Degrees of Difference: How is Martinsville like Fontana?

I love getting questions from readers because I always worry that the geeky stuff I find interesting is only interesting to me.  I love it even more when they not only give me a question, they also supply part of the answer!  This one has to do with the degrees of difference between Martinsville and Fontana.

Michael J. Clark asked a really good question about Martinsville and Fontana:

Why does Fontana (banking in the turns is 14 degrees) seem to have such higher banking than Martinsville (banking in the turns is 12 degrees)?  I would think the 2 degrees more that Fontana has wouldn’t look so dramatically different than Martinsville, but it really does.  I’m guessing it has to do with the fact that Fontana’s turns are about 10 car-widths wide (my estimate) compared to the turns at Martinsville, which seem to be about four car-widths wide.

Great question and another example (like race cars seemingly speeding up when spinning into the grass) of how our perceptions are often subjective.

We always talk about Martinsville being a “flat track”, which is sort of unfair.  It’s flat compared to Talladega and Daytona, but there are still twelve degrees of banking in the turns.  Nothing like a little trigonometry at the racetrack – what does twelve degrees look like?  Let’s start with some definitions so we’re all talking about the same things.

Track width is measured across the track surface and forms the hypotenuse of a right triangle.

Any right triangle can be described by the lengths of any two sides, or the length of one side and one angle.  Remember SOHCAHTOA? You can (finally!!) use your trig to reverse engineer the racetrack.

One degree isn’t really all that large.  A banking angle of one degree means that in order to get a rise of one foot, you need to have a run of about 57 feet.  One degree isn’t very much, as shown in my figure below.

The top picture shows what a banking angle of one degree would look like, with the rise of 1 foot and the run of 57 feet.

The bottom picture is a scale drawing of Martinsville Speedway, which has a track width of about 55 feet (although I think it is a little narrower in the corners).  The banking angle is variously given as 11 degrees or 12 degrees.  I’m using 12 degrees here because that’s what the official NASCAR site says.  Given the hypotenuse (track width) and the banking angle, I can back calculate to show that the rise is about 11.4 feet and the run is about 54 feet.

Now to Michael’s question.  The diagram below shows scale drawings of the banking at Martinsville and California and (just for comparison) Talladega.  I’m using the best numbers I can find on the web.  If someone has more accurate numbers, please let me know.  Kudos, by the way, to Talladega for having one of the best webpages of track data.

Michael has great instincts – the track at Fontana is two-to-three car lengths wider than Martinsville.  This means that the rise is seven feet (one Brad Daugherty) higher than Martinsville at the edge of the track. That increase in rise makes the banking look steeper because you’re looking up a greater distance.

(You always hear that Talladega is five stories tall.  I’m not sure what they’re counting in that calculation because I get 26 feet, which is pretty far short of five stories unless you have very short stories.)

In addition to the greater width, you also have to remember that there’s a huge difference in overall scale.  Martinsville was the second track I visited while writing The Physics of NASCAR – the first was Atlanta.  Martinsville was the track that made me love short tracks.  You get up close to the action and even though they’re not going 200 mph, when you’re that close to them going 100 mph, it seems really fast.  Short tracks are a great challenge to the crew chief (and the driver) because suspension movement is so much more important than aerodynamics.  And, of course, tempers seem to be proportional to the track length of the track:  at Martinsville, they are both really short.

But you have to realize just how much smaller Martinsville is than the California track.  The straights at Martinsville are 800 feet, while the backstretch at Fontana is 2500 feet.  Martinsville is .524 miles, which is 2777 feet.  If you unrolled the Martinsville track, you could just about fit the entire thing on Fontana’s backstretch.  The picture below is my attempt to make a to-scale drawing of the two tracks.  The banking at Fontana looks huge compared to the banking at Martinsville not only because the track is wider at Fontana, but also because the track is simply bigger.  When you look out into the turns, you simply see a lot more asphalt.

Side note:  The featured picture in the post at the top shows me trying to stand up on the 24-degree banking at Texas Motor Speedway, just to give you an idea of how steep 24 degrees actually is.  This was while we were shooting the Science of Speed video series.

So that’s the difference between the tracks at Martinsville and Fontana.  I’m told there is absolutely no comparison between their hot dogs.

Thanks for the question, Michael!  Questions (and suggestions for the Sirius radio “NASCAR Mythbusters” segment) are always welcome.  Click on the ‘contact’ tab above to send me an email.

I’m heading out to Joliet, IL to give my  Science of Speed talk at Joliet Junior College Friday October 26th at 7:00 p.m.  More information on how to get there can be found on my appearances page.  My talk is aimed at the average NASCAR fan and focuses on why it’s a lot harder to drive fast than most of us think.  Most people leave the talk with even more respect for what professional racecar drivers do.  I promise no pop quizzes, so please come on out and meet me!