What curve does a kayak make...

[JohnHuth]

Here's a figure, attached that illustrates what I'm saying and what I believe David's saying. The "GPS" is just a way of saying that you are always following a heading toward an waypoint on the far side of a crossing. It uses the waypoint feature - you punch in the lat/long of a location you want to head to, or choose it from a chart. The GPS then computes the heading to that point, assuming a fixed reference frame (ie. no current). But, if you are a die hard fan of GPS, just leave that concept aside and look at the concept of having a heading that always points to the waypoint on the opposite side. It's just a mental construct to aid visualization.

On the top illustration, I've broken the crossing into 5 discrete steps, where the arrow points to the landmark on the opposite side of the crossing at each stage. You physically change direction at each of those steps in order to compensate for the fact that the current has swept you downstream. The path will include paddling that will have both downstream and upstream components. In the lower case, one takes a ferry angle, which implies that there is no component of the path that is either upstream or downstream. For a fixed paddling speed, the ferry angle crossing will be faster.

This has nothing do with paddler A is an adonis and paddler B is a wimp, it's just a mathematical statement.

Now, to go to the other question of using the GPS as an aid to determine current and even ferry angle, I'll try to come up with some illustrations for that.

Waypointing.pdf

[djlewis]

Hi, John (Leon might want to ignore this post, as he has already rejected everything in it):

As far as the $100 bet is concerned, I think it misses the point David was trying to make.

Just for the record, here was my original bet with Leon -- it had nothing to do with any kind of contest on the water. Leon says you can use a GPS to stay on the theoretical best course from A to B, namely the straight line from A to B. The GPS somehow automatically adjusts for wind, current, sunspots, etc. You set A and B as GPS waypoints, look at the straight line on the GPS map display, and keep your GPS position on it (which modern GPSs apparently help you do). I agree and say...

The bet: You can use a compass (without a GPS) to do the same thing, in principal.

The method -- and mathematical proof of this statement, whose truth or falsity is the bet -- is simple. That theoretical straight line from A to B has another property, namely it is exactly the set of kayak locations on which the compass bearing from the kayak to B is the same as the compass bearing from A to B. So, just use your compass to always keep that bearing to B the same as it was when you started at A.

I'm not saying that is a great method in practice -- in fact it isn't, and neither is the GPS method. Both will produce a slightly zig-zag course, as I showed Lisa, though the zigs and zags with the GPS will typically be smaller than with the compass. The good method in practice is to set a correct ferry angle to start and keep reducing it linearly as you approach B. You can use the compass or GPS to monitor how you are doing on that.

And, as Jason pointed out, the best course from A to B is a straight line if and only if the current (and wind) between A and B are totally uniform. So when that's not true, the GPS waypoint/straight line method will not work, and neither will the simple compass bearing method, and even the ferry angle method will be quite a bit more complicated.

[lhunt]

But, if you are a die hard fan of GPS, just leave that concept aside and look at the concept of having a heading that always points to the waypoint on the opposite side. It's just a mental construct to aid visualization.

OK, maybe we're getting somewhere now, not sure. Us diehard fans (actually, I think there are many reasons not to use a GPS, this just isn't one of them...) know the GPS isn't pointing to a waypoint on the opposite side - that is, it isn't setting a heading that points directly towards the waypoint on the opposite side. You still think the GPS works just like a person who can see the tree and is paddling pointing toward it. Yes, if it worked that way you would get a curve - apparently a "pursuit curve" as stated.

Referencing your drawing, here is a thought experiment that might help: I put a GPS on my deck with a find on the tree. I start across the current, which is coming from the left. As I start to drift to the right, I look down and see my GPS pointer changing. I modify my heading so that the pointer is straight up to the top of the screen. Once I find the pointer has centered, I look up. Am I now pointing

• to the left of the tree,
• to the right of the tree, or
• right at the tree?

If you know the answer to this question, you understand how the GPS works. Please note that the GPS does not have a compass working at the time.

[lhunt]

The GPS somehow automatically adjusts for wind, current, sunspots, etc. You set A and B as GPS waypoints, look at the straight line on the GPS map display, and keep your GPS position on it (which modern GPSs apparently help you do). I agree and say...

