There's a fascinating article at Vanity Fair Magazine about the mid-air collision of a GOL Airlines Boeing 737 and N600XL, an Embraer business jet.

I compel you to read it and then come back and read the rest of this blog post. I wonder if the facts blow your mind as much as they do mine:

It is simply astonishing to me that:

this relatively "minor-appearing" damage to the Embraer led to the severing of the entire outboard section of the wing of a 737 (I guess its similar to what a micro-meteor can do to a satellite at speed).

What is amazing to think about is how literal milliseconds and hundredths of degrees over time and distance could have drastically changed this outcome.

I did some calculations and I determined that a change of heading of a mere 0.01 degrees, would, over the course of 200 miles, yield 175 feet of difference in course of the Embraer at the time of impact. I am not a pilot, so I do not know if that is within the margin of error of GPS or autopilot course tracking, however taking this out of the equation, say they enabled autopilot 10 seconds later?

If it were travelling 0.1 mile per hour faster or slower for 1 hour? 500 feet of difference. (constant 599.9 mph for the math), again, I don't know the granularity of autopilot with parameters such as head/tail winds, etc)

More simply visualized: if one of the pilots hesitated for three seconds before throttling up at take off at either airport? How much that would have altered the times of their course intersections. It would be like trying two people with hockey pucks sliding their pucks toward each other from opposite sides of a frozen lake half a mile wide and expecting them to collide, without knowing when the other would slide their puck or exactly where on the other shore the other person was positioned.

It boggles the mind.

It is simply staggaring that even in the absence of TCAS/ATC that such a collision could occur, given seemingly insignificant adjustments to the parameters involved. The single constant being their shared flight level of 37,000 feet, but a thousand other variables in the other dimensions (including time) could have played this out completely different, less tragic way.

(I'm not a mathmatician, either, so I used some basic trig for these)