Distinct Activities: Shackled by a Common Name?

[Andrew Troup]

What the treadmill belt simplification does fail to capture is: what if the direction, as well as speed of the belt, are constantly changing?

[Seaworthy Lass]

Originally Posted by Andrew Troup

What the treadmill belt simplification does fail to capture is: what if the direction, as well as speed of the belt, are constantly changing?

It doesn't matter, it just needs to be taken into account when making the calculations for the correct constant heading for the passage .

PS All this gets blown if reasonable estimates for tide cannot be made. Because there will always be errors in estimates for tide and boat speed, the it is unlikely the heading will be dead accurate, but it will still be a quicker than simply following a straight course over the ground. Calculations along the way allowing comparisons of actual and expected position at certain times will allow for recalculations of heading if time is of an essence and you can be bothered.

[boatman61]

Originally Posted by Andrew Troup

What the treadmill belt simplification does fail to capture is: what if the direction, as well as speed of the belt, are constantly changing?

Deep Sheeett..... zigzag belts no less..

[Jammer Six]

Would this be a bad time to point out that I don't need to know about great circle calculations, since my GPS does it for me?

[Hudson Force]

Originally Posted by Seaworthy Lass

................. All this gets blown if reasonable estimates for tide cannot be made. Because there will always be errors in estimates for tide and boat speed.................

I am also thrilled by this vigorous conversation, but it is essential that we are all speaking the same language. Let's agree to take this term "tide" off the table. Tidal changes represent a change in the depth of water at a location. This is usually represented by a number plus or minus from a comparison with the mean level. I believe those that are using this term are actually referring to the current drift. There are standard operational definitions used by international oceanogaphers that we should be using in order to effectively communicate.

[Andrew Troup]

I think it's not necessary to greatly complicate the treadmill thought experiment to embrace varying current direction;

given that ants are small, it could be a mini conveyor belt, sitting on a turntable at a Chinese restaurant for REALLY lazy diners.

[Andrew Troup]

Regarding terminology, it think its a fair point to suggest the use of the term current, but if the source of that current is purely (or overwhelmingly) tidal gradients, then "tide" seems like a fair contraction for the more comprehensive term "tidal current"

Usually, of course, there will be a regularly reversing component due to tide, superimposed on a more unidirectional and slowly varying component due to ocean thermal/coriolis circulation, wind-induced surface drift etc, and other generally unquantifiable possible additions like currents due to barometric pressure, water being transported inshore by wave action (causing rips) etc etc

I would hate to see a discussion on this point of terminology derail the discussion of an important conceptual principle, which falls into the rare category where, if it's argued to a standstill, only one side of the argument can prevail.

[Andrew Troup]

Hmm -- I retract my previous assertion that simply putting a turntable under the conveyor belt would be sufficient to cover changing directions as well as amplitudes of the current vector.

This is only the case if the pivot of the turntable is continually repositioned so that it is directly beneath the ant.

Bugger !

(I know this doesn't make any difference to the real world answer; it just makes it a bit harder to prove with a simple thought picture)

[Hudson Force]

Originally Posted by Andrew Troup

..............I would hate to see a discussion on this point of terminology derail the discussion of an important conceptual principle, which falls into the rare category where, if it's argued to a standstill, only one side of the argument can prevail.

Sure, I don't want to lesson the conversation by focusing strictly on terminology and there is good cause to identifly currents that result from tidal changes because of their uniquely timed reversing quality, but let's make sure we are talking about currents and their set and drift. Things are complicated enough without bringing in water level. Oh, no! Did I just suggest, "for simplicities sake"!

[Andrew Troup]

So, CaptForce, have you had time to digest #225?

which was directed squarely at the points you raised in #224

.... and, in #225, no 'tides' were mentioned

;-)

[Seaworthy Lass]

Originally Posted by CaptForce

Sure, I don't want to lesson the conversation by focusing strictly on terminology and there is good cause to identifly currents that result from tidal changes because of their uniquely timed reversing quality, but let's make sure we are talking about currents and their set and drift. Things are complicated enough without bringing in water level. Oh, no! Did I just suggest, "for simplicities sake"!

