometimes got pretty strong.  I felt pride seeing my country's servicemen and servicewomen at the ceremony.  I spoke to a couple of them afterwards, asking them where they were stationed and thanking them for their service.  The Royal Air Forces Association organizes the ceremony in the park each year.  It was moving hearing the names of the ten crew members who died in the crash, but well worth hearing every one of them.

A Delightful Hour of Music

My wife and I visited our favorite Peak District pub, the Fox House, the day before Valentine's Day.  She made the experience even more wonderful for me by telling me that she had purchased tickets for an upcoming concert.  After a great week of work in which I got to teach my first tutorial of the current semester, my wife and I made our way to The Crucible Theater for the concert.  What a lovely hour of music we experienced on a Saturday afternoon!

I love experiencing chamber music in person because of the intimate feel one has with the performers.  Unlike listening to the music on an iPod, watching a live performance affords one the chance to see how the performers experience the music.  It had been many years since I witnessed chamber music in person, mostly because of being a workaholic and using free time for family and martial arts.

Yesterday I was introduced to the music of Sterndale Bennett, who was born in Sheffield 200 years ago.  My wife and I sat in Tier 1, which was the top of the cozy theater.  Because we aren't from the UK, I told my wife that we were Tier 1 Imports (I got the expected eye roll after a corny joke!).  Before the music started, Tim Horton, the pianist, talked to the audience about Sterndale Bennett, his music, and the performers' interest in celebrating the 200th anniversary of his birth year.  How great to hear a Sheffield composer in a Sheffield theater!

The piece we heard was Bennett's Chamber Trio in A Op. 26.  Composed in 1839, the piece was positively delightful. I particularly enjoyed watching Gemma Rosefield on cello as she faced Benjamin Nabarro on violin.  During the second movement, the serenade, the string instruments were alternately plucked.  I had the image of two children talking back and forth with each other, two plucky children.  The piano was like a parent keeping the children from getting too wild.  I'm no musical expert, and I may have butchered what a connoisseur would describe for that second movement, but that was my honest feeling while watching it.  I could see Rosefield's face really well and she played with a lot of plucky passion.  She was fun to watch!  I will definitely check out more of Bennett's music.

After a brief intermission, a quartet prepared to play String Quartet in A Op. 41 No.3 by Robert Schumann.  I had heard this piece many years ago.  It was composed in 1842 during Schumann's "year of chamber music."  Joining Rosenfield and Nabarro were violinist Claudia Ajmone-Marsan and violist Ruth Gibson.  Prior to the beginning of the music, Nabarro regaled us with his obvious love and passion for Schumann's music.  He compared themes in the Bennett piece we had just heard with the Schumann piece we were about to hear.

I don't know why children were on my mind, but I had another thought of a child while listening to the Schumann piece.  It's great music with lots of passion from the quartet of performers.  During the third movement, the adagio molto, the viola seems a bit sad.  Gibson looked sad while playing.  As the fourth movement, the finale allegro molto vivace, got going, it looked like Nabarro's violin was talking to Gibson's viola, almost perking her up as the music progressed.  I had the image of the sad child in the third movement getting cheered up and joining the others in the fourth movement.  Again, a connoisseur might think I'm nuts for such imagery, but I'm sticking with it!

I thank my wife for a great Valentine's gift.  It was a delightful hour during which I could experience new feelings while encountering great music.

TV Filming Outside Our Front Door!

We saw signs on a street near our rental house about a week ago that informed us of filming to take place on the weekend.  My wife and I decided to check out the scene this past Sunday (14 February).  Right around the corner from our place is Sharrow Vale Road.  It's a neat road with lots of local shops.  Our neighbourhood pub, The Lescar, is visible from our house and sits on Sharrow Vale Road.  The TV filming took place on the part of Sharrow Vale Road nearest Hunter's Bar roundabout.  A butcher store got transformed as shown below (click on the image for larger view).

Note the television store to the right!  The show that was being filmed is called Brief Encounters and will be a six-part show on itv.  Click here for information on the show set in Sheffield in the 1980's.  My wife checked out the phone booth and cars that were brought in to give the street an '80s feel (click on the image for a larger view).

As someone who spent his teen years in the '80s, I began to feel my age seeing all that old stuff around!  A travel agency and a record shop were even created (click on the image for a larger view).

It was fun seeing the track on the street for filming, and it was great watching a scene being shot in the butcher shop.  Not so great was the monster light set up right outside our windows last night (Monday, 15 February).  I guess there was some filming taking place at night and they needed the streets lit up.

We'll check out the show when it airs and look for our neighbouring street.

Loving Science on Darwin Day!

How great was yesterday's announcement of the observation of gravitational waves?  We physicists knew there was an ardent search for what Einstein predicted a century ago, and there were rumblings last fall about a possible detection.  Learning of the news yesterday from the LIGO group made me proud to be a scientist.  I'm not an astrophysicist, and my research into the sports world certainly doesn't touch on anything like black holes merging together.  But like so many physicists, I studied general relativity in graduate school and have enough familiarity with the field to know how special yesterday's announcement was.  I am tickled to see something I studied many years ago now become part of observational science.  A nice read on the science behind yesterday's announcement may be found here.

How great is it to be a scientist?  It's wonderful!  I've had so many chills-on-the-spine moments in my life as I've learned about the natural world.  Any student of mine will recall a class where we were about to derive a famous result and I said something like, "Get ready to feel a chill run up your spine!"  As great as it is to learn and understand work done by those who came before us, it's an even bigger thrill to discover something new.  That "something new" doesn't have to be a discovery that gets you a call from Stockholm in a future October.  Learn how to make a car run more efficiently than today's most efficient cars.  Add a nugget of information to what's already known about designing a building to resist damage from earthquakes.  Gain insight into how a species of ants behaves when threatened by a predator.  I'm now grateful to those who developed technologies for plates and screws that assist in mending broken bones.  In my own work, I've gotten tingles on my spine as I discovered something new about how soccer balls move through the air and when I learned how to tease out what's important for winning Tour de France stages.

