How LORAN Worked

check that out. I mentioned that Loomis was instrumental in developing a technology called Lauren l O R A N. And today I'm going to talk about that technology in deeper detail and how it uses mathematics and radio signals to help ships navigate far off the coast, or rather how it used to do that, as the system has since been phased out, but more on that later. I do think that Lauren is pretty cool, and it does give me a chance to talk about mathematics a little

bit now, as we'll discuss in this episode. I won't go into incredible detail mathematically speaking, because it involves things like hyperbolas, which are way easier to talk about with the use of visual aids. However, first I should give some background on laur Anne. In the nineteen forties, there was no such thing as the Global Positioning System or GPS. You could not turn on a computing device and activate a helpful little app to see where you were on

the globe. No one had invented a rocket capable of reaching orbit, let alone put a satellite out in space at that point. Yet there was a need for reliable navigation systems for ships and later on for aircraft. This need was made more urgent when the Second World War began. So you had different systems that were already in place, but many of them relied upon the elements things like seeing where the sun was and making measurements using something

like a sextant. You had ships even leading up into World War Two that we're dependent upon these kind of systems, and for commercial ships that didn't have the benefit of military technology, this lasted even longer, and that was not ideal by n It seemed the question wasn't if the United States was going to be pulled into the Second

World War, but rather when. Because of this impending threat, several important people urged President Franklin Roosevelt to form a Special Scientific Council to head research and development projects in science and technology that could be useful during wartime. Among these people were Vanavar Bush, who served as scientific advisor

to the President. James Knant, who was president of Harvard at the time, and Carl Compton, who was president of m I. T. Roosevelt approved the plan, and the National Defense Research Council, or in d r C was born. The council looked at different technologies for detecting aircraft, often ships, and decided that microwaves were the most promising. Lead Carl Compton reached out to Alfred Lee Loomis to head up a special committee called the Microwave Committee to look into

the matter. Loomis and his team determined that microwaves could be ideal for a detecting aircraft, but that the US had no technology capable of emitting microwaves in the frequency range they desired and enough power to work properly. Meanwhile, in Great Britain, scientists had developed a magnetron capable of

creating powerful microwaves in those frequencies. Great Britain sent a group of scientists to the United States to try and develop a radar system that could take advantage of this technology. Sir Henry Tizard and his team brought over a cavity magnetron and Loomis invited the UK scientists to meet with the Microwave Committee. The committee convinced Compton to set aside a space at m I T for research and development with microwaves, and the m I T Radiation Laboratory or

rad Lab was born. Now, the reason they chose the name Radiation Laboratory was pretty interesting. It was all a matter of deception of misdirection. The lab did not want anyone associated with the Access powers to find out what they were working on, so the Allies could maintain an advantage during the war, especially when it came to navigation

and detection of aircraft and other vessels. So to that end they chose the name Radiation Laboratory for a siwhat paradoxical reason, or at least in retrospect, it seems paradoxical. It made it sound as though the lab was investigating nuclear science, as in things like nuclear power and potentially

a nuclear bomb. Not At the time, the prevailing feeling was that nuclear science was such a young discipline that would take too long to make any advances in the field that could possibly have an effect during the war, and and so they chose to disguise their efforts to advance radar technology by claiming to be a nuclear science lab, which I think is pretty wild, especially when you consider that the actual end of World War Two would be in large part due to the development of nuclear weapons.

The lab made significant contributions to science and technology, with numerous practical applications. Among them was the Long Range Navigation System or LAUREN. Now, the story of LAUREN really gets going on October first, nineteen forty, when the Army Signal Technical Committee met to create requirements for what it called

a precision navigational equipment for guiding airplanes. The committee was asking for a means to provide navigational assistance from a distance of five hundred miles, a flight ceiling of thirty five thousand feet, and inaccuracy of within one thousand feet at two hundred miles out. In other words, a planes navigator should be able to determine the planes position within one thousand feet of its act tool position while still two hundred miles out from the radio transmitters that are

beaming signals to the plane. Alfred Lee Loomis had a proposal to meet these requirements. He thought that this would originally be used for ships, not for aircraft because it would require building special receivers, and at the time, there wasn't really a practical way of building a receiver small enough to fit on an aircraft, which already had a pretty strict limit on how much weight and how much

space was available in them. Loomis had a clever idea that involved pairs of radio transmitting stations sending out synchronized signals. A receiver aboard a ship would pick up these signals, and by measuring the delay between the two signals, you could figure out your basic distance from the two transmitters. With a second pair of transmitters or a third transmitting tower, you could figure out your actual position. And it all had to do with the formulas for hyperbolas, which is