Sorry, my error, I meant "current", just got caught up with several references here to "tide" .

[Dockhead]

Originally Posted by CaptForce

Ah, now I think I see the problem and why so many seem to stick to an intelligent answer that I can not agree with. It's all because of the "for simplicities sake" and the simple example from the high school math teacher that does not wish to calculate the complexities of the real world. All those that are following the plan of maintaining a constant compass heading while crossing a current may remain satisfied with this procedure "for simplicities sake", but in the real world they will be taking a longer course on the sigmoid curve because the drift, if not the set also, will vary. Let me explain with one of the most common passages taken across a current. If you were to procede on a plan of crossing in a direction of 90 degrees M from Palm Beach, Florida across the Gulfstream to the Bahamas, you might, for simplicities sake determine that you will need to take a constant course of 115 degrees M at five knots, due to the average current set to the north at 2.5 kts, in order to reach your destination in the same manner as many suggest. The method is simple, but during the begining of the trip, when the current is less than the 5 kts at the center of the Gulfstrem, you would be making headway to the south of the rumbline course. Half way across the passage, when you are in the full five kt current, you will meet your rhumbline and then be moved north of your most efficient path. Finally, as you approach your Bahamian landfall and the current has weakened, you will arrive at your destination on the heading of 115M. This method works for "simplicities sake", but if you had elected to remain on the couse determined by your GPS you would arrive sooner and traveled in a straight line as you would constantly be recieving updates to change your required course vector as the strength of the current changed. Kudos to all the math teachers and all those correctly planning to cross an imaginary current that remains at a constant velocity for the passage. There is nothing wrong with taking the longer course if you value the method that gives you a simple answer. By the way, that treadmill analogy is excellent. Now, just imagine that the center of the treadmill is moving faster than the edges!

Nope, sorry, you've got it all wrong, and that such a smart and experienced person like you could fail to grasp it is a good illustration of why this is so hard to teach.

Try to think of it this way -- you sail through water, not over ground. The most efficient course is a direct course through the water -- a straight line. A straight line through water is a constant compass heading. The constant compass heading is emphatically not "for simplicity's sake" -- it is the direct route through water.

Now if the water moves around, that efficient course will describe a rambling path over the bottom. But that does not matter, because your boat is not attached to the bottom -- a mile sailed is a mile sailed through the water.

Let's take a real simple example -- you are sailing Needles to Cherbourg, 60nm, bearing 180. Your average speed is 5 knots, so 12 hours. You set out just as the tide is setting to the West, and it will run West for six hours, then turn East. It runs, let's say, an average of 2 knots in each direction.

Your fastest way to get there is to set your pilot to steer 180 and leave it there for 12 hours whereupon you will arrive in Cherbourg. As the tide runs West, it will sweep you off the rhumb line. 6 hours later, halfway across, you are 12 miles down Channel from the rhumb line. And that is just where you want to be. Because now the tide is turning, and it is sweeping you now directly to Cherbourg. You will see that your COG will now gradually converge with BTW, although your bow is still pointed 180, more or less at the Cap d' Hague. That's the way I will be sailing that passage.

That way one sails 60 miles through the water, which is the shortest possible distance, so 12 hours at 5 knots, and one is in Cherbourg.

Now imagine you tried to do what you just said -- stay on the rhumb line, for the shortest route over ground. You can do this -- just set your pilot on "Track" mode, and your pilot will do it automatically. To counteract 2 knots of current, the pilot will steer you at first about 35 degrees to the East of Cherbourg, a course of about 145, so your bow will be pointed way off to the East, and your SOG towards S will be about 4 knots. You will not get half way across the Channel in 6 hours, because you are crabbing along the rhumb line, stemming the tide. After six hours, you have only made about 24 miles of Southing, because you have wasted 1 mile out of 5 sailed just crabbing towards the rhumb line.

