sublynx
08-03-12, 01:04 PM
Underneath I describe a method that helps you estimate the quickest course that let's you pass a ship or convoy in a way that keeps you outside its detection range (whether detection range by sight or by radar). I write this at a computer with no SH3 so I'll show how it's done on Google Sketchup. You should be able to do this perfectly with SH3 navigation tools as well.
The example situation: you have stalked a convoy and plotted its course and speed as 295 true bearing, 7 knots. The convoy is now at a relative bearing of 87 degrees, range 10 kilometers. The fastest speed you can make in the prevailing winds and not wanting to risk engine failure is 15 knots. You want to pass the convoy keeping a range of 8 kilometers, thinking that at that kind of range they will not see you, but you can see them. This is how you determine your course:
http://i.imgur.com/TAnNJ.jpg
1. With the protractor, draw an angle of 87 degrees (representing the convoys relative bearing).
http://i.imgur.com/zTODg.jpg
2. Draw a line with a length of 10 (the units you use are not important, they may be meters or kilometres, or centimetres or miles, but you have to keep using the same unit). The line represents the distance from your U-boat to the target.
http://i.imgur.com/kZRan.jpg
3. From the end of the line you drew, draw another line using the protractor tool and the line tool. Angle 295, length 7 units, representing the convoy's course and speed. If you want to, you can erase the lines the protractor left to make the picture clearer.
http://i.imgur.com/2ttPM.jpg
4. Draw two circles around the starting point of the target ship's course/speed line. The other circle should have a radius of 8, representing the safety distance you want to keep to the convoy. The other circle should have a radius of 15, representing the speed you want to use while passing the convoy quickly but safely.
http://i.imgur.com/pM2w8.jpg
5. From the middle of the circle representing your ship draw a tangent touching the circle with the 8 kilometer radius. A tangent is simply a line that "just touches" the circle, a line that is closer to the circle than any other line could be. It doesn't have to be pinpoint accurate, just a close-by is quite enough.
http://i.imgur.com/3DxPW.jpg
6. Copy the tangent line you just drew. You can use the protractor to measure the angle or more simply just use the select tool and copy the line to the clipboard. Then paste it to the end of the line representing the course and speed of the convoy. Continue the line until it breaks the circle representing the 15 knot intercept speed we're using in this example.
http://i.imgur.com/5Imb4.jpg
7. The last thing to do is to draw a line from the starting point of the line representing the convoy's speed and course to the point where the copy-pasted line cuts the circle representing the 15 knot speed you are going to use. Measure the angle you got with the protractor.
I got about 27,5. That's the true bearing you should now use with the speed of 15 knots. Keeping that speed and course you should end up nicely just in front of the convoy, just outside the safety range of 8 kilometres that was used here.
There are slight variations in the results, depending on how accurately one has drawn the tangent, but it should be close enough. I have had error percentages of about 1 - 5 % in my paper calculations. I have had no time or opportunity to try these in the game, but if my calculations were correct, the method should bring results accurate enough. Keep in mind though, that the method is also affected by the accuracy of your initial target course and speed estimations and any zigzagging or wind speed changes during the passing of the target. Time compression also affects the speed you can keep, so if you use TC, check the speed gauge.
(Another thing to keep in mind: if you use SH3's in-game tools, remember that the method described here uses relative speeds and relative distances. I recommend drawing the picture somewhere else than the location of your U-boat. Otherwise you might mix up the lines and circles drawn here to the lines and circles that you have drawn to measure actual distances.)
More info on the method and similar ones can be found from a US Navy maneuvering board manual from 1941: http://archive.org/details/maneuveringboard00unit The method used in this thread is part of case VI, page 12.
Do keep in mind that I don't understand much about mathematics: I might have misunderstood the method. So if you try this, try it in a safe situation. If there are any questions on the mathematics or trigonometry behind this method, don't expect any answers: at least from me :88)
http://i.imgur.com/jPsjO.jpg
Here's one more thing that one might be able to do with Sketchup. It is possible to copy a maneuvering board in the background and keep using Sketchup. You can change the size of the background maneuvering board to match measurements and rings in the maneuvering board. One could for example draw a line representing 8 knots with the line tool's measuring function to a length of 8 meters. That length could also be made to match the maneuvering board's rings, for example a line of 8 units could be made to correspond with 4 rings.
