Big sky theory

Last updated

In aviation, the Big Sky Theory is that two randomly flying bodies are very unlikely to collide, as the three-dimensional space is so large relative to the bodies. Some aviation safety rules involving altimetry and navigation standards are based on this concept. It does not apply when aircraft are flying along specific narrow routes, such as an airport traffic pattern or jet airway.

Contents

The Big Sky Theory has been mathematically modeled, using a gas law approach. [1] This implies that collisions of aircraft in free flight should be extremely rare in en-route airspace, whereas operational errors such as violations of formal separation standards should be relatively common. Three critical parameters are the number of flying objects per unit volume, their speed, and their size. Larger, faster objects, flying in a traffic-rich environment are more collision-prone.

Military aviation tactics

The theory is also relevant in military aviation tactics, especially regarding targeting of aircraft and missiles by ground-based, non-guided weapons without visual spotting. For example, consider an F-16, which has a combined fuselage/wing area of roughly 670 square feet (62.2 square metres), and flying at 6,000 feet (1,829 metres) at night or above clouds. Ground-based, non-guided antiaircraft guns are firing randomly hoping to hit it. Their maximum slant range is 10,000 feet (3,048 metres).

There are 20,626 square degrees in the visible sky hemisphere, assuming no horizon obstructions. The 670 square ft (≈62 m²) aircraft would subtend an angle of 0.24 degrees at 6,000 ft (≈1,800 m). Therefore, the chance of a single randomly fired unguided shot hitting the aircraft would be one in 20626 / 0.24 / 0.24, or one in 358,090.

Targeted firing reduces these odds. By sound or by guessing, isolating the firing region to about one fifth of the sky might be possible. If you assume 10 guns firing 10 rounds per second over one fifth of the sky, perfectly coordinating their firing evenly across that region, and crudely tracking the aircraft as it flies over, the chance of hitting it would be 358,090 / 5 / 10 / 10, or one chance in 716 each second.

Flying at 500 mph or 805 km/h (733 ft/s or 223 m/s), each second the aircraft would cross seven angular degrees of sky. With a 10,000 ft (≈3,000 m) slant range, the anti-aircraft guns could cover a cone of sky 100 degrees wide, assuming a common gun location. Therefore, the aircraft would be within range for 100/7 or 14.3 seconds, and the total chance of hitting it during a single flyover pass would be 716 / 14.3 or one chance in 50.

When coordinating corridors for friendly artillery trajectories through airspace, it is sometimes assumed (rarely, and for emergency expediency) that similar unlikelinesses apply. This is often referred to as the "Big Sky - Small Bomb" theory.

Space warfare

Space warfare tactics are also affected by the Big Sky Theory, if unguided projectiles are used. At the vast engagement distances, the subtended angle of the target would be minuscule, and the projectile flight time to target would be great, possibly on the order of an hour or more. If the target vehicle randomly maneuvered every few minutes, the chance of a hit would be extremely small, even if many projectiles were fired. A space weapon using unguided kinetic projectiles flew on the Soviet Almaz military space station. [2]

Big ocean theory

There is a related marine concept called the big ocean theory. It holds that two randomly placed, randomly maneuvering vessels in an ocean are very unlikely to collide.

See also

Related Research Articles

<span class="mw-page-title-main">Missile</span> Self-propelled guided weapon system

In military terminology, a missile is a guided airborne ranged weapon capable of self-propelled flight usually by a jet engine or rocket motor. Missiles are thus also called guided missiles or guided rockets. Missiles have five system components: targeting, guidance system, flight system, engine and warhead. Missiles come in types adapted for different purposes: surface-to-surface and air-to-surface missiles, surface-to-air missiles, air-to-air missiles, and anti-satellite weapons.

<span class="mw-page-title-main">Surface-to-air missile</span> Ground-launched missile designed to attack aerial targets

A surface-to-air missile (SAM), also known as a ground-to-air missile (GTAM) or surface-to-air guided weapon (SAGW), is a missile designed to be launched from the ground to destroy aircraft, ground targets or other missiles. It is one type of anti-aircraft system; in modern armed forces, missiles have replaced most other forms of dedicated anti-aircraft weapons, with anti-aircraft guns pushed into specialized roles.

<span class="mw-page-title-main">8.8 cm KwK 36</span> 88 mm tank gun used by the German Army during World War II

The 8.8 cm KwK 36 was an 88-millimetre (3.5 in) tank gun used by the German Army during World War II. This was the primary armament of the PzKpfw VI Tiger I tank. It was developed and built by Krupp.

