

01022013, 03:43

#16

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Re: Single CTS or follow the Courseline?
In all of the problems we have been looking at the boat speed is given to us as a constant. First to avoid some terminalogy that I will use:
SOG  Speed over Ground
VTG  Velocity Track Made Good
VDR  Velocity and set of drift (assuming due to tidal current for these examples)
Vboat  Boat Speed
Positions
A  Departure point
B  Destination
C  RYA Tidal offset (this is to a full hour)
D  RYA  arc of distance traveled at Vboat and line AB
K  SWL tidal offset for duration of voyage
distances:
AB  rhumbline dist from A to B
AC  tidal offset at x hrs
CD  distance travelled though the water mass over x hours
AD  distance traveled along rhumb line over x hrs
AK  total tidal offset
KB  total distance travelled through the water mass
Using the RYA method
VTG (AD) = Vboat x (AD/CD)
Using the SWL method
VTG (AB) = Vboat x (AB/KB)
Note that given more than one curent your drift will vary with the current and your boat track will not follow the rhumbline. Your speed over ground will not be the same as the VTG. If you want, you can calculate one using the Law of Cosines using Vboat, VDR and the angle between the CTS and the tidal set for each tidal hour. It would not survive first contact with the elements!
Quote:
Originally Posted by Paul Elliott
You are correct. The CTS methods are using the V to B vector length and time to work out speed, or using length and speed to figure out the time, (where V is the end of the current vector and B is the destination). As has been shown, this plotted distance is *not* the throughthewater distance, so SOG should be used.
However, the actual SOG will be somewhat less than if we were actually sailing on the VB line, since our track will have a constantlyvarying currentinduced sideways ground vector.
I'm not sure how we work out the speed. It's probably SOG * cos(angle BAV), or BSP / cos(angle BAV). Someone should look into this. It could be important!
Or, if we calculate speed by looking at time and the distance AB (which is the actual throughthewater distance for the CTS method), then we can use BSP (speed through the water) in the calculations. I think that works. It's not how I was doing it though.

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01022013, 03:48

#17

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Re: Single CTS or follow the Courseline?
I just want to point out that I have retracted my statement quoted above. The distance along the CTS vector is indeed the distance sailed through the water, and so BSP is the proper parameter to use in the calculations.
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01022013, 04:15

#18

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Re: Single CTS or follow the Courseline?
Quote:
Originally Posted by bewitched
In recent months on this forum, there has been a growing support in favour of opting for a Single Course to Steer (CTS) method of navigation when sailing across a varying tidal flow. The proponents of this method claim that it is faster than ‘crabbing along the rhumbline’. Which perhaps could be more kindly termed navigate along the course line (NCL)?
In this thread I hope to present the case for my belief that NCL will normally be the fastest and safest way to complete a passage when compared to the CTS method.
Course to steer  two hours of tide  YouTube[/url] . It’s not a definitive explanation of the CTS method, but provides the basics of the technique which essentially sums the tidal vectors over x hours, adds the boatspeed (BSP) vector from the end of the tidal vectors to the intersect with the course line. This is the estimated position after x hours.
NCL: This method uses GPS data to ensure that the boat stays on the course line. In very simple terms, the technique involves ensuring that the course over the ground (COG) achieved matches the desired course. It is simply a case of following the course line that has been drawn on the chart as shown on the attached picture.
To avoid presenting the subject in one huge post, I will post separately for each major issue.
So first issue: Safety

