UPDATE:  I talked to a number of people this week while trying to resolve this because it was really bugging me not having a consistent answer.  They have some pretty convincing evidence that the angle was indeed significantly shallower than 90 degrees; however, if you run the numbers, I can’t get anything consistent with 100 g and a contact time of 0.008 seconds.  Just goes to show you what a challenge it is to try to figure out what happened without the evidence.  So despite how much it looked like a straight-on hit, it wasn’t.  It’s amazing to me that the camera provides such a distorted picture of reality.  I may never look at a NASCAR race the same way again unless I’m actually there.  So I’m wrong about the angle, but I think (unless I get data otherwise), I’m probably right about the time.  This is exactly why scientists have peer review.

Here’s where I think I got confused:  The attitude of the car (which way it is pointed) can be very different than the motion of the center of mass, especially when a car is sliding instead of rolling.  So even though the car hits head on, the center of mass can be at a shallow angle.

ORIGINAL POST:

While there is a lot of negative press about NASCAR keeping things “secret”, there really are some good reasons for not releasing crash information: One is simply that the data are pregnant with the potential for misuse. As is the case with everything from baseball to K-12 education, people want a single number to measure things against each other, even when it is meaningless to do so.

Sadler’s Pocono crash was really scary.  Thank goodness for the HANS device, the Hendrick carbon-fiber composite seat, and the redesigned car.  The folks at the NASCAR R&D Center – Tom Gideon foremost among them – have all the data (and the car) and will be analyzing it to learn even more about how we keep drivers safe.  Tom was one of the primary voices arguing for safety well, well before four NASCAR deaths in 2000-2001 made the need for action impossible to ignore.  Tom worked for GM Racing when racing safety wasn’t even on most people’s radars.  NASCAR didn’t start requiring black boxes on cars until the early 2000′s, but Tom was very active in advocating for black boxes in race cars in NASCAR and other racing series throughout his entire career.  He and John Melvin (another motorsports safety pioneer) gave a paper on the history of black boxes in motorsports at the last SAE Motorsports Conference.  (Indy cars were recording data as early as 1933!)  Tom is one of the good people in the business.

The biggest concern in a crash is the maximum force felt by the driver.  That force is the product of the driver’s mass times his acceleration.  Acceleration is how fast you change your speed, so we can also write the force in terms of the rate of change of the speed, or in terms of the acceleration. In the equation at right, the triangle v means the change in speed and the triangle t means change in time.  This equation says that if your change in speed is large (Δv large), it hurts. If you stop very quickly (Δt small), it hurts.

People talk about crashes in terms of “gs”. A ‘g’ is the acceleration due to gravity and it has a value of 32.2 feet per second per second, which means that, each second, your speed changes by 32.2 feet per second.  Everyone on Earth is (give or take a little depending on altitude) experiencing 1g of acceleration.  The force the Earth exerts on you is equal to your weight times the number of gs.

Let’s temporarily transport ourselves to another planet, exactly like Earth, but twice as massive. The doubled mass makes gravity twice as strong, so the acceleration due to gravity on this planet would be 2g.  If you weighed 150 lbs on Earth, you’d weigh 2 x 150 lbs = 300 lbs on this new planet.  (Don’t get me into the difference between mass and weight in the English unit system.  This is so much easier in the metric system.)  The ‘g’ is a handy unit:  multiply the weight of the object in pounds times the number of g’s  (unitless) and the product is the force.

Here are a couple caveats about “g” numbers:

1.  The black box is usually placed on the drivers’ side of the car, but it is attached to the car, not to the driver.  The car is designed to absorb the energy of the crash so that it is not transmitted to the driver. The seat is designed to absorb energy from the crash so that it is not transmitted to the driver.  The number from the black box isn’t necessarily an accurate measure of the driver’s experience.  If two cars’ black boxes have the same readings, but the drivers are in different types of seats, or the angles or speeds of the crashes are different, the drivers could experience very different forces.  The number is, however, a number that can be compared to other crashes in which the instrumentation was installed similarly.   NASCAR has a database of every bit of information they can gather from race car crashes and everything they learn during the investigation will be added to what they already know.

2.  You can not assume a spherical NASCAR driver (Make your own jokes here), or a spherical car.  The distance from axle to axle is 110 inches, so different parts of the car could experience very different forces.  The driver’s torso and head move very differently than his arms, for example.  The FIA (Federation Internationale de l’Automobile) is developing accelerometers (meters that measure acceleration) that fit into the radio earpieces drivers already wear.  These incredibly small devices can be less than a few millimeters cubed in volume.  If I were a driver, I’d want access to that technology so that I’d have an actual, real measurement of what happened to me.  Forget the car.  That is much more important than the deceleration of the car.  Something else we’ve learned is that the motion of the internal organs inside the body relative to the body is really important.  The driver may be strapped in securely, but remember that your brain, heart, lungs, stomach, etc. are basically floating around inside your body.  They don’t stop at the same time as the outside of your body.

