Distinct Activities: Shackled by a Common Name?

[Seaworthy Lass]

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 dies 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!

ROFL
I love it

Will have a drink for you tonight
Definitely worth all the head banging I was doing LOL.

[Dockhead]

Hah, this was easier than I thought.

I just broke up the distance into the same number of slices I had been previously slicing time into. So I was able to use the existing current tables, which are now perfect. Instead of solving for distance made good achieved in the given time frame, I solved for time to get across the given distance. So now I have the passage times to get to a waypoint 18.3303 miles across a body of water with unidirectional current varying smoothly from 0 to 4 and back to 0, average 4, according to various tactics of navigating.

So I now have mathematically perfect picture of Capt Force's scenario!

The results are as follows:

Constant heading boat -- passage time 4 hours
GPS track boat, four slices of 4.582576 miles each -- 4.1621 hours
GPS track boat, 48 slices of 0.381881 miles each -- 4.2486 hours
GPS track boat, 240 slices of 0.076376 miles each -- 4.2494 hours

When I say "mathematically perfect", I mean that we consider the GPS track boat to have an autopilot which makes corrections at certain intervals corresponding to our analysis frameworks. This is not artificial, because that is of course exactly the way autopilots actually work. They do not make continuous corrections -- they correct the course every certain period of time, with the result that the boat is actually sailing a constant heading course between the correction points.

The fact that the GPS track boat takes more and more time, the more frequent the course corrections occur is another demonstration of the constant heading principle. The GPS track tactic is more efficient, the more infrequent the course changes are, since it is (according to the model) sailing perfect constant heading legs between the corrections.

That is a very minor error of the model -- it assumes that every autopilot course correction results in a perfect constant heading course to the next correction point. In fact, autopilots correct for the current set of the previous period. The effect of this will be to very slightly overstate the efficiency of the GPS track tactic, this overstatement becoming vanishingly small with the finest analysis framework.

But I think I'm done with Capt Force now. I don't think there are any mistakes in the model now. If anyone finds anything, please let me know!

captforcescenario_distancesliced1.xls


Thanks again to Andrew Troup for the idea to slice distances and solve for time, instead of slicing time! It was a superbly elegant solution to the main problem of my previous version of this model.

P.S. -- for those of you got confused by my plug number for length of the rhumb line -- distance over ground to the waypoint -- note that this is a totally trivial question with this version of the model. You can put any distance whatsoever for distance to waypoint, and the model will show how long it takes each boat to get there. 18.3303 miles happens to get the fastest boat there in Capt Force's 4 hours, but if we abandon 4 hours, we can use any distance.

[Seaworthy Lass]

Originally Posted by Dockhead

........
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.

Yeah, well done for your perseverance! Persistence pays.
I gave up after I tried to demonstrate that vectors don't add up the way CaptForce thought.
Feeling very happy we have a convert. Welcome the the 'Single Course to Steer Club' CaptForce

PS I think Andrew must be asleep by now and missing all the excitement .

[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.

[conachair]

Originally Posted by Seaworthy Lass

So I have plotted out a scenario for you.
)

I hadn't thoughht about it too much, but 1st guess intuitively the boat would always be upstream of the rhumb line. Shows how wrong you can be Well done. Good to have a reason to get CAD back on the laptop as well.

Which was the orig hovercraft post again?






https://docs.google.com/file/d/0BxDI...VJeDRKLW8/edit
https://docs.google.com/file/d/0BxDI...5XYzRnRGM/edit

[Dockhead]

Originally Posted by conachair

I hadn't thoughht about it too much, but 1st guess intuitively the boat would always be upstream of the rhumb line. Shows how wrong you can be Well done. Good to have a reason to get CAD back on the laptop as well.

Which was the orig hovercraft post again?

Attachment 53049

Attachment 53050


https://docs.google.com/file/d/0BxDI...VJeDRKLW8/edit
https://docs.google.com/file/d/0BxDI...5XYzRnRGM/edit

Yep, I stepped in that one too. It seems counterintuitive. Still trying to get my head around it, especially the odd (it seems to me) fact that you cross the rhumb line in the middle, if the current is symmetrically unidirectional.

[conachair]

Anyone used the graph app in google chrome?

https://www.desmos.com/about

You should be able to graph all this kind of stuff, if you have several heads

Not sure exactly how it works yet, I keep getting 42 ...

[Dockhead]

Originally Posted by conachair

Anyone used the graph app in google chrome?

https://www.desmos.com/about

You should be able to graph all this kind of stuff, if you have several heads

Not sure exactly how it works yet, I keep getting 42 ...

The problem is not the graphs, but the math.

You can graph stuff very easily in Excel. But you have to give it a table with correct numbers To get the numbers, you have to have a better grasp of the math than most of us folks who have been out of school for a decade or three

Graphs are like computers -- garbage in, garbage out

[conachair]

Originally Posted by Dockhead

The problem is not the graphs, but the math.

You can graph stuff very easily in Excel. But you have to give it a table with correct numbers To get the numbers, you have to have a better grasp of the math than most of us folks who have been out of school for a decade or three

Graphs are like computers -- garbage in, garbage out

Yep, absolutely. It does seem a much easier way to play around with graphs though, once you sort out the maths

But then google knows all..

I've got circles, straight lines and bog standard sine waves so far, but that's the easy bit

[Seaworthy Lass]

Originally Posted by conachair

......
Which was the orig hovercraft post again?

The hovercraft scenario and all the data was repeated in post #519, so you don't have to go back far.

I would love it if someone would work it through from first principles as I did, then work it out following the RYA method in the youtube that GoBoating was using (and that I also repeated) and compare the two results.

