[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.