Helical Flight Logic
Regarding the recent midair collision between a commercial 737 and a Legacy executive jet over Brazil... It struck me that a simple change would greatly reduce the incidence of such events. The 737 was traveling eastbound at 37,000 feet; with modern avionics and GPS, this altitude is maintained almost exactly. (Next time you're on a plane with live flight statistics, note that the altitude is almost always an exact multiple of 1000 feet.) The Legacy was traveling westbound, and theoretically should have been flying at an even-numbered altitude; e.g., 36,000 or 38,000 feet. But transcripts show that it was nevertheless cleared for 37,000 feet, inadvertently putting it on a collision course with the 737 jet.
The quantization of altitude into units of 1000 effectively reduces the usable airspace from 3D to 2D, dramatically increasing the probability of collisions. But there is an easy way to not only reduce the random probability of collision (by allowing the full 3D space to be used), but indeed to lower the risk even further. Consider:
Planes traveling east (0 degrees) should fly at XX,000 feet.
Planes traveling north (90 degrees) should fly at XX,250 feet.
Planes traveling west (180 degrees) should fly at XX,500 feet.
Planes traveling south (270 degrees) shoud fly at XX,750 feet.
Furthermore, this system can be made continuous: planes traveling northeast should fly at XX,125 feet, and so on. It creates a continuous helical pattern, in which aircraft at similar altitudes will always be traveling in similar directions, thus dramatically reducing the chances of collision during the long stretches of flights where altitudes are maintained.
Update: Here's a detailed mathematical analysis of this idea.
The quantization of altitude into units of 1000 effectively reduces the usable airspace from 3D to 2D, dramatically increasing the probability of collisions. But there is an easy way to not only reduce the random probability of collision (by allowing the full 3D space to be used), but indeed to lower the risk even further. Consider:
Planes traveling east (0 degrees) should fly at XX,000 feet.
Planes traveling north (90 degrees) should fly at XX,250 feet.
Planes traveling west (180 degrees) should fly at XX,500 feet.
Planes traveling south (270 degrees) shoud fly at XX,750 feet.
Furthermore, this system can be made continuous: planes traveling northeast should fly at XX,125 feet, and so on. It creates a continuous helical pattern, in which aircraft at similar altitudes will always be traveling in similar directions, thus dramatically reducing the chances of collision during the long stretches of flights where altitudes are maintained.
Update: Here's a detailed mathematical analysis of this idea.
posted by Ben Weiss at
3:40 PM
3 Comments:
Hey Ben.... awesome blog. I enjoyed reading about the test drive! How cool!!!
If you come across a refurbished Macbook, would you let me know? Heading back to college in January, and am trying to find a great deal. ; )
Hope to talk to you soon...
Jon
You might not be aware, but there's already a system similar to this in place. Many aviation insiders watching that accident were appalled because of one of the aircraft was at a flight level that it wouldn't typically be cleared to (can't remember which off the top of my head).
The system as it stands now is set up such that below 13k feet, aircraft travelling VFR (visual flight rules) operate on the odd thousands + 500 ft when travelling between 000 and 179, and even thousands + 500 ft. when travelling on the western half of the compass. Aircraft who are flying under IFR (instrument flight rules) fly on the exact thousands in the same patter as VFR aircraft.
Above 13000 VFR aircraft essentially fly with the same directional rules as IFR aircraft, up to 18000 (Flight Level 180), this time 1000' of separation is in place.
Above FL180 aircraft are still separated by 1000', then above FL350 (~35k), the spacing increased to 2000' intervals. It's been a while since I learned this stuff, so I can't remember which direction uses each level, but it's 2000' separation. The increasing separation at higher altitudes is due to the inaccuracies that develop in altimeters.
There is a new development using more accurate instrumentation that allows for reduced separation (I can't quite remember the acronym, but it includes RS in it!), which enables a more efficient use of airspace above FL350 so that aircraft only need to be separated by 1000' vertically, and also a lower horizontal separation I believe.
So... what I'm saying is that you're idea is a good one. So good in fact, that it's essentially in place already. The only hitch in it is that 250' intervals is still within the deviation that occurs in altimeters at the high altitudes where airliners fly - some of the most congested airspace. I think the greatest saviour for dealing with aviation congestion will be when we do away with the airways system and rely on direct routings via GPS instead. This would have to be accompanied by an overhaul of existing ATC infrastructure in order for the control agencies to be able to cope with the new way aircraft would be routed, but it's well worth the cost.
Anywho, I enjoyed looking through your blog as well - hope you're having a great day!
Gord
Hi Gord,
Thanks for your comments. I'm pretty familiar with the existing system; it's major problem is that the more accurate the altimeters, the more dangerous the flying patterns! (aircraft flying at 000 and 179 headings would be at the same altitude, yet potentially on head-on collision courses.) With the helical system, the more accurate the altimeters, the safer the flying patterns.
With modern technology and GPS, altimeters are becoming more and more accurate, so the current system is actually becoming more and more dangerous; the helical approach avoids this; and if 250' intervals are too small, space them out to 500' or 1000' intervals. (I chose 250' for simplicity in illustrating the concept, but come to think of it, 250 meters is more realistic for 90-degree changes in heading. And of course, the helical system would be continuous; 125 meters for 45-degree heading changes, etc...) How does that sound?
-Ben
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