why laura and is also known as a hyperbolic navigation system. Now, I know all the mathematicians out there already have a firm grasp of what a hyperbola is, but for some of us we might need some instruction or refresher It's been more than twenty years since I took a mathematics course, and I needed a little reminder for myself. So here we go. Hyperbola is a symmetrical open curve that represents this set of points in a plane whose distances to two fixed points called folk i in that same plane

have a constant difference. So by a symmetrical open curve we mean you have two curved lines called branches or connected components. They are symmetrical, so they are mirror images of each other, with the open side of the curves facing outward from each other. They look kind of like infinite bows. As the arms extend out from the center of the hyperbola, which is called the vert vertex the

verticey ease of the hyperbola, they become less curved. So the further out the lines go, the more straight they appear. The two fixed points or foci, are each on the inside of one of those curves or branches. Now remember the branches represent a set of points. If you were to select any of those points along one of the curves, you can measure the distance between that point and the

two foci. The point will be closer to its own focus than the focus of the other curve, and you subtract one distance from the other and you take the absolute value, meaning you make it a positive value. So if it would have been negative, you change it to a positive You will then find the constant for that hyperbola.

If you were to pick any other point on that same curve and repeat this process where you measure the distance between that point and the FOLCA and it's foci and that point and the folk I of the other curve, and then subtract the two, you would still arrive at that same value. That woman, you take the absolute value. The folk I are in a position relative to the curves, so that the difference between the distance of any point on the curves and the folk I will always be

the same. The curves thus represent a selection of possible locations from the perspective of the folk I. Now that's the secret behind Lauren. But how well I'll tell you. But first let's take a quick break to thank our sponsor. Okay, So imagine you've got a coastline, and along this coastline you have transmitting towers that are paired together so that they send out a pulse of signals in perfect synchronization.

If you were on a boat out at sea equa distant from the two towers, you would receive both sets of signals at exactly the same time. But let's say you're a little closer to Tower A than you are from Tower B. What happens then, Well, Tower A and Tower B send out their signals at exactly the same time. It is synchronized, so you would receive Tower a's signals a little bit earlier than you would receive Tower b's signals.

That's because the signals from Tower B have to travel further than the signals from Tower A, and the signals are traveling at a constant rate of speed. So what speed is that, Well, it's the speed of light, because radio waves are electromagnetic radiation, as is light now in our atmosphere, because light does travel at different speeds through different media. In the vacuum of space, it's one speed. But in our atmosphere light travels at two thousand seven

kilometers per second. I'm really going to focus on kilometers for this. It makes it easier in the long run. So it's not like there would be a long delay between the two incoming signals. I mean that that speed. Unless you are really far away, you wouldn't be able to have a massive delay between the two. And if you were really far away, you wouldn't be able to

pick up the signals in the first place. So, uh, we're talking about a delay that's measurable in micro seconds, but with a Loran receiver that's long enough to do some serious calculations. Now, the two towers that are transmitting represent the foci of a hyperbola. So you're on this boat and your receiver picks up that you're getting the signals from Tower A let's say about two hundred micro seconds before you get the signals from tower B, so you are closer to Tower A by a factor of

two hundred micro seconds. You also happen to know how far apart Tower A and Tower B R because that's part of the whole system. You have to know the location of the transmitting towers and their distance relative to each other. Otherwise you don't have enough information to make any important determinations, and that information is freely available to anyone who's part of the Louran system. So you know the physical distance that separates these two folk i from

each other along the coast. Using those pieces of information, you can actually plot the hyperbola curves. So let's say the two towers are four kilometers apart. The speed of the radio waves is point to nine nine seven nine two kilometers per micro second, and the difference between the two sets of pulses was two hundred microseconds. We can calculate the constant of this hyperbola by using the equation

distance equals rate times time. The rate is the rate of the radio waves that's point to nine nine seven nine two kilometers per microsecond, and the amount of time that passes is two dred microseconds. That gives us fifty nine point nine five eight four kilometers. So let's just round it up. We're gonna call it sixty kilometers. That's your constant. Any point along the hyperbola will have a difference in distances from the two folk i of about

sixty kilometers. Now, that still doesn't tell you where you are in relation to anything else. It just tells you the relationship between the difference in distances between the two transmitters. However, knowing the constant gives you enough information to suss out the rest of the equation for the hyperbola. The equation