Jeff Thompson, who’s done some forensic engineering (working backward from the scene of an accident to figure out how the accident happened) did a crash analysis to better understand what exactly happened.  A couple people asked me what I thought about the accident, since their intuition didn’t jibe with Jeff’s results.  Our intuition about the physical world is often wrong, so when I got back into town on Wednesday, I started looking into the situation.  Incidentally, Jeff is part of a great outfit called ten80 education, which has developed a lot of really neat RC car activities for kids of all ages.  They are doing a really neat job using motorsports to get kids (and their parents) interested in racing.  Jeff is also one of the good people in the world in my opinion.

Let”s start by calibrating ourselves with something closer to our own experience.  If you slow from 60 mph to a stop in a tenth of a second, you experience an acceleration of 27.3 gs.  If you weigh 150 lbs, that’s 4,095 lbs.  If you can extend that time to two tenths of a second, you halve the acceleration to 13.6 gs and 2,047 lbs.  The figure of merit  most safety researchers use in a crash is delta v – the change in speed.  That’s proportional to the product of the acceleration times the time.  I’ve written the formula, so all you have to do is pull up Excel, plug in the time of the collision and the number of ‘gs’.  If you do that, you get the graph shown on the right. (If you click on the graph, you can get a larger version of it, which is a little easier to read.  This is true of most of the diagrams in my blogs.)

I’ve drawn three lines representing 80 g, 100 g, and 120 g.  The horizontal axis is the  collision time — the time during which the speed of the car is changing, which is usually the time during which there is contact between the car and the barrier.  If you use 100 gs and a collision time of about 30 milliseconds (three one-hundredths of a second), then the change in speed would only be about 66 mph.  This confused me a little because my perception from watching the video was that Elliott’s crash took place over a relatively long time (as crashes go).  That didn’t seem consistent with Elliott’s reaction, either.  The berm into which he crashed is an earthen mound surrounded by Armco barriers.  The mound is pretty wide, but if you look at the video, you can very clearly see dirt being ejected from the other side.  That’s good because that’s energy absorbed by the barriers.  (If this crash had been into a concrete wall, it would have been an entirely different story.)

Another reason I would argue that the crash was longer is that the car was severely smushed, which means the center of gravity traveled further than it would have if the car bounced right off the barrier.  One of the front wheels was pushed back at least a foot or a foot and a half.  The time it takes for the center of mass of the car to travel 2 feet at 180 mph is 0.016 seconds.  That doesn’t even begin account to account for the time it took to crush the front end of the car and how much that slowed the car down.

We can break the car’s speed into two parts: a part along the wall, and a part perpendicular to the wall, as Jeff did in his analysis.  I’ve shown the part parallel to the wall in blue and the part perpendicular to the wall in red.  The angle at which you hit is important because the change in speed — along and perpendicular to the wall — is proportional to the force felt.

I’ve shown two angles in my drawing. The one on the right is a relatively shallow angle. The blue arrow is large and the red arrow is small. This is good because the force you feel when you hit the wall is (more or less) proportional to the length of the arrow in that direction. You feel a small force when you skim the wall. When you hit it at an angle, the component perpendicular to the wall grows.
It gets slightly more complicated, as I’ve shown in the next figure. The directions change when the car bounces off the wall. If you just look at the part of the motion parallel to the wall, both arrows point in the same direction.  The component of the motion that is perpendicular to the wall changes direction. That means that you actually undergo a much larger change in speed. If you were going 60 mph to the right, and you bounced off a wall so that you were going 60 mph to the left, you’d have a perpendicular speed change of 120 mph.

In most crashes with a barrier, the car continues in the direction it was originally headed and the change in speed in that direction is usually pretty small compared to the perpendicular component.  It isn’t, however, necessarily negligible, especially if the car hits at an angle and the wall creates a torque that causes the car to spin.  The drawing at right doesn’t show much difference between the before and after longitudinal speeds ; however, if the car slowed down a lot during the collision, it is possible that the force parallel to the wall was not negligible.  The angle at which the car hit the wall is incredibly important:  A glancing blow vs. a head-on collision.

