Hyperbolic navigation is a class of radio navigation systems in which a navigation receiver instrument is used to determine location based on the difference in timing of radio waves received from radio navigation beacon transmitters.
Such systems rely on the ability of two widely separated stations to broadcast a signal that is highly correlated in time. Typical systems broadcast either short pulses at the same time, or continual signals that are identical in phase. A receiver located at the midpoint between the two stations will receive the signals at the same time or have identical phase, but at any other location the signal from the closer station will be received first or have a different phase.
Determining the location of a receiver requires that the two synchronized stations be tuned in at the same time so the signals can be compared. This reveals a difference in time, corresponding to a relative distance closer to one station or the other. Plotting all the locations where this time difference may occur produces a hyperbolic line on a chart. To take a "fix", a second station pair is also tuned in to produce a second such curve. The two curves will normally intersect at two locations, so some other navigation system or a third measurement is needed to determine the exact location.
Hyperbolic location systems were first used during World War I in acoustic location systems for locating enemy artillery. The sound of a shell being fired was received by several microphones, and the time of reception sent to a computing center to plot the location. These systems were used into World War II. The first hyperbolic radio navigation system was the World War II-era Gee, introduced by the Royal Air Force for use by RAF Bomber Command. This was followed by the Decca Navigator System in 1944 by the Royal Navy, along with LORAN by the US Navy for long-range navigation at sea. Post war examples including the well-known US Coast Guard Loran-C, the international Omega system, and the Soviet Alpha and CHAYKA. All of these systems saw use until their wholesale replacement by satellite navigation systems like the Global Positioning System (GPS) in the 1990s. Satellite systems are also based on the hyperbolic principle.
Basic concepts
Timing-based navigation
Consider two ground-based radio stations located at a set distance from each other, say 300 km so that they are nearly exactly 1 ms apart at light speed. Both stations are equipped with identical transmitters set to broadcast a short pulse at a specific frequency. One of these stations, called the "secondary" is also equipped with a radio receiver. When this receiver hears the signal from the other station, referred to as the "primary", it triggers its own broadcast. The primary station can then broadcast any series of pulses, with the secondary hearing these and generating the same series after a 1 ms delay.
Consider a portable receiver located on the midpoint of the line drawn between the two stations, known as the baseline. In this case, the signals will, necessarily, take 0.5 ms to reach the receiver. By measuring this time, they could determine that they are precisely 150 km from both stations, and thereby exactly determine their location. If the receiver moves to another location along the line, the timing of the signals would change. For instance, if they time the signals at 0.25 and 0.75 ms, they are 75 km from the closer station and 225 from the further.
If the receiver moves to the side of the baseline, the delay from both stations will grow. At some point, for instance, they will measure a delay of 1 and 1.5 ms, which implies the receiver is 300 km from one station and 450 from the other. If one draws circles of 300 and 450 km radius around the two stations on a chart, the circles will intersect at two points. With any additional source of navigation information, one of these two intersections can be eliminated as a possibility, and thus reveal their exact location, or "fix".
Absolute vs. differential timing
There is a serious practical problem with this approach - in order to measure the time it took for the signals to reach the receiver, the receiver must know the precise time that the signal was originally sent. This is not possible in the case of uncooperative signal sources (like enemy artillery) and until the 2000s, clock distribution was an unsolved problem until the widespread introduction of inexpensive GPS receivers.
In the 1930s, such precise time measurements simply weren't possible; a clock of the required accuracy was difficult enough to build in fixed form, let alone portable. A high-quality crystal oscillator, for instance, drifts about 1 to 2 seconds in a month, or . This may sound small, but as light travels , this represents a drift of 420 km each hour. Only a few hours of flight time would render such a system unusable, a situation that remained in force until the introduction of commercial atomic clocks in the 1960s.
However, it is possible to accurately measure the difference between two signals. Much of the development of suitable equipment had been carried out between 1935 and 1938 as part of the efforts to deploy radar systems. The UK, in particular, had invested considerable effort in the development of their Chain Home system. The radar display systems for Chain Home were based on oscilloscopes (or oscillographs as they were known at time) triggered to start their sweep when the broadcast signal was sent. Return signals were amplified and sent into the display, producing a "blip". By measuring the distance along the face of the oscilloscope of any blips, the time between broadcast and reception could be measured, thus revealing the range to the target.
