Will the Gen-6 Car Affect the Number of Cautions?

 Cautions, Edwards Carl, math, Racing, Tony Stewart  4 Responses »
Jan 252013
 

I love the Gen-6 car.  Not as much as I love the Nationwide cars (but that’s got more to do with what I drive than it does the cars).  The big question is whether the decrease in cautions is going to be changed because of the new car.Let’s start (as we usually do) with the new car.

Graph4Let’s start (as we usually do here) with the data.  I’ve tabulated the data for cautions for the last twelve seasons and found that cautions have been decreasing since 2005, as shown,  for both the Nationwide and the Sprint Cup series.

In order to compare the two series and to compare between seasons within a single series, I’ve plotted the number of cautions per 100 miles.

In 2012, the Sprint Cup series had 1.57377 cautions per 100 miles.  They drove 13725 miles total, so that was 216 cautions total.

In 2012, the Nationwide series had 2.23969 cautions per 100 miles.  They drove 8240 miles, with comes out to 189 cautions — essentially the same number of cautions per mile they had last year.

Conclusion #1.  If the Nationwide drivers had driven the same number of miles as the Sprint Cup drivers, they would have had 307 cautions.

You’ll notice that I’ve drawn lines through each set of data.  They aren’t just a best fit by eye – I actually did a non-linear least-squares fit that determines the line that goes closest to all the points.  The data are decidedly linear and, more importantly, there aren’t any bumps or jump in, say, 2008, when the COT (which I guess is now the Gen-5 car) was introduced, or in 2011 when the Nationwide car was changed.  The data remained pretty consistent.

Conclusion #2.  Cautions are not affected much by the car that’s being driven.  Sure, I expect there to be some driver errors when a car doesn’t handle the way the driver expects it to behave; however, these guys catch on really quickly, so that’s going to be maybe 5 cautions.  Five out of 216 is like 2.3 percent, which is well within the error in the fit parameters.

Why are the cautions decreasing?  I’ve gone into this before, but I believe it is essentially because the drivers have a lot more experience now than they did in previous years.  There are a lot of veteran drivers in the Cup series right now, and I calculated that if you add up all the races run by the current crop of drivers, they have run a total of about 1000 more races in 2011 than they did in 2005.  That’s a whole lot of experience, and it’s distributed amongst the drivers.   Compare just two drivers:  Tony Stewart had run 248 races in  2005 and at the end of 2012, had run 500.  Carl Edwards had only run 49 races in 2005 – compare that to the 301 races he’d run as of today.  (I am only counting points paying races.  If you could somehow quantify the number of practice laps, time testing, etc., I think that would only make my argument stronger.)

So, in short, I don’t expect there will be any significant change in cautions because of the new car — up or down.  What do you think?

 

Is There Really a Second-Place Curse?

 Clint Bowyer, Dale Earnhardt Jr., Denny Hamlin, Edwards Carl, Jeff Gordon, Jimmie Johnson, Kasey Kahne, Keselowski Brad, Kyle Busch, Mark Martin, Martin Truex Jr, math, Tony Stewart  No Responses »
Dec 072012
 

One of the commentators after the final race in Homestead mentioned that Jimmie Johnson should be happy he finished in third because it allows him to avoid the “dreaded second-place curse”.
Anytime someone says something like that, it makes me wonder whether there really is a curse, or whether that person had just been talking to Carl Edwards.  So I analyzed a little data and guess what… there really IS a second place curse.

I used data from the last twelve years — from racing-reference.info, bless them!  After trying a couple of different approaches to making the data easy to visualize, I ended up with something a little more complicated than I would have liked.

Bear with me – it’s not as yucky as it looks.  I have plotted on the horizontal axis the place in which a driver finished in the first year listed, which we’ll call “X”.  I then calculated the change in positions of the same driver the next year (X+1) and plotted that on the vertical scale.  So the first set of data has X = 2000 and X+1=2001.

  • A positive number on the vertical axis means that the driver finished better by that many places in the following year. For example, +5 means that the driver finished five places better the next year than they finished the year before.
  • A negative number on the vertical axis means they finished worse the next year. A -5 means they moved down five spots in the final standings.

I went through and removed any special cases — like Mark Martin running full time one year, but not the next, Busch brothers missing races (that’s a different kinds of curse), people retiring, etc.  The graph below summarizes the top 16 finishing places and the change in final standing over the last twelve years.

There’s an obvious statistical implication:  If you finish second, for example, you have only one place to move up and forty one places to move down.  You’re either going to win the championship next year, become second again, or move down.  The probability is that you’re going to finish worse than second.

