Position fix Methods: Doubling of the bearing at the bow (doubling of the four point bearing)

Good afternoon, so this is another in a series of position fixing method. This is called doubling the angle on the bow so This doubling of the angle on the bow will be also doubling the four-point bearing if The angle is at 45 degree, so I'll give you the theory of it. It is very easy to do. It's basic trigonometry Whenever the ship is passing Near a reference point maybe a lighthouse or a beacon or a Raycon Remember all this can be done only when you are using Reference point from a fixed position. You cannot use a bow for doing any of the position fixing on the charts So you take a bearing Then suppose this is your vessel you take a bearing towards the Beacon or lighthouse then note down your Logs distance don't take the log speed you should take the log distance then Suppose the angle is around 15 degree the first bearing was 15 degree then When it is 30 degree the next bearing is 30 degree this bearing is 30 This is 15, and this is 30 degree suppose. This is 15. This is 30 degree The second bearing note down the time and again note down the log distance so the basic trigonometry states that the distance traveled will be The distance between your vessel and the reference point at the time of the second observation So for this you have to take the log distance you won't take the log speed because It will change and also for this remember your core steered has to be the same and If there is going to be a small current that current won't matter too much if The time interval is short, so This is the basic theory of this I will show you in in practical example, so take the first bearing Write down the time take down log reading that is the distance then take a second bearing when the original bearing has doubled and Write down the log reading and the distance you traveled between both the bearing is Your range from the lighthouse So you got the range you got the bearing and you can cut the range and bearing and that is your position and you Can come back transfer your position line back, and you will get the first position. This is how it is done. This is doubling Angle on the bow so if it is doubling the four point you will take an bearing of an of of a Stationary object at 45 degree and when it is at 90 degree That is doubling the four point four point is basically 45 degree and doubling the four point is when the bearing is at 90 degree So this distance is basically this distance so you get the You have the bearing and you get the distance you can cut it. So this is how it is done I will show you in practical. Thank you This is an azimuth circle so in the azimuth circle you will be having a slit at one end and a thread on the other so how you take the bearing is you will be aligning the slit and the thread and the object and Once you align all three you will be getting your bearing from your compass repeater remember Azimuth circle has to be placed on top of the compass repeater That is a gyro repeater and once you get it how it is possible to read out the bearing is below there is a reflector with a small thread attached and this reflector will reflect the bearing onto a mirror and This mirror is the place you will be able to get the bearing and you can just read out the bearing This is how it works Ship's current heading is 3 1 1 This is chart number 3 9 4 6 it is the chart from Port Kalang to Malacca that is basically the Malacca Strait and we will be using The Raycon situated at Gosong Relic for doing our doubling of the bow. We will be using doubling of four points This is the Gosong Relic Raycon this is our four point bearing 2 6 6 degree and This is our current GPS time position and this is the log speed and distance as told the vessels heading is 3 1 1 degree and Since we will be using four point bearing four point is 45 degree. So The light is at 45 degree to our port side. So I will be minusing 45 degree So the bearing should be 2 6 6 degree My first bearing I will be taking at 2 6 6 degree Also the time I have written it is 1400 and the GPS lat-long is this why I have written the GPS lat-long is because we will finally compare if our position observed from doubling of the four point is accurate with the GPS and the log distance log distance is really important. This is the Log distance for the moment at 1400 the log distance was this now, let us Take the first bearing of 3 of 266 degree now, let us take the bearing My first bearing was 2 6 6 degree. So I will be taking 2 6 6 degree 2 6 6 is here So I will be taking 2 6 6 degree This is 2 6 6 degree Now I will be transferring this 2 6 6 degree to Gosong Relic since the Gosong Relic is a Fixed point There will be a star Denoting that it is fixed. You can see this. So it is a Raycon. Raycon means a radio beacon. It is basically a beacon So let me transfer 2 6 6 degree to Gosong Relic. So this will be my first bearing This is the center of the star. I am going to take it from the center From the center of the star. I am taking the first bearing first bearing is 2 6 6 degree so this is 1 4 0 0 now, I don't know where my vessel is. My vessel is somewhere along this bearing line Now I will take the second bearing. So let us go and take the second bearing This is a doubling of the four point bearing 2 2 1 degree and this is the current GPS position and time and log speed and distance Now my second bearing should be at 2 2 1 degree why because I will be doubling the four points doubling the four point is 90 degree and 3 1 1 was the heading 3 1 1 minus 90 degrees 2 2 1 degree also, I have taken down the time and the GPS lat-long again for comparison and The log distance the log distance is 3 7 4 0 3 point 2 So why I am taking it is I will get the log distance traveled as 6 decimal 9 mile and The log you can see as per the video it was constant at 