With very slight modification, the same display could be used to time the difference between two arbitrary signals. For navigational use, any number of identifying characteristics could be used to differentiate the primary from secondary signals. In this case, the portable receiver triggered its trace when it received the primary signal. As the signals from secondary arrived they would cause a blip on the display in the same fashion as a target on the radar, and the exact delay between the primary and secondary easily determined.
Position fix
Consider the same examples as our original absolute-timed cases. If the receiver is located on the midpoint of the baseline the two signals will be received at exactly the same time, so the delay between them will be zero. However, the delay will be zero not only if they are located 150 km from both stations and thus in the middle of the baseline, but also if they are located 200 km from both stations, and 300 km, and so forth. So in this case the receiver cannot determine their exact location, only that their location lies somewhere along a line perpendicular to the baseline.
In the second example the receivers determined the timing to be 0.25 and 0.75 ms, so this would produce a measured delay of 0.5 ms. There are many locations that can produce this difference - 0.25 and 0.75 ms, but also 0.3 and 0.8 ms, 0.5 and 1 ms, etc. If all of these possible locations are plotted, they form a hyperbolic curve centred on the baseline. Navigational charts can be drawn with the curves for selected delays, say every 0.1 ms. The operator can then determine which of these lines they lie on by measuring the delay and looking at the chart.
A single measurement reveals a range of possible locations, not a single fix. The solution to this problem is to simply add another secondary station at some other location. In this case two delays will be measured, one the difference between the primary and secondary "A", and the other between the primary and secondary "B". By looking up both delay curves on the chart, two intersections will be found, and one of these can be selected as the likely location of the receiver. This is a similar determination as in the case with direct timing/distance measurements, but the hyperbolic system consists of nothing more than a conventional radio receiver hooked to an oscilloscope.
Because a secondary could not instantaneously transmit its signal pulse on receipt of the primary signal, a fixed delay was built into the signal. No matter what delay is selected, there will be some locations where the signal from two secondary would be received at the same time, and thus make them difficult to see on the display. Some method of identifying one secondary from another was needed. Common methods included transmitting from the secondary only at certain times, using different frequencies, adjusting the envelope of the burst of signal, or broadcasting several bursts in a particular pattern. A set of stations, primary and secondaries, was known as a "chain". Similar methods are used to identify chains in the case where more than one chain may be received in a given location.
Operational systems Meint Harms was the first to have attempted the construction of a hyperbolic navigation systems, starting with musings on the topic in 1931 as part of his master's examination at Seefahrtschule Lübeck (Navigation College). After taking the position of Professor for Mathematics, Physics and Navigation at the Kaisertor in Lübeck, Harms tried to demonstrate hyperbolic navigation making use of simple transmitters and receivers. On 18 February 1932 he received Reichspatent-Nr. 546000 for his invention.
Gee
The first operational hyperbolic navigation was UK's Gee, first used experimentally by RAF Bomber Command in 1941. Gee was used both for bombing over Germany as well as navigation in the area of the UK, especially for landing at night. Several Gee chains were built in the UK, and after the war this expanded for four chains in the UK, two in France, and one in northern Germany. For a period following the formation of the International Civil Aviation Organization in 1946, Gee was considered as the basis for a worldwide standard for navigation, but the VHF omnidirectional range (VOR) system was selected instead, and the last Gee chain was eventually shut down in 1970.
Gee signals from a given chain were all sent on a single frequency. The primary station sent two signals, the "A" signal that marked the beginning of a timing period, and the "D" signal which was essentially two "A"s to mark the end. In every period, one of the two secondaries would respond, alternating their "B" and "C" signals. The resulting pattern was "ABD…ACD…ABD…" A wide-band receiver was used to tune in chain and the output sent to the operator's oscilloscope. As the chains were closely spaced in frequency to allow them to be received by a single tuner, this sometimes resulted in the signals from several chains appearing on the display. To distinguish the chains in these cases, a second "A" signal, the "A1" or "ghost A", was periodically keyed in, and the pattern of flashing on the display could be used to identify the chain.
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. They would then tune a local oscillator that triggered the oscilloscope's trace so that it matched the clock at the primary station (which could, and did, change over time). Next, they would use a variable delay that was added to the local oscillators signal to move the entire display back or forth 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.