Transcripts
1. Introduction : Hi, my name is Nicole and welcome to my class grade, we will get to know how to find compass error by CVD, MVT rule. So C stands for combust. D stands for deviation. M stands for magnetic, V stands for variation, and T stands what true. But before getting into these terminologies, we will get to know some basic definitions. So we will cover definitions first. And I will tell you one important formula by which we will be able to find a compass error. And then we will see some solved examples. So let's get started.
2. Definitions Part 1 : So our first definition is an axis. So the axis of earth is a diameter about which it wrote it. So this is a diameter of a circle. It is considered as an art. And the diameter, ok. So the diameter of Earth about which it rotates is known as an axis. So if I take a tennis ball and if we insert a rod inside it, crossing from 1 to another point. And if you have that tennis ball around that born, then that porn which is intersecting the spear or a ball from a center, right? That pool will be our axis. So similarly, the diameter, if we extended over here, then we can consider our earth is rotating like this around the, this single line. So this diameter is known as an axis. So second definition is poles. What are the geographic poles? So the geographic poles of the earth are two points there. The axis meets Earth's surface, right? So if we draw a line extending from this diameter, then it will be touching Earth's surface is at 2. This one is first one and this one is second. So the two points where the axis meets earth surveys are known as poles and they are named as North Pole. And other one is South Pole. Okay? Next definition, our third definition is a great circle. A circle on the surface of Earth, or a sphere whose plane will pass through the center of that spear. So if you consider this as a center and you see a circle here, this is a front portion and this is a backward portion. So a circle on a sphere on a surface of Spear, who's plane will pass through the centre of the sphere or an earth. It will be known as a great circle. So it can be horizontal, it can be vertical also. It can be transverse also. So however, it may be our denial unless the plane of that circle, if it is passing through the center, then it is known as a grid circa. Okay? Next definition, our fourth definition is a small circle. A circle on a surface of a sphere or earth, whose plane does not pass through the center of spear or Earth, is known as a small circle. So if I draw a circle over here, okay? Which is extremely backwards, okay? So this one is a small circuit. It will not be known as a great circle because its plane does not pass through the center. Similarly as a great circle, this can also be horizontal, is, can be here. What is Can we hear, right? It can be vertical, it can be here, or it can be here. It can be here, and it can be transverse also. It can be here, it can be here. Ok? So until, and unless, if the plane of that circle is not passing through the center, then it will be known as a small circle. And if a plane is passing through the center, then it will be known as a great circle. Okay? Now our fifth definition is equator. So the equator is a great circle. Okay? That means its plane is passing through the center. The equator is a great circle on surface of earth, the plane of which is perpendicular to the earth's axis. So you see a circle over here. If we draw a plane of it, it will be crossing the center, as well as the plane will be perpendicular to the axis of Earth. So this will be our equator. So I'm repeating a definition of equator once again. The Equator is a great circle on surface of earth, the plane of which is perpendicular to the earth's axis. Okay? And the equator divides it into two parts. That is Northern Hemisphere and southern hemisphere. Okay? So our next definition, six definition is are parallels of latitude. So I'll explain it to you on another diagram. So in this diagram you can observe here, see this is a circle whose plane is passing through the center, right? So it is a great circle. But you see a circle similarly over here, cause Glenn is not passing through the center of Earth. So this one is known as a small circle. This one is a great circle. Similarly, this one is a small soccer. Ok. So parallel of latitude. What is a parallel of latitude? Are a small circles on surface of the plane of which is parallel to the equator. So those are a small circles whose plane will not cross the center, but those will be parallel to the equator plane of equator. So if I draw a circle over here, okay? So it will be a small circle because it is not crossing a center, right? But it is parallel to the equator, then it is known as parallel of latitude. So this circle over here is parallel to the equator, as well as its plane is not crossing the center. That's why this one is a parallel of latitude. This one is also a parallel of latitude. Our next definition, or seventh definition is meridians. So meridians are Samy grid circle on odd surface. Now what is the semi great circle? It is a half portion of a great circle. So if we draw a circle over here. And if we extend it backwards, so if we raise the backward portion, then it remains only a half circle, right? But whose plane will pass through the center? So it will be a great circle, but a half circle, right? So it is a saving rates uncle. And what is the property of that semicircle? It is joining the two poles of Earth, that is known as meridian. So the entire definition becomes meridians are saving rates, circles on the art, joining two poles. Okay? And the other half is also known as other semi-circle that enjoining to poll, but that is counted on the other side. So meridians are always counted as a semi grid circle. They are not counted as an entire circle. But equator or a parallel of latitude is counted or an entire basis. It is not