Distinct Activities: Shackled by a Common Name?

[Dockhead]

Originally Posted by Andrew Troup

And I answered your question, for the GPS track boat.

I then answered a question you didn't answer, because your question didn't seem to me to provide any basis for comparison with your four hour scenario.
And I answered for both boats, because I thought the entire point of the exercise was to compare the two tactics.

That's a long answer: the short answer is that I was trying to be helpful.



Ummmm... two reasons:

1) I was trying to meet CaptForce, to the extent possible, on his own territory. He, unlike you, was not convinced that the water based method was mathematically perfect - or, at least, that it was any better than the rhumb line. Presumably, he remains unconvinced, but that's his prerogative. I've done all I'm going to do.

2) Have you already forgotten that we all made prize dicks of ourselves through having not the faintest idea what the ground track looked like for the constant heading transit?

Also: What if there are places en route we do not want to go ?

I like to know whereabouts on the chart I'm going, thanks very much. My spreadsheet provides a prediction of where I can expect to be at any stage of a constant heading transit; I can compare this against the GPS to find out how accurate the current data are proving to be.

In any case, I wanted to be sure I was correct to change sides, in favour of CF's 'S' curve

(you need to remember that at the time when I put the spreadsheet together, nobody else had come on board with his provocative idea. In abstract theory, I had pretty much convinced myself, but I wanted a second opinion, from a practical worked example)

3) OK, so I lied about 2 reasons:

So that the relative progress of the two competing boats could be meaningfully compared at any point.

4) It also provided a cross check that the constant heading boat ends up back on the rhumb line (and crosses it midway, and runs parallel to it at the quarter and three-quarter marks).

As for "breaking my head":

If there's one thing this exercise has (re)taught me, it's the perils of seeking the easiest answer.

In any case, it was not difficult with distance slices, especially in comparison with trying to reconcile time slices with a current which varies as a function of distance, which presumably you somehow found a way to do.

Last point first:

Don't break your head with a complicated approximation, when you have a simple precision available to you. It increases noise in the system and risk of mistakes.

That being said, of course it is interesting to see what the ground track is for a constant heading boat. If your model did that well, then that's useful. And you can easily check your model against the mathematically perfect water-based calculation.

For this task, best of all would be a CAD program, which would plot this up in a jiffy. If only I had the skills -- I have AutoCad but it's not going to be worthwhile for me to learn how to do this right this minute. Made some forumite knows how to plot this in AutoCad? Would really do a service to the poor sufferers on this thread.

Kudos to you for distance-slicing. That's the perfect solution to this problem. Now I'm going to redo my model using that technique.

The other thing I want to do is to correct my currents -- they are perfectly linear but have a small flat top and two small flat ends, which I don't like. This will make a microscopic difference in the overall passage speeds, but I want to eliminate it as a possible source of the perplexing quicker passage of the one-minute GPS track boat compared to the five-minute GPS track boat, which violates my hypothesis about smaller triangles = slower, which after much thought I am convinced must be right.

I lack just that much trig to be able to do the currents as a sine wave -- it's probably dead simple if you know the one tiny secret. Argh. I was hoping someone with more math would have just popped that into my model over night, but noooo . . . .

[Dockhead]

Originally Posted by Andrew Troup

1) I was trying to meet CaptForce, to the extent possible, on his own territory. He, unlike you, was not convinced that the water based method was mathematically perfect - or, at least, that it was any better than the rhumb line. Presumably, he remains unconvinced, but that's his prerogative. I've done all I'm going to do.

Yes, but Capt Force correctly calculated the passage of a constant heading boat!!!

His formula is very simple and has a very simple error --

He assumes that all the little triangles of the GPS track boat add up to be the same as the one big triangle of the constant heading boat.

That is his mistake and the source of all of our problems -- they do not add up!! Dave pointed out that this is because squares don't progress linearly. I guess that's the correct mathematical way to look at it.

I know they don't add up not because of math, but because the water track is longer, and we use speed through water as a constant. To my mind this is dead obvious and dead simple, but Capt Force doesn't want to hear about water tracks. So I guess any further argument with him should be using Dave's point, or just the demonstration which ALL of our models show a considerable advantage for the constant heading tactic, compared to GPS track.

