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The turn (symbol tr or pla) is a unit of plane angle measurement that is the measure of a complete angle—the angle subtended by a complete circle at its center. One turn is equal to 2π radians, 360 degrees or 400 gradians. As an angular unit, one turn also corresponds to one cycle (symbol cyc or c) [1] or to one revolution (symbol rev or r). [2]
If every internal angle of a simple polygon is less than a straight angle (π radians or 180°), then the polygon is called convex. In contrast, an external angle (also called a turning angle or exterior angle) is an angle formed by one side of a simple polygon and a line extended from an adjacent side. [1]: pp. 261–264
Diagram showing the path of a driver performing a U-turn.A vehicle with a smaller turning diameter will be able to perform a sharper U-turn. The turning radius (alternatively, turning diameter or turning circle) of a vehicle defines the minimum dimension (typically the radius or diameter) of available space required for that vehicle to make a semi-circular U-turn without skidding.
Flight path angle γ: is the angle between horizontal and the velocity vector, which describes whether the aircraft is climbing or descending. Bank angle μ: represents a rotation of the lift force around the velocity vector, which may indicate whether the airplane is turning.
A standard rate turn is defined as a 3° per second turn, which completes a 360° turn in 2 minutes. This is known as a 2-minute turn, or rate one (180°/min). Fast airplanes, or aircraft on certain precision approaches, use a half standard rate ('rate half' in some countries), but the definition of standard rate does not change.
The relationship between speed and tilt can be calculated mathematically. We start with the formula for a balancing centripetal force: θ is the angle by which the train is tilted due to the cant, r is the curve radius in meters, v is the speed in meters per second, and g is the standard gravity, approximately equal to 9.81 m/s²:
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Two angles that share terminal sides, but differ in size by an integer multiple of a turn, are called coterminal angles. The reference angle (sometimes called related angle) for any angle θ in standard position is the positive acute angle between the terminal side of θ and the x-axis (positive or negative).