welcome to part 1 of the series of videos I'm making on the topic of a lurancy Laura and C as you know stands for long-range navigation so basically Lauren stands for long page navigation and these videos are in a series of three parts discuss or this is part one actually this video will discuss understanding the hyperbolic system understanding the hyperbola and the hyperbolic system as well as the transmission of the radio waves how it all works in the case of Lauren see part two will be discussing the working of the Lauren C specifically so I'll be putting Part one and Part two together where you understand how the hyperbolic system and transmission radio waves actually fit into the working of T Lawrence E and then part three will be another video where I'll be discussing about the errors of the Lorenz C and how to go about correcting those errors of the Lauren C so there will be three videos you know I hope you watch all the three videos to actually understand how the Lawrence C operates now if you straightaway go and look at Part two this will not work very well for you you have to understand part one you have to understand the principles of the hyperbolic system and the transmission of radio waves before you actually try to understand how it all fits into the working of the Lorenz C so do not skip parts so in that in that respect I will be putting out this video first and then after some time I will put out part two things in poetry so that you have some time to understand it as you proceed on to the next video so let's get started with understanding the hyperbola so as you probably know that like I said there Lauren is the stands for a long-range navigation and the system basically works on a low frequency of 100 kilowatts signals that are transmitted from one master and two three or four slaves or secondary stations called a chain now the time difference in arrival of receive signals from any pair of stations is measured using various electronic techniques in the ship's receiver which can then be converted to distance differences and hence you what you get is a hyperbolic lattice of lines of constant time difference which is used to plot the line of positions of them now what you see on your slide is the basic hyperbola now you can see a hyperbola is actually can be described as a line joining places where the difference in distance from two fixed points which are also known as the foci focus is the singular and foci is of course the Perl so the two fixed points and the difference between the two fixed points is a constant so what you see in the figure here points a and B are the foci and points a P naught P 1 P 2 and P 3 are joined by a curved line for this curved line to be a hyperbola the distance from any point on the line to a minus the distance from the point to B must be the same so for example the distances a P naught and B P naught when subtracted will give exactly the same value as the difference between a P 1 minus V P 1 so the ratio of the difference in distances will be the same here you can see that a and B are exactly 6 units of distance apart so a family of hyperbola is now drawn where the difference in distance between points a and B is 0 units one two and three units respectively or etcetera so you can see you are able to construct a family of hyperbolas each with different this of distance from the two foci now notice that when a hyperbola of zero difference is constructed it will be at right angles to the line joining the foci and this line is known as the baseline so you will see in my next video I often refer to the baseline as B slash lvl that is the baseline also make a note that the hyperbola gets further apart as you move away from the baseline and that there is also a hyperbola extending the baseline as this line will also be a constant difference of distance from the two foci the hyperbolic pattern shape also becomes a very important so you can see here that if the since you are measuring a difference of value a given fraction or a percentage of that difference value this translates into a larger distance when plotted on the Earth's surface especially when the observer moves further from the pair of beacons or the observer is approaching the baseline extension accuracy in the center of the pattern is good but it gets worse as you move outwards and round towards the baseline extension if the two foci are used to produce the family of hyperbola or transmitting stations also imagine them to be the transmitting stations and you have a means available to measure the difference in distance to the two transmitters then a hyperbola could be constructed and used as a position line and this is what we will see in part 2 of the video where you will see how I put this into the theory or into the working of the currency so radio waves are used to generate the patterns and the rate of propagation of low frequency relative energy over the sea is constant and predictable so Lawrence II uses low frequencies of about 100 kilohertz right now remember all hyperbolic radio navigation systems are based on the principle that radio frequency energy is propagated through space with a finite and known velocity alright so that is the principle will be used or will be using to understand the working of the radio wave now if the two foci are the two transmitters and if a third transmitter is added to the system then each pair of transmitters would produce a family of hyperbola and a position line from each family could be obtained so the intersection of the hyperbola from the two different families would be your position when a group of transmitting stations are used collectively to give a number of position lines they are referred to as a chain the systems make use of the property of low frequency radio waves that the rate of propagation of the scene is constant and practical lurancy uses this time difference system however the transmissions from each of the stations have to be synchronized to ensure accuracy therefore one of the stations in each chain is designated as the master station and each of the other transmitting stations you can call them as slaves so this method of using the ranges from two transmitters has been used in a number of now which have now become obsolete systems such as Omega and taker but they are still being used by the Lawrence II system I remember when I was located I had to read about the Omega and they take a system as well but these days and not so much anymore all right however as you will see in my part two of the video I'll also show you how the invention of accurate atomic clocks which are also used for the GPS systems have ensured that method of synchronization of these transmissions is no longer necessary so like I said before deca and Omega over the the now-obsolete or redundant systems which relied on the ability of the receiver to discriminate between the faces of two identical signals but with now with the invention of atomic clocks and their introduction for DeLorean C system that synchronization requirement is not there anymore