To look at the data in a slightly different way, I plotted it the same way they plot the daily activity of the the stock market:  the symbol shows you the average.  One line extends up to the maximum increase in position and one line extends down to the largest drop in position.

 

The first-place curse

In fact, if we’re going to call dropping in the standings a “curse”, then there is clearly a first-place curse that affects everyone except Jimmie Johnson.  Mose drivers who win the championship one year inevitably finish worse the next year.  When I say ‘drop in points’, it’s not a huge drop:  nine places was the most anyone who finished first dropped.

The average first time finisher fell almost five positions.  That’s including four consecutive ’0′s due to Jimmie Johnson.  If we exclude Jimmie just because what he did was really unprecedented (and unlikely to be duplicated), the average first-place finisher falls almost seven positions the next year – about the the same as the second-place driver.

The second-place curse

Second place shows a very similar story, only worse.  There is only one case in twelve years in which the second place finisher one year won the championship the next year.  That was Jimmie Johnson.  Whoops – Rick pointed out my mistake.  It was 2001 -2o02 and the driver was Tony Stewart!  On average (including Jimmie), the second place finisher finishes about seven positions lower the next year.

The three biggest drops in point standings (-15, -13, -11, -9 and -7) are due to Martin, Edwards, Biffle, Edwards and Hamlin.  There are no extenuating circumstances like crew chief changes, owner changes, etc. on which to blame the drops.  Four out of five of those drivers were all driving for Roush at the time… maybe there’s a Roush curse?

The bad news for Jimmie Johnson… and everyone else who made the chase

Here’s the bad news for Jimmie:  Yes, he avoided the second-place curse; however, no third-place driver has gone on to finish first or second the next year.  The best they’ve done was to match their third-place finish.

Yep, perhaps there’s a third-place curse as well, as third-place drivers finish an average of three places lower the following year.

In fact, you don’t find a finishing position in which there is an average probability of bettering your finish until 7th place.  On the graph above, you can see that the majority of finishes were improvements, although without one -11 change, it would be a much more positive number.  After that, it’s an oscillation between slightly better and slightly worse.

A caveat of this data analysis is that the Chase sort of messed things up going out past 10 because a driver in the Chase can’t finish lower than 10th, even if he misses races or otherwise would have fallen much lower without the Chase format.

 

Cautions: A New Low for NASCAR

 Cautions, NASCAR, Racing, Statistics  2 Responses »
Nov 212012
 

At the start of the season, the big news was that cautions were remarkably down from last year.  As I showed, this isn’t a new trend – it’s a continuing trend since 2007.  Since the season’s data are now complete, I thought it was time to revisit the data.

Plotted at right are the caution data from 2012 compared to the data from the previous six years.  I’ve normalized the cautions to cautions per 100 miles to account for the changing lengths of some races over the years.

Note how the data jump around pretty wildly until about race 10.  That is because averages are only meaningful when you’re averaging enough information.  When you average a small number of measurements, the average fluctuates until you get enough data that the numbers mean something.  You can’t predict anything from the first five or ten races.  Please remember that next year when the prognosticators tell you someone’s season is over just after first Martinsville.

The 2012 data are the green triangles – a whopping decrease in cautions from 2011!  In absolute numbers, there were a total of 218 cautions this year compared with 278 in 2011 and 265 in 2010.  Where were the biggest numbers of cautions?

Highest Lowest
Race Month Cautions/100 miles Race Month Cautions/100 miles
Bristol August 4.87  Fontana  March  0.388
Martinsville October 4.18  Texas  April  0.400
Martinsville April 2.58  KansasHomestead  AprilNovember  0.750

The Nationwide Series didn’t experience the same drop in cautions – in fact, they had just about the same numbers of cautions this year as they did last year.  The tracks with the largest caution rates per 100 miles for Nationwide are:

Highest Lowest
Race Month Cautions
/100 miles		 Race Month Cautions/100 miles
Bristol August 6.77  Fontana  March 1.33
Phoenix November 4.90  Iowa  September  1.37
Kansas OCtober 3.88  Dover  September  1.50

Here’s the updated graph, showing cautions per 100 miles since 2001.  You’ll notice that 2012 marks a new low for the Cup Series.

I’m still working on the analysis, but I think my original theory holds for why the number of cautions has been decreasing:  we simply have more drivers with more experience.  There are a lot of veterans and fewer rookies.  The average time each driver has been driving in the series is higher, which means that the drivers are simply better.

