Definition
A family of open curves formed by lines of equal time difference between signals received from two fixed transmitter stations. In long-range radio navigation systems such as Loran, each curve represents all the points where the time difference between paired station signals is the same. By measuring time differences from two or more pairs of stations, an aircraft's position is fixed at the intersection of two hyperbolic curves.
Plain English
Curved lines on a navigation chart that show every point where the timing difference between two radio stations is the same. Where two of these curves cross is your position.
Context Anchor
Seen in discussions of older long-range radio navigation systems, especially systems that compared signals from pairs of ground stations.
Derivation
From the Greek hyperbole, meaning 'a throwing beyond' or 'excess.' The mathematical hyperbola gets its name because the curve is defined by a constant difference between distances to two fixed points. In navigation, the 'difference' is a time difference between two station signals, which traces out the same shape.
Why Pilots Care
Understanding the hyperbolic principle explains how systems like Loran fixed an aircraft's position before GPS, and why two pairs of stations were needed to get a usable fix.
Analogy
Imagine marking every place where you are exactly 5 miles farther from one town than from another town. Those places would form a curved line, not a straight line. Hyperbolic curves work the same way with radio signals instead of towns.
Grounding Statement
Picture two radio towers sending pulses. If you are anywhere along a certain curved line between them, the pulse from one always arrives the same fraction of a second before the other. That curved line is one hyperbolic curve.
Intuition Check
Do not read hyperbolic curves as curved flight paths. They are position lines created by comparing two signal sources.
Example Sentence 1
Loran-C used hyperbolic curves printed on charts so the pilot could plot a position from the station time differences shown on the receiver.
Example Sentence 2
Hyperbolic curves allow position fixes from signal time differences without requiring direct distance to each station.