Kudos to Bewitched for a very intelligent and wellreasoned argument of the problem!
I'm glad also that he has resigned from the Flat Earth Society and now understands that a constant heading course is always faster!
Now we get to more subtle questions about whether it is (a) worthwhile; (b) usable at all given quality of tide data; or (c) safe. There are no pat answers to those questions, which depend on the circumstances.
As to whether or not it is safe  I think that's the easiest question. If you need to follow a straight line through obstacles or through a narrow gap somewhere or a narrow channel, then obviously you need to sail the rhumb line and forget about the efficiency of constant heading passages. I like to use "track mode" on my pilot in such cases.
As to whether or not it is worthwhile or practical, it really all depends on the currents. If they are weak, and/or they tend towards consistent rate and direction over the whole passage, then a constant heading strategy brings little result, becoming zero result with either zero current or absolutely consistent rate and direction. At a constant rate and direction, a constant heading strategy will anyway take you right down the rhumb line.
But if the current varies, a rhumb line course will be a zig zag through the water, and will take longer and be harder to sail. Is it worth it? Well, you might have no choice if you have a narrow pass between obstacles. But a rhumb line passage through moving water is just like a zig zag passage through still water  if you really need to sail N way over there in order to get around that shoal, before turning E to your destination  well, you have to do what you have to do. Sailing a rhumb line path through moving water is exactly the same thing  fine if you must do it, but rather stupid otherwise  UNLESS the current is very weak and/or very consistent.
In order to know the extent to which it is worth it or not, I guess it makes sense to play with the models. I have posted a spreadsheet with open formulae which anyone can download and plug in any combination of values they like.
As to whether tides are knowable enough to sail an efficient CTS passage, I guess that also depends on where you are. In our part of the world, the tide atlases are accurate to some tenths of a knot, and definitely plenty accurate enough to make a CTS passage worthwhile. And anyway  how accurate does the data need to be, to give you a better chance, than intentionally sailing a zigzag through the water by doing a rhumb line passage? I think not very. If you are even only right about the direction of the aggregate vector you are already ahead of the game, in many cases. A straight line through the water will often be better than an intentional zigzag, even if you are off by a bunch of degrees in calculating your Course to Steer
We could work up some examples to demonstrate this.
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01022013, 06:20

#20

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Re: Single CTS or follow the Courseline?
Quote:
Originally Posted by Dockhead
I'm glad also that he has resigned from the Flat Earth Society and now understands that a constant heading course is always faster!

Really?
Here's the situation  your destination is 12 NM due East. Your boat speed is 5 kts. Tidal set is to the south (180º) 2 kts first hour, 3 kts second hour, 2 kts third hour.
I submit it's faster to crab along the 'rhumbline.' Prove me wrong.
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01022013, 06:30

#21

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Re: Single CTS or follow the Courseline?
Quote:
Originally Posted by Lodesman
Really?
Here's the situation  your destination is 12 NM due East. Your boat speed is 5 kts. Tidal set is to the south (180º) 2 kts first hour, 3 kts second hour, 2 kts third hour.
I submit it's faster to crab along the 'rhumbline.' Prove me wrong.

I'm just getting off a train and onto a ferry to the IOW. I'll dig up the spreadsheet when I get there and prove it.
What is the case, mathematically  these are the laws:
1. Constant heading is always the fastest away across any still or moving body of water.
2. Rhumb line course will just equal constant heading course in only two cases: (a) still water; and (b) constant rate and set of a current over the whole passage. That is because in those two cases, and in none others, a rhumb line course exactly equals a CTS course  they coincide.
The reason for this is that the shortest distance between any two points is a straight line. We sail in water, not over ground. A constant heading is a straight line through water. Ergo, a constant heading is always the fastest way  anything else is crooked path which is, mathematically, longer.
We exclude the case of back eddies or inconsistent currents where it can be profitable to sail an odd course to get a lift. We assume uniformly moving body of water. We do not consider any effects of wind. We are also using planar geometry  we assume the ocean is a plane, which of course it is not, although at these distances it is close enough.
I think you know all of that well enough, and probably better than any of us! You're just trolling for a good proof, I suspect. That's ok  I'll bite
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01022013, 07:03

#22

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Join Date: Sep 2009
Posts: 885

Re: Single CTS or follow the Courseline?
Quote:
Originally Posted by Dockhead
Constant heading is always the fastest away across any still or moving body of water.

I think there are quite a few big 'IFs' that need to be added to that statement. Some of which are:
IF you have accurate tide data available
If you have accurate leeway data available. (TWA=70deg, TWS = 18kts, moderate sea, No.2 headsail, full main, what is the magnitude and angle of leeway generated on your boat?)
If you predict the weather and sea state correctly across the whole passage.
There is also the inconvenient issue that the NCL boat will normally achieve a faster BSP. Which may make for a tricky apples to apples comparison
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01022013, 07:08

#23

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Join Date: Sep 2006
Posts: 3,303

Re: Single CTS or follow the Courseline?
Quote:
Originally Posted by Lodesman
Really?
Here's the situation  your destination is 12 NM due East. Your boat speed is 5 kts. Tidal set is to the south (180º) 2 kts first hour, 3 kts second hour, 2 kts third hour.
I submit it's faster to crab along the 'rhumbline.' Prove me wrong.