Degrees of Difference: How is Martinsville like Fontana?

 Auto Club Speedway of California, Martinsville, math, Talladega, Texas Motor Speedway, Trigonometry  1 Response »
Oct 252012
 
DLPTXTrackBanking

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!

 

 

The Six-Year Downward Caution Trend: In the Nationwide Series, too!

 Cautions, Consipracies  1 Response »
May 242012
 

Just out of curiosity, I decided to do a similar analysis on the Nationwide Series caution record as I did on the Cup record.  My intent was that if there was something specific to the Cup series – the new car, the Chase, etc.), it would show up because the Nationwide would follow a different trend.  Not at all!  Remember that I’m plotting number of cautions per 100 miles run.

No too surprisingly, the Nationwide Series has more cautions than the Cup Series; however, the cautions are decreasing much faster in the Nationwide Series than in the Cup Series.

Taking the linear trend to its logical extreme, we can expect the first caution-free season in 2018 for the Cup Series and 2030 for the Nationwide Series!

How Likely are You to Win the TNT Million Dollar Challenge?

 Daytona, math, Probability  No Responses »
Jun 292011
 

TNT is offering a million dollars to anyone who picks the top ten drivers – in order – at any of the six races they broadcast.  You have up until 25% of the race has been run to lock in your selections, which means up to mile 100 at Daytona this weekend.   How likely are you to win?

You have a 1 in 43 chance of picking the first driver correctly.  There are now 42 drivers left and you have a 1 in 42 chance of picking the second driver correctly.  When you calculate the probability of doing two things, you multiply the probabilities.  It makes sense that there ought to be less probability of picking two numbers in a row than of picking one, right?  So the odds of picking two drivers in the right order is 1 in (43 x 42) or 1 in 1,806.

Continuing this pattern…

# picked in right order

 Calculation Chances are …
1 1 in 43 1 in 43
2 1 in (43 x 42) 1 in 1806
3 1 in (43 x 42 x 41) 1 in 74,046
4 1 in (43 x 42 x 41 x 40) 1 in 2,961,840
5 1 in (43 x 42 x 41 x 40 x 39) 1 in 115,511,760
6 1 in (43 x 42 x 41 x 40 x 39 x 38) 1 in 4,389,446,880
7 1 in (43 x 42 x 41 x 40 x 39 x 38 x 37) 1 in 162,409,534,560
8 1 in (43 x 42 x 41 x 40 x 39 x 38 x 37 x 36) 1 in 5,846,743,244,160
9 1 in (43 x 42 x 41 x 40 x 39 x 38 x 37 x 36 x 35) 1 in 204,636,013,545,600
10 1 in (43 x 42 x 41 x 40 x 39 x 38 x 37 x 36 x 35 x 34) 1 in 6,957,624,460,550,400

That’s one in 6.9 quadrillion to get all ten in the right order.

Is Picking Them in Order Harder?

What if TNT had just said you had to get all ten, in no particular order?

If you look at ten numbers, there are ten ways of picking the first number, nine of picking the second, etc. That multiplies out to there being (10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1=) 3,628,000 different ways of organizing ten numbers in every which way possible.

If TNT had decided that you only needed to get the drivers right, but not the order, your chances would increase to a whopping 1 in 1,917,334,783.

But there aren’t Really 43 Drivers Capable of Placing in the Top Ten…

OK, in reality, the odds are a little better.  The calculation above assumes that the finish is a totally random event and we know that it’s not because there are 7-9 start and parkers.  Realistically, you’re picking from maybe 35 cars (8 S&Ps), so the odds for getting all ten in the right order if you’re only picking from 35 drivers are 1 in 818,441,006,423,040. or 1 in about 818 trillion.

But there aren’t Even Really 35 Drivers Capable of Placing in the Top Ten…

Yeah, the husband tried to make the argument that you’re really only choosing from about 17 or maybe 20 drivers.  Five words:  Regan Smith and Trevor Bayne.

Just for comparison…

Odds of being struck by lightning are 1 in 576,000.
Odds of being killed by lightning are about 1 in 2,320,000
Odds of a meteor landing on your house: 1 in 182,138,880,000,000

So you’ve got a better chance of a meteor landing on your house than winning that million dollars.

Often for promotions like this (free televisions if it snows 10 inches on New Year’s Day!!), a company will take out an insurance policy.  They’ll pay some amount of money to hedge against paying more.  The people at the insurance company who figure out how much to charge them use these types of calculations to figure out the risk.  I’m guessing TNT wouldn’t want to pay much of a premium because the odds are clearly in their favor.  But it’s a great promotion.