11.7 knots. So let us take the second bearing Second bearing is 2 2 1 degree 2 2 1 comes here 2 2 1 So to take 2 2 1 I will be just taking it aligning it on the compass rose So this should be 2 2 1 you can see it is 2 2 1 now I will be transferring 2 2 1 bearing on to go song really Rick So again, I am transferring you can see The middle that's the star From the star. I will be just transferring the 2 2 1 degree So this is my second bearing this happened at 1 4 3 5 Now, I don't know where my ship is My ship is somewhere on this first bearing line and again, it is somewhere on the second bearing line how to calculate the range from this recognized as I have told you before I Have got the log distance. The log distance is 6 decimal 9 mile Why that's the distance travel between That doubling of the four points. So 6 decimal 9 mile. I will be taking From the latitude scale. So latitude scale is available here So I will be taking 6 decimal 9 This is 1 2 3 4 5 6 and 7. So I will be taking just below sir Just above 7 so it will be 6 decimal 9 6 decimal 9 will be this Since I got 6 decimal 9. I Will be placing it on the center of Gosong relief this is the Gosong relief I will be placing it on the center of it and Cutting it here you can see I got a position somewhere here now this is my range and Bearing My course is somewhere here. So I got My first bearing here and the second bearing here the distance I traveled should be 6 decimal 9. This should be 6 decimal 9. I will again confirm it. It is 6 decimal 9 you can see 6 decimal 9 So after 6 decimal 9, I cut it. This is my exact position at 1 4 3 5 So this is 1 4 3 5 position this I got by cutting the range. I Got from the distance calculated and the bearing the second bearing. So this is my Second portion and to the second portion. I'll be just doing 3 1 1 I'll be back tracing. I know my course is 3 1 1 So I'll just confirm the 3 1 1 again take the 3 1 1 3 1 1 this is 3 1 1 and this 3 1 1 I'll be transferring back to the second bearing line from To the first bearing line from my second bearing line. You can see this so this Where it meets the first bearing line is my portion at? 1400 so this is my portion at 1400 as observed from my Doubling of the bow or doubling of the four-point calculation so 1400 portion and 1435 portion now, let us compare both these portion with the GPS portions my first first portion at 1400 as per GPS is 102 degree 3 decimal 9 3 decimal 9 is 1 2 3 4 so 3 decimal 9 is here 3 decimal 9. I am taking this should be 3 decimal 9 and My long latitude is 2 degree 7 decimal 4 2 degree 7 decimal 4 5 6 7 decimal 4 so 7 decimal 4 So once I plot that position this should have been my GPS portion vessel was on track So this is my GPS position you can see the bearing is the same you can see at 1400 I was here and My bearing to that was basically 2 6 6 degree. So that means This is okay. Now. My second position is 2 degree 12 decimal 4 north and 101 degree 57 decimal 9 that means 58 So 101 degree 58 58 is 58 58 and 2 degree 12 decimal 4 2 degree 12 decimal 4 11 12 12 decimal 4 I'm just plotting the position Let us see where our ship was at 1435 again, she was on track So this is my portion at 1 4 3 5 you can see there is no error in our bearing because both times We were on the bearing line. That means the GPS position at 1435 gave us the bearing at 221 and at 1400 the bearing was 266 now The question comes why is an error of around? There is an error here. So this error is nearly 0.6 Miles that means it is six cables. Why this error came is a question now I'll show you and explain why this error came This is my GPS log. So You can see the date just so that you can confirm that. It's the same day 24th, October 1400 my GPS speed was 13 decimal 1 and at 1500 my GPS speed was 14.0. That means if you take an average by interpolating at 1435 my speed should have been around 13.5 this 13 to 13.5 was the speed but as per my log my speed was 11 decimal 7 can see this and For the whole calculation we had used our log distance Can see so the log distance we used had an error. Why this error came? It's not because of the fault in our ships log it was because The Malacca Strait is having Tidal streams the so we were having favorable tidal stream and since that we are having favorable tidal stream our speed had increased by nearly eleven point seven and thirteen point five So as an average one point eight one point one point eight so in 35 minutes, I Am having an error of around 0.6 or 0.7 miles This mile this difference that had happened was just because of the error of the ship's distance traveled by log and the ship's real distance traveled by the GPS being different if The eleven point seven we got as the log speed had been the same Distance we had covered over ground Then this error wouldn't have come and Practically Our calculation would have shown our ship's position to be accurate. So this error around 0.6 to 0.7 has transferred because of The speed over ground being different from the speed over water Remember log speed is speed over water and GPS speed is speed over ground So log speed is not taking into account any of the tide current wind or Anything that is affecting going to affect the ship that is the reason that error is Something we could not calculate you can always use the tidal stream Calculation to calculate how much current you are going to get or use this to find the set of the current That's a different calculation, but I believe that you got a good understanding of how to do doubling of the bow and in this case doubling of the four-point bearing and Also, remember if you are taken doubling of the bow and if you are taken short intervals of time then the error Error would have been minimized because there is Going to be slight difference between the speed or ground and speed or water. I Believe you got a good understanding Thank you