Hyperbolic navigation refers to a class of navigation systems based on the difference in timing between the reception of two signals, without reference to a common clock. This timing reveals the difference in distance from the receiver to the two stations. Plotting all of the potential locations of the receiver for the measured delay produces a series of hyperbolic lines on a chart. Taking two such measurements and looking for the intersections of the hyperbolic lines reveals the receiver's location to be in one of two locations. Any other form of navigation information can be used to eliminate this ambiguity and determine a fix.
Hyperbolic System Principles:
The principle on which all hyperbolic navigation and positioning systems operate is essentially the same. If two transmitters radiating a radio wave in the same phase are located at the ends of a baseline, as shown in the diagram below, then a receiver in the centre of the baseline will receive the wave in the same phase since the time-of-flight of the wave to the receiver from both transmitters is the same. Applying this principle in reverse, if the receiver is receiving the two waves in phase, then it must be located either at the centre of the baseline or somewhere along the perpendicular line l - l'.
Operating System:
The operator initially tuned in their receiver to see a stream of pulses on the display, sometimes including those of other chains which were nearby in frequency. He would then tune a local oscillator that started the trigger of the oscilloscope's trace so that it matched the clock at the master station (which could, and did, change over time). Next he would use a variable delay to move the start of the signal so one of the "A" pulses was at the very left side of the 'scope (the action is identical to the "horizontal hold" dial on an analog television). Finally the speed of the trace across the display would be tuned so the D pulse was just visible on the right. The distance of the B or C pulse from the A pulse could now be measured with an attached scale. The resulting delays could then be looked up on a navigational chart.
Loran Overview:
f the positions of the two synchronized stations are known, then the position of the receiver can be determined as being somewhere on a particular hyperbolic curve where the time difference between the received signals is constant. In ideal conditions, this is proportionally equivalent to the difference of the distances from the receiver to each of the two stations.
So a LORAN receiver which only receives two LORAN stations cannot fully fix its position—it only narrows it down to being somewhere on a curved line. Therefore, the receiver must receive and calculate the time difference between a second pair of stations. This allows to be calculated a second hyperbolic line on which the receiver is located. Where these two lines cross is the location of the receiver.
In practice, one of the stations in the second pair also may be—and frequently is—in the first pair. This means signals must be received from at least three LORAN transmitters to pinpoint the receiver's location. By determining the intersection of the two hyperbolic curves identified by this method, a geographic fix can be determined.
Future Of Loran:
With the perceived vulnerability of GNSS systems, and their own propagation and reception limitations, renewed interest in LORAN applications and development has appeared.Enhanced LORAN, also known as eLORAN or E-LORAN, comprises an advancement in receiver design and transmission characteristics which increase the accuracy and usefulness of traditional LORAN. With reported accuracy as good as ± 8 meters, the system becomes competitive with unenhanced GPS. eLORAN also includes additional pulses which can transmit auxiliary data such as DGPS corrections. eLORAN receivers now use "all in view" reception, incorporating signals from all stations in range, not solely those from a single GRI, incorporating time signals and other data from up to 40 stations. These enhancements in LORAN make it adequate as a substitute for scenarios where GPS is unavailable or degraded.
List Of Loran-C Transmitter:
A list of LORAN-C transmitters. Stations with an antenna tower taller than 300 metres (984 feet) are shown in bold.
| Station | Country | Chain | Coordinates | Remarks |
