Big Sky Theory - Military Aviation Tactics

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.

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.