I guess I mostly agree with this, except for 2 things. One is the "somehow" statement: The GPS simply responds to your current course, thereby correcting for whatever happens to be messing with your course. It's pretty simple. The other issue I have is that you never have to set "A". The only "A" is your current location. The beauty of this is that if you drift off course from inattention, doing a rescue, avoiding rocks, etc., etc., etc., the GPS will happily compute the new heading that will give you a straight line from your new "A".

And, as Jason pointed out, the best course from A to B is a straight line if and only if the current (and wind) between A and B are totally uniform.

OK, I understood when Jason pointed out that it's OK to let a current push you to the right as long as you know another current is going to push you back again. I'm willing to believe that. I now understand (I think) that you are also saying it's OK to let a current push you to the right as long as you know there is less of a right-hand current later on when you have to paddle back to the left to get where you want to go. Hmm... maybe. But if it's wind you're talking about I'm less sure - not so predictable. And I'm sure there's some mathematical sweet spot for how much drift to allow for how much difference in currents and all that. Some skepticism here, but I won't say you're wrong.

That theoretical straight line from A to B has another property, namely it is exactly the set of kayak locations on which the compass bearing from the kayak to B is the same as the compass bearing from A to B. So, just use your compass to always keep that bearing to B the same as it was when you started at A.

Sorry, I know I'm quoting you out of order, but this is the one I don't get. If I read it carefully, then paraphrase, it sounds like you are saying simply pick a direct compass heading and stick with it, regardless of changes in wind or current. I find that hard to believe. If the wind or current pushes you off to the right, regardless of your heading, you won't get there. Actually, last time we talked about this I think you said later that the thing was to compute a ferry angle then reduce it linearly. Which means you need to know the strength of the current or wind ahead of time, I think. But, as you say, we've seen this movie, so I won't try to play it again :-) Of course you can do a good job with a compass and a chart - people do it all the time and it's amazing. I think I'm just saying the GPS is easier and somewhat more accurate.

Anyway, that's it for now, I guess. Thanks very much for the discussion!

Lisa

[leong]

Gentlemen and Lisa,

Well, unlike my friend Lisa, I’m really not enjoying this discussion. It’s too frustrating for me that people don’t understand some simple facts. The more that I read this thread the more do I realize that you gentlemen probably do not read it carefully and probably do not understand the basic principal of using a GPS as Lisa and I explained several times. That’s why I proposed a bet to see if you really would stand behind your misunderstanding. The bet is really just an experiment to prove the truth. You don’t like my experiment, then propose another. Sometimes only the results of an experiment will convince you that a method works. The betting game aside, below are the relevant facts and some other comments addressing prior posts in this thread:

1. Following the arrow of a GPS doesn't result in a pursuit curve with respect to the fixed earth coordinate system. Instead it results in a straight line from the starting position to the waypoint (okay, you could call it the pursuit curve of a dog chasing a stationary dead rabbit). Yes, the heading in earth coordinates continually changes in the presence of cross wind and current, but the track over ground is a straight line. Both Lisa and I know this well, but I'm not sure that the others do. Stop your arguing about zigging and zagging and the other mumbo jumbo having nothing to do with this subject. It’s all garbage below the noise level and not worth considering. Just look at a real track over ground that Lisa provided. As they say, the proof is in the pudding.

2. To follow the GPS's arrow you don't need to have any knowledge (or estimates) of current, wind, boat speed, ferry-angle, or peanut butter. You don’t use the GPS as a compass (you couldn’t care less about the compass heading for this purpose). You don’t estimate the angle of the correct track. You could teach a monkey to follow this arrow. What can be easier for the user? Why can't you guys recognize this simple fact! All the pedantic stuff being thrown out is irrelevant to how the GPS works. It's as if stated that the product of two negative numbers was positive and you guys tried to prove or disprove it using Fourier transforms. No, better yet; think of driving a car on a curvy road. The driver doesn’t need to know anything at all about Newtonian mechanics; of course, the car’s reaction (to the road and the driver) certainly follows Newton’s laws of motion.

