Inaccurate RYA Teaching : CTS - Quest For a New Method

[Seaworthy Lass]

There has just been a heated discussion on this thread:
http://www.cruisersforum.com/forums/...ame-94879.html

In this thread I went head to head with an experienced RYA instructor who up until proven wrong (he was five degrees off using the RYA method on a very simple short exercise) was heatedly insisting the RYA was using a mathematically perfect model for determining the CTS (course to steer) for a passage.

The instructor had earlier provided me with a link to a YouTube video which illustrates the RYA technique:
YouTube
It is useful to view this if you haven't already.
As an aside, note in this video how the arced off distance travelled vector lies quite a distance from the destination point and no attempt is made to see if this point falls closer to the destination point B after the next hour or even the following one, where this point would end up past B. Selecting the point closest to B (whether it falls before or after B) would at least improve the technique, but that is a separate issue. The technique is essentially flawed.

I am starting a new thread as I think this is a very important issue and as it risks being lost over time in a very long thread, it needs to be continued here without the other navigational discussions that are going on concurrently and distracting from this issue.

Flaws with the current RYA method:
The RYA determine the CTS to get to a point near the destination point, not actually to it. They then extrapolate the data. Sometimes that works just fine, sometimes it will be substantially out (extrapolations are often not valid, as shown in the example I set the RYA instructor where his computed heading was five degrees out), sometimes it will be dramatically out.

The instance where it will fail dramatically is where the sum of the vector positions ends up perpendicular to the destination point and exactly above or below it. In this case the arc off of the distance travelled from the tip of the sum of the current displacement up until then does not reach the rhumb line. If the next arc off of the current is perpendicular to B (the destination) it hits the rhumb line twice, equidistant from B.
These two lots of D could be wildly different - it is even possible for them to be more than 90 degrees apart!!!! Pointless choosing either of them, the correct CST is exactly halfway between them then. These type of tidal/current situations may not crop up, but any method should work with ANY data thrown at it .

This extreme case was pointed out to me by a CF member who sent me a PM shooting holes in one of the methods I proposed for determining CTS.
By the way, would you like to come out of hiding yet and take kudos for pointing me in the right direction? (No pun intended). You were inspirational! Many thanks for taking the trouble to sit and look at my model carefully and see it was based on false principles. You were the only one who also recognised I was on to something and had a close look at what I was proposing and told me to go back to the drawing board. Many thanks

The following post will describe my method. It removes the need to draw a rhumb line at all. I am throwing it out for consideration. If anyone can pick flaws in it (please please try) it will have to be revised yet again, but I am hoping this time it is right .