| Afif | Saudi Arabia | Saudi Arabia South (GRI 7030) Saudi Arabia North (GRI 8830) | 23°48′36.66″N42°51′18.17″E | 400 kW |
| Al Khamasin | Saudi Arabia | Saudi Arabia South (GRI 7030) Saudi Arabia North (GRI 8830) | 20°28′2.34″N44°34′51.9″E | |
| Al Muwassam | Saudi Arabia | Saudi Arabia South (GRI 7030) Saudi Arabia North (GRI 8830) | 16°25′56.87″N42°48′6.21″E | |
| Angissq | Greenland | Shut down on 31 December 1994 | 59°59′17.348″N45°10′26.91″W | used until 27 July 1964 a 411.48 metre tower |
| Anthorn | United Kingdom | Lessay (GRI 6731) | 54°54′41.949″N3°16′42.58″W | Master and Slave on 9 Jan. 2016. Replacement for transmitter Rugby[50] |
| Ash Shaykh Humayd | Saudi Arabia | Saudi Arabia South (GRI 7030) Saudi Arabia North (GRI 8830) | 28°9′15.87″N34°45′41.36″E | |
| Attu Island | United States | North Pacific (GRI 9990) Russian-American (GRI 5980) | 52°49′44″N173°10′49.7″E | demolished in August 2010 |
| Balasore | India | Calcutta (GRI 5543) | 21°29′11.02″N86°55′9.66″E | |
| Barrigada | Guam | shut down | 13°27′50.16″N144°49′33.4″E | |
| Baudette | United States | North Central U.S. (GRI 8290) Great Lakes (GRI 8970) | 48°36′49.947″N94°33′17.91″W | |
| Berlevåg | Norway | Bø (GRI 7001) | 70°50′43.07″N29°12′16.04″E | |
| Bilimora | India | Bombay (GRI 6042) | 20°45′42.036″N73°02′14.48″E | |
| Boise City | United States | Great Lakes (GRI 8970) South Central U.S. (GRI 9610) | 36°30′20.75″N102°53′59.4″W | |
| Bø, Vesterålen | Norway | Bø (GRI 7001) Eiði (GRI 9007) | 68°38′06.216″N14°27′47.35″E | |
| Cambridge Bay | Canada | shut down | 69°06′52.840″N105°00′55.95″W | free-standing lattice tower, used as NDB |
| Cape Race | Canada | Canadian East Coast (GRI 5930) Newfoundland East Coast (GRI 7270) | 46°46′32.74″N53°10′28.66″W | used a 411.48 metre tall tower until 2 February 1993, uses now a 260.3 metre tall tower |
| Caribou, Maine | United States | Canadian East Coast (GRI 5930) Northeast U.S. (GRI 9960) | 46°48′27.305″N67°55′37.15″W | |
| Carolina Beach | United States | Southeast U.S. (GRI 7980) Northeast US (GRI 9960) | 34°03′46.208″N77°54′46.10″W | |
| Chongzuo | China | China South Sea (GRI 6780) | 22°32′35.8″N107°13′19″E | |
| Comfort Cove | Canada | Newfoundland East Coast (GRI 7270) | 49°19′53.65″N54°51′43.2″W | |
| Dana | United States | Great Lakes (GRI 8970) Northeast US (GRI 9960) | 39°51′7.64″N87°29′10.71″W | |
| Dhrangadhra | India | Bombay (GRI 6042) | 23°0′16.2″N71°31′37.64″E | |
| Diamond Harbor | India | Calcutta (GRI 5543) | 22°10′20.42″N88°12′15.8″E | |
| Eiði | Faroe Islands | Eiði (GRI 9007) | 62°17′59.69″N7°4′25.59″W | |
| Estartit | Spain | Mediterranean Sea (GRI 7990) (shut down) | 42°3′36.63″N3°12′16.08″E | |
| Fallon | United States | U.S. West Coast (GRI 9940) | 39°33′6.77″N118°49′55.6″W | |
| Fox Harbour | Canada | Canadian East Coast (GRI 5930) Newfoundland East Coast (GRI 7270) | 52°22′35.29″N55°42′28.68″W | |
| George | United States | Canadian West Coast (GRI 5990) | 47°03′48.096″N119°44′38.97″W | |
| Gesashi | Japan | North West Pacific (GRI 8930) East Asia (GRI 9930) | 26°36′25.09″N128°8′56.94″E | |
| Gillette | United States | North Central U.S. (GRI 8290) South Central U.S. (GRI 9610) | 44°0′11.21″N105°37′24″W | |
| Grangeville | United States | Southeast U.S. (GRI 7980) South Central U.S. (GRI 9610) | 30°43′33.24″N90°49′43.01″W | |
| Havre | United States | North Central U.S. (GRI 8290) | 48°44′38.58″N109°58′53.3″W | |
| Hellissandur | Iceland | shut down on 31 December 1994 | 64°54′14.793″N23°54′47.83″W | 411.48 metre tall tower, now used for longwave broadcasting of RÚV on 189 kHz |
| Helong | China | China North Sea (GRI 7430) | 42°43′11″N129°6′27.07″E | |
| Hexian | China | China South Sea (GRI 6780) | 23°58′3.21″N111°43′9.78″E | |
| Iwo Jima | Japan | shut down in September 1993. Dismantled | 24°48′26.262″N141°19′34.76″E | used a 411.48 metre tall tower |
| Jan Mayen | Norway | Bø (GRI 7001) Ejde (GRI 9007) | 70°54′51.478″N8°43′56.52″W | |
| Johnston Island | United States | shut down | 16°44′43.82″N169°30′30.9″W | |
| Jupiter | United States | Southeast U.S. (GRI 7980) | 27°1′58.49″N80°6′52.83″W | |
| Kargaburun | Turkey | Mediterranean Sea (GRI 7990) (shut down) | 40°58′20.51″N27°52′1.89″E | |
| Kwang Ju | South Korea | East Asia (GRI 9930) | 35°2′23.69″N126°32′27.2″E | |