3. John said, “As far as the $100 bet is concerned, I think it misses the point David was trying to make.” I’m not trying to address any of the points David is trying to make. I’m only trying to state what the GPS does and show how easy it is to use it. Everything else, including the differential equations of Pursuit Curves is irrelevant to me as far as how the GPS works.

4. John, if you think you can come up with a better experiment to demonstrate that a compass (almost) equals a GPS for navigation in varying currents and winds then be my guest. I’ll be happy to disprove it with a real world experiment. You can use an expert level navigator for the compass side of the experiment. I’ll teach you (in about 10 minutes) how to use a $100 GPS and you’ll easily beat the expert navigator.

5. John said,” Now, using a GPS to assess current set and drift is doable. You paddle out into your stream, and just set there. Leave the GPS on, and it will give you, effectively the current set and drift, as this is just the direction you're moving and speed. OR....you can use a heading that's based on your GPS' compass referenced to true north as you cross, but then you'll find your 'true' heading (i.e. wrt a fixed reference) deviates from that due to the effect of current. If you adjust your heading (direction in which you're paddling) so that the 'true' heading is pointing at the waypoint you've programmed in, you'll have just found a ferry angle using the GPS.” Again this is all irrelevant. For the purpose of navigation to a waypoint you don’t need to access current set, side drift, compass heading, true heading, deviation, ferry angle or peanut butter. Just read what Lisa and I said!

6. John said, “If you head in that direction as the GPS "thinks" it should if you were not in a current stream, then you will find yourself continually adjusting the heading from the GPS, as you will get swept downstream and the GPS will want to compensate for that.” If everything were constant and perfect once you headed in the direction of the GPS’s arrow you wouldn’t ever have to look at the GPS again (because the GPS’s arrow gave you the ferry-angle adjusted correct heading that will take you to the waypoint along a straight line). But nothing is perfect (even if you use a compass). Every stroke you take causes the kayak to yaw back and forth and eventually due to this (and winds and waves) will move you slightly off of the straight line. But the GPS’s human in the loop feedback control system corrects this (a monkey can easily do it).

7. John said, “All David is saying is that if you, instead, calculate your compass heading, assuming that there is a uniform current, you'll take a straight line path, rather than the pursuit curve that results from following the multiple headings the GPS will give you in trying to direct you toward the waypoint on the far side. This is faster.” No, that is baloney! Even in calm water the kayak yaws, the compass wobbles, etc. and you have the same problem as you claim you do with the GPS. However, following the GPS’s arrow constitutes a closed loop system that corrects itself. The tiny zig-zags are a fact of life, even if you use an inertial navigation system (even like the one I worked on for the US Navy).

8. John said, “What I think Leong is saying is that a) there are other factors, like non-uniform current and waves and wind (true) and there are ways of using the GPS to determine current and even take it into account (true), although those are not "smarts" built into the GPS - it is using the GPS as an instrument to determine current and even help you figure out an optimal ferry angle.” I’m not saying anything like that. As I stated above, you don’t need to determine current and figure out an optimal ferry angle or anything of that sort. You can do it if you’re not busy paddling along at 6 mph in heavy conditions with a strong cross current, but it's not necessary and the results will have no practical use if you're following the GPS's arrow.

9. I think I said enough for now.

[leong]

Here's a figure, attached that illustrates what I'm saying and what I believe David's saying. The "GPS" is just a way of saying that you are always following a heading toward an waypoint on the far side of a crossing. It uses the waypoint feature - you punch in the lat/long of a location you want to head to, or choose it from a chart. The GPS then computes the heading to that point, assuming a fixed reference frame (ie. no current). But, if you are a die hard fan of GPS, just leave that concept aside and look at the concept of having a heading that always points to the waypoint on the opposite side. It's just a mental construct to aid visualization.

On the top illustration, I've broken the crossing into 5 discrete steps, where the arrow points to the landmark on the opposite side of the crossing at each stage. You physically change direction at each of those steps in order to compensate for the fact that the current has swept you downstream. The path will include paddling that will have both downstream and upstream components. In the lower case, one takes a ferry angle, which implies that there is no component of the path that is either upstream or downstream. For a fixed paddling speed, the ferry angle crossing will be faster.

