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The Navigation paradox states that increased navigational precision may result in increased collision risk. In the case of ships and aircraft, the advent of Global Positioning System (GPS) navigation has enabled craft to follow navigational paths with such greater precision (often on the order of plus or minus 2 meters), that, without better distribution of routes, coordination between neighboring craft and collision avoidance procedures, the likelihood of two craft occupying the same space on the shortest distance line between two navigational points has increased.
Robert E. Machol attributes the term "navigation paradox" to Peter G. Reich, writing in 1964, and 1966, who recognized that "in some cases (see below) increases in navigational precision increase collision risk." In the "below" explanation, Machol noted "that if vertical station-keeping is sloppy, then if longitudinal and lateral separation are lost, the planes will probably pass above and below each other. This is the ‘navigation paradox’ mentioned earlier."
Russ Paielli wrote a mid-air collision simulating computer model 500 sq mi (1,300 km2) centered on Denver, Colorado In Table 3 Paielli notes that aircraft cruising at random altitudes have five times fewer collisions than those obeying with only 25 ft (7.6 m) RMS of vertical error discrete cruising altitude rule, such as the internationally required hemispherical cruising altitude rules. At the same vertical error, the prototype linear cruising altitude rule tested produced 33.8 fewer mid-air collisions than the hemispherical cruising altitude rules.
Paielli’s 2000 model corroborated an earlier 1997 model by Patlovany showing in Figure 1 that zero altitude error by pilots obeying the hemispherical cruising altitude rules resulted in six times more mid-air collisions than random cruising altitude non compliance. Similarly, Patlovany’s computer model test of the Altimeter-Compass Cruising Altitude Rule (ACCAR) with zero piloting altitude error (a linear cruising altitude rule similar to the one recommended by Paielli), resulted in about 60% of the mid-air collisions counted from random altitude non compliance, or 10 times fewer collisions than the internationally accepted hemispherical cruising altitude rules. In other words, Patlovany’s ACCAR alternative and Paielli’s linear cruising altitude rule would reduce cruising midair collisions between 10 and 33 times, compared to the currently recognized, and internationally required, hemispherical cruising altitude rules, which institutionalize the navigation paradox on a world wide basis.
The ACCAR alternative to the hemispherical cruising altitude rules, if adopted in 1997, could have eliminated the navigation paradox at all altitudes, and could have saved 342 lives in over 30 midair collisions (up to November 2006) since the Risk Analysis proof that the current regulations multiply midair collision risk in direct proportion to pilot accuracy in compliance. The Namibian collision in 1997, the Japanese near-miss in 2001, the Überlingen collision in Germany in 2002, and the Amazon collision in 2006, are all examples where human or hardware errors doomed altitude-accurate pilots killed by the navigation paradox designed into the current cruising altitude rules. The current system as described by Paielli noted as examples that nuclear power plants and elevators are designed to be passively safe and fault tolerant. Reactivity control rods fall into the reactor to cause a shutdown on loss of electrical power, and elevator fall-arresting brakes are released by torque from support cable tension. The navigation paradox describes a midair collision safety system that by design cannot tolerate a single failure in human performance or electronic hardware.
To mitigate the described problem, many recommend, as legally allowed in very limited authorized airspace, that planes fly one or two miles offset from the center of the airway (to the right side) thus eliminating the problem only in the head-on collision scenario. The International Civil Aviation Organization's (ICAO) "Procedures for Air Navigation--Air Traffic Management Manual," authorizes lateral offset only in oceanic and remote airspace worldwide. However, this workaround for the particular case of a head-on collision threat on a common assigned airway fails to address the navigation paradox in general, and it fails to specifically address the inherent system safety fault intolerance inadvertently designed into international air traffic safety regulations. To be specific, in the cases of intersecting flight paths where either aircraft is not on an airway (for example, flying under a "direct" clearance, or a temporary diversion clearance for weather threats), or where intersecting aircraft flights are on deliberately intersecting airways, these more general threats receive no protection from flying one or two miles to the right of the center of the airway. Intersecting flight paths must still intersect somewhere. As with the midair collision over Germany, an offset to the right of an airway would have simply changed the impact point by a mile or two away from where the intersection actually did occur. Of the 342 deaths since 1997 so far encouraged by the lack of a linear cruising altitude rule (like ACCAR) improvement to the fault intolerance of the hemispherical cruising altitude rules, only the head-on collision over the Amazon could have been prevented if either pilot had been flying an offset to the right of the airway centerline. In contrast, ACCAR systematically separates conflicting traffic in all airspace at all altitudes on any heading, whether over the middle of the ocean or over high density multinational-interface continental airspace. Nothing about Reduced Vertical Separation Minima (RVSM) system design addresses the inherent vulnerability of the air traffic system to expected faults in hardware and human performance, as experienced in the Namibian, German, Amazon and Japanese accidents.
- Machol, Robert E., Interfaces 25:5, September–October 1995 (151-172), page 154.
- Reich, Peter G., "A theory of safe separation standards for air traffic control," RAE Technical Reports Nos. 64041, 64042, 64043, Royal Aircraft Establishment, Farnborough, United Kingdom.
- Reich, Peter G., "Analysis of long-range air traffic systems: Separation standards—I, II, and III," Journal of Navigation, Vol. 19, No. 1, pp. 88-96; No. 2, pp. 169-176; No. 3, pp. 331-338.
- Paielli, Russ A., "A Linear Altitude Rule for Safer and More Efficient Enroute Air Traffic," Air Traffic Control Quarterly, Vol. 8, No. 3, Fall 2000.
- Patlovany, Robert W., "U.S. Aviation Regulations Increase Probability of Midair Collisions," Risk Analysis: An International Journal, April 1997, Volume 17, No. 2, Pages 237-248.
- Patlovany, Robert, W., "Preventable Midair Collisions Since 26 June 1997 Request Denied for Notice of Proposed Rulemaking (NPRM) 28996 Altimeter-Compass Cruising Altitude Rule (ACCAR)," Preventable Midair Collisions Since 26 June 1997 Request Denied for Notice of Proposed Rulemaking (NPRM) 28996 Altimeter-Compass Cruising Altitude Rule (ACCAR)
- Langwiesche, William, "The Devil at 37,000 Feet", Vanity Fair, January 2009 
- Werfelman, Linda, "Sidestepping the Airway," AeroSafety World March 2007, pages 40-45, Flight Safety Foundation .