It was sad

It was sad,….

A lot more was lost this week than just a race team. In a time long, long ago, in a place that now seems far, far away, 1958, Richard Petty began his racing career.

Years ago a popular "gather-'round-the-campfire" song for children at summer camp was a tune which had a chorus of,…

It was sad (…oh, it was sad)

It was sad (…it was sad)

Oh, it was sad when the great ship went down,…

An oddly haunting refrain about the sinking of the Titanic.

A great ship went down this week, Richard Petty Motorsports, RPM. Only a couple of years more than a decade ago companies stood in line, literally, to pay (a lot) to have a little decal on the B pillar of the 43 car. But times change and somehow RPM didn't, they stayed in Level Cross when all the other teams set up shop in the Concord-Mooresville area. NASCAR entered the engineering era, driven in no small part by Hendrick who hired Gary Eaker from the GM wind tunnel to run their aerodynamics program--with Ray Evernham who obsessed about data for an up-start kid named Jeff Gordon; the age of specialization produced a string of championships.

The change was so dramatic that by 1994 Earnhardt Sr. remarked "there ain't gonna be no more Alan Kulwicki's."  As prophetic as the grammar was bad, the age of the lone owner, builder, crew chief, driver was over.

Where RPM had been fast on the track they were now slow on the learning curve. By the time RPM did move to Concord it was too little too late. Like watching a Greek tragedy unfold, this day of final doom seemed inevitable when RPM merged with GEM, Gillett-Evernham Motorsports, the sorry remnants of what had been Evernham Racing. GEM was anything but a gem, as Gillett seems to have gone from junk bond scandal to hockey to football teams in England (otherwise called soccer) to NASCAR, each step along the way building a larger house of cards on ever larger amounts of debt.

The sad part is that by the time RPM tried to join the modern era the choices were so slim it made the GEM deal seem like a good idea, or the grasp of a drowning operation clutching at anything still afloat.

It is impossible to imagine that Jack Roush ever wanted to beat Richard Petty as a car owner this way--on the track, yes, every week--by scheming mortgage deals: never.

NASCAR has become a "product," fueled entirely by sponsor dollars, defined by marketing, the great ship of racing has slipped beneath the sea,…

It was sad (…oh, it was sad)

It was sad (…it was sad)

Oh, it was sad when the great ship went down

Deep Thought on Big Hits

Deep Thought reflects on more than an 80 g acceleration, theta, and dt

For a very funny "Onion" sort of piece by Jeff Meyer go to  http://www.frontstretch.com/jmeyer/30604/

And now the real Deep Thought
There are three parts to determining what effect an acceleration has on an object, including a human body: magnitude (how much acceleration); direction (an angle, theta); and the time duration of the acceleration, dt.

Numerous medical studies have shown that a human can withstand surprisingly high accelerations, more than 100 g's (one hundred times the acceleration of gravity) provided that the duration is very short (on the order of a millisecond, 0.001 seconds).


While NASCAR has indicated the magnitude of the acceleration sustained by the 19 car, they've said nothing about where the accelerometers were placed, the direction of the acceleration or the duration of the acceleration. But then, high g accelerations make for good headlines.

The 19 car was sliding down the track as well as heading for the Armco barrier.

 
 
 
 Note the location of the TV camera and the extreme foreshortening of its images.






Looking at the event area in more detail, indicates the path and orientation of the 19 car as it slid and rotated, heading for the Armco barrier.

Acceleration is a change in direction and/or speed of an object. Mathematically if one looks at the velocity of the car going into the impact event and the velocity of the car leaving the impact event it is possible to construct a moment diagram of the event itself.

Momentum is shown in a flat plane, with two directions X (along the Armco barrier) and Y (perpendicular to the Armco barrier); the Z direction, straight up, is the angular momentum of the object (rotation). If one takes the sum of the momentum vectors, they must close, that is the sum of momentum going in minus momentum leaving must equal zero. The dV vector is the change in velocity during the impact event.




From what little information is available on You-Tube videos it would appear that the total acceleration for the center of gravity of the 19 car was on the order of 110 g's.

The duration was very short, video frame rate is 30 frames per second, the 19 car changes from going forward to going backward between two frames, i.e., 0.033 seconds. The peak acceleration probably lasted for less than 0.008 seconds.