counted as a CME RED circular, Okay? Now our eighth definition is prime meridian. So Prime Meridian is a meridian wished process to the Greenwich city. So if we consider this meridian, the meridian which is passing through the Greenwich city, then this meridian will be our Prime Meridian, which is counted as 0. And all the meridians which are other than this are named east, our waste from the Prime Meridian. So all the meridians which are lying on the eastern side of this meridian, it will be counted as east. All the meridians which are lying on the western side of this meridian will be counted as waste. Ok. So I'll show you how entire meridian diagram will look like. I will take you to the, another diagram. So this is how all the meridians will look like these RS saving great circles which are joining tuples, okay? And this is our equator. Okay? So this is how all the meridians will look like. And if we consider this as a green, which are a prime meridian, then all the meridians which are on eastern side will be counted as East. And all the meridians which are on western side will be counted as west. Okay? So our next definition, that is our ninth definition is geocentric latitude. Okay? Or we will just say the latitude of a place. Okay? So I'll take you to the next diagram for it. So a latitude of a place, I'll tell you that a definition and then I will explain it to you. A latitude of a place is an arc of a meridian, or the angle at the center of Earth. Contained between the equator and the parallel of latitude. Okay? So if we see an object over here, that is o, ok, we have an object over here. And we want to know what is a latitude of this particular place. So it will be counted as an arc of a meridian, which is extended a bit when equator and the parallel of latitude crossing by that place causing from that place, okay, which will be parallel to, which will be a small circle who is parallel to equator, Right? So the arc of a meridian contained between equator and parallel of latitude of that place. Or it will also be counted as an angle contained at the center of Earth, which is contained between the equator and the object. So this angle or this arc will be a latitude of a police. Ok? Similarly, if we want to know what is a longitude of a place, the definition of longitude is the angle between the plane of equator, OK? Angle between the plane of equator and the vertical that at that place. Okay? So a vertical is nothing but a meridian solute, I'll tell you this in a simple way. So the latitude of a place is the arc of an equator, okay? Is our of an equator or the angle at the polls content between the prime meridian and the meridian of that place. So our configurator will be this. So if this line is considered as a prime meridian, that is counted as 0, right? And we will count all the meridians with respect to this prime meridian. So the arc of an equator contained between the Prime Meridian and meridian of that place. So this arc or angle at the pole, which is contained between the prime Vertica Prime Meridian and a meridian of that place. So this angle or this arc will be known as a longitude of a police. So if we want to know the position of this place, then it will be an arc or angle at center, which is latitude, and arc of equator, or angle at pole, which is longitude. So by latitude and longitude, we will get to know the position of a place. Okay? Now, coming back, are coming back to our next definition. That is our tenth definition. Is difference in latitude. That is also known as dilemma. I'll explain it to you here. Difference in latitude is arc, offer Meridian or angle at the center of Earth, contained between two parallel of latitude through to two places. So if we have another object which is here. Okay, we will call it o2. Ok? This will be one, this will be CO two. Now, we want to know the difference in latitude. Okay? So latitude of this place will be an arc of meridian which is contained between up parallel of latitude and equitable correct. Or angle at the center. Right? So angle at the center will be like this. This is O2 and openness, this one. So difference in latitude will be this arc, which is a difference of if we consider this point is t0, it will be a difference of A0 over two equal to this arc. Okay? So I'll explain you and a perfect definition that d lambda between two places, if arc of a meridian or angle at the center. Okay, so if we take a difference of 010, it will be this angle, right? So the difference in latitude between two places is arc of a meridian or angle at the center of Earth, contained between parallels of latitude through those two places. So this one is one parallel of latitude passing through object two. And this one is a parallel of latitude parsing through object O1. So the difference between these two will be known as difference in latitude, which is written as d lack. Okay? Now next definition is DeLong. Day-long is difference in longitude. So similarly, like latitudes, if we have an object O2 over here, right? The meridian which will be passing through that object will be drawn like this. A semicircle that is joining tuples. So difference in longitude between two places is shorter arc of an equator. The shorter arc, because longitude of this place will be this entire arc, correct. And longitude of this place will be this arc. So the difference between these two Rs, that is a shorter version of equator. This is known as a dialogue or this angle. And this angle difference between angles at the pole, right? That means this angle. This angle will be known as a difference in longitude. Ok, so the definition becomes the DeLong between two places is shorter arc of the equator or the smaller angle at the bone contained between the meridian passing through these two places. So this meridian is passing through 01 and this meridian is passing through 02, right? So this will be r d for, this will be our dino.