This has nothing do with paddler A is an adonis and paddler B is a wimp, it's just a mathematical statement.

Now, to go to the other question of using the GPS as an aid to determine current and even ferry angle, I'll try to come up with some illustrations for that.

John,

I just looked at the two figures in the waypointing.pdf that you linked. There’s one big problem with the figure. The one labeled “GPS waypointing” is a pursuit curve, it’s not the curve that you’d get by following the arrow of a GPS! The second curve is correct for both GPS waypointing and ferrying. I don’t know who created the PDF but let me make one thing perfectly clear: if the originator of the PDF doesn’t agree that this is an error then he is ignorant about how GPSs work. Why don’t you inform him of his mistake? I give you permission to reference me for finding the error. Better yet, I’ll provide an actual GPS track in a strong cross wind showing that it is indeed straight with a fixed earth coordinate system. Perhaps the author was using a GPS that uses an internal compass … that screws everything up.

Still respectfully,

Leon

[djlewis]

Referencing your drawing, here is a thought experiment that might help: I put a GPS on my deck with a find on the tree. I start across the current, which is coming from the left. As I start to drift to the right, I look down and see my GPS pointer changing. I modify my heading so that the pointer is straight up to the top of the screen. Once I find the pointer has centered, I look up. Am I now pointing

• to the left of the tree,
• to the right of the tree, or
• right at the tree?

If you know the answer to this question, you understand how the GPS works. Please note that the GPS does not have a compass working at the time.

From what's been said so far, I would have thought that the arrow is directing you back to your original, A to B (A = where you started, B = the tree) straight line course, and that means correcting for your rightward drift, so #1 -- left of the tree.

But your statement below about resetting A to your current location would lead me to say #3 -- directly at the tree.

The other issue I have is that you never have to set "A". The only "A" is your current location. The beauty of this is that if you drift off course from inattention, doing a rescue, avoiding rocks, etc., etc., etc., the GPS will happily compute the new heading that will give you a straight line from your new "A".

However, I am skeptical that is what happens because, if the GPS always sets a straight course from "here" to B, it is doing no more than mimic a visual "always paddle directly toward B" strategy (maybe in dark or fog when you can't see B with your eyes), and that strategy gets you a pursuit curve.

So, I'm guessing that the first case holds, and #1 happens, that is, you will be directed to get back on the original straight line from A to B.

And the compass can, in principal do that same thing. It doesn't give you a direction to point to do that, you just overcorrect on your own until the bearing to B is what is was to begin with, that is, you are back on the original straight line from the original A to B.

BTW, your surprise (doubt?) that this compass method works is roughly equivalent to your (and Leon's) contention that the GPS is automagically correcting for drift. It is doing that, in effect, but mathematically all it's doing is keeping you on the original straight A to B line. And so is the compass method.

PS -- We definitely should get together on the water and hash this out. Unfortunately, other obligations are keeping me land-bound for the time being. But I think we could meet somewhere in town with a GPS, compass and pencil and paper and do about the same thing.

[djlewis]

Referencing your drawing, here is a thought experiment that might help: I put a GPS on my deck with a find on the tree. I start across the current, which is coming from the left. As I start to drift to the right, I look down and see my GPS pointer changing. I modify my heading so that the pointer is straight up to the top of the screen. Once I find the pointer has centered, I look up. Am I now pointing

• to the left of the tree,
• to the right of the tree, or
• right at the tree?

If you know the answer to this question, you understand how the GPS works. Please note that the GPS does not have a compass working at the time.

Here's a page from a Garmin manual which, I think, illustrates my understanding well.

If you are talking about a Bearing Pointer, then the GPS will direct you always directly toward the destination, and you'll get a pursuit curve. But if you are following a Course Pointer, then you will always be on the straight, A to B line, and will take an optimum track.

