Brain hurts - Working out course to steer

[cyan]

Funny stuff.
(Complaints about thread drift well after the end of any drift, keeping the drift alive)
Speaking of drift...
What was the final answer to the old vector debate: single heading to cross a steady current channel vs variable heading for a straight path over ground?
Yeah, I read both threads. Must have missed the answer.

[Dockhead]

Originally Posted by cyan

Funny stuff.
(Complaints about thread drift well after the end of any drift, keeping the drift alive)
Speaking of drift...
What was the final answer to the old vector debate: single heading to cross a steady current channel vs variable heading for a straight path over ground?
Yeah, I read both threads. Must have missed the answer.

It's not really a debate. There's only one right answer.


There's a chapter on it in the RYA Navigation Handbook, for anyone who can't pick the right answer out of this thread, or the thread which was linked near the beginning.

[cyan]

Thanks for the reference.
That linked thread included some incorrect statements, and indeed a debate, warranted or not.
Pretty sure the RYA Handbook is reliable.

[Dockhead]

Originally Posted by cyan

Thanks for the reference.
That linked thread included some incorrect statements, and indeed a debate, warranted or not.
Pretty sure the RYA Handbook is reliable.

The linked thread is still open, so in case you want to challenge something you think is incorrect, you can reply to anything you find in there.


The problem of navigating across changing currents is an evergreen topic, which never stops being interesting.

[captwylie]

Originally Posted by valhalla360

For a slow displacement boat...if you are figuring a 6hr run, start 3hr before slack and point her in the right direction and keep a steady heading. Odds are pretty good that the currents will switch part way thru and line you back up with your destination.

Use the free charting software on your tablet to check periodically you aren't too far off.

Problem with coastal situations is things change too much and to unpredictably...If you run the math assuming a 6kt cruising speed but the wind only gives you 4kt...all your math is going to be wrong because you won't be in the same current. Also in most areas, you won't know the exact current each combination of time and location anyway. A little closer to a shoal and the current could be faster or slower and may even change direction.

In the end, you make a rough guesstimate and adjust based on what happened.

I agree. I allow a few degrees for deviation and each time I check my position I make corrections. Its kind of like the way we used to weigh hogs. We would balance a large board on a rock. We would then place the hog on one end of the board and then stack rocks on the other end until it balanced out. Then we would estimate the weight of the rocks.

[Q Xopa]

Originally Posted by cyan

Thanks for the reference.
That linked thread included some incorrect statements, and indeed a debate, warranted or not.
Pretty sure the RYA Handbook is reliable.

Hmm interesting. I in the aviation game, and this isnt considered either. I guess it is less relevant at aircraft speeds. But it in this age of going to great lengths to minimize fuel costs it would be interesting to see what the possible fuel savings could be.

Honestly I dont think it has been thought of. Kinda suprising really. But like most things its always been done that way so thats how we do it.

So forgetting for a minute about rumb lines, SOG, Speed through the water, Great circle, tide or current predictions etc.

Thinking a bit out of the box here but, perhaps naively, I might have a solution?

To me the most important number should be 'rate of closure'. Ok I dont know if its a real term, or best description but Im sure you understand what I mean. I have no doubt someone smarter than me will have a better one. 'Rate of closure' maximized will take you to destination in the fastest, ie the most efficient route. I guess it is the best compromise between shortest distance {GC) and fastest speed through the water.

What about if we had OpenCPN, or some smart program, had a 'rate of closure' to destination/ waypoint number.

Anyone know of an existing plotter or program that can display this?

Should be simple enough. Its only a current/ live speed from current GPS point to the destination point.

Taking this concept a little further. Im not a programmers you know what, but I doubt it is difficult to have your program set to determine and disply the maximum rate of closure number and a heading that matches.

If the above can be done it should be easy enough to drive your autopilot to this heading on a live basis.

Boats are always swinging around the autopilot 'null', sensing a deviation, then applying a correction.

I might be missing something obvious here as Im not that smart.

Just a crazy thought.

[Dockhead]

Originally Posted by Q Xopa

. .. . To me the most important number should be 'rate of closure'. Ok I dont know if its a real term, or best description but Im sure you understand what I mean. I have no doubt someone smarter than me will have a better one. 'Rate of closure' maximized will take you to destination in the fastest, ie the most efficient route. I guess it is the best compromise between shortest distance {GC) and fastest speed through the water.


. . .



I might be missing something obvious here as Im not that smart.


.

This is not be any means a stupid thought at all.


By "rate of closure" you're meaning VMG to your waypoint (or VMC as is sometimes said now), and I think this is a the same term in aviation.


If the current is constant, then a constant heading which produces COG=BTW will get you fastest to the destination, although you will get greater VTC -- for a time -- by steering further down in relation to the current. But the VTC will fall constantly as you get nearer the waypoint, as the bearing changes. If you keep changing your heading, this will be slower. The fastest route is always a constant heading -- this is an axiom -- because the shortest distance to any destination is a straight line through the water.