I am convinced the RYA method is not a precise formula as GOBoating keeps insisting, but a rough approximation to get you on the rhumb line hopefully not too far from the destination. The heading needs to changed well before if there is any component of the current running with you, as that places you off to the side aiming to a point behind the destination.

The heading also needs to be altered significantly if the current in the final hour of your journey is predicted to be significantly different than the average current over the part of the journey before you hit the rhumb line. I am not talking about unexpected current, but the predicted one.

In the hovercraft example if GoBoating persisted in following the course to steer that the RYA method determines, he would pass up current of the destination and never reach it!

The RYA method does NOT give you the quickest route to the destination and it also does not give you a course to steer to get you to the destination (as GoBoating keeps repeating it is), it just gets you close. It is, however, a GREAT way of getting close if you have very complex current vectors that would otherwise need to be resolved.

The method is very useful, but its limitations need to be recognised particularly if you are teaching the subject (and I am talking limitations even when you have perfectly accurate data to work with - if that was only possible in the real world!)

[conachair]

Originally Posted by Seaworthy Lass

The hovercraft scenario and all the data was repeated in post #519, so you don't have to go back far.

Just had a quick look at that, there's data missing so you are limited to working out the first 4 hours. If you assume the 5th hour has no wind then from drawing and Pythagoras I make the arrival time to be 4.71 hours.
SQRT(16*16+10*10) (10 is the sum of the wind vectors)

I think the RYA way is as accurate as you can go with the data available in the examples so far. It's that last hour you don't know about, Dave's sketch looks like it gets you back on the rhumb line after 4 hours, the 4.7 hour assumes no wind so you don't get back to the rhumb line until the destination.



Anyway, people keep giving me free boat show tickets so off for some more expensive guiness in the company of seldom seen sailor mates

catch up later, desmos graphs here we come


(Ah, just seen #403, you've done all that already )

[Wotname]

Originally Posted by Seaworthy Lass

............
The RYA method does NOT give you the quickest route to the destination and it also does not give you a course to steer to get you to the destination (as GoBoating keeps repeating it is), it just gets you close. It is, however, a GREAT way of getting close if you have very complex current vectors that would otherwise need to be resolved.

The method is very useful, but its limitations need to be recognised particularly if you are teaching the subject (and I am talking limitations even when you have perfectly accurate data to work with - if that was only possible in the real world!)

The RYA method seems to be in a similar vein as say using 22/7 as the value of pi. That is, a good approximation and quite useful, just not exact by any means.

[four winds]

Great thread, been reading carefully and learning much, thanks.

I'm not doing open water passages at present, just day sailing. But I've learned a ton about the relationship of one's path through the water compared to the path over ground. And this will help even in my day sailing efforts.

I have a math background but didn't feel qualified to participate with such knowledgeable people debating. About four pages back I finally chose sides and should apologize to Seaworthy for not stating so publicly. Her graphs and text were the easiest to digest for me and helped me get a handle on the issues.

CaptForce's last post was perfect.

Thanks for the lively, courteous, enlightening debate. (not saying the debate is over, never is)

[Seaworthy Lass]

Originally Posted by conachair

Just had a quick look at that, there's data missing so you are limited to working out the first 4 hours. If you assume the 5th hour has no wind then from drawing and Pythagoras I make the arrival time to be 4.71 hours.
SQRT(16*16+10*10) (10 is the sum of the wind vectors)

Yep . I agree, we must have just rounded off the figures differently, I had 4.72 hours.

The RYA method calculated five hour seven minutes and what GoBoating refuses to recognise is that that is the time take to arrive at a point upcurrent of the destination (he will never pass through the destination point). He insists I am the one who will not arrive following a steady course of an offset of 32 degrees (B is due east of A magnetically, this makes my compass heading 58 degrees, GoBoatings offset is 38.7 degrees making his compass heading 51.3. This is not an insignificant difference).

Originally Posted by conachair

JI think the RYA way is as accurate as you can go with the data available in the examples so far. It's that last hour you don't know about, Dave's sketch looks like it gets you back on the rhumb line after 4 hours, the 4.7 hour assumes no wind so you don't get back to the rhumb line until the destination.

It is not the we "don't know about it" it is that the RYA method completely ignores the predicted current in the final bit of the journey (and in this case it was not an insignificant bit, it was 3.51 miles out of a 16 mile journey!).
If the data is available for the first four hours of this journey, then it is also available for the 5th hour. The RYA is simply ignoring it.
This is precisely why the RYA method is not precise. It does NOT have us arriving at the destination as GoBoating also insists it does.

In addition GoBoating is also insisting he will not arrive on the the rhumb line at the four hour mark. This is incorrect. He certainly does! This is the whole thrust of the RYA exercise, to get you on the rhumb line close to the destination every single time.
Unfortunately the method is not always successful at getting you close to the destination when you arrive at the rhumb line (the hovercraft case illustrates one such example).

Originally Posted by conachair

Jcatch up later, desmos graphs here we come
(Ah, just seen #403, you've done all that already )

Yep, demo graphs are there, including a dotted line indicating the chartplotter track.

[Seaworthy Lass]

Originally Posted by Wotname

The RYA method seems to be in a similar vein as say using 22/7 as the value of pi. That is, a good approximation and quite useful, just not exact by any means.

It is far more erratic than that.

It will be absolutely precise if the current for the last part of the journey happens to be the EXACT average of the current predicted for the first bit of the journey.

It could be well and truly out otherwise - in this case an 'arrival time' of 5 hours 7 minutes is calculated, when you actually never pass through the destination point if you keep heading along compass course the RYA method calculates you should.

The correct arrival time is 4 hours 43 minutes and you DO actually arrive and you have followed a constant compass heading (and a constant speed as the example specifies) for the entire journey .