<span class="mw-page-title-main">R4M</span> Rocket

R4M, abbreviation for Rakete, 4 kilogramm, Minenkopf, also known by the nickname Orkan due to its distinctive smoke trail when fired, was a folding-fin air-to-air rocket used by the Luftwaffe at the end of World War II.

<span class="mw-page-title-main">Flight level</span> Measure in aviation

In aviation and aviation meteorology, a flight level (FL) is an aircraft's altitude at standard air pressure, expressed in hundreds of feet. The air pressure is computed assuming an International Standard Atmosphere pressure of 1013.25 hPa (29.92 inHg) at sea level, and therefore is not necessarily the same as the aircraft's actual altitude, either above sea level or above ground level.

<span class="mw-page-title-main">Rocket launcher</span> Portable device that propels unaimed rocket

A rocket launcher is a weapon that launches an unguided, rocket-propelled projectile.

<i>Lexington</i>-class aircraft carrier Pair of aircraft carriers for the United States Navy during the 1920s

The Lexington-class aircraft carriers were a pair of aircraft carriers built for the United States Navy (USN) during the 1920s, the USS Lexington (CV-2) and USS Saratoga (CV-3). The ships were built on hulls originally laid down as battlecruisers after World War I, but under the Washington Naval Treaty of 1922, all U.S. battleship and battlecruiser construction was cancelled. The Treaty, however, allowed two of the unfinished ships to be converted to carriers. They were the first operational aircraft carriers in the USN and were used to develop carrier aviation tactics and procedures before World War II in a series of annual exercises.

<span class="mw-page-title-main">Sukhoi Su-15</span> Soviet interceptor aircraft

The Sukhoi Su-15 is a twinjet supersonic interceptor aircraft developed by the Soviet Union. It entered service in 1965 and remained one of the front-line designs into the 1990s. The Su-15 was designed to replace the Sukhoi Su-11 and Sukhoi Su-9, which were becoming obsolete as NATO introduced newer and more capable strategic bombers.

<span class="mw-page-title-main">Aeroméxico Flight 498</span> 1986 mid-air aircraft collision and crash in Cerritos, California, US

Aeroméxico Flight 498 was a scheduled commercial flight from Mexico City, Mexico, to Los Angeles, California, United States, with several intermediate stops. On Sunday, August 31, 1986, the McDonnell Douglas DC-9 operating the flight was clipped in the tail section by N4891F, a Piper PA-28-181 Cherokee owned by the Kramer family, and crashed into the Los Angeles suburb of Cerritos, killing all 64 on the DC-9, all three on the Piper and an additional 15 people on the ground. Eight on the ground also sustained minor injuries. Blame was assessed equally on the Federal Aviation Administration (FAA) and the pilot of the Cherokee. No fault was found with the DC-9 or the actions of its crew.

<span class="mw-page-title-main">1996 Charkhi Dadri mid-air collision</span> November 1996 mid-air plane collision in northern India

On 12 November 1996, Saudia Flight 763, a Boeing 747 en route from Delhi, India, to Dhahran, Saudi Arabia, and Kazakhstan Airlines Flight 1907, an Ilyushin Il-76 en route from Chimkent, Kazakhstan, to Delhi, collided over the village of Charkhi Dadri, around 100 km west of Delhi. The crash killed all 349 people on board both planes, making it the world's deadliest mid-air collision and the deadliest aviation accident to occur in India. The crash was caused by failure of the Kazakh crew to maintain the correct altitude, because of confused dialogue with the tower communicated via the radio operator.

<span class="mw-page-title-main">Folding-Fin Aerial Rocket</span> Air-to-air rocket, air-to-surface rocket

The Mk 4 Folding-Fin Aerial Rocket (FFAR), also known as "Mighty Mouse", was an unguided rocket used by United States military aircraft. It was 2.75 inches (70 mm) in diameter. Designed as an air-to-air weapon for interceptor aircraft to shoot down enemy bombers, it primarily saw service as an air-to-surface weapon. The FFAR has been developed into the modern Hydra 70 series, which is still in service.

