Editing Decca Navigator System (section)

== Principles of operation ==
=== Overview ===
[[Image:Crude loran diagram.PNG|thumb|right|''The Decca Navigator principle.'' <br> The phase difference between the signals received from stations A (Master) and B (Secondary) is constant along each hyperbolic curve. The foci of the hyperbolas are at the transmitting stations, A and B.]]

The Decca Navigator System consisted of individual groups of land-based radio transmitters organised into ''chains'' of three or four stations. Each chain consisted of a [[master station]] and three (occasionally two) secondary stations, termed Red, Green and Purple. Ideally, the secondaries would be positioned at the vertices of an equilateral triangle with the master at the centre. The baseline length, that is, the master–secondary distance, was typically {{convert|60-120|nmi|km}}.

Each station transmitted a continuous wave signal; comparing the relative [[phase (waves)|phases]] of the signals from the master and one of the secondaries produced a relative phase measure that was presented on a clock-like display. The phase difference was caused by the relative distance between the stations as seen by the receiver. As the receiver moves these distances change and those changes are represented by the movement of the hands on the displays.

If one selects a particular phase difference, say 30 degrees, and plots all the locations where that phase difference occurs, the result is a set of [[hyperbola|hyperbolic]] ''[[lines of position]]'' called a ''pattern''. As there were three secondaries there were three patterns, also termed Red, Green and Purple. The patterns were drawn on [[nautical chart]]s as a set of hyperbolic lines in the appropriate colour.

Navigators determined their location by reading the phase difference from two or more of the patterns from the displays. They could then look at the chart to find where the two closest charted hyperbolas crossed. The accuracy of this measurement was improved by choosing the set of two patterns that resulted in the lines crossing at as close to a right angle as possible.

=== Detailed principles of operation ===
When two stations transmit at the [[phase-locked loop|phase-locked frequency]], the difference in phase between the two signals is constant along a hyperbolic locus. However, if two stations transmit on the same frequency, it is impossible for the receiver to separate them. Instead, each chain was allocated a nominal frequency, known as 1''f'', and each station in the chain transmitted at a harmonic of this base frequency, as follows:

{| class="wikitable"
|-
! Station!! Harmonic !! Frequency (kHz)
|-
| Master || 6''f'' || 85.000
|-
| Purple || 5''f'' || 70.833
|-
| Red || 8''f'' || 113.333
|-
| Green || 9''f'' || 127.500
|}

The frequencies given are those for Chain 5B, known as the English Chain, but all chains used similar frequencies between 70&nbsp;kHz and 129&nbsp;kHz.

Decca receivers multiplied the signals received from the Master and each Slave by different values to arrive at a common frequency ([[least common multiple]], LCM) for each Master/Slave pair, as follows:

{| class="wikitable"
|-
! Pattern !! Slave Harmonic !! Slave Multiplier !! Master Harmonic !! Master Multiplier !! Common Frequency
|-
| Purple || 5''f'' || ×6 || 6''f'' || ×5 || 30''f''
|-
| Red || 8''f'' || ×3 || 6''f'' || ×4 || 24''f''
|-
| Green || 9''f'' || ×2 || 6''f'' || ×3 || 18''f''
|}

It was phase comparison at this common frequency that resulted in the hyperbolic lines of position. The interval between two adjacent hyperbolas on which the signals are in phase was called a ''lane''. Since the wavelength of the common frequency was small compared with the distance between the Master and Slave stations there were many possible lines of position for a given phase difference, and so a unique position could not be arrived at by this method.

Other receivers, typically for aeronautical applications, divided the transmitted frequencies down to the basic frequency (1''f'') for phase comparison, rather than multiplying them up to the LCM frequency.

=== Lanes and zones ===
[[File:Admiralty Chart No 1607 Thames Estuary Southern Part, Published 1967.jpg|300px|thumb|right|A 1967 [[Admiralty chart|Admiralty]] Decca Chart of the Thames Estuary, marked with red and green lanes and zones.]]
Early Decca receivers were fitted with three rotating ''Decometers'' that indicated the phase difference for each pattern. Each Decometer, which could be read to a resolution of a centilane, drove a second indicator that counted the number of lanes traversed &ndash; each 360 degrees of phase difference was one lane traversed. In this way, assuming the point of departure was known, a more or less distinct location could be identified.

The lanes were grouped into ''zones'', with 18 green, 24 red, or 30 purple lanes in each zone. This meant that on the baseline (the straight line between the Master and its Slave) the zone width was the same for all three patterns of a given chain. Typical lane and zone widths on the baseline are shown in the table below (for chain 5B):

{| class="wikitable"
|-
! Lane or Zone!! Width on Baseline
|-
| Purple lane || 352.1 m
|-
| Red lane || 440.1 m
|-
| Green lane || 586.8 m
|-
| Zones (all patterns)|| 10563 m
|}

The lanes were numbered 0 to 23 for red, 30 to 47 for green and 50 to 79 for purple. The zones were labelled A to J, repeating after J. A Decca position coordinate could thus be written: Red I 16.30; Green D 35.80. Later receivers incorporated a microprocessor and displayed a position in latitude and longitude.

=== Multipulse ===
''Multipulse'' provided an automatic method of lane and zone identification by using the same phase comparison techniques described above on lower frequency signals.

The nominally continuous wave transmissions were in fact divided into a 20-second cycle, with each station in turn simultaneously transmitting all four Decca frequencies (5''f'', 6''f'', 8''f'' and 9''f'') in a phase-coherent relationship for a brief period of 0.45 seconds each cycle. This transmission, known as Multipulse, allowed the receiver to extract the 1''f'' frequency and so to identify the lane that the receiver was in (to a resolution of a zone).

As well as transmitting the Decca frequencies of 5''f'', 6''f'', 8''f'' and 9''f'', an 8.2''f'' signal, known as Orange, was also transmitted. The beat frequency between the 8.0''f'' (Red) and 8.2''f'' (Orange) signals allowed a 0.2''f'' signal to be derived and so resulted in a hyperbolic pattern in which one cycle (360°) of phase difference equates to 5 zones.

Assuming that one's position was known to this accuracy, this gave an effectively unique position.

=== Range and accuracy ===
During daylight, ranges of around {{convert|400|nmi|km|-1}} could be obtained, reducing at night to 200 to {{convert|250|nmi|km|-1}}, depending on propagation conditions.

The accuracy depended on:
* Width of the lanes
* Angle of cut of the hyperbolic lines of position
* Instrumental errors
* Propagation errors (for example, [[skywave]])

By day these errors could range from a few meters on the baseline up to a nautical mile at the edge of coverage. At night, skywave errors were greater and, on receivers without multipulse capabilities, it was not unusual for the position to jump a lane, sometimes without the navigator knowing.

Although in the days of differential [[Global Positioning System|GPS]] this range and accuracy may appear poor, in its day the Decca system was one of the few, if not the only, position fixing system available to many mariners. Since the need for an accurate position is less when the vessel is further from land, the reduced accuracy at long ranges was not a great problem.