Compound Collision Course Method

[Pisces]

Originally Posted by JoeCorrado

Doesn't it take FOUR brain cells to perform any type of trig function?

Is it cheating to use a 21st century calculator to do the math and just pretend like you have a math wiz doing the calculations for you, or is long hand absolutely required for the sake of realism?

K.I.S.S.

It's a personal choice. But since it is usually much easier to just spin a wheel making numbers align, than it is to punching numbers (and risk starting over if you punch in the wrong one) on a calculator, I try to find a more authentic way. But yeah, when testing methods out I too use a calculator to make sure the intermediate steps are dead-accurate.

Solving something graphically is perfectly acceptable. But the drawing tools can induce major inaccuracy in certain situations. Like in this case, two relative bearings that are close together. The point where they cross could be a very slender 'X'. This would lead to a wildly changing intercept angle (W).

[Diopos]

Originally Posted by Pisces

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Solving something graphically is perfectly acceptable. But the drawing tools can induce major inaccuracy in certain situations. Like in this case, two relative bearings that are close together. The point where they cross could be a very slender 'X'. This would lead to a wildly changing intercept angle (W).

Yeap, that is a limitation of many graphical methods, more so with SH4's nav tools. The only way to eliminate the effect is to allow the data points to "spread out" a bit (more points and/or larger "sampling" intervals). I'm certain that this would be a problem in RL nav plotting work, too.

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[Rockin Robbins]

In general, graphical solutions expose defects in the numbers too! In this condition, with a long narrow triangle, it is child's play to see in the graph how even a tiny difference in one parameter can result in a huge difference in another. That shows a method VERY intolerant of error.

Let's take the triangle where you have a target at an AoB of 10º. There's your long narrow triangle, with you crawling at a knot or so to track the collision course of your normal speed target. Here's where the narrow triangle bites! A lousy quarter knot difference in your speed would change your target speed result by 1.44 knots! In other words, using the collision course method on an 80º AoB target to derive target speed multiplies any error in your speed by almost six times in the resulting target speed! That is terrible precision.

Since we can only be accurate to about a half knot, that means that we can only measure the target speed to an accuracy of +-2.88 knots. That's not acceptable. Long narrow triangles mean either great precision or lousy precision, depending on which leg of the triangle you are. If you're the short leg, as in the slow speed of the sub compared to the high speed of the target, you can toss that method out the window for now and use something else until your leverage is much better.

Using just the numbers gives you no obvious clue when your method is full of holes or when you've made a critical error that results in a miss. Graphical methods are self-validating. If it's tough to accurately draw that long narrow triangle, that MEANS SOMETHING. Pay attention!

On the other hand, if the angles are larger, the figure is much easier to draw and slight errors don't make much difference in the graphical result, that means that your solution is very error tolerant and you can proceed with confidence. So Diopos is exactly right: spread those data points out. Widen those triangles!

So rather than numbers being superior, there is more information in a graphical solution which can markedly improve your success rate if you understand what you are looking at. It is the numbers which deceive, by looking precise when they are not.

Insert discussion of the concept of significant figures here. 5<>5.0.

[Pisces]

Originally Posted by Rockin Robbins

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So rather than numbers being superior, there is more information in a graphical solution which can markedly improve your success rate if you understand what you are looking at. It is the numbers which deceive, by looking precise when they are not....

I didn't mean to imply that numbers are superior. I completely agree that a graphical representation would immediately show the defects of a situation intolerant of errors. Which is less apparent if you use just numbers. Drawing with the map tools would enhance error simply by errors in placement and orientation of lines and angles. And that is something I would like to avoid if I'm trying to understand how it works exactly

[Rockin Robbins]

No doubt understanding the problem both from a graphical and mathematical basis helps with understanding the situation. Many times I'll take a graphical situation and then mathematically calculate my error tolerance to see if it's worthwhile to shoot. I did that with the Mark 1 version of the fictitious course brainstorm, finding that the method sucked but if I could reduce to a range of 500 yards I would hear booms. Of course so would a blind chimpanzee, but you gotta salvage what dignity you can!

[Diopos]

Still brainstorming on CCCM: Link

Geometrical solutions expanded to include:

1. change in sub's direction,
2. non "sequential" collision runs
3. multiple collision runs
4. "diverging" target situations

Still not formulated as an """official""" method, but you can experiment with it.
It is a long read, but give it a try anyway!

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