Richmond Redux: Relative Velocity

NOTE: Some clarifications added 1:00 p.m. 4/30/12. Thanks to all the commenters, especially @nateryan!

I think Dave Moody did a good job breaking things down. The situation is confounded because there were so many different complications. Who from NASCAR is duly authorized to tell a spotter/crew chief/driver their position? Is it the team’s responsibility to make sure they are lined up the right place or NASCAR’s?  Should NASCAR have held off another lap to make sure that the teams knew what was going on?

The only thing this blog attempts to show is that one should never accept what one sees without questioning it because there are often explanations for why what we think we saw isn’t actually correct.  See my take on technology and data in motorsports.

Of all the things I am mandated to teach in intro physics, the problem where you are swimming across a river and there is a current and you have to figure out at what angle you swim so that you counteract the current and go directly across the water is my absolute least favorite.  I am hard pressed to find a case in which my students have cause to need to know how to do this.

Richmond may have given me a new way of teaching the importance of relative motion.  Although the magnitude of the speed does have an effect on interest, when you come down to it, the crux of racing is whether Car A is running faster than Car B.  It doesn’t matter if Car A is running 180 mph and Car B is running 179 mph, or if Car A is running 150 mph and Car B is running 149 mph.  You win because you are faster than the other car.

Although the restart controversy regarding the 14 and the 99 seems to be more a matter of a communications screw up (both cars claim they were told they were P1), it raises an interesting issue in terms of what we perceive vs. what actually is.  Even sat at a train crossing and had the momentary feeling that the train was standing still and you were moving sideways? Here’s a series of animations I put together really quickly. See if they do the job.

Take a look at the video below and decide which ball is accelerating and which ball is moving at constant speed.

Clearly, the blue ball is accelerating and the yellow ball is moving at constant speed. You can see this more clearly by marking the ball every ten frames, as I’ve done below. Exact same motion, but with markers:

The hallmark of acceleration is that the distance traveled over the same time interval increases. See how the blue balls are more and more spaced apart? That’s acceleration in a nutshell.
Now try this one: Which ball is accelerating this time?

The yellow one, right? Let’s try it again with the markers.

You can see from this that the yellow ball was actually moving at constant speed. The blue ball was decelerating. Because the 14 spun its wheels, it was not accelerating and that made the 99 look like it was accelerating even faster. If you had a frame-by-frame video of the actual restart, you could do the exact same type of analysis with the actual cars and settle for sure whether the 99 was accelerating prior to the starting box.

We judge things by how they look relative to other things. To be a good judge of relative motion, you have to reference your observations to something fixed – like the lines on the animation, or a track wall, or something that isn’t also moving.

This simple demonstration isn’t meant to call into question whether the penalty was right, or who screwed up – just to make people realize that what you see isn’t always what happened.

Is More Data Always Better?

Saturday’s race in Richmond was a festival of miscues.  Carl Edwards mistakenly thought he was leading, then he jumped the restart, although he wasn’t the one to lead the restart because he wasn’t the leader.  One would think we have the data that could prevent incidents like this.  We probably do.  But do we want to use it?

NASCAR Timing and Scoring

A transponder is a device that translates one type of signal into another.  For example, the track position of the cars is measured using induction from loops of wire embedded in the track and translated into an electrical signal that is passed along to timing and scoring.

Like computers, timing and scoring systems merely report exactly what they are asked to report.  The official timing and scoring system works on the basis of ‘scoring loops’ – which are literally loops of wire embedded in the track.  The number of loops in the track depends on the track.  There are more loops at longer tracks and fewer at shorter.  The loops are in the main part of the track and embedded in Pit Road (which is how they catch speeders). The two faint lines running along the track at right (from top to bottom of the photo) are a scoring loop in Pit Road at Charlotte Motor Speedway.

When a caution flag appears, everything goes back to the situation at the last scoring loop passed.  Even if car A passes car B, if it happened in-between scoring loops and a caution comes out, car B is still the leader.  Television replay is used in the last laps of the race.  Timing and scoring has a discrete number of measurements around the track.

There are, of course, more measurements available.  Television shows you much more frequently updated data from a different system.  How many times have you watched the tracker on television (or Pit Command) and seen the lead switch back and forth during caution as the drivers sped up and slowed down while scrubbing tires?

If Car A passes Car B, that information is updated immediately on the television system.  The official scoring loop system is updated only after a scoring loop is passed.  This is why there was so much confusion Saturday night.  With a penalty on the 48 team, the 99 team thought they were the leader – as reflected by the scoring pylon and, it seems, the officials on the spotter’s stand.  See Bob Pockrass’s story for a detailed explanation.

We Have the Technology: Why Don’t We Use It?

I received a lot of comments to the effect of “NASCAR has more detailed data – we know that because we see it on television and RaceView/Pit Command.  Why don’t they use it?” Two comments.

1.  The official timing and scoring is based on the track scoring loops.  Television replays are used at the end of the race, but the rest of the data you see on television is informational.  It is not the data of record.

2.  I interviewed some people from SportVision (the company that provides the television with the information you see) earlier this year in the context of whether it was possible for teams to intercept data.  Their tech people repeatedly made the point that they acquire such a huge amount of data that analyzing it in real time in any reliable detail is not feasible at present.  They transmit a subset of that data directly to the television, but I was under the impression that the data you’re getting from Race View may not give you results  accurate enough to base race calls on during a race.

This raises a much larger question:  Do you want a sport where technology contradicts what the audience thinks they saw?  It sure looked at thought Carl Edwards obviously accelerated way before the starting box – but we know that human perception is not objective and not always accurate.  Your perception was affected to a large extent by the fact that Stewart spun his tires and didn’t accelerate.