for an east west hyperbola. So if you were to plot this on the old X Y axis, you know, a good old grid, then this would be the ones that would face left and right, a north south hyperbola would face up and down along the y axis as opposed to left and right along the X axis. So when you plot and east west hyperbola on an x y axis, the equation for a hyperbola is X squared divided by A squared minus Y squared divided by B

squared equals one. That's your your hyperbola equation. Now, if this were an up down a north south hype perbola, you would actually have Y squared over A squared minus X squared over B squared equals one. Just a little bit of mathematics for you. The A, by the way, represents the vertices. The that would be the the center of the hyperbola. That that point where it has the curve where it curves around the very center of that is the the of Both of those curves are the vertices,

and the B represents the covertices. Describing that as a little more tricky without visual aids. So just go with me on this if you want to really understand what this is. There's a video I highly recommend. I found it extremely useful. The video that you can find is on YouTube. I have no connection to the person who makes this video or the company that makes this video.

I just found it very useful. The title of the video is applying hyperbola as navigation, and it's by think Well VIDs, and you can see this applied specifically for the purposes of navigation. That even use an example very similar to what I'm talking about, although he uses miles rather than kilometers. Uh. If you check that out, you'll be able to see this in action, and it'll be much easier for you to visualize since I'm working just

from an audio format here. The point being that once you figure out the equation for the hyperbola, you can plot out all those points on a map that have this this constant this constant difference of of distances between the two folki. So you get that curved line that represents all of those physical points on the map. We call this the Loran line of position. By itself, that information isn't that useful because you don't know exactly where along that line your position is. You just know that

it has to be one of those points. Based on the math, you could be anywhere along that curve. Well, if you're on a boat, you would presumably be anywhere out over the ocean, because if the curve extends out over the land, you probably aren't there if you're in a boat. If you are there, then you don't really need to worry about your position so much, because chances are it's not really changing. Boats don't move well on land.

What you need now is either a third tower that's pulsing the same synchronized signal, or, as the original design of Laurent intended, a second pair of transmitting towers. So with a third tower, let's remember our first two towers were Towers A and B. Uh this would be Tower C. You would run the same calculations with regard to the ship and Tower A. That will produce a second hyperbola, one in which the curve of that second hyperbola will

intersect with the curve from the first hyperbola. If you were using a second pair of towers, we'll call these towers D and E, you would repeat the process you did for Towers A and B, measuring the difference in time it takes towers Tower D signal to get to you compared to Tower E signal. That would let you plot out a second hyper bluff, and you would still see a second set of points representing your possible location.

More importantly, they would intersect with your first set of points, and it's at that intersection where the two lines cross that your location would have to be. That's the only place your ship could be, because the mathematics would tell you that you have to exist along both of these curved lines simultaneously, and they only intersect at one point.

That point is your location. So by using a Loran receiver and taking in transmissions from different towers and applying a little math, you can figure out exactly where you are out in the ocean, even if land isn't in sight and the sky is overcast. By sending out these pulses with identify irs, you'll know where you are in relation to where you're headed and can make course corrections and take the measures to pilot your ships safely toward

its destination. This is particularly useful during wart wartime, when you might have to worry about enemy ships patrolling certain areas of the seas and being able to navigate around them. Now, the theory behind Lauren was solid. The math works. The trick then was to make it a practical technology. Knowing that the theory was sound was one thing, but to put it into practice to actually build stuff that could use it. That was another and that presented a bit

of a challenge. If the committee could find a way to synchronize transmissions from radio towers hundreds of miles apart, the scheme would work. But that synchronization was absolutely critical because without it, the difference in time between the two signals would be meaningless. The receiver would have no way of knowing the relationship between time and distance if the two sets of signals weren't sent out at exactly the

same time. The team requested about four hundred thousand dollars worth of equipment on December uh well in December, in order to carry out an experimental run to determine if the mathematically attractive solution was actually feasible in the real world. And if we just that four hundred thousand dollars for inflation, that would be about seven point two million dollars worth

of stuff in today's money. The team looked for suitable spots to construct the transmission towers, and at first they they considered some mountain peaks along the coast, but then they found two former Coastguard lifeboat stations that had fallen into disuse. One was outside Montauk Point, Long Island and

the other off of Fenwick Island, Delaware. The two locations were two d nine nautical miles apart from one another, and they weren't too far from the headquarters for the project, which was in the Bell Telephone Laboratories in New York. The earliest tests concentrated not on synchronization, which was an area that Alfred Lee Loomis was particularly intrigued by as he had a fascination with timekeeping, but rather in how