When the tide turns, you are in the wrong place. Because now the tide, which had been sweeping you West, is now trying to take you to the East, but you are directly N of Cherbourg, on the rhumb line. So now you're going to do the opposite of what you did the previous 6 hours -- you will point your bow to the W, about 35 degrees off of S or about 215 when the tide is running 2 knots and your boat speed is 5 knots. You will again crab along the rhumb line making about 4 knots SOG towards Cherbourg. You will not be in Cherbourg after 12 hours, you will have made only about 48 miles made good after 12 hours, with 12 miles still to go. The tide will turn yet again, and again you will point your bow towards the W and again you will stem the tide, crabbing along the rhumb line.

You will have sailed a straight line across the ground, but you will have sailed 15 extra miles through the water, about 75 in all, which will take you 3 extra hours since your boat cannot feel miles over ground.

I will have sailed a huge long distance across the ground, in a long "S" curve, getting up to 12 miles XTE at one point, but I will have sailed exactly 60 miles through the water -- which I say again, is the only way any boat can sail -- boats don't have legs which reach down to the bottom. I will arrive in Cherbourg after 12 hours, 3 hours ahead of you.

Got it now?

In your Gulf Stream example, you will be crabbing back and forth staying on the rhumb line, sailing a longer distance through the water, changing heading all the time as the current gets stronger and weaker, rather than sailing the one true CTS which will let the current take you right to your destination, a shorter distance through the water.


Both of these examples assume perfect knowledge of the currents, and of our average passage speed -- of course we don't have perfect knowledge. Still, we know that sailing along the rhumb line is the wrong way to cross a moving body of water, and becomes a radically wrong way to do it, the more varied the current is. Even approximate knowledge of the motion of the body of water gives us enough to calculate a CTS and sail more efficiently.

I don't think I've been more than 2 miles off in my last 10 Channel crossings, and I'm usually within a mile, after one mid-Channel correction.

[noelex 77]

Let's do some simple calculations for a passage. I am sure doing the calculations will convince the doubters that Dockhead is correct.
We are traveling due north to a destination 60Nm away.
We a motoring at a constant STW of 5 knots.

The current will be as follows
1st hour 1K due west
2nd hour 2k due west
3rd hour 3k due west
4th hour 3k due west
5th hour 2k due west
6th hour 1k due west

7th hour 1k due East
8th hour 2k due East
9th hour 3K due East
10th hour 3K due East
11th hour 2K due East
12th hour 1K due east

After the 12th hour for subsequent hours there is no current.


Calculate the length of time the passage will take for:
A) steering a constant due North compass course ( swinging east and then back on course)
B) steering a constant COG ( with zero cross track error)


OK let's hear those answers.Preferably with a bit of working out to show how you arrived at the number.

[Seaworthy Lass]

Originally Posted by Andrew Troup

......
(I know this doesn't make any difference to the real world answer; it just makes it a bit harder to prove with a simple thought picture)

The easiest thing I can think of is that the shortest distance between two points is in a straight line. When sailing the straight line is relative to the water, not relative to the ground. Therefore for shortest time is taken following one constant heading all the way .

PS I was typing while you posted Dockhead. You explained it well.

[Andrew Troup]

Nice real life example, Dockhead, and it was an asymmetrical one, to boot, scotching one misconception.

The value of the thought experiment continues to intrigue me, though.

I think it's thrown up, for me, a problem with the 'constant heading' model, in the case where (tidal) current direction is changing rather than simply reversing.

Lets assume the conveyor belt's frame is sitting on an ice rink, and at various pre -planned times, some kind person reorients the frame in a new (also preplanned) direction. NOTE: in such a way as not to move the ant at that moment in time.

This will not matter to our ant, who continues crawling towards a spot painted on the far side of the belt. Provided the changes of direction have been correctly factored into the maths used to position that spot, so that the spot ends up corresponding to the exit point on the rink at the time the ant arrives, the model still works. The ant's path ON THE BELT remains a straight line, hence shortest possible path.

The problem is that unlike the ant, we sailors do not have an aiming spot. We are relying on a compass bearing, and while that's a perfect proxy for an aiming spot if the belt is always oriented (say) North/South, it's not if the belt slews to a new axis. If our ant continued crawling (say) NE, he would no longer be crawling towards the aiming spot, and consequently his trail would no longer be a straight line.

So I respectfully disagree with Seaworthy Lass in post #227, for the moment at least.