Editing Loran-C (section)

===Hyperbolic navigation===
[[File:Crude LORAN diagram.svg|thumb|right|A crude diagram of the LORAN principle—the difference between the time of reception of synchronized signals from radio stations A and B is constant along each hyperbolic curve; when demarcated on a map, such curves are known as "TD lines". "TD" stands for "Time Difference".]]
In conventional navigation, measuring one's location, or ''taking a fix'', is accomplished by taking two measurements against well known locations. In optical systems this is typically accomplished by measuring the angle to two landmarks, and then drawing lines on a [[nautical chart]] at those angles, producing an intersection that reveals the ship's location. Radio methods can also use the same concept with the aid of a [[radio direction finder]], but due to the nature of radio propagation, such instruments are subject to significant errors, especially at night. More accurate radio navigation can be made using pulse timing or phase comparison techniques, which rely on the time-of-flight of the signals. In comparison to angle measurements, these remain fairly steady over time, and most of the effects that change these values are fixed objects like rivers and lakes that can be accounted for on charts.

Timing systems can reveal the absolute distance to an object, as is the case in [[radar]]. The problem in the navigational case is that the receiver has to know when the original signal was sent. In theory, one could synchronize an accurate clock to the signal before leaving port, and then use that to compare the timing of the signal during the voyage. However, in the 1940s no suitable system was available that could hold an accurate signal over the time span of an operational mission.

Instead, radio navigation systems adopted the ''[[multilateration]]'' concept which is based on the difference in times (or phase) instead of the absolute time. The basic idea is that it is relatively easy to synchronize two ground stations, using a signal shared over a phone line for instance, so one can be sure that the signals received were sent at exactly the same time. They will not be received at exactly the same time, however, as the receiver will receive the signal from the closer station first. Timing the difference between two signals can be easily accomplished, first by physically measuring them on a cathode-ray tube, or simple electronics in the case of phase comparison.

The difference in signal timing does not reveal the location by itself. Instead, it determines a series of locations where that timing is possible. For instance, if the two stations are 300&nbsp;km apart and the receiver measures no difference in the two signals, that implies that the receiver is somewhere along a line equidistant between the two. If the signal from one is received exactly 100&nbsp;μs after, then the receiver is {{convert|30|km}} closer to one station than the other. Plotting all the locations where one station is 30&nbsp;km closer than the other produces a curved line. Taking a fix is accomplished by making two such measurements with different pairs of stations, and then looking up both curves on a navigational chart. The curves are known as ''lines of position'' or LOP.<ref>{{Cite book| author=Appleyard, S.F. |author2=Linford, R.S. |author3=Yarwood, P.J.| title=Marine Electronic Navigation |year=1988 | publisher=Routledge & Kegan Paul| pages=77–83 | isbn=0-7102-1271-2|edition=2nd }}</ref>

In practice, radio navigation systems normally use a ''chain'' of three or four stations, all synchronized to a ''master'' signal that is broadcast from one of the stations. The others, the ''secondaries'', are positioned so their LOPs cross at acute angles, which increases the accuracy of the fix. So for instance, a given chain might have four stations with the master in the center, allowing a receiver to pick the signals from two secondaries that are currently as close to right angles as possible given their current location. Modern systems, which know the locations of all the broadcasters, can automate which stations to pick.