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Old 04-25-2019, 05:10 AM   #1
Join Date: Jan 2013
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Default Improving the 4-bearing method (with ownship moving) using relative plotting

Anyone tried the 4-bearing method must be impressed by the amount of plotting it required if your boat is moving. Here I want to propose an improvement using relative plotting to make plotting much easier.

This is inspired by relative plotting used by the USN Maneuvering Board manual, especially in this case (

If you keep a constant speed and course, the 4th bearing extrapolated by the previous 3 bearings is exactly the same as if you plot all the bearings from the same point. The formula to get an extrapolated 4th bearing is shown below. One may found that this is the exact same formula if ownship is not moving.

Now you may plot the bearings from the same point, as if ownship is stationary. By using any stationary 3-bearing method, the direction of target relative motion can be determined. Then you can use it to extrapolate the 4th bearing.

If you don't like plotting, you can just code the formula into a calculator, like I did. But I didn't use the idea of Spiess TMA since it has limitations.

Special thanks to Pisces' link (

Last edited by ljqcn101; 04-26-2019 at 01:50 AM.
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Old 04-25-2019, 06:14 AM   #2
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By knowing the 4th bearing and the extrapolated 4th bearing, we can triangulate the target position.

By knowing the target position, we can calculate the length of target relative motion between times, using the range at the extrapolated 4th bearing. Then the relative speed of the target can be determined.

From any point 'e', we can draw an vector 'er' representing ownship course and speed.

From point 'r', draw the target relative motion and relative speed as a vector, pointing to 'm'.

Now we get 'em' as the target true course and speed.

All speeds are proportional to a predefined scale. Same to range/distance.

Last edited by ljqcn101; 04-25-2019 at 10:08 PM.
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Old 04-25-2019, 07:47 AM   #3
Neptune's daughter
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Alternatively, two Uboats in a wolf pack can triangulate very quickly (6mins?) and get true course and speed.

Did it last night with McDewgle and it worked brilliantly.
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