A high-energy turn (HET) was a maneuver that allowed one to turn a starship very rapidly. The odds of success varied greatly upon the mass of the starship in question. By using additional energy, the ship could be made to turn at a much higher rate than usual. This allowed a ship to make up to a 180° turn nearly instantaneously. As one might expect, this was not good on the ship. The hull, systems, and crew took a tremendous strain. Eventually this strain would result in a breakdown. Some ships were better at making HETs without having a breakdown and ships with superior flight controllers could make more HETs without suffering a breakdown. It was also called a "warp turn" because performing an HET required the generation of a warp field. (RIS Bouteina, Star Fleet Battles)
Even ships as massive as PumwI'-class prison ships could perform HETs; however, the last recorded use of an HET on a ship of that class resulted in a fifty-fifty chance of success. (RIS Bouteina: "Eidolon")
It was generally not recommended to perform a high-energy turn while under cloak, as doing so would damage the cloaking device. Also, the Norexan-class ship was capable of a high-energy turn. (RIS Bouteina: "The Whole Kitten Kaboodle")
Ships of the Stoneship-class could perform a HET at 0.75c within a 100 km radius. (Star Trek: The Stoneship Files: "Highly Illogical")
External link[]
High-energy turn article at Memory Beta, the non-canon Star Trek wiki.