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The Science of Fast

Will You Be Able to Tell if NASCAR Cars are Slower in 2019?

Montage of speed-related pictures

When is the answer to better racing slower cars? It just might be for NASCAR.

Note: This post analyzes the change in speed due to the new rules package. Please don’t interpret it as my defending the rules change. I won’t be making up my mind on whether this package ‘works’ until after Phoenix at the the very earliest. I share some of the drivers’ worries that instead of a level playing field, we’re going to get random winners. But I’m going into it with an open mind and we’ll see.

Why Slower?

For years, NASCAR has battled ‘the passing problem’. Teams have made huge gains in aerodynamic downforce over the years. These gains don’t just affect peak speed: If you have more grip, you can corner faster. Higher corner entry speeds narrow the racing groove, which makes it difficult to pass. The theory is that decreasing corner entry speeds will widen the groove and allow for more passing.

Aerodynamic downforce (Fd) depends on speed (v) squared.

F_d \propto v^2

The squared is important:

  • If you double the speed, you get four times the downforce.
  • Conversely (and more relevant to our purposes), to reduce the downforce by a factor of 2, you only have to reduce the speed by a factor of the square root of two (which is 1.41)

The graph below compares the mechanical grip of the car (i.e. its weight) with its aerodynamic force. The weight doesn’t change with speed, but the aerodynamic downforce does. The faster you go, the larger the fraction of your downforce that is aerodynamic.

A graph comparing mechanical and aerodynamic grip.

NOTE: These numbers are for an earlier rules package, but they give you an idea of how significant aerodynamic grip is.

The easiest way to slow down a racecar is to decrease its engine power. That’s why NASCAR is using differently sized tapered spacers at different tracks in 2019.

A bar graph showing how the effective horsepower changes with various sized tapered spacers and restrictor plates

So Why Give the Cars More Downforce?

It seems counterintuitive that, at the same time they took away engine power, they increased the spoiler and splitter sizes. That’s because the situation is much more complex that simply total downforce. Different corners of the car experience different forces.

  • When turning left, the mechanical load shifts to the outer wheels and the inner wheels lose grip.
  • When accelerating, the rear wheels gain grip and the front wheels lose it.
  • When braking, the front wheels gain grip and the rear wheels lose grip.
  • The aerodynamic downforce depends on the attitude of the car, so when the car turns, brakes, or accelerates, the aerogrip of each wheel changes.
  • Proximity to another car (or a wall) near a car also changes the aerodynamic forces on the car.

Remember that the goal isn’t simply lowering speeds: It’s lowering corner entry speeds. You don’t need to slow the cars down everywhere. Also, you want the cars to have enough stability to be able to race close to each other. That’s the only way they can pass.

So NASCAR took away horsepower, but made a number of other aerodynamic tweaks. NASCAR took from the engine, but gave back a little of what they took on the body.

How Much Slower?

All some NASCAR fans heard was that they were dropping 200 hp and there was a hew and cry from some NASCAR fans that this rules package would Ruin. NASCAR. Forever.

In reality, the change in average lap speed at the affected tracks is likely to be in the 7- 12 mph range. Some people still think that’s a big deal.

But can you even tell whether a car is going 200 mph or 190 mph?

CAVEAT: Record books record average lap speeds. If you slow corner speeds, average lap speed will slow, but we don’t know how much slower the cars will be on the straightaway — if they are slower at all. Everything from here on out is dealing with average lap speed.

CAVEAT 2: As I’ve discussed before, the speeds reported are not measured. Lap times are measured and the average lap speed is calculated using the standard track length. That doesn’t account for different lines around the track. I’m using speed here because that’s what people complain about, but it would be the exact same analysis if I used lap times.

Speed vs. Time

One of the very first equations you learn in physics is the equation that relates average speed (v) to distance (x) and time (t):

x=vt

The television broadcasters like to show this formula when talking about pit road speed and, much to my consternation, someone gets it wrong at least once every year. So watch for it and inundate them on twitter if they do it again this year.