Does this mean you shouldn’t play?  Heck no – TNT isn’t charging you to enter, so get your best guess together and see if you can beat the odds.

RANDOM NOTES

Look at this cool project from Clemson and DuPont to take middle and high school teachers to the racetrack and teach them about science!  Way to go, Tigers.

The probability of becoming a saint is estimated at about one in 20 million, but if you’re Jacques Villeneuve, the odds rise to one in a flying pig.

Gratuitous link to The NASCAR Insiders just because their Wednesday Q&A is always worth checking out – it is a blog I always learn something from!

Daytona this weekend – read all about drafting vs. bump drafting, why you’re likely to see two but not three cars drafting together, why NASCAR limits radiator pressure to try to keep the two-car draft to a minimum, and why drivers shift to the right to get air to the engine if they’re turning left.  Or take a look at the Science of Speed video on drag and drafting.

 

100 Million vs. 78 Million is not the Numbers Question for FOX vs SPEED

 math, Media, NASCAR, Uncategorized  3 Responses »
Jun 212011
 

The NASCAR pundits have again simplified a complex situation.  Incorrectly.

(Of course, at least they got the network right!  I got FOX and ESPN confused.  This is the problem with a 60-hour a week job and trying to blog about something utterly unrelated in the meantime.  My excuse is that I have a $3.5 million proposal due this week.  The same math holds, regardless of whether it is FOX or ESPN. Thank you Michael!)

The NASCAR Net is a-twitter since FOX floated a trial balloon about moving races from ESPN FOX to SPEED.  I’ve heard the argument over and over, in print and on radio that this is a bad idea because EPSN FOX is in 100 million homes and SPEED is in “only” 78 million homes.  They argue this would be a decline of 22 million potential viewers.  The question not being asked how many of those 22 million ESPN FOX watchers are actually potential viewers?

Point number 1:  Diehard NASCAR fans are going to find the race on television wherever it is.  Rabid fans are going to get whatever cable package they need in order to watch races, or they’re going to find a local sportsbar that carries the race.  Casual and incidental viewers are the ones that will make a difference in numbers.

Point number 2:  A very small fraction of households receiving a network watch it.  The highest rated race of 2010 on ESPN was August Pocono, with 6.3 million viewers.  Let’s assume an average of 2 people per household, so if ESPN is in 100 million households, that corresponds to roughly 200 million viewers.  ESPN pulled in 3.2% of the viewers who had the option of watching the August race at Pocono.

SPEED is in 78 million households, so assuming the same two people on average per household, there are 156 million potential viewers.  If SPEED captured the same 3.2% of their possible viewers, that would be 5.0 million viewers.  The difference is 1.3 million viewers — if you are willing to ignore point 3.

The numbers for FOX – let’s leave out the Daytona 500, which was 13.3 million and I bet FOX isn’t going to move that – are similar.  The highest rated race was April Talladega, with 8.45 million viewers.  Out of the 200 million possible eyeballs, that’s 4.2%.  4.2% of SPEED’s viewing audience is 6.55 million viewers, so again, we need an increase of about 1% to match FOX’s numbers.

Point 3:  Consider the demographics of FOX viewers vs. SPEED viewers.  SPEED is a motorsports channel.  I would think you’d be more likely to get a motocross fan to watch NASCAR than an average television viewer.  Which network is more likely to promote the race during other shows?  Which network is more likely to have the schedule freedom to do extended pre- and post-race shows?  All SPEED would have to do to equal the viewership from ESPN would be to attract 0.86% of the remaining viewers and about 1% to equal the viewership from FOX.  We’re really talking more like a difference of 2 million than 22 million.

There are many factors besides numbers, but numbers aren’t as big a factor as some are trying to make them out to be.

Just for fun, here are some stats for ESPN and SPEED viewership. They are from 2006-2007, but that’s the latest I have easy access to.

Category ESPN SPEED
Men 69% 80%
Women 31% 20%
18-34 28% -
35-54 39% -
55+ 33 -
18-49 - 69%
25-54 - 63%
$75,000/year + 43% 38%
$50,000/year + 62% 61%

The Math of Fuel Mileage

 Engines, Fuel Mileage, Kansas, Pocono  6 Responses »
Jun 102011
 

The gas needed to do one lap at a one-mile track fits in this quart bottle

I guess when you have people feeding you all the numbers you need through your earpiece, you think they’re easy to come by.  That’s the only explanation I can figure out for the snarky comments by television commentators about crews not being “smart enough” to figure out how much gas to put in the car so that it doesn’t run out before the end of the race.  There have been a lot of fuel mileage races the last few weeks.  Pocono is traditionally also highly likely to be a fuel mileage race, so let’s clarify how easy (or hard) it is to not run out of fuel.