How great is it to be writing about science on Darwin Day?  Luminaries like Charles Darwin and Albert Einstein helped establish science as how we come closest to truth in the natural world.  It matters not what we were told as children; it matters not what we were told in school; it matters not what our peers told us.  Even if some or most of what we've been told in the past is true, the point is that we need not take seriously claims that are not supported by data and evidence.  And you know what's great about that idea?  Allow me to use a bigger font.

Anyone can be a scientist and investigate the natural world.

How great is that idea?  If you are of the opinion that gravitational waves don't exist, make an effort to prove your opinion.  If you show that Einstein was wrong on this and that yesterday's announcement was in error, and you have data and evidence on your side such that the physics community comes around to your way of thinking, expect a call from Stockholm someday.  As much as teachers come across as authority figures, and it is immensely valuable to teach students what has come to be thought of as true, there are no authority figures in science.  Darwin may seem like the ultimate authority figure, but you don't have to take evolution to be fact simply because someone tells you it's true.  Read about all the research that has been done to establish evolution as true as gravity.  Investigate the natural world yourself and put Darwin's ideas to the test.  If you have problems with what scientists have told us for the past quarter century about our climate, investigate Earth's climate yourself.  Scepticism and scrutiny are needed for good science.  Keep questioning until data and evidence point you in the direction of truth.  And definitely don't fill voids in our knowledge with whatever comforts you or might seem like good ideas.  Test your hypotheses and never be afraid of being wrong.  We can learn a lot from being wrong!

How great is it to be alive and be doing science?  It's a wondrous feeling!

Wet and Windy in Southeast Wales

Today's entry in my sabbatical journal concerns my family's short trip to southeast Wales (Sunday, 7 February to Tuesday, 9 February).  Our trip timing wasn't great as Storm Imogen greeted us on two of our thee days.  But rain and wind weren't so severe as to dampen our enjoyment.  We stayed in Tintern, which is in the county of Monmouthshire.  The beautiful Welsh village sits on River Wye, which nearly flooded its banks while we were there.  If you are ever in Tintern, I highly recommend staying in The Tintern Rectory Bed & Breakfast with its interesting hosts and numerous delicious breakfast choices.

We toured Chepstow Castle in Chepstow, which is also in Monmouthshire.  Castle construction began just a year after the Battle of the Hastings.  Below is a photo of me standing in front of the castle's entrance (click on the image for a larger view).

You can see that rain was part of our visit.  My family enjoyed touring the magnificent castle, especially my daughters, who loved hiding in little nooks and crannies.  The image below shows the large castle interior (click on the image for a larger view).

River Wye can be seen off to the right.  We mostly had the castle to ourselves.  Nothing like some rain and wind to get rid of lines!

On the day after our trip to Chepstow, we visited Tintern Abbey, which is walking distance from the bed & breakfast.  The glorious abbey dates to the 12th century.  Check out the photo below (click on the image for a larger view).

So much beautiful architecture and clever engineering to witness at Tintern Abbey.  I was particularly intrigued by the drainage system.  I'm always fascinated by how people solved problems so long ago.

We visited northern Wales seven years ago, and now we've gotten a glimpse at the southern part.  We heard Welsh spoken a little in the north, but not at all in the south.  Perhaps we can sneak a trip into the middle of Wales before we leave Europe.

Can Peyton Manning run 17 mph?

That was the question put to me by the Tampa Bay Times.  During the AFC title game in which Manning's Broncos defeated the Patriots, a replay showed Manning running for a first down in the 3rd quarter and hitting 17 mph (27 kph) on a speedometer graphic.  To test the NFL's speed claim, I needed to analyse video of the play.  The best video I could get, however, was from the normal view we see on television (only quick looks from other angles).  That side view meant that I could determine the component of Manning's velocity parallel to the sideline, but not perpendicular to it.  Click here for the article and you will see images I used of Manning in motion.  From the 23-yard line to the 27-yard line, Manning was running mostly parallel to the sideline, but he did drift slightly toward the sideline while running those four yards.  That part of his run represented the best shot I had at seeing Manning running parallel to the sideline, so that my speed calculation could be compared to what the NFL found.  My guess is the NFL used overhead images, which would have been nice to analyse.

To give you a better feel for why it is challenging to determine speed from video, consider the screen capture below (click on the image for a larger view).

You can see the NFL's speedometer showing Manning running at 17 mph.  There is, of course, error associated with that number.  What I really want you to see is the orange arrow I put on Manning.  That shows approximately the direction of his velocity vector as he ran past the 21-yard line.  My modelling of the run, therefore, began after he squared his shoulders and got moving more parallel to the sideline.

I found a maximum speed of a little more than 16 mph (26 kph), and I estimated an error of no more than 10%.  Given what I had to work with, I would say the NFL's speedometer was reasonably accurate.  But as I mentioned above, an overhead view would have allowed me to determine his velocity vector instead of just the component of that vector parallel to the sideline.

Manning is listed at 6' 5" (1.96 m) tall and he's been a great athlete most of his life.  Athleticism and a long stride length help with speed (just ask Usain Bolt, whose height is about the same as Manning's).  Still, hitting 16 mph - 17 mph certainly isn't bad for a guy nearing 40 years old!