Jeff makes a very important point I wouldn’t have thought to consider:  He notes that we have to take into account the orientation of the camera with respect to the  collision.  Have you ever looked at something exactly head-on?  It’s impossible to tell how far away it is.  The lack of perspective, he argues, makes the angle look very different than it is.  I’ve reproduced his sketch from his blog at left  (How I wish I had one-tenth his drawing skill!) His analysis comes up with an impact angle of 18 degrees, a change in perpendicular speed of 56 mph and a collision time of 0.008 seconds.  Those numbers just didn’t “feel right” to me.

Knowing the impact angle precisely is critical.  Calculating the perpendicular speed depends on taking the sine of the impact angle. Sine is a very nonlinear function (well, duh…), so not having an impact angle introduces significant error in the numbers.  The table below shows how the perpendicular speed changes with angle.  A change in angle of three degrees changes the perpendicular speed pretty significantly.  A change of 10 mph in impact speed corresponds to 21g if you assume a collision time of 0.01 seconds, (or 7 g if you assume a collision time of 0.03 seconds).  The sine of 90 degrees is 1, so a head on collision would correspond to a 180-mph perpendicular impact.

The video sure looks like Elliott hit at a 90-degree angle, but Jeff made his argument well.  Still, the 18-degree number was really bothering me, so I spent some more time looking at the video of the race and perusing Google Earth to try to understand where exactly the accident happened.  The video revealed that Google Earth isn’t necessarily very recent: the picture of the track doesn’t exactly match what the television shows.  In particular,  there are two perpendicular pieces of wall that run from the barrier to the access road that are not shown on Google Earth.  (You can see one of them in the still below).  So the angle of the bend might be different from what I’ve calculated, which is about 167 degrees.

The angle of the barrier isn’t the critical thing: the angle of impact is.  Here, the video gives us some additional information.  First, when the car hit the barrier, it sent dirt flying (the dirt is mounded a little over the Armco.)  Conservation of momentum allows us to use the dirt to tell us something about which way the car hit the barrier

That, in combination with the skid marks coming in, shows that Elliott actually hit the barrier pretty much head on, as shown in the diagram below (pulled from the ESPN coverage during the red flag.)  I think this makes it pretty clear that Elliott’s car was forced into making a hard turn and he hit the barrier nearly perpendicularly. (Thanks to Dr. Bob for watching out of the corner of his eye during the race and insisting that there were clearer pictures of the skid marks.  I was in an airplane during the race.)

You’d really like to slow down the car prior to its hitting anything.   Most large tracks have removed most of their infield grass because the coefficient of friction (especially when the grass is wet) is much lower than it would be on asphalt (even wet asphalt).  A high coefficient of friction (often attained with gravel traps, which aren’t great for the car, but much better than hitting the wall) helps scrub off some of the speed so that you’re not going as fast when you hit.  The explanation I heard is that Pocono is a designated wildlife refuge and that makes it difficult for them to remove grass.

If you were wondering (as I was) how Pocono installs 25 acres of solar cells and can’t pave over infield grass because it’s an environmental refuge, the answer is that the solar forest was put on some existing parking lots.  Major kudos to Pocono for taking this expensive, but important step to green.  More on that in another blog!

Let’s revisit the graph that tells us how speed change and time are correlated.  Here’s an expanded version of my earlier graph.  Let’s assume the worst possible case:  180 mph in and 180 mph out at a 90-degree angle (that’s exaggerated because a lot of energy was transferred to the barrier, but for the sake of worst-case argument…), this would suggest that the time of impact would have been a tenth or two-tenths of a second.  Reviewing the video, that’s not unreasonable.

We can never make racing 100% safe.  Buddy Baker mentioned on his Sirius radio show that the hardest hit he experienced was due to a stuck throttle at Martinsville, a track where speeds are rarely high and the thought of putting SAFER barriers around the inside seems almost silly.  Virtually all types of motorsport have had a reactive attitude toward safety, making changes only after something serious happens.  The sign that this attitude is changing is that the seriousness of the incidents that spawn changes has decreased.  (See Las Vegas and Watkins Glen for example.)  Pocono announced they were going to make changes in the interior barriers after the last race, but there simply wasn’t time to do it before this race.

There is no reason why the highest-speed tracks shouldn’t be required to have SAFER barriers around the entire racing surface, inside and outside.  Yes, it’s very expensive.  In Pocono’s case, there aren’t even existing walls on which to build the barriers, and it is not a coincidence that the fastest tracks are frequently also the longest.  But perhaps NASCAR should set a goal that Elliott’s impact remains the hardest the sport ever sees.

It’s really easy to knock NASCAR.  It’s equally important to praise them when they get stuff right.  Kudos to NASCAR for all they’ve done – requiring the HANS, doing series research into safer seating, and designing the new car – that allowed Elliott to walk away from what could have been a disaster for the sport.  Here’s hoping they continue moving in a proactive manner when it comes to safety.