Doing a proper CTS, based on tidal stream vectors for the whole passage, uses the information you have about FUTURE changes of the streams, to steer the optimum course, or as close to the optimum course as the quality of your information will allow.



This would be true for aviation as well, even if there is less need for it (shorter passages, no regularly reversing air streams), so I bet the same practice must exist somewhere in aviation.





To the Great Circlists: You may read "constant heading" in the above as "range of heading corrected for great circle effects", that is, a range of heading which will keep you in a straight line through the water, considering the curvature of the earth. But keeping in mind that we are talking about unsteerable tenths or hundredths of degrees for any conceivable passage where you may be doing a CTS calculation.

[Q Xopa]

Yeh youre right VMG, that rings a bell. But its not a normally displayed or considered value.

Its a FMS (Flight Management System) in aircraft. But its essentially all the same thing.

Yes of course aircraft arent subject to regular Tidal streams. But they are still effected by changeable currents of air they are flying through. So its comparable.

Yes agreed about being preferable to set yourself up for future tidal streams. But the problem here is as you say the quality of your information. As others have said many places have little to none accurate tidal information.

Yes I agree changing your heading through the water will slow you down.

I havent got this completely clear in my head yet but I think maximizing VMC would keep you on a constant heading. Even if the currents are reversing.

Yes also agree about straight line through the water being fastest. Even if the water parcel we are moving through is moving in changing directions and speeds which are all but impossible to predict.

Im not understanding exactly what youre saying about VTC decreasing closing on your waypoint. I understand your deviation distance (angles are the same) decreases as you get nearer your waypoint.

As you say you cant go Great circle on a constant heading because of changing mag variation. But for short distances its negligable.

[Dockhead]

Originally Posted by Q Xopa

. . . I havent got this completely clear in my head yet but I think maximizing VMC would keep you on a constant heading. Even if the currents are reversing.

If the current is constant, and your heading is constant, your VMC (for clarity -- VMG to the waypoint) will fall as the bearing to the waypoint changes (falling eventually to 0 then minus), and in most cases (depends on the angle of the current) you will have to gradually turn towards the waypoint in order to keep VMC at its maximum.

Originally Posted by Q Xopa

Yes also agree about straight line through the water being fastest. Even if the water parcel we are moving through is moving in changing directions and speeds which are all but impossible to predict.

Yes, absolutely. That straight line might be unknowable, if we don't have information, but just because we don't know it, doesn't mean it doesn't exist


It's important to note that even a pretty rough guess gives good results for typical CTS problems. I used to do my Channel-crossing CTS calculations by hand and using off the cuff approximations when reading the tidal diamonds (for off angles, and days between springs and neaps), and used to do very well indeed. The biggest unknown for that passage is actually your passage speed, but if you do three runs at a range of speeds, you can correct as you go along, as you get to know better what your average speed is, and this works really surprisingly well.

Originally Posted by Q Xopa

Im not understanding exactly what youre saying about VTC decreasing closing on your waypoint. I understand your deviation distance (angles are the same) decreases as you get nearer your waypoint. . .

That was discussed above. I just meant that if you pick a heading which, at the start of the passage, gives you max VMC, this will necessarily decrease as you approach the waypoint, actually it will decrease during the whole passage. This assumes that the max VMC heading gives you COG not equal to bearing to waypoint (not true only if the waypoint is directly downstream). So the waypoint bearing will change, and the difference between COG and BTW will increase, which, geometrically, reduces VMC for a constant SOG.

[El Pinguino]

Originally Posted by cyan

I think you make a good point regarding 100 mile CTS work, and nobody here was calling people names that I know of.

I am simply suggesting that navigation students might be best served if they are told the full truth about the rhumb line-- being a good estimate most of the time. There were incorrect rhumb line assumptions stated in this CTS discussion, and pointing that out now is not meant to be insulting whatsoever.

For the record, those crazy souls who sail from Cape Horn to Cape Town would be adding 200 nm to their cold weather adventure if they believed a rhumb line represented the shortest distance. I wouldn't wish another 200 miles of such a journey on anyone.

For the record... those crazy souls follow neither rhumb or GC.... they typically go through Le Maire - if the tide suits- and get north as fast as their little legs will carry them before turning right. Pure Great Circle isn't used at all between 'the capes'....'composite' maybe between some... 'pure' across the Great Australian Bight or across the Tasman ...

I see no great circles here

https://maps.sail.cloud/home/event/19

There is however a lot to be saved by commercial ships in the middle latitudes... even New York to Cape Town there is a saving of about 50 miles....
that is a lot of fuel on a big ship.
I would imagine every ship bound from anywhere between Bahia Blanca to the top end of Brazil towards the Cape of Good Hope would be steering a great circle.... automatically in many cases...

