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Old 01-04-10, 08:03 PM   #48
Pisces
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The time between taking the bearings MUST be the same. The longer the time the better the AOB accuracy will be. With just a few degrees of initial bearing change the drawing becomes almost useless. The math behind it needs to 'measure' the accelleration of bearing change. You cannot see that with almost parallel bearings.

The crew calls out the bearing right on the exact degree. (Hmm, how unrealistic! Try measuring by listening yourself. ) So if you make sure your uboat doesn't turn during the whole process then you can get the first 2 bearings very accurately. From that follows a time period that you need to wait for the 3rd bearing. You do not need to get to the second, but to 10 seconds is close enough if the whole time-span between bearing 1 and 2 is more than 10 minutes. Unfortuneatly, the 3rd bearing-time doesn't neatly fall on an exact bearing when the time runs out, but somewhere in between. If the time runs out closer to the next bearing call out than it does to the one before you might need to draw the bearingline in the second half of the degree maybe even round up to the next. Especially very small or very large AOBs (0-10 or 170-180) take very long to change one degree.

Lets give some examples.

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Assume for a moment you hear a contact. You do not know it yet but at the first bearing the target has an AOB of 41 degrees (closing).

You wait until it has moved 5 degrees exactly (cheating with the crew's call outs). How much time this takes is entirely dependant on speed and range. But you can certainly draw this out on the map or a piece of paper (sharp pencil and protractor and compass works more accurate than the game map).

I promise that you will find the bearing has changed 11 degrees to bearing 3 after the second time interval, if drawn accurately. (How do I know? Check and make this!)

But now, lets say we didn't pay attention when listening to the sound, or didn't draw the 3rd bearing accurately. Instead we draw the 3rd bearing line 12 degrees further from the 1st bearing, not 11. That should have produced a drawing with an AOB at the 1st bearing of 26 degrees. That's 15 degrees wrong. (Not bad you might say, but you have to take into consideration you were cheating with the bearing call outs)

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Ok, now same situation: AOB 20, but you waited longer and got 10 degrees between the first 2 bearings. Draw it out and you will find the 3rd bearing is (almost) 24 degrees away from the 1st. The bearing accelerated an additional 2 degrees (2 times as many degrees: 10=2x5, 11x2=22 24-22=2), enough to refine the bearing preciscion limit of 1 degree.

But again we forked up with the 3rd bearing. We measured and have drawn it to 25 degrees. Do Nefelodamon's drawing and see it comes up with an AOB of 36 instead. That's 5 degrees error in AOB. So, now with twice as many initial degrees (between bearing 1 and 2) we reduced the AOB error to one third.

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Another situation: Assume AOB at 1st bearing is 85 degrees (almost at closest point, about to move away from you)

You wait for the first 5 degrees to get bearing 2. (Shouldn't take long. Guess what the AOB is at that point )

Ok you wait another period like that, and at bearing 3 it should be 10 degrees further from the 1st. (For the math wizards, what sort of triangle does it remind you of?)

But instead, we draw the 3rd bearing at being 11 degrees, as Bernard had navigator duty at the time. This should produce a drawing that has an AOB at the 1st bearing of 41 degrees. ....YIKES!! That looks way out of whack! 44 degrees error from the real thing!

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Ok, we wait a longer period to improve that error. As we seriously need it this time. (even if we cheated with the call-outs)

10 degrees to the 2nd bearing. Unfortunately, that doesn't change the picture that much. An accurate drawing would put the 3rd bearing at 19.7 degrees from the 1st. That is too close to 20 (double the amount of bearing drift) to see the acceleration (actually, decceleration this time) of bearing change.

Instead we wait until the bearing has drifted 20 degrees for bearing 2. Ok that is better. This should put bearing 3 at 37 degrees from bearing 1. As a side note, did you notice the bearing change has slowed down. 37 degrees is less than the double of 20 (40). ...

But here we mess up again. We measured or drawn bearing 3 not at 37 but at 38. This produces a drawing that has an AOB of 79 degrees at bearing 1. Yeah!!! that's much more like the real thing. Only 6 degrees error from the real AOB of 85 degrees at bearing 1


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In conclusion: If the target is still far away, starting out with a small AOB, the effect of bearing error isn't that much. If you cheat by taking the time between the exact bearing call-outs you (can) do as-good-as the rough course indications of mapcontacts. If you measure bearings by listening yourself you need to take into account bearing errors of atleast 1 degree. And therefore you need to allow more time between the bearings to let the bearing change acceleration show through.

You can't know before hand what it's AOB is when you first hear it. It could just as easily be as close as it will ever get to you. And from that follows an AOB close to 90 degrees. Due to the math and geometry behind it this creates excessive sensitivity to bearing errors, even if cheating with exact bearing call-outs. For these situations you must allow longer periods between bearings (more degrees) to let bearing acceleration/decceleration to show through. Use short periods initially to get a rough idea, but double up the bearing changes to refine the AOB.

Keep note of the exact times at which bearings are reported. This way you can re-use bearing 3 of a short period drawing, as bearing 2 for a 'twice-as-long-period' drawing.

Patience is a virtue and asset!
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Last edited by Pisces; 05-30-10 at 09:47 AM.
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