3. Definitions Part 2 : This will be a part two of our definitions. And in this part we will cover two definitions. First is nautical mile, and another one is not. So I'll tell you what the definition of a nautical mine first. So the nautical mile at any place is length of the arc of a meridian. So we have an arc of a meridian over here substituting an angle of one minute at the centre of curvature of that place. Okay? So basically I will explain you the diagram first. Then I will explain you what is the meaning of nautical miles. Okay? So our Earth is not an entire sphere, okay? It has a lesser area at the pose. So it is known as in a standard terms as an oblate sphere on it, or it is not a complete sphere. It is an obligate spirit. It is slightly curved. The insight at both the poles. So if we expand the North hemisphere, then it will be not a complete circle over here. It will be like this. So our poll will reside over here. Now, here is one confusion. So if we think as per the definition, the definition says are performed meridian at that place S tending angle of one minute. So we know we have 90 parallel of latitudes, right? So one degree parallel of latitude will be somewhere here. Two degrees will be some year. 45 degrees will be somewhere here. 80 degree will be somewhere here. And 90 degree will be our pole. Now, since the Earth is not entire sphere, the area that the pole is lesser than the area at the equator. So how it will be done, right? This is the main question. So if we consider and the pole where the curvature is least, the nautical mile measured on an, an actual Earth. If we expand this and if you go on an actual earth, right? So one-minute area, if we measure it physically, it will be 1.7861 meter at the pole, where the curvature is least. And add the equator where the curvature is the maximum, is it Largest? There will be measurement 1.9842 meters. So we will not be having an exact value, two major or nautical mile worldwide, right? So taking into consideration these two possibilities, we have came down to one standard unit value that will be used for a nautical mile with an average of these two, that will be 1.3852 meters. So standard value of one nautical mile is 1.3852 meters. Or a weekend say 1.8523 kilometres. That is known as one nautical miles. Okay. And our second second definition is not. So we measure a speed of a vehicle in kilometer per hour. That means how many units of kilometers done in unit time, right? Similarly, in shipping terms, nautical mile isn't unit to measure a distance, right? So how many nautical miles? The unit nautical mile done n unit r is known as not. So this is a unit of a speed which explains nautical mile per r that is known as not.
4. Definitions Part 3 : In the Part Three of definitions, we will be covering our direction measurement. So this is an art. And this is a meridian which is running from north to south. That enjoining are tuples, and this is a parallel of latitude of this exact place. So if we expand the surface of Earth, because art is having so much of area. So if we expand this area and we go by zooming in into this place, practically displays will look like this. It will be looking like a cross at that place. Okay? So directions are measured as an angle in degrees and minutes with reference to the geographic north. So our meridian will be this north to south, right? And the meridian will always be pointing towards the north because is, because it is running from north to south, right? So all the directions are major as an angle in degrees and minutes with reference to the geographic north. Okay? So if we have an object over here, then we will draw a line from our place that is a center. We have standing over here, right? This is our parallel of latitude and this is our meridian, This is our longitude. So we'll draw a line from our place to that place. And the direction of that place will be an angle extending from north, which is always a clockwise. This will be a direction of this object which we are observing. So this will be a 45 degrees. So if we have an object over here, then it will be counted as 80 degrees from North. If we have an object over here, then it will be counted as 170 degrees. If you have an object over here, then always remember, the counting is always done clockwise from the north. So even if we have object over here, we will not count it from anticlockwise side. We were always counted from clockwise site. So the object over here will definitely become a 230 degrees. Okay? If we have an object over here, then it will become a clockwise direction that will be 300 degrees. So it will be counted as 3-0 0 degrees. An object over here, the direction of that object will not be counted from north in anticlockwise direction. It will be always counted in clockwise direction. So the direction of this object becomes 359 degree. And the objects which are lying over here, the direction of it will be either 360 or we can call it as 0 degrees because this is our starting point. Okay? So this is how the direction of any object or any lighthouse or a ship or anything we can say it is measured in this way. So now, if