Black triangle (UFO)
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Black triangles are a class of unidentified flying objects, or UFOs, with certain common features which have reportedly been observed during the 20th and 21st centuries. Media reports of black triangles originally came from the United States and United Kingdom. 
Reports generally describe this class of UFOs as large, silent, black triangular objects hovering or slowly cruising at low altitudes over cities and highways. Sightings usually take place at night. These objects are often described as having pulsing colored lights that appear at each corner of the triangle.
Black triangle UFOs have been reported to be visible to radar, as was the case with the famous Belgian UFO wave. During these incidents, two Belgian F-16s attempted to intercept the objects (getting a successful missile lock at two occasions) only to be outmaneuvered; a key conclusion of the Project Condign report was that no attempt should be made on the part of civilian or RAF Air Defence aircraft to outmaneuver these objects except to place them astern to mitigate the risk of collision. 
UK Ministry of Defence Report Findings
Declassified research (subject to a Freedom of Information request) from the UK Ministry of Defence report UAP in the UK Air Defence Region, code named Project Condign and released to the public in 2006, draws several conclusions as to the origin of "black triangle" UFO sightings. Their researchers conclude that most, if not all, "black triangle" UFOs are formations of electrical plasma, the interaction of which creates mysterious energy fields that both refract light and produce vivid hallucinations in witnesses that are in close proximity. Further it suggests that "the majority, if not all, of the hitherto unexplained reports may well be due to atmospheric gaseous electrically charged buoyant plasmas"  which emit charged fields with the capability of inducing vivid hallucinations and psychological effects in witnesses and are "capable of being transported at enormous speeds under the influence and balance of electrical charges in the atmosphere." The researchers note that plasmas may be formed by more than one set of weather and electrically charged conditions, while "at least some" events are likely to be triggered by meteor re-entry in scenarios where meteors neither burn up completely nor impact, but rather break up in the atmosphere to form such a charged plasma. These plasma formations are also theorized to have the effect of refracting light between themselves, producing the appearance of a black polygonal shape with the lights at the corners caused by self-generated plasma coloration (similar to the Aurora Borealis). 
The report states: "Occasionally and perhaps exceptionally, it seems that a field with, as yet, undetermined characteristics, can exist between certain charged buoyant objects in loose formation, such that, depending on the viewing aspect, the intervening space between them forms an area (viewed as a shape, often triangular) from which the reflection of light does not occur. This is a key finding in the attribution of what have frequently been reported as black 'craft,' often triangular and even up to hundreds of feet in length." These plasma formations also have the effect through "magnetic, electric or electromagnetic (or even unknown field), appears to emanate from some of the buoyant charged masses. Local fields of this type have been medically proven to cause responses in the temporal lobes of the human brain. These result in the observer sustaining his or her own vivid, but mainly incorrect, description of what is experienced. This is suggested to be a key factor in influencing the more extreme reports found in the media and are clearly believed by the 'victims.'
Recently un-redacted sections of the report state that Russian, Former Soviet Republics, and Chinese authorities have made a co-ordinated effort to understand the UAP topic and that Russian investigators have measured (or at least detected) 'fields' which are reported to have caused human effects when they are located close to the phenomena. According to the Ministry of Defence researchers, Russian scientists have connected their UAP work with plasmas and the wider potential use of plasmas and may have done "considerably more work (than is evident from open sources)" on military applications, for example using UAP -type radiated fields to affect humans, and the possibility of producing and launching plasmas as decoys. 
On March 30, 1993 multiple witnesses across south-west and west England saw a large black triangle at low speeds. Analysis of the sightings by Nick Pope concluded that the object moved in a north-easterly course from Cornwall to Shropshire over a period of approximately 6 hours.
The sightings report clearly visible objects over densely populated areas and highways, mostly in the United States and Britain, but other parts of the world as well. A geographic distribution of U.S. sightings has been correlated by a currently inactive American-based investigative organization, the National Institute for Discovery Science, which led to a July 2002 report which suggested that the craft may belong to the U.S. Air Force; however, a subsequent report in August 2004 by the same organization (NIDS) found that the rash of sightings did not conform to previous deployment of black project aircraft and that the objects' origins and agendas were unknown.
