Thursday, August 5, 2010

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.

Monday, August 2, 2010

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.