we want to know what is an intro course of our ship, then consider this diagram. This is our ship heading into this direction, okay? Now, we want to know what is a true cores of our ship. So the definition of true cost is the angle at the ship, angle extended at the ship between the true north and ships him. So likewise, this diagram, we will draw a crossover here, okay? So this will be our meridian, and this will be r parallel of latitude, okay? At our place. So our meridian will always be pointing towards north. And if we want to know the direction in which our ship is heading, we will simply draw an angle between the true north and ships head and it will be R through course. So the definition one summer, once again, I am repeating is the angle at the ship between that true north and the ships here is known as the ships through course. Okay? Now we will know what is a true bearing. So if we see an object over here, ok, whether it be a lighthouse or any other shape or any other fishing boat. So if we want to measure a direction of it, then we will not count it from the head of ship because all the directions are measured from true north. So the angle extended from true north, which is clockwise, till that object will be our true bearing. So this one will be around one to 0 degrees. So this will be our bearing, a True bearing of this object. In this scenario, if we want to know, the truckers, similarly draw a meridian and a parallel of latitude. Okay? In this scenario or ship series here, right? We will not count it anticlockwise, will count it clockwise from here. And this will be, this angle will be the direction true cost of our ship. This will be around 300 degrees through. So this is the true course. And if we find any object over here, then we will not count it from ships Here. We will always counted from true north. So this is a true naught. From here, it will be around 050 degrees. So this is a true bearing. So this is the difference between true cores and True bearing.
5. Variation and Deviation : Now we will get to know about the magnetic meridian and variations. So as we all know, the axis around which the Earth rotates, touches the two points on the earth, which one is not born and so forth. So these are geographic south pole and geographic North Pole. Now, if we take a magnet which is freely suspended into an air, if you are tired by rope or something. And if we freely suspended in the air, then it will be directing towards a single direction. The north end of the magnet will be directing towards the north pole, and the south end of the magnet will be directing towards the south proof. So this south and north, both the North and South Pole directed by the magnet, are not exactly the geographic poles. Those are magnetic poles of Earth because Earth is having its own magnetic field, and that is why the magnetic north and magnetic south poles are slightly different from the geographic northern geographic south pole. And this is why the variation comes into place. So as we all know that the line, a Samy, great circle joining north and south pole is known as a meridian. So similarly, the same regret circle joining magnetic north and magnetic south will be known as a magnetic meridian. And the variation will be an angle which is subtended between the magnetic meridian. And our two meridian will be our variation. So the definition of variation is the angle between the true meridian and magnetic meridian is known as variation. Ok? So variation is different and at different places, it is termed east or west. Howard is named east or west. I'll tell you if the magnetic north lies on the right-hand side of true north, then the variation is named as East. Whip them. Magnetic north lies on the left-hand side of the true north, then the variation is named as west. So this is how the variation is named. Now, our next definition is deviation. I'll explain it to you on another diagram. So this is our compass needle. And as we all know, that it will be aligning with the magnetic meridian due to the magnetic field of Earth. So this is aligning with them magnetic meridian, This is a magnetic meridian and this is our compass needle. Okay, so now if we have a magnetic field which is very near to the campus around here. Okay? So if we have a magnetic field around here, then it will be acting on this compass needle. So it will cause to deflect the compass needle slightly towards him. So if we have a compass needle like this, it will be slightly deviated towards the magnetic field, which is near to that compass. So the definition of deviation becomes the angle between the magnetic meridian and the North-South line of a compass car. So that means if the compass needle is deviated somewhere here, then the compass north-south line will be like this, right? So the angle between the magnetic meridian and the North-South line of compass is known as baby insulin. And Howard is named. It is named If the compass needle is directing on the right-hand side of magnetic meridian, that it will be named as is. And if it is on the left-hand side, then it will be known as west. So this is the definition of deviation.