Rendlesham Forest incident
A pyramid-shaped craft was reported to have landed near an American air base at Rendlesham Forest in Suffolk, England on December 27, 1980. Military personnel reported having approached at least one landed craft in the forest and observed it in great detail before it once again took flight. Another craft was observed landing in an open field near the base and then taking off at incredible speed. Between 2002 and 2005, reporter Bryant Gumbel hosted a series of exclusive SciFi Channel documentaries, one of which, entitled UFO Invasion at Rendlesham, focused on this incident. Gumbel interviewed some of the men involved with the sighting, and the documentary toured some of the scenes, attempting to gather evidence that something landed in the forest. The History Channel also aired an episode of UFO Files on the incident, calling it "Britain's Roswell".
Four US military personnel went to investigate what they believed to be a possible downed aircraft in the forest when they saw unexplained lights; they then saw a series of lights whilst in the forest. Only one of four personnel who went to investigate the lights claimed to have actually seen an actual craft, but this account emerged some time after in the initial incident, causing issues with its veracity and reliability. In particular, the craft was not witnessed by the three others who went with him that night. Natural phemomena such as a nearby lighthouse and barking Muntjac deer have been offered as explanations for what was seen and heard. MoD papers on the subject say nothing occurred that night which was of concern to British airspace security.
Belgian Air Force report
On March 30, 1990, citizens of the city of Eupen spotted what appeared to be a large black triangular craft hovering silently over the city for several minutes. Local police officials arrived on the scene and reported observing the object as it appeared to hover over apartment buildings. One officer reported that the object released a red glowing disk of light from its center which flew down to the ground and darted around several buildings before disappearing.
Phoenix Lights incident
One of the more famous appearances of these craft was during the event known as the "Phoenix Lights", where multiple unidentified objects, many of them black triangles, were spotted by the residents of Phoenix, Arizona and videotaped by both the local media and residents with camcorders across multiple evenings beginning on Thursday, March 13, 1997. Some lights drifted as low as 1000 feet and moved far too slowly for conventional aircraft and too silently for helicopters. Some of the lights appeared to group up in a giant "V" formation that lingered above the city for several minutes. Many residents reported one triangle to be over a mile wide that drifted slowly over their houses blocking out the stars of the night sky. Other reports indicated the craft were spotted flying away from Phoenix as far away as Las Vegas, Nevada and Los Angeles, California.
An official report made by the Air Force about the incident concluded that the military had been testing flares launched from conventional aircraft during that time. Eyewitnesses confirmed military jets were scrambled from nearby Luke Air Force Base, but instead of launching flares, they were seen chasing after some of the objects.
The next few nights, in an attempt to recreate the incident, local pilots flew prop-planes over the city in a "V" formation, but the sounds of their engines were easily heard. The original lights made no sound. Flares were also deployed above Phoenix. Comparison of the video taken of the lights (which appeared at night) against daytime images of the same scene show that the lights "disappear" at the exact moment they are shown to fall behind a mountain range. The mountains were invisible against the night sky. There were apparently no reported radar sightings of the objects which appears to be consistent with the flare theory.
Southern Illinois incident
The "St. Clair Triangle", "UFO Over Illinois", "Southern Illinois UFO", or "Highland, Illinois UFO" sighting occurred on January 5, 2000 over the towns of Highland, Dupo, Lebanon, Summerfield, Millstadt, and O'Fallon, Illinois, beginning shortly after 4:00 am. Five on-duty police officers around these locales, along with various other eye-witnesses, sighted and reported a massive, silent, triangular aircraft operating at an unusual treetop level altitude and speeds. The incident was examined in various television shows including the ABC special Seeing is Believing with Peter Jennings, an hour-long Discovery Channel special UFOs Over Illinois, an episode of the Syfy series Proof Positive and a half-hour-long independent documentary titled The Edge of Reality: Illinois UFO, January 5, 2000 by Darryl Barker Productions.
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- Summary of the Black Triangle UFO phenomenon at Space.com
- UAP In the UK Air Defence Region Full Text (PDF)
- Treatise on Black Triangle UFO Sightings
- Mysterious Dudley Dorito UFO spotted over UK skies for the third time in three years, Daily Mail, 11/17/2010