It’s not like this is a difficult formula to remember. Speed is measured in miles per hour. To get a distance (in miles) from miles per hour, you have to multiply by time. Scientists call this dimensional analysis. Regular people call it common sense.

Our perception of speed is really our perception of the time it take an object to traverse a distance. Since the distance the racecars travel doesn’t change, what we’re really talking about is how we perceive time.

What is Time, Anyway?

There’s a philosophical answer to that question and a physics answer. Let’s go with the physics answer first.

The second was originally defined at 1/86,400 th of a mean solar day. (‘Mean’ meaning ‘average’, not ‘cruel’.) This was slightly less than robust, so in 1960, the world agreed that:

One second is the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom when the cesium atom is ata temperature of 0 Kelvin.

National Institutes of Standards and Technology

Believe it or not, that is actually much clearer than the first definition. But for us, it doesn’t really matter because what’s important here is how we perceive time, not the actual time.

Time vs. Time Perception

While the second is a very precisely defined quantity, your perception of it differs if you are getting married or sitting in the dentist’s chair. They may both last the same time, but it sure doesn’t seem like it. And there are people who devote their lives to trying to understand why this is.

The study of time perception requires psychology, linguistics and neuroscience. It considers time, not the objective way we measure it, but the way human beings experience it. And human beings’ experience of time is highly subjective.

  • People tend to remember relatively recent events happening further back in time then they actually happened; conversely, events from the far past are often remembered as being more recent.
  • Vierodt’s law says that shorter intervals tend to be overestimated while longer intervals tend to be underestimated.
  • How long you perceive a task to take depends on how motivated you are to do it and whether you are focused on doing the task or just having it done.
  • Your emotions and mental state can change how you perceive time.
    • People who are depressed tend to more accurately estimate the passage of time.
    • Fear tends to make time seem longer.
    • Even something like very loud or very high pitched noises can skew our perception of time. You will perceive a loud car as being faster than a quiet car

Hence my husband’s suggestion that all NASCAR really needs to do is add 10 deciBels to the engine so everyone would think the cars were faster.

The Data

The only numbers we have with the new rules package so far come from the late-January test at Las Vegas Motor Speedway. So let’s use LVMS as our test track and take a look at historical pole speeds. (Data from the good folks at racing-reference.info, as always.)

The history of pole speeds as a function of time at Las Vegas Motor Speedway
The red square represents the 2018 fall race.

If we consider only data after the track was reconfigured in 2006, you can see that the pole speed increased almost 15 mph from 2008 (182.3 mph) to 2016 (196.3 mph). The most recent pole speed (fall 2018) was 188.1 mph. The pole speed that spring was 191.489 mph.

Now let’s look at the data from the January testing sessions. There were three test sessions and 50 total runs. These are the top speeds for each car from all three sessions.

A histogram of the top speeds for the January 2019 test at Las Vegas Motor Speedway

Of the 50 runs reported

  • 22 (44%) were between 177 mph and 178 mph.
  • Only 5 runs (10%) were above the median speed
  • This leaves 22 runs (44%) below the median range.
  • The highest speed in a team car was Jimmie Johnson on Thursday morning, at 178.885 mph.

OUTLIER EXCLUSION: Ross Chastain reached 183.16 mph on Thursday morning, but a) that was in the heavily instrumented Chevy Wheel Force car and b) No one else got anywhere near that speed during the entire test. I’m being conservative and going with Johnson’s speed.

That’s the Clock: What About Me?

What would you see if you were sitting in the stands at LVMS?

The front straightaway at Las Vegas is about 1800 feet. How long does it take to drive that distance?

The time it takes to go 1800 feet at different speeds from 178 to 188 mph.
  • If you drove at last year’s pole speed (188.1 mph), it would take 6.524 seconds to make it all the way from Turn 4 to Turn 1.
  • If you drove at the top speed in the testing session (178.885 mph), it would take you 6.861 seconds.