Average mileage under green is about 4 miles per gallon.  At a one-mile track, than means one lap (one mile) requires one quarter of a gallon, which is one quart.  A car running out of gas coming out of turn four is short by probably a cup of fuel.   On the one hand, it’s amazing that it takes a whole quart of gas to do one lap.  On the other hand, the fuel cell holds 18 or 19 gallons.  Let’s say they get 18.5 gallons in the fuel cell – that’s 74 quarts, so you’re talking being off by 1/74th of a tank, which is a pretty narrow margin of error.

For comparison, a passenger car getting 32 mpg would need only a half a cup of gas to do a lap at Phoenix.  Although much more fuel efficient, the television ratings would likely be much lower.

There are some other considerations.  Here are two that are hard to quantify:

  • The pickups on the fuel cell can’t pull all the gas out of the tank, no matter how much swerving the driver does.  There’s likely to be some fuel in the fuel cell that just doesn’t make it to the engine.  It is a small fraction of the fuel cell, but  if we’re talking about 8 ounces of fuel being the difference between making it and not, small amounts matter a lot.
  • The driver’s ability to save fuel varies, depending on the driver and if he’s racing hard or if he’s able to set his own pace.  If he’s racing hard with another driver, he’ll likely get less than the expected fuel mileage.  If he’s skilled (getting off the throttle earlier going into the corner and getting onto the throttle later coming out of the corner), he might save a lap or two or three worth of gas.  It’s the same principle as you and I not stomping on the gas or the brake to be more fuel efficient.  When the crew chief asks the driver how much gas he’s saved, the only thing the driver can do is guess.  The more experienced the driver, the better feel he is likely to have for how much gas he saved.

One of the biggest challenges for the crew chief is calculating the actual gas mileage.  Let’s say you or I are calculating the fuel mileage of our car.  We go to the gas station and fill up the car.   The next time we stop for gas, we figure out how many gallons it takes to fill the tank back up and how far we drove.  For example:

I fill up my tank.  300 miles later, I stop for gas again and find that I need 10 gallons to fill up the tank.  It took me 10 gallons to drive 300 miles, which means my gas mileage is 30 miles per gallon.

OK, that’s not perfectly accurate because what does “fill up” mean?  Some people top off the tank and others stop as soon as they sense it is close to full.  There’s some variation in the fuel pumps as to where the pump shuts off automatically.  300 miles on the expressway is different than 300 miles in town.  If you want a meaningful number that characterizes your own gas mileage, you need to measure it consistently over a period of time and use an average.  Of course, that’s not possible in NASCAR.

But at least you and I get a decent measurement of how much gas we put in the car.  NASCAR teams don’t get to measure how many gallons of fuel goes into the car: They get to measure how many pounds of fuel went into the car.

A NASCAR fuel can holds about 12 gallons of fuel.  Gas weighs about 6 lbs per gallon, so the full gas can holds 76 lbs of gas.  The can itself is about 20-25 lbs, so round numbers, 95-100 lbs total. (Thanks to the NASCAR Insiders for the numbers.  I am writing this from a neuroscience retreat and don’t have my notes handy.)

Before each pit stop, the team weighs each one of the gas cans.  Let’s say one of them weighs 96 lbs.  The car comes in to pit, they add fuel and then weigh each gas can again.  Let’s say that the can weighs 36 lbs after a stop.  The change in weight is 96 lbs – 36 lbs = 60 lbs.  At 6 lbs per gallon, you can infer that the can is missing 10 gallons.

Note that I very carefully said ‘the gas can is missing 10 gallons’ because we have no assurance that all 10 gallons went into the car.  You’ve seen gasoline spill out everywhere when the gasman pulls the dry break away from the fuel cell inlet.  That happens even more with the new dry breaks because they are a little trickier to put in place and pull out than the old gas cans were.

The crew chief looks down and makes a mental estimate of how much fuel is spilled, converts the masses from the cans into gallons and comes up with a number for how much fuel he thinks is in the car.  From that, he estimates how many laps they can run.  If you want to see a frustrated crew chief, look for the gas man with the raised eyebrows and the shrugging shoulders.  He thinks he got it full… but he’s not sure.  That’s actually sometimes worse than the one who knows he didn’t get it full.  Sometimes it’s better to know the answer, even if it’s bad, than to be unsure.  The scales in the pits have at least one decimal place, and my friend Josh (a member of the ex-Elliott crew chief club) suggests that the better teams have almost certainly moved to scales with two decimal places.