6. CDMVT Rule : Now here is c, d, M, d rule. So to find the compass error, we have to use this theory MVT rule. What does this CDM VET stands for? If c stands for campus, D stands for deviation. M stands for magnitude. That is a magnetic direction. V stands for variation. And T's transport through bathing or approvals. Okay? Now, if we remember this formula, we will be able to find campus data already V, It's an aura variation in easy formula. It's simply FDA, campus era is east, then the compass will have unleashed value. And the compass error, if it is West, the compass bearing will be best. That means it will be having a higher volume, higher value. So, and how can we apply deviation and variation? It is similar to this formula. So if we have a compass bearing as 050, that is a compass bearing. And if we have a deviation as two degrees is the same formula will be applied in case of deviation also. So if dv is sin, is east, then the compass will be list. So compostable beliefs than magnetic sort, it is least less dual degrees then magnetic, that means magnetic, we'll do degrees higher than compass. So the magnetic direction or magnetic cores or magnetic bearing will become 052 degrees. If my animator, okay. This one is compass bearing. This one is a magnetic barrier, or we can save this as a course as a magnetic cuz if we have it as two degrees west, If we have a deviation as two degrees west, then according to this formula, if the compass error will not talk about composition, and because we are talking about deviation, if the deviation is west, then compass will be best. That means compass will be having higher value. So if this has higher value than magnetic by Hamas degrees, by two degrees, that means we have to subtract these two from 050. Magnetic will become 0 for a degrees if we have deviation as west. Okay, now we want to find a True coarse ora probate and then we will get to know about variation also. So if we have a variation as five degrees east, okay? So if you have a variation has five degrees east, then cell formula will be applied of East. East is leased and the rest is best. So if it is east. We'll believed that true. Okay, so if magnetic is least that men's proof is higher by five degrees. So even add a five degrees and 05 to sort it will become 057 degrees to if we have variation taste. And if we have a radius and as five degrees wet, then by this formula, if the variation is west, then the magnetic Viterbi best, that means it will be having a higher value. So if this one is higher than, T2 will be less than. So we even subtract five degrees from 0 forehead to get our answer. So if you subtract five degrees, it will be 0 for three degrees too. So if we have a deviation east, then compass will release than magnetic. And if a variation is then magnetic will be less than two. Ok? And if we have deviance and as west, then compass will be best than magnetic. If we have a variation rest, we will have a magnetic best NANDA through so resultant arrow. We want to know our resultant error, how to find a compass resultant air. So the resultant error will be algebraic addition of these two. Okay? So if we have a two degrees east deviation and five degrees east variation, so we will write it down. Deviation is two degrees is, and variation is five degrees less, sorry, five degrees is. So algebraic sum of these two will be seven degrees to the east. This will be our compass arrow. So if we have composite risk seven degree, we can cross check this formula. If error is East Campus is least now our error is on east side. So combustion would be leased by Drew. By how many degrees? 70 degree. So this is 057 R2 value and 050 as our campus when, so this is least that drew by seven degrees. Now, algebraic same of some of the west sides also, if we have a deviation as two degrees west, and if we have variation as fine degrees west, then the algebraic sum of these will become a campus era. And that will be seven degrees west. So now, as per this formula, cross-linking, if error is West, Campus will be best, campus will be higher. So Aaron is West by seven degrees. So campus should be higher by 70 risk prompt through. So we have 043 as our approval you, and we have 050 as our campus value. So that is higher by seven degrees from not, right? So now if we have a different directions of dBs and invariant set, how will we do it? So as I told you, it is an algebraic sum of variation and deviation. So if we have deviation as three degrees to east, and if we have a variation as seven degrees to west, then our resultant error will become a subtraction. If we have a different signs. If it is a west deviation is deviation, then it will also be a substrate secretase, an algebraic sum. So it will be a subtraction and the direction will be offer higher volume, higher value. So compass error will become in this case, is four degrees to West. And if we have 050 as campus course, how much r two will be? If compass error is west, then compass will be best. Proof will be less. So true when B is 046 degrees, this is our groovy hearing. This will be our answer. So this is how cd, MVT rule is applied. C stands for campus, D for deviation, M for magnetic V4 variation, and T for true. And the single formula for this is if Aaron is East, Campus will be list. If a1 is West, TEN campus will be best.