The short of the whole story is that the track needs to be modified, the grass area between the track and the Armco barrier is less than 100 feet, not enough to slow a car while sliding through wet grass. One of the many people who have emailed me since my previous blog post suggested sand traps such as you see in F1 tracks, good idea but not enough room. The Pocono track back stretch is scary narrow for cars going 180 or 200 mph.

Now on to Watkins Glen and the fact that in the early days of auto racing, all courses were road courses.

Reconstructing the 19 car

Mathematics gives you X-ray vision

Even better than the comic book version of Superman's X-ray vision mathematics makes it possible to "see" what is otherwise invisible.

The wreck of the 19 car at Pocono on Sunday was spectacular and perhaps an engineer's view might add a bit more insight beyond what was on television. For all the cameras the television networks bring to a race the wreck of the 19 car nearly escaped notice, until the aftermath became apparent. Search as they might it seems as if there were no images leading up to the impact of the 19 car with the inside wall (Armco barrier) on the back stretch of the Pocono track. However, mathematics allows one to look back in time and reconstruct the event with some degree of veracity.

There's an entire branch of engineering studies called "accident reconstruction" and having worked in that business this is a quick summary of what I saw on TV. Ordinarily a report on an accident would entail hundreds of hours of collecting data, detailed examination of the pieces of evidence (car parts, skid marks, measurement of impact points along the wall, etc.) followed by hundreds of hours of calculations. What follows is the result of a few calculations and measurements done from images gleaned from You-Tube postings on the internet.

After the parts stopped flying around, the 2 car and the 19 car were fairly well demolished, the 19 car showing much the worse of the bargain. This image is from Turn 2, the Tunnel Turn at Pocono which is patterned after one of the Indy 500 turns, in fact it is just about a perfect replica. The final skid marks of the 2 car are easily seen in this picture with the remnants of the 19 car sitting in the middle of the track some distance back.

A map of the track traced from a Google image provides some orientation of where this took place.

 

 

 

 

 

A more detailed sketch is shown here of the location of where the event with the 2 and 19 cars took place 19; again traced from a Google map and matched up with images from You-Tube postings.

 

Several images of the area were posted during the TV broadcast, some apparently taken from a helicopter.

 

 

 

 

 

A couple of salient features are immediately apparent; the skidding trail left by the 2 car, the engine block of the 19 car at the edge of the track, and the skid marks of the 19 car in the grass and on the track.

 

 

 

 

 

 

 

 

The scale of the track and camera angles were deceptive in the TV broadcast, things were not exactly what they seemed to be at first glance; particularly the impact angle of the 19 car. Translating the information in this photo to the traced map yields the following results.

The foreshortened view of the TV camera looking down the back stretch was particularly deceptive, not by intention but rather it provided the only images available. The 2 car in the middle left of the image is more than 400 yards from the camera, and the 19 car almost at its impact point in the lower right of the frame is 200 yard from the camera.

 

 

 

 

 

From the camera angle it appears as if the 19 car plows square, head on into the wall; the skid marks shown in photographs of the area indicate that the 19 skidded some distance from its impact point to its final resting point (FRP), and at a fairly shallow angle to the inside wall (Armco barrier) of the track.

 

The reflected angle of an impact is roughly equivalent to the incident angle, i.e., an object bounces off a wall, or fence, at about the same angle as it approached. You can conduct a simple experiment to verify this effect. The shallower, flatter, the angle is of the thrown ball with respect to the ground, the flatter the rebound is.

With a bit of trigonometry and a momentum diagram it is possible to reconstruct the approach of the 19 car to its impact point.

When this information is added to the TV image, the result is a bit different than first impressions. The 19 car appears to be driven straight into the Armco barrier of the inside wall of the track.

But it isn't.

The angle with the wall is actually about 20 degrees.

The 19 car rotates after its impact, although due to the low friction in the grass its center of gravity travels in nearly a straight line, like an Olympic racer on skates who falls in a corner, their body continues to slide on almost a straight line even though they're rotating as they skid.

The swirling skid marks in the helicopter view picture evidence the rotation of the 19 car as well as the fact that the front end damage is much greater on the right front than the left, and the engine didn't leave the car until about 200 ft after the impact point (when the 19 car went over the access road).