[Wotname]

I'm backing Seaworthy on the Hovercraft challenge; I haven't done a full analysis but a thumbnail calculation seems to me that she is on the money (and her method is intuitively correct to my mind).

As for the rest of the problems posted - they are interesting but too challenging for my grey (gray?) matter

[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 )

[Seaworthy Lass]

Originally Posted by Wotname

I'm backing Seaworthy on the Hovercraft challenge; I haven't done a full analysis but a thumbnail calculation seems to me that she is on the money (and her method is intuitively correct to my mind).

As for the rest of the problems posted - they are interesting but too challenging for my grey (gray?) matter

Thanks Wotname.
You are the first person to say my calculations are correct. Everyone has stayed strangely silent except for GoBoating who is disputing me vehemently (which is of course the basis for a good debate which I have enjoyed LOL).

[conachair]

Originally Posted by goboatingnow

No in a simple one hour plot the boat runs down the rhumb. In a case where there are multiple vectors of differing angles the boat does not run down the rhumb. ( which is a safety issue. ) all the vectors in line is a simple case.

Agree with that, of course. It was the "D is merely a vector addition vertices. You are not physically there." bit which was confusing.

Irrespective of where D is. The key is that you ARE plotting speed vectors. That is you lay down distance per unit time. That's speed Seaworthy

I can't see how you come up with that. You start with a velocity vector, speed (in Kn or Nm/H) of tide and direction, then constrain the time to 1 (hour) leaving you with a unit of distance, Nm/1. This is what you plot, distance and direction.

Otherwise the scale of the vectors wouldn't matter as long as they were all the same scale but not necessary the same scale as the chart, all you would get would be a CTS, no idea where you would be after the 3 hours or however many you plotted.

[Wotname]

Originally Posted by Seaworthy Lass

Thanks Wotname.
You are the first person to say my calculations are correct. Everyone has stayed strangely silent except for GoBoating who is disputing me vehemently (which is of course the basis for a good debate which I have enjoyed LOL).

We will celebrate or sink together

[Andrew Troup]

Originally Posted by Dockhead

.....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.

If you feel that way, I'm surprised you didn't challenge my explanation in post 377, in which I carefully spelled out the simple reasons why I considered the symmetrical S curve to be exactly correct.

(For reasons entirely separate from the analysis --which, I revealed, confirmed that track)


I think, by persisting in hanging onto your very wrong mental picture of the track across the ground, you've made my point more powerfully than I ever could:

It seems to me there's a dangerous tunnel vision associated with using the 'through the water' model, for the reason that it's exact and easy and elegant, to the exclusion of slightly messier, deeply counterintuitive, and potentially consequential considerations of the track across the ground.

To me that's the single most important learning from this scenario. But I've said that before (sigh)

[Seaworthy Lass]

Originally Posted by Wotname

We will celebrate or sink together

Cracking open bottle of Limeburners sounds like an excellent idea either way .

[Andrew Troup]

Dockhead

I'd always planned to port my data across to a CAD package when I get a bit of spare time, hopefully might get to it this weekend.

It won't be AutoCAD, though... (although I own it and can drive it after a fashion, I detest using it, with considerable passion)

[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]

Originally Posted by Andrew Troup

Dockhead

I'd always planned to port my data across to a CAD package when I get a bit of spare time, hopefully might get to it this weekend.

It won't be AutoCAD, though... (although I own it and can drive it after a fashion, I detest using it, with considerable passion)

Can't wait to see that. A CAD program will do in a trice what we have been busting our heads doing crudely, almost by hand. Very cool.

Meanwhile I'm redoing my GPS track boat passages using distance slicing . Brilliant idea of yours.

[conachair]

Originally Posted by Dockhead

Can't wait to see that. A CAD program will do in a trice what we have been busting our heads doing crudely, almost by hand. Very cool.
.

On it Hard drive reformat means a bit of work though, google sketchup doesn't really cut it so I need to track down an install copy of vectorworks again...

[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.

captforcescenario2.xls

[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!