7. Solved Examples : Here we will have a look at some examples. Here. Examples are NCD m, v d format. And we'll find out what is N a either. Okay? So our first example is we do not have a compass course. We have only deviation that is three degrees west. We do not have our magnetic cause. We have a variation as five degrees is, and we have a true cores as 097 degrees. So we have to find what is a compass course, what is a magnetic cores and what is an error? As we all know, if variation is east, then a magnetic will be list that true. So if it is five degrees east, we will subtract five degrees from 097, so it will become 092 degrees as magnetic goods. Okay? So our magnetic courses 092 because our variation is five degrees east. Now if we find, if we want to find a compass course, then if deviation is East, Campus is list, if deviation is West, Campus is best. So deviation is West. That means compass will be of higher value. By how many degrees? Three degrees. So we will add three degrees into 092. So our compass course will become 095 degree, that is our compass codes. Now we want to know what is an error. So it has an algebraic sum of deviation and variation. What is deviation? Three degrees west, variation is five degrees east. So we will subtract these and East sign will be given because five is a higher value. So if we subtract these two, the error will become two degrees. Two is now we will crosscheck with Era and true can come pass. So if we have error as East Campus will be list. So we have 097095 parties, at least by two degrees. Now we're looking at, get down to our second example. We do not have a compass course, we have a deviation magnetic variation. We don't want our true and we have, we do not have an error. So deviation is West, that means compass will be best. So we will add five directories in 17 five, so it will become 180 degrees. That will be our compass course. Now we have variation as ten degrees west. That means magnetic will be best. Campus will be, sorry, true will be least magnetic will be best proven buildings. So we will subtract ten degrees from magnetic. So this will become one, 65 degrees. That will be our true goals. Now, our error will be algebraic sum of deviation and variation. So if we add up these two because these two are having a same sign, our compass error will be 15 degrees to vest. Now we will cross check whether it is correct or not. If error is west campus a little bit best by how many degrees? 15 degrees. So we have a true as 165 and we have Compass as 180, that Miss compass is best by 1-5 degrees. Now here, we do not have a deviation. Do not have a variation, we do not have a era, we only have a campus cause magnetic cores and protocols. Now, we will apply a formula of East is East and West is best. So as we know, if deviation is east, then compass will be list then magnetic here, campuses list than magnetic by how many degrees? Five degree. So R Thevenin deviation in this case will be five degrees. Two is same. Here. If variation is east, the magnetic will be least. If variation is best, magnitude will be best. Now here, magnetic is at least than true by how many degrees? Five degree. So here our variation will become five degrees is. And if we want to know the campus error, then it will be an algebraic sum of these two that is same signs we will add up and we'll give a sign of east. So our compass error will become ten degrees to east. We will crosscheck with true and campus. We have a true as 135 and compass as one-to-five. So that means air and is East Campus is leased by ten degrees from true cores. Next example, we have a campus cause we haven't deviation. We don't have a magnetic, we have variation, we do not have a true constant, we do not have encompassed era. So now we have deviation as poor degrees. East. Deviation is campus will be list, so magnetic will be 197 degrees. Okay? Now variation we have as West, that means magnetic will be best. That means true will be lesser than magnetic. So we will subtract these three degrees from magnetic. Sar, true will become 194 degrees. Okay? And certain air will be algebraic sum of deviation and variation. So we have different signs. We will subtract them and give a sign of higher value. So if we subtract three and to answer will be one degree and the sign-off higher value will be given to campus era. So our error will be one degrees to west. Now we will crosscheck, hybridize one degrees to West, that Miss campus should be best by one degree from true. So we have one line for as are true and we have, we have 19, five as our company. Now, our last example. And you do not have a campus course. We have deviation, we have magnetic cause, we have a variation. We do not have a true value and we do not have an air. So if deviation is East Campus will be list. So we will subtract five degrees from to 97, it will become 292 degree. This will be our compass cause now we have variation as east, that means magnetic will be list. So we will add this five degrees into two, 97, sorry, it will become 302 degrees. So 3-0 two degrees will be r glucose. And if we want to find out the resultant era, then it will be erudition. Algebraic sum of these two. That means five degrees plus phi degrees will be ten degrees. Today is no cross-checking with Compass and true error as East Campus will be leased by how many degrees? Ten degrees. So we have proved as trees that are two and compass as tuna and two, that means campuses less by ten degrees from true. So this is how we solve examples.