Do the decimal places really matter?  Turns out they do.  Sunoco provides NASCAR teams with the exact density of the gas on race day, and they provide it to two decimal places.  So instead of 6.00 lbs/gallon, they’ll tell you 5.94 or 6.06 lbs/gallon.  If you weigh 60 lbs of gas, that’s 1o gallons @6.00 lbs/gal vs. 10.6 gallons @6.06 lbs/gal.  Remember that on a one mile track, one lap requires 0.25 gallons.  That 0.6 gallons difference is more than two laps on a one-mile track.

One more thing that’s different this year.  Here’s your word to impress people with this week:  Hygroscopic (hi-grow-skop-ick).  It means very attractive to water.  Ethanol – and 15% of the NASCAR fuel is ethanol – is highly hygroscopic.  If you turn your back on ethanol for even a moment, you turn back and there it is sucking up water.  We use ethanol in the lab to clean things and we actually have to use acetone afterward to get rid of the water the ethanol leaves.

Two issues with hygroscopicity:  First, you’re getting water in the fuel and water isn’t combustible.  You put the same volume of liquid in the cylinder and you get less power because some of the molecules turn into steam instead of combusting.  So you need more rotations to get the same power and thus you’re using fuel at a different rate.

Second, water has a different density than the hydrocarbon fuel molecules (or the ethanol), so the amount of gas you’re getting in the car is different that what you think.   Density changes with temperature, so if you think about a race like Kansas, where it was really hot, or like Charlotte, when the temperature varied quite a bit from start to finish, you might experience meaningful changes in the density over the course of a race.  Even if you did all the calculations successfully, you might still be surprised because one of the inputs was off. Also, when the temperature rises, more water can be absorbed by the ethanol.  The water molecules hang out in the gas, pretending they belong there.  But when it cools down, the water can separate from the fuel, so it’s possible to have liquid in the tank, but not have a lot of fuel.  This is a tremendous unknown that the teams have no experience with and it may account for why there have been so many fuel mileage surprises.

A lot of factors go into correctly calculating fuel mileage.  I think if you really want to get it right, you’d want to use a model that involves calculus.  And I bet there are at least a couple teams doing that.  You can make little widgets for things like fuel consumption or gear ratios and rpm using something as simple as Excel.  I know NASCAR likes to portray itself as simple, but let’s give the folks sitting with all the computers up on the pit box their due.

A few misc notes:

  • Happy to hear that Chad Johnston is getting a shot at crew chief for the 56 team.  Chad was the engineer for Elliott Sadler’s team when I was following them around for the Physics of NASCAR book.  Chad is a talented guy who reminds me a little of Rodney Childers – not self-promoting, doesn’t talk when he doesn’t have anything to say, but when he has something to say, make sure you listen.
  • I wish the story about what happened to the Second Chance Motorsports Nationwide crew at Chicago got just a small fraction of the attention Richard Childress/Kyle Busch did.  It’s sad, but there are so many people trying to get into NASCAR that there will always be some people who will work for someone who doesn’t have a history of treating people right.
  • BTW – I’m tired of hearing about RC/KyBu… you can stop now.
  • Here are a couple neuroscience tidbits I learned this week.  Perhaps the most useful thing was that if you get eight hours of sleep, but it’s not continuous (think new moms), your reflexes and ability to think are comparable to someone seriously sleep deprived.  The least useful (but perhaps most interesting) piece of information was that rodents lack the ability to vomit.  If you want to test whether a drug induces nausea, you use ferrets because they barf pretty readily.  Moral of the story:  If you’re going out drinking, take the rat as your bar buddy and let the ferret be the designated driver.  (The second moral is that if you went into physics because you have a queasy stomach, watching that talk right before lunch was maybe not the best thing to do.)
  • Where have I been?  Well, the last year or so I’ve been dealing with some really, really serious medical issues and it’s been all I can do to get through the day.  Blogging was one of the many things in my life that just seemed to require too much energy to manage.  I’m starting to feel better now – sometimes I would go so far as to say “inspired” – so I’m hoping my comeback will keep.  Thanks to the many online buddies who have kept me in their thoughts and brightened my days.  You don’t know how much you have been appreciated.