far they could broadcast the radio signals. They tried several different wavelengths to see which ones could perform best under different situations, and they discovered that longer wave length radio waves seemed to travel further at night, and shorter ones seemed to travel further during daylight hours, and that kind of suggested to them that maybe they should compromise and go with a medium wave length signal that would perform the best under most circumstances. They also did not test

it with a ship at sea at first. Rather, they created a Loran receiver and they mounted it aboard a humble station wagon that traveled as far away as Springfield, Missouri. Now I have to say more about the development of Lauren in just a second, but first let's take another quick break to thank our sponsor. As work continued on the lor End project, the group began to work on a way to synchronize signals, because without synchronization, these equations

are not going to create an accurate hyperbola. The solution was called a two trace indicator technique. A trace is a type of log or record of events. A common reference time acts as the anchor point for the traces, which can then be analyzed against each other to determine how close to synchronicity the two transmitters are and adjustments

can be made. Eventually, they created a time keeping algorithm that was accurate enough that were in a wrist watch, you could go for a full decade without losing a minute on it. By January ninety two, the project was able to create a system that had an average error in the line of position of about two and a half miles or around four kilometers, which sounds like an awful lot, but when you're thinking about the distances that these various craft were traveling, it was actually pretty good.

The remaining challenge was one that was solved relatively easily, The problem was the receivers would pick up two signals of different amplitudes, meaning different strength of signal, and the difference in amplitudes made it more difficult to measure the time difference between the signals accurately. So to fix this, the team built in differential gain control to help boost a low signal or dampen a powerful one, so that

the calculations could be made more easily. Successful tests with ships and blimps convinced the U. S. Army and Navy to fund the construction of transmission stations for a larger tests in the Northwest Atlantic in nineteen two. Work continued in America, Canada, and Greenland to build out transmission stations. The project was a success, and work soon extended to other parts of the coast, as well as over in the UK. The application proved to be a sound one.

Advancements in receiver technology allowed aircraft to use the same system a little bit later, which became incredibly useful during the war. Planes and ships could meet at rendezvous points that previously have been would have been impossible to achieve. Uh they were able to pair together different navigation systems, some of them were more accurate at closer ranges, and Lauren was more accurate at long range, so using the

two together was really helpful. By the end of n more than three thousand naval ships and thirty thousand planes had Laura end technology aboard. After the war, the system was recognized as being so useful as to be instrumental in the shipping industry moving forward, and the US Coast Guard even produced a short film to convince shipping companies to adopt Lauren technologies for the purposes of navigation. Lauren

stations were manned by military personnel, primarily the Coastguard. Now according to the Coastguard blog site, an assignment to a

lur End station could be pretty lonesome. The crews tended to range in size between eight and twenty five people, and typically the person put in charge was a junior officer who had maybe served a tour of duty aboard a ship and now was put in charge of an office, and frequently this would be the highest military officer rank in the area, not meaning that the rank was particular really high, but rather that these stations were in pretty

remote spaces, sometimes so much so that the only communication you had with the outside world was the radio and frequently you had to have all your supplies shipped to you on a regular basis. In fact, the blog post said that for a lot of these people, the day when a shipment came in would be a really big day if you were on if you're posted to one of these places, because you would actually get to speak to people who weren't on your crew, and that could

be a real relief. Just imagine spending time was set up to seven to twenty four other people, and those are the only people you ever get to see. Ever, on top of that, the junior officers sometimes had to act as a representative of the US military and uh two people who were native to the areas that they

were stationed in. So in some cases it wasn't so remote that you didn't have other people around you, but it was in a territory that did not belong the United States, and there you are as an official of the U. S Military, and you have to, you know, serve as a representative of your country. So that put a lot of extra pressure on you. It was pretty interesting. Now.

On a blog post for the Coast Guard, Lieutenant Connie Brish said that a typical description of a tour of duty at a Lorentz station would be quote hours of boredom punctuated by moments of sheer panic end quote. Now, the staff's primary function was to make sure that the transmitters were working properly. That required standing watches, in which staff would literally remain in the room monitoring the equipment for the transmitter to verify that everything was still working

as planned. It wasn't until a more advanced of Lauren called Lauren C automated enough of the functions to remove that necessity, and Laurence would not see wide deployment in the UH in the consumer world, especially until the nineteen seventies. Now, the original No Lauran system was later called Lauren A. Lauren B was the designation of a different version of Lauren which used the phase of the signals as the means of measuring time differences between the two received signals

rather than comparing the actual timing of the pulse envelopes themselves. So, in other words, the original version of Lauren was all about when did this set of signals get to you? When did this pulse arrive to your receiver, and how does that compare to when this second pulse arrived to your receiver. It was just based upon that the order of operations of when a pulse of signals arrived to you.

