Big sky theory
Encyclopedia
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 (or applies less) when aircraft
are flying along specific narrow routes, such as an airport
traffic pattern or jet airway.
The Big Sky Theory has been mathematically modeled, using a gas law approach. This implies that metal-on-metal collisions of aircraft in free flight
should be extremely rare in en-route airspace
, whereas operational errors (violations of formal separation standards
) should be relatively common. Three critical parameters are the number of flying object(s) per unit volume, their speed, and their size. Larger, faster objects, flying in a traffic-rich environment are more collision-prone (per unit time).
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.
Of course firing is not truly random, even if the aircraft cannot be seen. By sound or just guessing, isolating the firing region to about ⅕th(one fifth) of the sky might be possible. If you assume 10 guns firing 10 rounds per second over ⅕th(one fifth) of the sky, and 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 antiaircraft 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.
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.
Aviation
Aviation is the design, development, production, operation, and use of aircraft, especially heavier-than-air aircraft. Aviation is derived from avis, the Latin word for bird.-History:...
, 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 (or applies less) when aircraft
Aircraft
An aircraft is a vehicle that is able to fly by gaining support from the air, or, in general, the atmosphere of a planet. An aircraft counters the force of gravity by using either static lift or by using the dynamic lift of an airfoil, or in a few cases the downward thrust from jet engines.Although...
are flying along specific narrow routes, such as an airport
Airport
An airport is a location where aircraft such as fixed-wing aircraft, helicopters, and blimps take off and land. Aircraft may be stored or maintained at an airport...
traffic pattern or jet airway.
The Big Sky Theory has been mathematically modeled, using a gas law approach. This implies that metal-on-metal collisions of aircraft in free flight
Free flight (air traffic control)
Free flight is a developing air traffic control method that uses no centralized control . Instead, parts of airspace are reserved dynamically and automatically in a distributed way using computer communication to ensure the required separation between aircraft. This new system may be implemented...
should be extremely rare in en-route airspace
En-route chart
In aviation, an en-route chart is an aeronautical chart that guides pilots flying under Instrument Flight Rules during the en-route phase of flight.-Overview:...
, whereas operational errors (violations of formal separation standards
Separation (air traffic control)
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 wake turbulence....
) should be relatively common. Three critical parameters are the number of flying object(s) per unit volume, their speed, and their size. Larger, faster objects, flying in a traffic-rich environment are more collision-prone (per unit time).
Military aviation tactics
The theory is also relevant in military aviationMilitary aviation
Military aviation is the use of aircraft and other flying machines for the purposes of conducting or enabling warfare, including national airlift capacity to provide logistical supply to forces stationed in a theater or along a front. Air power includes the national means of conducting such...
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
Fuselage
The fuselage is an aircraft's main body section that holds crew and passengers or cargo. In single-engine aircraft it will usually contain an engine, although in some amphibious aircraft the single engine is mounted on a pylon attached to the fuselage which in turn is used as a floating hull...
/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
Anti-aircraft warfare
NATO defines air defence as "all measures designed to nullify or reduce the effectiveness of hostile air action." They include ground and air based weapon systems, associated sensor systems, command and control arrangements and passive measures. It may be to protect naval, ground and air forces...
guns are firing randomly hoping to hit it. Their maximum slant range
Slant range
In radio electronics especially radar terminology, slant range is the line-of-sight distance between two points which are not at the same level relative to a specific datum....
is 10,000 feet (3,048 metres).
There are 20,626 square degrees
Degree (angle)
A degree , usually denoted by ° , is a measurement of plane angle, representing 1⁄360 of a full rotation; one degree is equivalent to π/180 radians...
in the visible sky hemisphere
Sphere
A sphere is a perfectly round geometrical object in three-dimensional space, such as the shape of a round ball. Like a circle in two dimensions, a perfect sphere is completely symmetrical around its center, with all points on the surface lying the same distance r from the center point...
, 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.
Of course firing is not truly random, even if the aircraft cannot be seen. By sound or just guessing, isolating the firing region to about ⅕th(one fifth) of the sky might be possible. If you assume 10 guns firing 10 rounds per second over ⅕th(one fifth) of the sky, and 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
Slant range
In radio electronics especially radar terminology, slant range is the line-of-sight distance between two points which are not at the same level relative to a specific datum....
, the antiaircraft 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 warfareSpace warfare
Space warfare is combat that takes place in outer space, i.e. outside the atmosphere. Space warfare therefore includes ground-to-space warfare, such as attacking satellites from the Earth, as well as space-to-space warfare, such as satellites attacking satellites.It does not include the use of...
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
Kinetic energy
The kinetic energy of an object is the energy which it possesses due to its motion.It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes...
projectiles flew on the Soviet Almaz
Almaz
The Almaz program was a series of military space stations launched by the Soviet Union under cover of the civilian Salyut DOS-17K program after 1971....
military space station.