OK, here's a proof of sorts. I'm on another computer and can't post a scan of my work, but I'll walk you through it. I am doing this stepwise, treating each hour (or fraction) independently.
First, the easy "crabbing along the rhumbline" solution.
Hour 1: (5 kts BSP, crosscurrent of 2 kts). I didn't bother to work out the CTS angle, but we have a triangle with 2 miles for the current, 5 miles for the CTS, and progress along the rhumbline of 4.583 miles (square root of the sum of the squares).
Hour 2: the triangle is 3 miles (current) 5 miles (CTS) and 4 miles along the rhumbline.
Final 0.7456 hour: the triangle is 1.491 miles (current), 3.728 miles (CTS), and 3.417 miles (along the rhumbline).
The total distance along the rhumbline is 12 miles, the CTS distance is 13.643 miles, and the elapsed time is 2.746 hours.
Now, we see how far we can get in the same time (2.746 hours), with a constant CTS:
Vectors are 6.491 miles (current), 12 miles (rhumbline), and 13.730 miles (CTS, 2.746 hours @ 5 kts). The end of the CTS vector is 0.087 miles *beyond* the destination.
We reach the destination sooner with a constant CTS, than by crabbing. The distance sailed crabbing is longer than the constant CTS distance.
Does anybody see a flaw in my analysis?
Please note that this is purely a math exercise, and this assumes perfect information and performance. But I think this is a good place to start when you are trying to analyze this stuff.
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01022013, 07:38

#24

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Re: Single CTS or follow the Courseline?
Here you are:
lodesmanscenario10.xls
Two boats set out at the same time, each traveling at 5 knots through the water towards a destination 12 miles away due E. Southgoing tide at 2 knots first hour, 3 knots second hour, 2 knots third hour.
One boat calculates a CTS of 90  25.18 degrees, sets off, and arrives at the destination in 2.65 hours after sailing 13.26 miles through the water.
Another boat sets out along the rhumb line, making hourly course corrections. It arrives in 2.7457 hours.
The assumptions are rather artificial  the current runs steady at 2 knots, then in an instant accelerates to 3 knots, then back to 2. But it does not really change the result. In fact this approach exaggerates the efficiency of the rhumb line passage.
If we have the current increasing steadily, either as a triangle wave as per my Captain Force analysis, or as a sine wave (thanks to Hapless Seagull for the math), we can analyze the rhumb line course more realistically, and we can try the rhumb line course with more frequent course corrections (down to 1 minute in the Captain Force analysis). All of this makes the rhumb line course look worse and worse.
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01022013, 07:48

#25

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Re: Single CTS or follow the Courseline?
Quote:
Originally Posted by bewitched
I think there are quite a few big 'IFs' that need to be added to that statement. Some of which are:
IF you have accurate tide data available
If you have accurate leeway data available. (TWA=70deg, TWS = 18kts, moderate sea, No.2 headsail, full main, what is the magnitude and angle of leeway generated on your boat?)
If you predict the weather and sea state correctly across the whole passage.
There is also the inconvenient issue that the NCL boat will normally achieve a faster BSP. Which may make for a tricky apples to apples comparison

Why in the world would the NCL boat achieve a faster BSP? uzzled:
As to the rest of it  why don't you quantify it? We've all had to brush off our high school trig and do some math. Why don't you make a mathematical case for, for example, if you are off by 1 degree in your CTS calculation, you will already lose your advantage, in this or that scenario. That would be interesting.
My challenge to you is this. Lodesman threw his gauntlet, and we picked it up. Now I'm throwing mine: I say it will be a rare case where intentionally sailing a zig zag through the water will be more efficient than sailing even an imperfect CTS passage. Prove me wrong!
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01022013, 08:07

#26

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Re: Single CTS or follow the Courseline?
Sorry, there was a formula error in my last calculation. Corrected:
lodesmanscenario11.xls
So the CTS boat needs a CTS of 90  28.23, sails 13.62 miles through the water arriving in 2.72 hours.
Rhumb line boat is the same.
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01022013, 08:36

#27

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Re: Single CTS or follow the Courseline?
There's no doubt in my mind that simply sailing the rhumb line can have tactical advantage. In some scenarios I can see that the attempt to steer Rhumblinecourse results in the boat being nearer to destination than the OverallCTS boat for much of the passage.
TACTICALLY, this means the rhumbline boat may get to a stronger breeze, sooner and thereby cleantheclock of the CTS boat
The usage of the word "current" is best changed to "Drift" hereafter as a reminder. But it gets too complicated as an exact factor and so, using the current as the major factor is just fine. add a "windage" factor if you must.
SWL was pretty plain in saying "Flat Calm, motoring..." in her examples .
as a favour, please stick with this one model for awhile. I never get a chance to think when folks are flinging up various inputs to prove a point.
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01022013, 09:16

#28

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Re: Single CTS or follow the Courseline?
Quote:
Originally Posted by Dockhead
Sorry, there was a formula error in my last calculation. Corrected:
Attachment 53883
So the CTS boat needs a CTS of 90  28.23, sails 13.62 miles through the water arriving in 2.72 hours.
Rhumb line boat is the same.