<span class="mw-page-title-main">M982 Excalibur</span> 155 mm guided artillery shell

The M982 Excalibur is a 155 mm extended-range guided artillery shell developed in a collaborative effort between the U.S. Army Research Laboratory (ARL) and the United States Army Armament Research, Development and Engineering Center (ARDEC). The Excalibur was developed and/or manufactured by prime contractor Raytheon Missiles & Defense, BAE Systems AB and other subs and primes in multiple capacities such as Camber Corporation and Huntington Ingalls Industries. It is a GPS and inertial-guided munition capable of being used in close support situations within 75–150 meters (250–490 ft) of friendly troops or in situations where targets might be prohibitively close to civilians to attack with conventional unguided artillery fire. In 2015 the United States planned to procure 7,474 rounds with a FY2015 total program cost of US$1.9341 billion at an average cost of US$258,777 per unit. By 2016, unit costs were reduced to US$68,000 per round. Versions that add laser-guidance capability and are designed to be fired from naval guns began testing in 2015. By October 2018, over 1,400 rounds had been fired in combat.

<span class="mw-page-title-main">Allegheny Airlines Flight 853</span> 1969 mid-air collision

Allegheny Airlines Flight 853 was a regularly scheduled Allegheny Airlines flight from Boston, Massachusetts, to St. Louis, Missouri, with stops in Baltimore, Maryland, Cincinnati, Ohio, and Indianapolis, Indiana. On September 9, 1969, the aircraft serving the flight, a McDonnell Douglas DC-9, collided in mid-air with a Piper PA-28 light aircraft near Fairland, Indiana. The DC-9 was carrying 78 passengers and 4 crew members, and the Piper was leased to a student pilot on a solo cross-country flight. All 83 occupants of both aircraft were killed in the accident and both aircraft were destroyed.

In aviation, a mid-air collision is an accident in which two or more aircraft come into unplanned contact during flight. Owing to the relatively high velocities involved and the likelihood of subsequent impact with the ground or sea, very severe damage or the total destruction of at least one of the aircraft usually results.

<span class="mw-page-title-main">Separation (aeronautics)</span> Concept for keeping aircraft safe distances apart

In air traffic control, separation is the name for the concept of keeping an aircraft outside a minimum distance from another aircraft to reduce the risk of those aircraft colliding, as well as prevent accidents due to secondary factors, such as wake turbulence. Separation can also apply to terrain, obstacles, and controlled airspace, wherein an aircraft must stay at a minimum distance from a block of airspace; as an example, all aircraft must be approved by the controller who "owns" the airspace before the aircraft is approved to enter that sector.

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, 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.

<span class="mw-page-title-main">1956 Grand Canyon mid-air collision</span> Mid-air collision on June 30, 1956 over the Grand Canyon

The Grand Canyon mid-air collision occurred in the western United States on Saturday, June 30, 1956, when a United Airlines Douglas DC-7 struck a Trans World Airlines Lockheed L-1049 Super Constellation over Grand Canyon National Park, Arizona. The first one fell into a canyon and the other one slammed into a rock face. All 128 on board both airplanes perished, making it the first commercial airline incident to exceed one hundred fatalities. The airplanes had departed Los Angeles International Airport minutes apart for Chicago and Kansas City, respectively. The collision took place in uncontrolled airspace, where it was the pilots' responsibility to maintain separation. This highlighted the antiquated state of air traffic control, which became the focus of major aviation reforms.

Deflection shooting is a technique of shooting ahead of a moving target, also known as leading the target, so that the projectile will "intercept" and collide with the target at a predicted point. This technique is only necessary when the target will have significantly displaced its position during the time the projectile would take to reach the target, which can become the case over very long distances, due to fast moving targets, or while using relatively slow projectiles.

<span class="mw-page-title-main">Precision-guided munition</span> "Smart bombs", used to strike targets precisely

A precision-guided munition is a guided munition intended to precisely hit a specific target, to minimize collateral damage and increase lethality against intended targets. During the First Gulf War guided munitions accounted for only 9% of weapons fired, but accounted for 75% of all successful hits. Despite guided weapons generally being used on more difficult targets, they were still 35 times more likely to destroy their targets per weapon dropped.

In aerial gunnery, gun harmonisation, convergence pattern, convergence zone, convergence point or bore-sight point refers to the aiming of fixed guns or cannon carried in the wings of a fighter aircraft.

References

  1. Knecht, W.R. (2001). Modeling the Big Sky Theory. Proceedings of the Human Factors and Ergonomics Society 45th annual meeting, 87-91, Santa Monica, CA: Human Factors and Ergonomics Society.
  2. Oberg, James (1999). "The Nature of Space Power" (PDF). Space Power Theory. National Space Studies Center / US Air Force Academy. p. 53. Archived from the original (PDF) on 2018-07-12. Retrieved 2013-01-18.