Relevance to cruising yachtsmen? about zero...

Now here is a thought.... what does your chartplotter work in? OK Opencpn gives you the choice while the original Cmap software used to display the rhumb line but show GC initial course....

Thread drift?... well I didn't start it...

[Q Xopa]

Originally Posted by Dockhead

If the current is constant, and your heading is constant, your VMC (for clarity -- VMG to the waypoint) will fall as the bearing to the waypoint changes (falling eventually to 0 then minus), and in most cases (depends on the angle of the current) you will have to gradually turn towards the waypoint in order to keep VMC at its maximum.









Yes, absolutely. That straight line might be unknowable, if we don't have information, but just because we don't know it, doesn't mean it doesn't exist


It's important to note that even a pretty rough guess gives good results for typical CTS problems. I used to do my Channel-crossing CTS calculations by hand and using off the cuff approximations when reading the tidal diamonds (for off angles, and days between springs and neaps), and used to do very well indeed. The biggest unknown for that passage is actually your passage speed, but if you do three runs at a range of speeds, you can correct as you go along, as you get to know better what your average speed is, and this works really surprisingly well.







That was discussed above. I just meant that if you pick a heading which, at the start of the passage, gives you max VMC, this will necessarily decrease as you approach the waypoint, actually it will decrease during the whole passage. This assumes that the max VMC heading gives you COG not equal to bearing to waypoint (not true only if the waypoint is directly downstream). So the waypoint bearing will change, and the difference between COG and BTW will increase, which, geometrically, reduces VMC for a constant SOG.

Yes I have no doubt that even a WAG is going to have you ahead of the guy in the same model boat leaving the marina at the same time as you and happily follows the chart plotter track.

Even just being aware of this gives you an edge on most of the fleet.

[Dockhead]

Originally Posted by Q Xopa

Yes I have no doubt that even a WAG is going to have you ahead of the guy in the same model boat leaving the marina at the same time as you and happily follows the chart plotter track.

Even just being aware of this gives you an edge on most of the fleet.

Indeed!


I think the first thing actually is not falling into the trap of thinking that the problem with moving water is just getting COG to equal BTW. Very many people just don't do any navigation anymore -- they try to let the plotter do everything. This is one problem which the plotter can't solve! That's also what makes it interesting.

[Q Xopa]

Originally Posted by Dockhead

Indeed!


I think the first thing actually is not falling into the trap of thinking that the problem with moving water is just getting COG to equal BTW. Very many people just don't do any navigation anymore -- they try to let the plotter do everything. This is one problem which the plotter can't solve! That's also what makes it interesting.

Im not convinced that if the plotter was programed to maximise VMG it wouldnt work.

Not that I dont believe you, more I didnt unstand your reasoning.

I think we're both singing the same tune mostly, but I am a few steps behind you.

[Dockhead]

Originally Posted by Q Xopa

Im not convinced that if the plotter was programed to maximise VMG it wouldnt work.

Not that I dont believe you, more I didnt unstand your reasoning.

. . . .

These problems are also fun because the answers are often non-obvious, or counter-intuitive, and sometimes require a lot of thought to figure out.


You can work on this one yourself -- plot out some passages where you steer to max VMC and see where you end up.


The answer is not immediately obvious, but I think this one can be solved by logic.



One thing to define is what you mean by this -- set a constant heading at that heading which, at the start of the passage, gives you max VMC? Or keep steering to keep that VMC at max?


The first will obviously not work -- because you'll just sail past the destination and never arrive.



The second is more subtle, but I think you will see that it won't work, if you think about it. Here is the point -- steering this way maximizes the MOMENTARY VMC, without regard to the future. That's by definition -- the future is not considered at all, when you steer this way. So this course will give up FUTURE VMC, and a disproportionate amount of it, by putting you downtide from your destination, in order to get higher VMC in the moment. A bad bargain.


That's the abstract logic; but I think you will see that it actually works this way, if you'll plot out a few passages.


A good disproof of this would be to consider the case of absolutely constant current. We know that if the current is constant, then the straight water track coincides with the straight ground track, and you sail along the the rhumb line*. We all know that this is fastest. But you will obviously not be sailing max VMG to the destination, sailing like that. The max VMC heading at the beginning of the passage would have you heading off downtide from the destination at a high SOG. But you will be losing ground against the current which you have to make up later, so you will end up with drastically reduced VMC, later in the passage, which more than wipes out the gain in VMC at the beginning.


Logical? As I said, you can plot out a few example passages to see for yourself, whether it's really like this, or not.