I see where I made my error  oops. I have been proven wrong  the CTS is 2 minutes quicker.
Quote:
The assumptions are rather artificial  the current runs steady at 2 knots, then in an instant accelerates to 3 knots, then back to 2. But it does not really change the result. In fact this approach exaggerates the efficiency of the rhumb line passage.

Seriously this is the scenario that you call artificial? It is indeed fairly likely that you could start out as tidal current increases to its maximum then decreases. When the set comes from a constant direction, the CTS doesn't have very much of an advantage, certainly when you consider that for a couple minutes saved on passage, you'll have to plot three separate CMGs (for navigational safety). I still haven't had a very good answer as to what you do on a CTS when a fix puts you off your planned CMG? Do you steer to regain or maintain your planned CTS?
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01022013, 09:42

#29

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Re: Single CTS or follow the Courseline?
Quote:
Originally Posted by Lodesman
I see where I made my error  oops. I have been proven wrong  the CTS is 2 minutes quicker.
Seriously this is the scenario that you call artificial? It is indeed fairly likely that you could start out as tidal current increases to its maximum then decreases. When the set comes from a constant direction, the CTS doesn't have very much of an advantage, certainly when you consider that for a couple minutes saved on passage, you'll have to plot three separate CMGs (for navigational safety). I still haven't had a very good answer as to what you do on a CTS when a fix puts you off your planned CMG? Do you steer to regain or maintain your planned CTS?

Nothing wrong with it being artificial! It's easier to analyze. Sound mathematical principles will deal with scenarios both artificial and natural.
Yes, for a slightly varying current coming from one direction, a CTS course will give only a small advantage. At some point it's hardly worth doing. I think everyone agrees about that.
What do you do IF a fix puts you off your planned track? No IF but WHEN
You NEVER make a sharp correction to get back to your planned ground track. Not efficient. From any given point, the fastest way to get to your destination is a straight line through water, so ideally you rerun all the numbers and calculate a new CTS. When I'm crossing the English Channel, I always do a complete rerun in the middle, just to check, if not to correct.
If you're not too far off, you just stay on your original CTS. It will come out in the wash at the end.
You will have a builtup error in any case  greatest source by far is variance in planned speed. You make your destination some place which will be somewhat uptide of your destination at the time of your arrival, in any case  margin of error. For NeedlesCherbourg, 1 mile if you have great confidence in your calculations, 2 or 3 if less. That should put you at least slightly uptide despite the accumulated pool of errors.
Then one hour out when you've just got one tide to go, or maybe half an hour out if things have gone really well, you abandon your constant CTS and go over to more ordinary method of matching COG to BTW, or simply put your pilot on "track mode". From slightly uptide of your destination, you just glide right in. It's very satisfying when it comes off, and it most always does
As as a result of all these fascinating discussions, with a lot of stimulation and inspiration from Capt Force, Andrew Troup, Hapless Seagull, and especially, Seaworthy Lass, I have perfected my hand methods, thoroughly figured out the theory, and even blown the cobwebs off my high school trig. And ironically, I guess, immediately abandoned hand methods. I bought the Neptune program ( PASSAGE PLANNER PLUS), which runs a CTS with near mathematical perfection using the high resolution UK Hydrographic Office 5minute tide data. Effortlessly. So you can run several scenarios, and rerun everything midpassage without any trouble at all.
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01022013, 10:18

#30

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Re: Single CTS or follow the Courseline?
Quote:
Originally Posted by Lodesman
I still haven't had a very good answer as to what you do on a CTS when a fix puts you off your planned CMG? Do you steer to regain or maintain your planned CTS?

Yes, you may have to plot a separate track for each tide segment if you suspect you will have a significant XTE and/or your CTS will take you near potential hazards. Every situation will be different. If you use OpenCPN to graphically do the RYA or SWL methods it is just a few more mouse clicks. What you do if your fix is off would depend on the magnitude of the displacement. You could rerun the CTS from your position, make a small correction back to your next next CMG waypoint if you calculated them,
Unlike Dockhead, I have had little experience with having to deal with significant tides. Instead of dusting off cobwebs, I have been learning lots of theory. I will be sticking to the hand methods for now. However, putting the trig into a spreadsheet makes some of the recalculating much quicker.
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