So while the 19 car took a huge hit, the perpendicular impact speed with the wall was probably on the order of 50 to 60 mph not 150 or 170 mph, the forward speed of the car.

While a 50 or 60 mph hit is huge, one should temper the comments on the structural integrity of the new NASCAR design a bit. Most new street cars with the latest air bag technology would have protected the driver in this impact just as well; the best of new cars also include crumple zones at the front of the car to dissipate energy in a collision. A passenger car is designed so that in a frontal impact the engine subducts under the vehicle, then front frame bends and crushes, leaving the passenger compartment intact. When I worked at Ford my office was next to the full-scale crash test facility (where the crash test dummies take one-way rides) and it was very instructive to examine the results of their tests.

 

 

Kepler in 1590 Explains Darlington in 2010

Kepler Explains Darlington

    The mascot for Darlington is a revised Kepler with a little help from the Hubble telescope and a large inspirational contribution from Gerrit Dou.

Kepler, an astronomer of the late 1590's, made the observation that "all things happen for a reason, and those reasons are the fundamental forces of the universe. If you duplicate the reasons you replicate the results."

This simple statement by Kepler essentially started all of modern science and mathematics.
Although known as an astronomer Kepler never made any observations of his own, his eye-sight was terrible; he worked out the mathematics from other people's data; notably that of Tycho Brahe. Delightful book, Heavenly Intrigue by Anne-Lee Gilder and Joshua Gilder, which suggests that Kepler may have murdered, poisoned, Brahe in order to gain possession of the trove of celestial observation data collected by his employer, Brahe.

One of the interesting bits Kepler gets credit for discovering is the fact that the quantity of

(V ^2 ) r,.. this is velocity squared, i.e., velocity multiplied by velocity then multiplied by radius r,

is the same for all planets; V is the velocity of the planet orbiting the sun, squared, multiplied by the mean radius, r, of its orbit yields the same number for all the (then known) planets. Kepler couldn't explain why this might be true, it was just a fact of observed data. The explanation would have to wait for almost 100 years and Newton, Leibnitz and the Bernoulli's.


The planets are held in their orbit by gravity; a race car is able to navigate a turn due to the pull of the wheels keeping it on the track which provides the same function as gravity does for the planets. Race cars can navigate a corner faster if a track is banked, higher banking allows higher speeds; and larger radius turns also allow higher speeds. If we write these processes into an equation and call it the Kepler Index, KI, then

where QS is the qualifying speed of a track, the Greek letter Beta, B, is the banking angle of the turns and r is the radius of the turns.

The Kepler Index, KI, is essentially the same number for all tracks,... except the SMI trio of Atlanta, Charlotte and Texas (more on that in the next post).

 Moreover, Qualifying Speed can be fairly well predicted from the banking angle and radius of the turns on a track.

Whereas the size of the track alone is not very useful in predicting qualifying speeds but it is informative; note the difference between the qualifying speed at Pocono with its three distinct corners compared to the symmetrical tracks of Indy, and Daytona, with all three tracks the same size, 2.5 miles around 1 lap.

TV does not convey the distinctive nature of the various tracks, the contrasting differences are astonishing. Darlington is shown outlined in Black and it is easy to see why it was called the first super speedway, it's nearly the size of Atlanta. But note it is not symmetrical, turns 1 and 2 are much larger in radius than 3 and 4, moreover, turns 1 and 2 are more steeply banked (by 2 degrees) and the straight-a-ways are nearly flat. Richmond, site of last week's race is shown in the infield of Darlington, and Martinsville, the week before just outside the Darlington and Atlanta outlines.

This whole configuration would fit inside of the Talladega infield,….twice.


The asymmetry of Darlington is what makes it so challenging, turns 1 and 2 can be driven at a much higher speed than 3 and 4, not only because of the radius but the flatter banking of 3 and 4 also contributes to lower cornering speeds. If Richmond was the test of brakes and gear choice, then Darlington is the consummate test for the vehicle dynamics engineers and people who run the 7 post rigs. This is ultimate and confounding set-up problem for weight balance, springs, shocks, anti-sway bar, roll center, camber, and polar moment of inertia,..this is math modeling nirvana.

The races are much more distinctive than what a viewer would imagine by watching the race on TV.