* To the great circlists: I think I found a much better way to explain why all navigators ignore great circle on all passages of less than many hundreds of miles, and many passages of even thousands of miles. What is a "line"? Mathematically, a line has no width. But in the real life of real navigation, a line, like a course line, like a rhumb line, might be considered to be as wide as what we can practically steer. So if the apex of a great circle course is say 20 meters from the idealized rhumb line, or even a cable or two, then the rhumb line and the great circle course is the same -- because you can't steer the difference between them, even if you wanted to bother with it. The great circle path is contained within the rhumb line, if you consider the rhumb line to be as wide as what you can realistically perceive and steer.


It is true that a constant heading is not an exactly straight path through water, except in a few special cases (along the equator; along a meridian; etc.). But when steering a great circle would require you to hold a course to tenths or hundreds of a degree, it IS, for all practical purposes, a straight line, and the navigator correctlytreats it as a straight line, unless he is just trying to show off.


It's a bit like Newtonian physics. We know now that Newtonian physics isn't exactly right. Newtonian physics aren't right at all at the atomic level, and they are very slightly not right at a macro level. But we don't use quantum mechanics at all when we engineer a bridge -- all the assumptions are based on classical Newtonian physics, even though we know they aren't precisely correct. It would be bad engineering to attempt to introduce quantum effects, into engineering a bridge, as a useless complication greatly increasing design costs and the risk of an error, and for no benefit at all, since the differences between quantum physics and classical physics for these problems are practically meaningless, even if they are not non-existent.

[El Pinguino]

Originally Posted by Dockhead

* To the great circlists: I think I found a much better way to explain why all navigators ignore great circle on all passages of less than many hundreds of miles, and many passages of even thousands of miles. What is a "line"? Mathematically, a line has no width. But in the real life of real navigation, a line, like a course line, like a rhumb line, might be considered to be as wide as what we can practically steer. So if the apex of a great circle course is say 20 meters from the idealized rhumb line, or even a cable or two, then the rhumb line and the great circle course is the same -- because you can't steer the difference between them, even if you wanted to bother with it. The great circle path is contained within the rhumb line, if you consider the rhumb line to be as wide as what you can realistically perceive and steer.


It is true that a constant heading is not an exactly straight path through water, except in a few special cases (along the equator; along a meridian; etc.). But when steering a great circle would require you to hold a course to tenths or hundreds of a degree, it IS, for all practical purposes, a straight line, and the navigator correctlytreats it as a straight line, unless he is just trying to show off.


It's a bit like Newtonian physics. We know now that Newtonian physics isn't exactly right. Newtonian physics aren't right at all at the atomic level, and they are very slightly not right at a macro level. But we don't use quantum mechanics at all when we engineer a bridge -- all the assumptions are based on classical Newtonian physics, even though we know they aren't precisely correct. It would be bad engineering to attempt to introduce quantum effects, into engineering a bridge, as a useless complication greatly increasing design costs and the risk of an error, and for no benefit at all, since the differences between quantum physics and classical physics for these problems are practically meaningless, even if they are not non-existent.

Nothing wrong with overthinking stuff if it keeps one amused I guess...

Why did navigators back in the dream time not use great circle for legs of less than 600 miles and often longer? Because they knew the gain was not worth the effort.

For longer runs there may have been a very small gain but still not worth the trouble of working it out... and most were quite frankly a little bit afraid of GC calculations... dunno why.... calculate the distance on day one with the Haversine formula and use the ABC tables to get the initial course and thereafter just use the ABC tables with L/L of destination substituted for the GP of the heavenly body to update your course to steer. Use the Traverse table to calulate your Days Run...

These days you will find that most ships are using GC much of the time regardless of distance.

Another small point is that while GC in high lats may be good while eastbound... its often not so good westbound on a/c weather... and not only will you not use the GC you will not use the Rhumb line track either..
More than a few years ago I recall reading a paper written by the master of a Belgian bulker running from Hay Point, NQ, to Northern Europe around the Cape of Good Hope.. with the permission of his owners he once took his ship from Hay Point north of Australia ( via Torres Strait) ... and demonstrated that despite being much longer than going south it was the better way to go.... later with a much larger ship he went north of New Guinea... same result..... no slow steaming to weather, no extreme wear and tear on ship, etc etc...
Bit like east v westbound in the Sopac... and would you use GC from the Canaries to the West Indies?

On a yacht it is all neither here nor there.... handy in a strategic sense but not in a tactical one.... if in the southern ocean choose a limiting lat... use GC to get down to it.... then its all to do with the weather...

So... does your plotter display GC courses or Rhumb line course?... as stated before my old Cmap kit showed a rhumb line on the chart but GC course and distance to go...

Easy way to check.... select two way points a good distance apart ( 1000 miles?) in a moderately high lat.... both waypoints in the exact same lat.... course should be 090/270... if it isn't then you are being shown GC courses...

It is far easier for a computer to calculate GC using the Sine formula than for it to produce 'Rhumb Line' info... with all that 'meridional parts' non sense...