There are however some quirks in using the maneuvering board background, for example the dark area in the screenshot that I don't know how to get rid off or even if it is possible to get rid of it.
The example situation: you have stalked a convoy and plotted its course and speed as 295 true bearing, 7 knots. The convoy is now at a relative bearing of 87 degrees, range 10 kilometers. The fastest speed you can make in the prevailing winds and not wanting to risk engine failure is 15 knots. You want to pass the convoy keeping a range of 8 kilometers, thinking that at that kind of range they will not see you, but you can see them. This is how you determine your course:
http://i.imgur.com/TAnNJ.jpg
1. With the protractor, draw an angle of 87 degrees (representing the convoys relative bearing).
http://i.imgur.com/zTODg.jpg
2. Draw a line with a length of 10 (the units you use are not important, they may be meters or kilometres, or centimetres or miles, but you have to keep using the same unit). The line represents the distance from your U-boat to the target.
http://i.imgur.com/kZRan.jpg
3. From the end of the line you drew, draw another line using the protractor tool and the line tool. Angle 295, length 7 units, representing the convoy's course and speed. If you want to, you can erase the lines the protractor left to make the picture clearer.
http://i.imgur.com/2ttPM.jpg
4. Draw two circles around the starting point of the target ship's course/speed line. The other circle should have a radius of 8, representing the safety distance you want to keep to the convoy. The other circle should have a radius of 15, representing the speed you want to use while passing the convoy quickly but safely.
http://i.imgur.com/pM2w8.jpg
5. From the middle of the circle representing your ship draw a tangent touching the circle with the 8 kilometer radius. A tangent is simply a line that "just touches" the circle, a line that is closer to the circle than any other line could be. It doesn't have to be pinpoint accurate, just a close-by is quite enough.
http://i.imgur.com/3DxPW.jpg
6. Copy the tangent line you just drew. You can use the protractor to measure the angle or more simply just use the select tool and copy the line to the clipboard. Then paste it to the end of the line representing the course and speed of the convoy. Continue the line until it breaks the circle representing the 15 knot intercept speed we're using in this example.
http://i.imgur.com/5Imb4.jpg
7. The last thing to do is to draw a line from the starting point of the line representing the convoy's speed and course to the point where the copy-pasted line cuts the circle representing the 15 knot speed you are going to use. Measure the angle you got with the protractor.
I got about 27,5. That's the true bearing you should now use with the speed of 15 knots. Keeping that speed and course you should end up nicely just in front of the convoy, just outside the safety range of 8 kilometres that was used here.
There are slight variations in the results, depending on how accurately one has drawn the tangent, but it should be close enough. I have had error percentages of about 1 - 5 % in my paper calculations. I have had no time or opportunity to try these in the game, but if my calculations were correct, the method should bring results accurate enough. Keep in mind though, that the method is also affected by the accuracy of your initial target course and speed estimations and any zigzagging or wind speed changes during the passing of the target. Time compression also affects the speed you can keep, so if you use TC, check the speed gauge.
(Another thing to keep in mind: if you use SH3's in-game tools, remember that the method described here uses relative speeds and relative distances. I recommend drawing the picture somewhere else than the location of your U-boat. Otherwise you might mix up the lines and circles drawn here to the lines and circles that you have drawn to measure actual distances.)
More info on the method and similar ones can be found from a US Navy maneuvering board manual from 1941: http://archive.org/details/maneuveringboard00unit The method used in this thread is part of case VI, page 12.
Do keep in mind that I don't understand much about mathematics: I might have misunderstood the method. So if you try this, try it in a safe situation. If there are any questions on the mathematics or trigonometry behind this method, don't expect any answers: at least from me :88)
http://i.imgur.com/jPsjO.jpg
Here's one more thing that one might be able to do with Sketchup. It is possible to copy a maneuvering board in the background and keep using Sketchup. You can change the size of the background maneuvering board to match measurements and rings in the maneuvering board. One could for example draw a line representing 8 knots with the line tool's measuring function to a length of 8 meters. That length could also be made to match the maneuvering board's rings, for example a line of 8 units could be made to correspond with 4 rings.
There are however some quirks in using the maneuvering board background, for example the dark area in the screenshot that I don't know how to get rid off or even if it is possible to get rid of it.