CTS vs Following Rhumb Line - DILUTED THREAD

[Seaworthy Lass]

Originally Posted by Dockhead

......But my darling -- Capt Force was not correct about the symmetrical sinusoid shape for the chart plotter track for a constant heading boat in a unidirectional current. It's symmetrical only in a symmetrical changing current. For a unidirectional current, the vast majority of the passage is spent on the upstream side of the rhumb line. You fall off downstream of the rhumb only just at the end -- if the current is unidirectional like in Capt. Force's scenario.

OK Dockhead, when I replied that this wasn't correct and that the track was symmetrical for a mirror imaged current all from one direction, I could feel your skeptism all the way here in Greece LOL.

So I have plotted out a scenario for you.
16nm passage due north magnetic
Boat speed constant 2.83 knots (I know its a weird figure, but I am getting tired of plotting and this made it easy).
Current from east to west magnetic (direction all the same).
Strength over 8 hours:
I knot, then 1 again, then 2 then 4 then 4 then 2 then 1 then 1.
Total displacement due to current 16 nm.
So heading is 45 degrees.

You spend eactly half the time upstream and half the time downsteam, NOT most of the time upstream as you said.

This is the plot over the eight hour passage. The dotted line is the charplotter track, showing it crosses the track over to the other side at the halfway point . You now need to watch out for those downstream obstructions after the half way mark .

Note the red line is a constant 2.83 nm at 45 degrees. The displacent due to current is the blue line (I have even now learned to put three arrows correctly on this vector )

[Dockhead]

Originally Posted by Seaworthy Lass

OK Dockhead, when I replied that this wasn't correct and that the track was symmetrical for a mirror imaged current all from one direction, I could feel your skeptism all the way here in Greece LOL.

So I have plotted out a scenario for you.
16nm passage due north magnetic
Boat speed constant 2.83 knots (I know its a weird figure, but I am getting tired of plotting and this made it easy).
Current from east to west magnetic (direction all the same).
Strength over 8 hours:
I knot, then 1 again, then 2 then 4 then 4 then 2 then 1 then 1.
Total displacement due to current 16 nm.
So heading is 45 degrees.

You spend eactly half the time upstream and half the time downsteam, NOT most of the time upstream as you said.

This is the plot over the eight hour passage. The dotted line is the charplotter track, showing it crosses the track over to the other side at the halfway point . You now need to watch out for those downstream obstructions after the half way mark .

Note the red line is a constant 2.83 nm at 45 degrees. The displacent due to current is the blue line (I have even now learned to put three arrows correctly on this vector )

Argggggh -- that is embarrassing!

It doesn't make sense to me, but I will immediately concede the argument. I confess I have not given any serious thought to the question of the constant heading boat's ground track, as it is entirely irrelevant to the problem. Should not have shot from the hip!!! Get burned every time that way!

[Dockhead]

OK, now I'm VERY happy! Nice after the humiliation of being shown to have been completely wrong about the ground track of the constant heading boat.

I have solved my current gradient problem on my time-sliced analysis. It was actually quite easy -- I used something similar to my formula to determine a linear progression of the current at the beginning of every period analyzed. Then I simply averaged the current at the beginning of the period under analysis and at the beginning of the next period. Simples! So now I have a perfect triangle wave for the current -- a perfectly legitimate model of a continuously increasing starting at zero and peaking at 4, and then decreasing continuously to zero. In fact this is probably the most literal interpretation of Capt Force's scenario.

Now here's the good part!! After eliminating the little plateau I had before, the model now shows that the smaller the units analyzed, the slower the GPS track boat goes. This fits my hypothesis which I think must be true.

New results, expressed in terms of distance made good towards the waypoint in four hours:

Constant heading boat: 18.33 miles (arrives in port)
GPS track, one hour analysis: 17.7980 miles made good
GPS track, five minute analysis: 17.5927 miles made good
GPS track, one minute analysis: 17.5913 miles made good

Hurrah!

So I now think that this is a perfectly valid analysis of Capt Force's scenario, preserving his 4 hour parameter. We fill in the blank of how far away is the waypoint? With 18.33 miles (we can use any number, but this one is convenient).

It shows that the constant heading boat gets there, with the GPS track boat more than half a mile behind, and more and more the finer we analyze its path.

This model slightly understates the effect of current on the GPS track boat. I will solve that in the next iteration, where I will use Andrew's distance-slicing technique.

Attachment 53046

[Hudson Force]

When I had last visited this site Dockhead had posed the question regarding what would happen to the vessel crossing a passage on the GPS track with a maximun current at the midway point that equaled the speed of the boat. As distance remains speed times time, it can be seen that when the speed falls to nil, the time to the destination becomes infinite. With this in mind I'll share the following story.