Lauren B was more about the phase of the signals and using that to determine the time difference as opposed to just this signal got to me first, and that actually improved the accuracy of Lauren in many ways. The United States Air Force was experimenting with a variation of Lauren C Lauren C, which also fall the approach that Lauren B was attempting to make. Lauren B never really got to see much use. It was kind of phased out pretty quickly, and Laurence took its place. Uh. Laurence

used that same approach. And then there was a variation of Lauren C from the United States Airforce called Lauren D that was used as a means to create guidance systems for the military and actually saw some limited use in the Vietnam War. And Motorola introduced a navigational system that was not directly related to the other Laurens systems, but because it used a pulse chain technology, it ended up getting the nickname Lauren F, though again it wasn't

really connected to the other versions of Lauren. While Laurence was superior to Lauren A, it was also more expensive to implement. It was more expensive to buy the receivers and install them on your equipment, so not everyone immediately switched over to Lauren C. Some people said, well, Lauren A works just fine and the system is still in place. Both systems are working together or at least concurrently, so

I don't have to switch over. The companies that did make the switch would frequently offload their old Lauren A equipment, making Lauren A readily available and relatively inexpensive, which extended its useful life quite a bit. The Coast Guard eventually chose to discontinue Lauren A in all but a few spots in the world in the late nineteen seventies and early nineteen eighties, kind of forcing a switch over to Lauren C, And that was largely from an administrative standpoint.

You wanted to have something that was more automated and you didn't have to dedicate as much staff to actually manning these stations. A different technology eventually began to displace Lauren altogether, and that was the Global Positioning System, or GPS. Through the use of satellites in orbit, it became possible to determine one's position on the planet with pretty good accuracy.

But until the year two thousand, the GPS approach had a built in limitation designed to keep accurate information out of the hands of people who might use it to harm the United States. And this was called selective availability, and it would introduce time varying errors on purpose to reduce the accuracy of signals to about a hundred meters if you were using civilian GPS. If you had military GPS,

this selective availability was not active. The whole selective availability purpose was to prevent bad actors from being able to use GPS to hone in on sensitive US sites like

military bases. And in two thousand, President Bill Clinton signed an agreement that turned off selective availability and reduced the introduced errors to zero, meaning that you no longer had any purposeful time varying errors inserted into the GPS signals, giving citizens the opportunity to receive much more accurate GPS readings and making stuff like real time mapping apps possible because imagine using a real time mapping app and it's still got the selective availability uh turned on and so

you know that sometime within a hundred meters you need to turn right, but you aren't exactly sure where. It might be a hundred meters ahead of you, might be a hundred meters behind you, it might be somewhere within that range, and you don't know if you've passed the street already or not. Obviously, that would limit the usefulness of GPS, but because we got rid of selective availability in two thousand, we now can use apps that rely on GPS that are far more accurate to just a

couple of meters. GPS became ubiquitous rapidly, and Loran was phased out over time, but there has been talk of developing a new LORAN system called e Loran or Enhanced Lauren. That version would allow for a positional system accurate to within eight meters, making it a potential backup should GPS fail or should people try to block or jam GPS signals.

There's been reported GPS interference over the Black Sea, and there's been reported GPS blocking UH technologies around North Korea, so this would be a way of getting around that. You could not block it in the same way that you would with GPS signals. The UK went so far as to allocate resources to building out such a system, though the government would eventually reverse that decision in two thousand fifteen after France and Norway ended their Laura and transmissions.

And that's the story of Lauren, the really important technology overseen by the Microwave Committee and then the Radiation Laboratory of m T, which in turn was reporting to Alfred Lee. Loomis, the guy I talked about last week, and I thought it was pretty fascinating. I love watching the videos of how this technology worked and the actual way of plotting where you were on the map. It was a pretty

fascinating use of mathematics and technology. So I highly recommend you go check out some of those videos so that you can get a visualization on what I've been chatting about. It's pretty fascinating stuff. If any of you have any suggestions for future episodes of tech Stuff, maybe it's a technology, maybe it's a company, maybe it's a person in tech I should talk about, you should send me those suggestions. Likewise, if you think of someone I should interview or have

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There's a chat room you can join in on and I would love to see you in there, and I will talk to you again really soon. For more on this and thousands of other topics. Is that how stuff works dot com eight