| Lampedusa | Italy | Mediterranean Sea (GRI 7990) (shut down) | 35°31′22.11″N12°31′31.06″E | |
| Las Cruces | United States | South Central U.S. (GRI 9610) | 32°4′18.1″N106°52′4.32″W | |
| Lessay | France | Shut down on 31 December 2015 Lessay (GRI 6731) Sylt (GRI 7499) | 49°8′55.27″N1°30′17.03″W | |
| Loop Head | Ireland | Lessay (GRI 6731) Eiði (GRI 9007) | (Never built) | 250 kW |
| Malone | United States | Southeast U.S. (GRI 7980) Great Lakes (GRI 8970) | 30°59′38.87″N85°10′8.71″W | |
| Middletown | United States | U.S. West Coast (GRI 9940) | 38°46′57.12″N122°29′43.9″W | |
| Minamitorishima | Japan | North West Pacific (GRI 8930) | 24°17′8.79″N153°58′52.2″E | used until 1985 a 411.48 metre tall tower |
| Nantucket | United States | Canadian East Coast (GRI 5930) Northeast U.S. (GRI 9960) | 41°15′12.42″N69°58′38.73″W | |
| Narrow Cape | United States | Gulf of Alaska (GRI 7960) North Pacific (GRI 9990) | 57°26′20.5″N152°22′10.2″W | |
| Niijima | Japan | North West Pacific (GRI 8930) East Asia (GRI 9930) | 34°24′12.06″N139°16′19.4″E | |
| Patapur | India | Calcutta (GRI 5543) | 20°26′50.627″N85°49′38.67″E | |
| Pohang | South Korea | North West Pacific (GRI 8930) East Asia (GRI 9930) | 36°11′5.33″N129°20′27.4″E | |
| Port Clarence | United States | Gulf of Alaska (GRI 7960) North Pacific (GRI 9990) | 65°14′40.372″N166°53′11.996″W | uses a 411.48 metre tall tower Demolished 28 April 2010 [51] |
| Port Hardy | Canada | Canadian West Coast (GRI 5990) | 50°36′29.830″N127°21′28.48″W | |
| Rantum (Sylt) | Germany | Shut down on 31 December 2015 Lessay (GRI 6731) Sylt (GRI 7499) | 54°48′29.94″N8°17′36.9″E | |
| Raymondville | United States | Southeast U.S. (GRI 7980) South Central U.S. (GRI 9610) | 26°31′55.17″N97°49′59.52″W | |
| Raoping | China | China South Sea (GRI 6780) China East Sea (GRI 8390) | 23°43′26.02″N116°53′44.7″E | |
| Rongcheng | China | China North Sea (GRI 7430) China East Sea (GRI 8390) | 37°03′51.765″N122°19′25.95″E | |
| Rugby | United Kingdom | Experimental (GRI 6731) (shut down at the end of July 2007) | 52°21′57.893″N1°11′27.39″W | |
| Saint Paul | United States | North Pacific (GRI 9990) | 57°9′12.35″N170°15′6.06″W | |
| Salwa | Saudi Arabia | Saudi Arabia South (GRI 7030) Saudi Arabia North (GRI 8830) | 24°50′1.46″N50°34′12.54″E | |
| Searchlight | United States | South Central U.S. (GRI 9610) U.S. West Coast (GRI 9940) | 35°19′18.305″N114°48′16.88″W | |
| Sellia Marina | Italy | Mediterranean Sea (GRI 7990) (shut down) | 38°52′20.72″N16°43′6.27″E | |
| Seneca | United States | Great Lakes (GRI 8970) Northeast U.S. (GRI 9960) | 42°42′50.716″N76°49′33.30″W | |
| Shoal Cove | United States | Canadian West Coast (GRI 5990) Gulf of Alaska (GRI 7960) | 55°26′20.940″N131°15′19.09″W | |
| Soustons | France | Shut down on 31 December 2015 Lessay (GRI 6731) | 43°44′23.21″N1°22′49.63″W | |
| Tok | United States | Gulf of Alaska (GRI 7960) | 63°19′42.884″N142°48′31.34″W | |
| Tokachibuto | Japan | Eastern Russia Chayka (GRI 7950) North West Pacific (GRI 8930) | 42°44′37.2″N143°43′10.5″E | |
| Upolo Point | United States | shut down | 20°14′51.12″N155°53′4.34″W | |
| Værlandet | Norway | Sylt (GRI 7499) Ejde (GRI 9007) | 61°17′49.49″N4°41′47.05″E | |
| Veraval | India | Bombay (GRI 6042) | 20°57′09.316″N70°20′11.73″E | |
| Williams Lake | Canada | Canadian West Coast (GRI 5990) North Central U.S. (GRI 8290) | 51°57′58.78″N122°22′1.55″W | |
| Xuancheng | China | China North Sea (GRI 7430) China East Sea (GRI 8390) | 31°4′8.3″N118°53′8.78″E | |
| Yap | Federated States of Micronesia | shut down in 1987. Dismantled | 9°32′44.76″N138°9′53.48″E | used a 304.8 metre tall tower |
Resolution:
Points of zero phase difference are referred to as 'lanes'. It is not necessary to rely on these however since the receiver can measure phase differences at points in between lanes. The maximum resolution of the system is expressed as the smallest distance within a lane that can be measured and is limited by a number of factors. In the case of HiFix the maximum resolution of the system is given as 0.01 lane, which at an operating frequency of 1900kHz would be 1.6 metres. Since the distance between hyperbolae and hence lanes increases with distance away from the transmitters, the accuracy of the system reduces in proportion. The operator would have to take this into account when a fix is obtained.