Dockhead was enjoying one of those Bahamian fruity rum drinks at anchor and wondering what ever happened to CaptForce. It seemed long ago when they had both left Lake Worth inlet at Palm Beach for the point due east at Grand Bahama Island, Now, just back from the dinghy dock in Hopetown Dockhead was looking over a copy of the Miami Herald.

There on page nine was the answer. CaptForce's vessel "Aythya" had been found adrift off the Carolinas without food, water or fuel. His dessicated remains clutched his deck log in one hand and a plate with the breastbone of a bird at the other hand.

His log entries told of his dogged attempt to remain on the rhumbline to Settlement Point on Grand Bahama even when the ovwhelming current forced him to head due south.

He had written with some hope after he had apparently overtaken Dockhead during the passage. There was an account of seeing Dockhead off his starboard bow and soon thereafter on his port quarter. Dockhead was being set north by the strong current, but, still making way east on his constant heading.

As the wind had died CaptForce was using the last of his diesel fuel to maintain. As his velocity to the east was lost, his time to his destination became infinite. Desparate with hunger he had netted a weary crow that had landed on the deck.

In the still of the doldrums and drifting toward Cape Hatteras he flung the dried breastbone of the crow on the plate where it struck with a sound not unlike the drop of a penny!

[Dockhead]

Originally Posted by CaptForce

When I had last visited this site Dockhead had posed the question regarding what would happen to the vessel crossing a passage on the GPS track with a maximun current at the midway point that equaled the speed of the boat. As distance remains speed times time, it can be seen that when the speed falls to nil, the time to the destination becomes infinite. With this in mind I'll share the following story.

Dockhead was enjoying one of those Bahamian fruity rum drinks at anchor and wondering what ever happened to CaptForce. It seemed long ago when they had both left Lake Worth inlet at Palm Beach for the point due east at Grand Bahama Island, Now, just back from the dinghy dock in Hopetown Dockhead was looking over a copy of the Miami Herald.

There on page nine was the answer. CaptForce's vessel "Aythya" had been found adrift off the Carolinas without food, water or fuel. His dessicated remains clutched his deck log in one hand and a plate with the breastbone of a bird at the other hand.

His log entries told of his dogged attempt to remain on the rhumbline to Settlement Point on Grand Bahama even when the ovwhelming current forced him to head due south.

He had written with some hope after he had apparently overtaken Dockhead during the passage. There was an account of seeing Dockhead off his starboard bow and soon thereafter on his port quarter. Dockhead was being set north by the strong current, but, still making way east on his constant heading.

As the wind had died CaptForce was using the last of his diesel fuel to maintain. As his velocity to the east was lost, his time to his destination became infinite. Desparate with hunger he had netted a weary crow that had landed on the deck.

In the still of the doldrums and drifting toward Cape Hatteras he flung the dried breastbone of the crow on the plate where it struck with a sound not unlike the drop of a penny!

ROTFLMAO!

The most hilarious, wittiest, and best concession speech I ever read! Love it!


I have to say, Capt Force, that we all owe you a huge debt of gratitude!

You stubbornly challenged something all the rest of us took for granted, and forced us to think it through to a level of detail we had never ever imagined even existed. In the process of pompously pontificating on various aspects of the problem, every one of us, including Dave (!) had brain farts, made mistakes, and learned the hard way that none of us understood it at all as well as we thought we did, including even Dave, who teaches this ****!!!

I might have to rate this as the single best thread ever on CF, at least in terms of how much people learned from it.

[Seaworthy Lass]

16 November 2013

The above 50 posts were all consolidated from this thread:
http://www.cruisersforum.com/forums/...ame-94879.html

Apologies if they are a bit disjointed, there were about 800 posts in the original thread and it was hard to wade through. If you want to go back and read the tale in its entirety, start at about post #180.

This thread followed on and was also interesting:
http://www.cruisersforum.com/forums/...ine-97251.html

The thread outlining the methods to calculate CTS (the RYA method and mine) can be found here:
http://www.cruisersforum.com/forums/...hod-96579.html

CTS vs. following the rhumb line has been debated ad infinitum. This thread was composed simply to make all the arguments easier to follow.

Hope you enjoyed the read and if you were a "follow the rhumb line" person before, you have now been converted .

Cheers
SWL

[foolishsailor]

Should be consolidated into a Manual and sent off to RYA - with a note

"How do you like these apples, bitches!"

[s/v Moondancer]

Dockhead and Seaworthy Lass instead of all this theory stuff we need a practical test conducted in a F6-7 in the English Channel in Spring on a spring tide in the rain to windward.

In separate boats you need to clear the Needles at dawn and without using a GPS, there are lots of big lighthouses to triangulate off, get to Cherbourg before the pubs shut!

Been there! Done that!