A difference in speed of 9.236 mph corresponds to a difference in time down the frontstretch of about a third of a second (337 milliseconds). The blink of an eye takes about 300-400 milliseconds.

via GIPHY

The difference we’re talking about ‘slowing the cars down’ is

  • About a third of a second down the frontstretch
  • A little less than 2 seconds over a 1.5-mile lap
  • 8.9 minutes over the course of a 400-mile race.

Will I Notice That?

Yes — because you’ll be looking for it.

Unfortunately, we can’t do the experiment because you already know the cars will be slower. Your expectations impact what you see. To really test this, we’d need to have you at a track, have a driver make laps at two different speeds and ask you which one was faster and by how much. And we’d have to do it with maybe a thousand people to get a range of opinions.

It would be like when you visit the eye doctor and do the ‘Which is clearer: 1 or 2’ thing. When we’re close, I can’t tell much of a difference. I bet you’d see the same thing with the track experiment.

In general, people aren’t very good at estimating speeds. A 2016 study from the Centre for Accident Research and Road Safety (in Australia) found that drivers did a miserable job estimating how fast trains were coming when approaching railroad crossing.

When the train was 350 m (382 yards) away

  • Drivers estimated a train going 130 km/h (~81 mph) was only going 90 km/h (56 mph) — a 29% error in judgement.
  • That means the drivers thought they’d have 14 seconds before the train got there when, in reality, they only had 10 seconds.

The farther away the train was, the worse their speed estimates were. When the train was 1100 m (1200 yards) away and going 130 km/h (~82 mph), people estimated the train was only going 75 km/h (47 mph) – a 44% error in judgement.

The lesson here might be that if you think you just have time to scoot past a train crossing before the train gets there, you probably don’t.

A 2009 paper in the journal Vision Research found that people are also very bad at estimating the speed of a flying object, such as a ball. And there are plenty of studies that show that people have a really, really hard time interpreting the motion of accelerating objects, even if those objects are moving slowly.

The takeaway: If you’re one of those people who’s already convinced that the cars are going to be slower and it’s going to ruin your enjoyment of the sport, it’s very likely that this is exactly what is going to happen.

But Is Racing Really Just Speed?

I’d argue no. So would NASCAR, because the entire point of this speed-reduction exercise better racing at intermediate tracks.

I love the people who call into radio shows and say that NASCAR should just use a rules package that is fast and allows for close racing. Believe me, if that were possible, they’d already have done it. That’s what they’d like, too. But the laws of physics say otherwise. And the laws of physics always win.

If all you care about is how fast the cars go, you’d probably find drag racing more your, uh, speed. If you want fast stock cars, follow the folks setting land speed records — like Bob Keselowski, who shattered the all-time stock car speed record by 30 mph at the Bonneville Salt Flats last September by running 271.84 mph.

The best part of this story is that this Dodge Charger was driven in a 2010 Martinsville race, crashed, and repaired. The second-best part is the headlines: “Retired NASCAR Cup Racer Makes 271.89-MPH Pass, Smashes Class Record at Bonneville” and “1989 ARCA Champ Keselowski Sets Speed Records in Utah“. That’s Bob Keselowski on the left and, I think, Bobby Gerhart on the right, who was there to earn his license.

NASCAR fans have been complaining about lack of passing for years. NASCAR has made a number of attempts to address it given the constraints of time and money. I guarantee you that all of this is being taken into account as they design the Gen-7 car.

For me, watching two cars run fender to fender as one tries to pass the other is the best part of racing. It’s good at Bristol at 100 mph and it’s good at Texas at 200 mph. And if I get a choice between Texas at 200 mph with minimal passing and Texas at 190 mph with more passing, I’ll take the latter, thanks.

In summary, the world is not fair. No one’s figured out a way to get high speeds and passing with the current car. Sure, you could solve the problem by throwing money at it, but that’s not a possibility in the current climate. What you see is highly influenced by what you expect to see. So I encourage you to go into Atlanta with an open mind and fingers crossed.

Thanks to @dmcgrew, who figure out I’d transposed the digits in the calculation of time and had 6.681 instead of 6.861. I can’t blame this one on Excel. I messed up typing! Thank you, Drew!

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