The original calculation by Kepler from the Brahe data would yield the following graph (augmented by modern data for the three planets discovered since 1600).

The real painting of the "Astronomer by Candle Light" is by Gerrit Dou (in 1665); this detail is from a photograph taken by the J Paul Getty Museum ©.

And, finally, we have a new use for old incandescent light bulbs: turn them into oil lamps.

Talladega pas de deux: why restrictor plates necessitate contact drafting

The official Talladega mascot:

Pas de Deux (pronounced as "pah-day-due"), Part 2

Restrictor plates necessitate contact drafting

Engine horsepower is not a single number, but rather a function of speed (engine RPM) and typically has a humped shape; power output increases with engine speed up to a peak and then drops off.

 
The actual horse power numbers for any given engine and differential gear ratio are a closely guarded secret by each shop. Even though we've seen the actual numbers this is a confidentiality we're not about to breach here so we'll show hp qualitatively (no numbers) but accurately.


A car must be pushed to ram it through the air; the required push (a force) increases proportionally with the square of speed, that is: Force, F = n x (speed x speed).

   
 

 
This diagram shows the pressure on and around a car going 190 mph, high pressure on the front of the car, low pressure behind it.
 
 
 
 
 
 
 
 
 

 
 Those pressures applied over the frontal area of the car determine the aerodynamic drag.  (Red is high pressure, blue is low pressure)










It is often informative to also look at the pressures on the surface of the car as well.

The power consumption (force x speed) due to aero drag increases with the cube of speed, that is: (speed x speed x speed), so it increases dramatically with speed, and it just keeps on going up. At 190 mph the force required to ram a NASCAR Cup car through the air is on the order of 700 lbs or more.

The net power (engine less aero drag) describes what is left for accelerating the car.

A plot of the difference between the two curves illustrates the frustration of drivers with restrictor plate racing, when the two curves cross there is zero left to accelerate the car and when the net power gets to zero that's as fast as the car will go.

 Note also as the car approaches its terminal speed, the available power for acceleration is also approaching zero, i.e., the car becomes more and more "sluggish," it has no "throttle response," you push the accelerator pedle farther down but the car doesn't go any faster.

The only way to go faster is to reduce aerodynamic drag, hence, the newly realized pas de deux of two cars running nose to tail, literally touching and both cars together ramming the combined block through the air. Notice that the high pressure area on the nose of the second car fills in the low pressure void behind the lead car.

The result is to reduce the overall drag of the two cars together.

Even though the two cars together are not a smooth shape as one can see with the turbulence over the back of the lead car and on the front of the second car, but the combination of two cars pushing together has twice the horse power of one.

Moreover, the two cars have much less drag than the sum of two individual cars, about 27% less drag as shown in these studies.

As a result of the lower aerodynamic drag the speed at which the net power for accelerating the car is zero has increased in the pas de deux, contact drafting.   Thus, two cars together go motoring right by a single car or a long string of cars.

While one might think that if two are good, then three should be better, but the dynamics of getting three cars actually touching nose to tail doesn't work. It is physically impossible to keep the front and back contact forces on the middle car centered for any period of time as the cars do bounce around more than a little. Even though the Talladega track is one of the smoothest tracks on the NASCAR circuit, the cars are not on rails and they move relative to each other. As soon as the forces on the middle car are not centered it turns the middle car around. Thus, three cars trying to run as a trio ends up either being two in a pas de deux plus a third as a trailer, or all three do get together and it's called a wreck.

A surprisingly small gap between the cars is sufficient to mitigate the drag reduction compared to two cars in contact with each other. The pas de deux with a trailer just isn't as streamlined as two.

Don't expect to see too much of the pas de deux formation at the Daytona race in July because the Daytona track is much rougher than Talladega so it is much more difficult to keep two cars in actual contact,…but I bet they'll try. With the repaving at Daytona now scheduled to be completed for the 2011 races it may then make DIS the second pas de deux track, sort of a pas de deux of pas de deux racing.

Next week will be the opposite end of the spectrum of tracks, Richmond, where the turns are the tightest (365' radius), except for Martinsville (188' radius), and the banking at 14 degrees is less than half that of Talladega; the race at Richmond is all about brakes and the right gear to accelerate. This is the track where the race car engineers get to show their skills, it's all in the set-up.