NASCAR is data intensive like few other sports.  NFL fans don’t need to know how fast two players were going when they collide – they just need to see that player B stopped player A.  Being a data geek, I want to get my hands on all the data I can; however, given the numerical literacy level of the country (A huge number of people can’t understand even basic charts and graphs), basing a sport more and more on technology is dangerous.  Technology can enhance your enjoyment of a game – like seeing the speed at which a fastball hurtles across home plate – but I don’t think most people want to have to follow the numbers that closely just to understand what is going on.



Infographic: Bristol: Old, New and Newer

In response to requests about how the ‘new new Bristol’ compares with the ‘new Bristol’ and the ‘old Bristol’, here’s a comparison.  For more on the changes, see my earlier post.  The light blue triangle shows the constant 36-degree banking of the ‘old Bristol’.  The black line shows the progressive banking (24-30 degrees) that was introduced in 2007 and the red line shows how (I think) they are modifying the highest groove only.  Note that there seems to be some disagreement about the actual banking values.  I’m using the values the track uses.

Kansas Wrap Up: What Caused all the Engine Failures?

The defining characteristic of the Kansas race was the surprising number of engine problems.  Many of those problems can be attributed to the change in rear gear from a 3.89 to a 4.00.  At  190 mph at a track like Kansas, your wheels make 2270 revolutions per minute (rpm).  If you watch the telemetry on the television broadcast, you know that the engine is rotating around 9500-9900 rpm.  Since the engine is attached to the wheels, there has to be something to change the rotation rate between the engine and the gears.

Gearing Up

That something is the transmission and the rear gear.  As shown at right (with the values given for a Corvette ZR-1), the engine rotation passes through the transmission and then through the rear-end gear before reaching the wheels.  A 4.00 gear means that the ratio of rpm in to rpm out is 4.00:1.  It takes four revolutions of the input to produce one revolution on the output.  If you have something rotating at 8000 rpm and you add a 4.00 gear, then the rotation is reduced to 8,000 rpm/4.00 = 2,000 rpm.

Note that NASCAR does not allow 5th or 6th gears and does not allow overdrive (when the first number is smaller than the second).  The lowest gear you can have is 1:1 in NASCAR.

Let’s compare running at 190 mph with the two different gears.  Last year, a 3.89 gear was used. At 180 mph, you’d better be running in 4th gear (which means 1:1 and the speed coming into the rear end gear is the same as that coming from the engine.  The engine speed required to go 190 mph is this 3.89*2270 rpm = 8830 rpm.  This year, with a 4.00 gear, you’d need to be running at 9080.  If you’re running 200 mph, last year you needed 9293 rpm and this year it would be up around 9556 rpm.  You’re basically running 250 rpm (or so) higher this year than last year at the same speed.

Andy Randolph, Engine Technical Director at ECR Engines tells me that engines were running at 9800 rpm for sustained times.  Although the engine rotates that fast at some places, doing it continuously places huge stress on the mechanical parts – that’s why most of the failures were due to mechanical breakage.  (Because I know he’s too modest to mention it, I’ll point out that none of the engines that had problems at Kansas were from ECR.)

The Math

For those of you wondering about where my numbers come from, here’s a calculation I did for Las Vegas.  The only difference is the slight variation in tire circumference.  If you plug in the numbers to the formulas and don’t get what I got above, I probably screwed up on the calculator.

Left-side and right-side tires have difference circumferences.  The circumference of a left-side Vegas tire in 2008 was 87.4″, while the right-side tires had a circumference of 88.7″.

To calculate how many times the tires rotate each minute, I first convert the speed into inches per minutes.  I know to use those units because I’m trying to get an answer in revolutions per minute, so I need to convert hours to minutes. I also know that every time a right-side tire makes one complete rotation, it has traveled 88.7 inches, so I’m going to convert miles to inches because I know I will need that later. Convert 45 mph to inches:

45 mph corresponds to 47,520 inches per minute. Looking at the right-side tires (for no particular reason), the car travels 88.7 inches every time it makes one full rotation. The number of times the tires rotate each minute is 536 rpm, as shown below.




Bristol: Banking vs. Distance

Bristol Motor Speedway announced that they are grinding down the upper groove of the track to decrease the progressive banking.  My (to-scale!) sketch of what I think they are doing from the press conference and the tweets (thank you so much Nate Ryan!) is below.  The 2007 re-do introduced progressive banking, with essentially three lanes.  The lowest lane had 24 degree banking and the upper lane (nearest the wall) had 30-degree banking.  I’m guessing that the middle lane was 27 degrees – haven’t been able to verify this, but it’s probably not far off.  (My values are from the Bristol Motor Speedway website.)

The change (again, I’m inferring this from the press conference and tweets) is to decrease the banking on the upper lane.  Assuming they make the banking the same as the middle lane (their graphics seem to suggest this), the new surface would look something like the line in red.

Why does this make a difference?  Briefly, banking helps a car turn.  A car driving into the page needs a force left to make a left turn.  The banking provides additional force, which adds to the force provided by the tires.  The force scales like the speed squared – the more turning force, the faster you can go.  All other things equal, a car goes faster on higher banking.

If a track is uniformly banked, going around the outside of the track gives you no advantage:  you have the same turning force, but the outside of the track forces you to drive a further distance.

By putting the progressive banking at the edge of the track, you increase the distance the car has to travel:  the advantage in speed you get from the additional banking is (somewhat) offset by the longer distance.  How effective this is at creating more grooves depends on the relative advantage of distance vs. speed.

There are other factors, such as how much rubber is laid down in each groove, and setups that may make the car handle better in one part of the track than the other, that have to be considered.