[Seaworthy Lass]

Originally Posted by s/v Moondancer

Dockhead and Seaworthy Lass instead of all this theory stuff we need a practical test conducted in a F6-7 in the English Channel in Spring on a spring tide in the rain to windward.

In separate boats you need to clear the Needles at dawn and without using a GPS, there are lots of big lighthouses to triangulate off, get to Cherbourg before the pubs shut!

Been there! Done that!

Hi Moondancer
This is not just theory. Dockhead has dozens of Channel crossings under his belt and uses a single CTS to cross very efficiently and accurately. He has reported that although his XTE (cross track error) may be up to 10 nm during the journey, as he is swept by current from one side of rhumb line to the other, he is usually with a nm of his destination at the end.

This technique is of real value and can shave a lot of time off a journey .

[s/v Moondancer]

Yes, I know, I have done it many times, but why has it taken over 1,000 posts to explain that?

The real point is that all this theory is fine but once you get out there and the electronics are down then you need seamanship not theory.

[Seaworthy Lass]

Originally Posted by s/v Moondancer

Yes, I know, I have done it many times, but why has it taken over 1,000 posts to explain that?

The real point is that all this theory is fine but once you get out there and the electronics are down then you need seamanship not theory.

This is not just theory, this is practical technique. And it is even more, not less valuable when your electronics are down as you are just steering one heading all the way, not continually tweaking the heading to stay on the rhumb line you can see on the chart plotter.

All this is of even greater importance when the current does not roughly cancel out over a journey.

And this CTS is NOT something your GPS or chart plotter will tell you (although there are now programs that will). It is something you calculate manually and all people navigating tidal waters would find it very beneficial to be familiar with the technique.

[foolishsailor]

Originally Posted by Seaworthy Lass

And this CTS is NOT something your GPS or chart plotter will tell you (although there are now programs that will). It is something you calculate manually and all people navigating tidal waters would find it very beneficial to be familiar with the technique.

Exactly!

This is what I love about this and the LBE theead. They actually illustrate that seamenship and navigation, outside that provided by chartplotters, is still required to optimize ones course.

You will get there if you just use you gps and chartplotter - but you will get there faster, and safer, using the fleshy bit between the ears.

...unless you can afford one of those really fancy predictive plotters that you can plugin tidal streams and realtime weather microforecasts to give you a moment by moment course and tack option...

...but who has one of those...

[Hudson Force]

I was pleased to see this revisited and very enlightened by the whole original thread. I am so thankful for those that persisted and allowed me to learn!

[goboatingnow]

I should point out that neither the RYA method or SLs method have been tested for accuracy. That's requires comparing projected end points of both methods agsinst end point accuracy achieved using a demonstrably better method. Like a computer program using small smaller tidal data points.

Dockhead I believe was going to undertake this , but I think it may have been more time consuming then originally thought.

I would contend , emphatically that the real life error circle of arrival at the destination is greater then either RYA or SLs system. ( In the vast majority of real life situations) In which case while SLs method demonstrates more precision it has not demonstrated more accuracy.

To illustrate a cheap 5 digit multi meter with 5% accuracy and a A three digit one with 5% accuracy. The 5 digit one is more precise , but not more accurate.

We await a peer review study.

Dave

[Dockhead]

Originally Posted by goboatingnow

I should point out that neither the RYA method or SLs method have been tested for accuracy. That's requires comparing projected end points of both methods agsinst end point accuracy achieved using a demonstrably better method. Like a computer program using small smaller tidal data points.

Dockhead I believe was going to undertake this , but I think it may have been more time consuming then originally thought.

I would contend , emphatically that the real life error circle of arrival at the destination is greater then either RYA or SLs system. ( In the vast majority of real life situations) In which case while SLs method demonstrates more precision it has not demonstrated more accuracy.

To illustrate a cheap 5 digit multi meter with 5% accuracy and a A three digit one with 5% accuracy. The 5 digit one is more precise , but not more accurate.

We await a peer review study.

Dave

I think that in general this is right, and that it is am important insight.

The only thing I would say is that SWL's method is inherently more accurate, and is no more trouble than the traditional method, so the accuracy is without any cost. Therefore, I am convinced that it is superior.

Another thing I would say based on experience -- although they are on the one hand too precise, as variations speed and steering accuracy and wind direction will inevitably conspire to mess them up, at the same time, none of these methods is actually precise enough, because they don't consider the fact that the currents are not precisely perpendicular (and deviations of current direction have a big effect on the results), and because they use coarse-grained current data from tidal atlases.

When I realized all of that, I just stopped doing it by hand altogether and started using a computer, which has been vastly better, not too mention easier.

Using a computer, you deal with unexpected changes in wind or boat speed by rerunning the numbers every couple of hours, which only takes a few seconds. It works a treat; I'll never go back.

The computer also deals brilliantly with the situation which is impossible to do by hand -- strong rotary currents like in the Channel Islands.