 

 

 

 

 

Again, these CFD studies in SolidWorks by FastTrack Racing Challenges for participating junior high and high school teams are possible due to the generous support of SolidWorks (visit their web site and look at the full software package at SolidWorks.com) and in particular thanks to Marie Planchard, their director of worldwide education markets.

Talladega Pas de Deux: why two is the magic number at 'Dega

The official Talladega mascot should be:


Pas de Deux (pronounced as "pah-day-due")

Merriam Webster dictionary defines "pas de deux" as


1. a dance or figure for two performers

2. an intricate relationship or activity involving two parties or things

A funny thing happened in Alabama on Sunday. Suddenly for the first time in memory two cars in a pas de deux outran an entire string of cars at "the big track." Until now a long string of cars-- 5, 10, 15 or more cars-- always had the advantage,…a huge advantage because a string of cars always had less overall drag than one or two alone. But on Sunday suddenly we saw two cars outrunning the freight train; how is that possible when it never worked before?

As many TV commentators remarked repeatedly, "the closing rate of the two cars over the rest of the field is incredible," as much as 15 mph or 22 ft per second, a car length per second. When you're only 3 feet away from another car, they're going 180 mph and you're doing 195, closing on them at 22 ft per second makes the slower car appear as if it is sitting still.

Several factors explain the two car run away: Talladega was repaved in 2006 and the surface is unusually smooth, allowing cars to get very close to each, nose to tail, and stay that way for long periods of time. The geometry of the CoT has the nose and tail of the car at essentially the same height so the trailing car can literally push up against the lead car and shove it. Previously with the car dubbed the Twisted Sister if the trailing car pushed this hard on the lead car they'd lift the rear wheels of the lead car off the ground and they'd both wreck.

Also the CoT with a spoiler on it has a very different wake than with the wing (red is highest speed air flow down to blue which is the lowest speed air flow).

There's a very distinctly larger area of low speed wake behind the race car with the spoiler compared to the race car with the wing. The result is that the two cars can actually touch and stay in contact which reduces the overall drag of the two car duet, considerably, by perhaps as much as 30%.

Power consumption increases with the cube of speed (speed x speed x speed) so the observed difference of two cars together at 195 mph vs one car or a string of cars at 180 mph should have required (7.415/5.832) 27% more power to go that much faster, but actually what happens is that the two cars linked together in a pas de deux have 27% less drag as shown in these studies.

While the two cars have a huge speed advantage there is very little air flow reaching the front of the trailing car, which means that the engine of the trailing car will quickly overheat because cool fresh air is not getting into the radiator. This limits how long the two cars can continue their pas de deux, and from watching the race one would deduce that a couple of minutes is about as long as two cars can stay in contact (NASCAR Cup cars can run 2.2 laps at Talladega in two minutes).


Harvick played the final lap pas de deux perfectly, and then at the last possible moment swung around his dance partner (McMurray) to win the race by a mere 0.011 seconds.

After the race Jamie McMurray was quoted, saying, "it's hard to explain to you guys that aren't in cars, but when there's someone directly behind you and they pull their car out of line really fast, it's like you pull a parachute in your car. It literally feels like you lose 3 or 5 mph immediately, and when that happens, the car that's doing the passing just has the momentum."

It doesn't just feel like the car slows down, it actually does slow down. The aerodynamic drag on a car is the difference in pressure on the front of the car, minus the pressure on the back of the car, and that difference of pressure applied over the frontal area of the car is the drag force (pressure multiplied by area equals force), perhaps 700 lbs or so on a car going 190 mph.

When the cars are nose to tail the low pressure area behind the lead car is filled in by the high pressure area on the front of the second car.

But when the trailing car gets out of line to go around the lead car, suddenly there's a low pressure area behind the lead car and the drag force on the front car suddenly increases by as much as 400 lbs. This has the same effect as throwing an anchor out, it slows the lead car by as much as 5 mph almost instantly.

These CFD studies in SolidWorks by FastTrack Racing Challenges for participating junior high and high school teams are possible due to the generous support of SolidWorks (visit their web site and look at the full software package at SolidWorks dot com) and in particular thanks to Marie Planchard, their director of worldwide education markets.