--David

[JohnHuth]

David -

Exactly! The point is not whether there are more sophisticated functions in a current day GPS. It is a "manner of saying" that if you paddle in the direction of the bearing to the object on the far side, you'll end up with a pursuit curve, which is longer than the ferry. Again, it's simply a statement of math.

It would be the first case in David's manual, if you want to reference a GPS-like analogy. As a matter of usage one should really say "GPS device" rather than GPS as GPS is the system, not the device.

My old Garmin etrex vista only could display a 'bearing' as the direction of travel. I'd happily admit that there are other features on newer GPS devices.

But, again, if you maintain a heading equal to the bearing to an object on a crossing in the presence of current you will get a pursuit curve, and if you compensate for the current you'll get the straight line. The pursuit curve is longer.

[JohnHuth]

Just to help the discussion, let me suggest something along these lines

1.) Do we now agree on the construction that the pursuit curve, which is derived from a continual set of headings equal to the bearing to an object on the opposite shore in the presence of current is longer than a heading that takes into account current? No words about GPS devices.

If so....then item

2.) We can compare the features on different GPS devices. I'm sure the newer ones have many nifty features. In my old Garmin etrex vista, it could only point toward a waypoint and couldn't compensate for current. It could also display a compass simultaneously. I'm sure newer GPS units can do many things.

item 1.) is a pretty clear statement of math. item 2.) has more to do with features on a device, and they will certainly vary with time. So, it would be OK to say "my GPS device has these features..." but it does not follow that all GPS devices have (or had) identical features. People relate their experience, so it would be reasonable to say "you may not be familiar with GPS device X which has the following features.... "

[leong]

John,

You can see by the time of this post that I couldn’t sleep. What kept me up all night is your inability to understand the simple operation of the GPS that Lisa and I have been describing over and over, ad nauseam. The path is a straight line (testing has proved it).

Allow me to give it another try (hopefully the last). Pretend you are a GPS sitting on a kayak. Because of the satellite signals, etc. you know as a function of time the following items: 1. The fixed position of the waypoint chosen. 2. The position of the kayak. 3. The velocity vector of the kayak (which is the vector addition of the kayaks forward speed vector and any movement vector of the kayak due to wind and current). With this information, it should be easy to calculate the heading angle that the kayak should move along in order to be consistent with the ferry-angle that would move the kayak along the track-over-ground from the kayak’s current position to the target. Even a lowly retired mathematician like me can do the simple math. This doesn’t prove that I’m right about how the GPS works, but at least it proves the plausibility.

Answering another question, I am using the course pointer which results in a straight line to the target as long as you keep the arrow pointed to the top of the screen. Why in the world would I want to go on a pursuit curve to waste energy.

So what's your problem guys. My GPS was purchased last year for about $100 and that's how it works. Lisa's GPS was purchased more than 4 years ago and that's how her's works. If you guys want to argue that there are crummy GPSs that don't work that way then so what? There are obsolete cars on the road too, but would you buy one? Just go out and buy a good GPS (one for kayak use).

So, I guess you now admit that Lisa and I have been right all along. You can always (think) that you've won an argument by basing it on false premises. I think that Lisa is owed an apology and I'd appreciate it if you thank her for the free GPS lessons.

Quod erat demonstrandum

Leon

[JohnHuth]

Leon -

Here's where I think the nut of the problem is:. My old Garmin Etrex Vista *only* pointed to a waypoint with no calculation whatsoever that factors in additional motion. So, the idea that my GPS device *only* points to a waypoint is what obscured the conversation. Now, I'm perfectly willing to be taught that a new GPS device factors in additional things that can be calculated, like current. But, the way it was phrased was to say "you just don't understand how GPS works", as opposed to "you may not realize that current GPS devices have the following features..."

At least the way I was approaching the problem was based on the experience with my old device, which was probably less sophisticated, being older.

I'm assuming that everyone, however, agrees with the assertion that the 'continually heading along the bearing that points directly across' is longer than factoring the ferry angle. Right?

I certainly apologize for not appreciating the capabilities of your GPS device.

I for one will not be contributing to NSPN website for some time to come, however, as the tone of the dialog on here is just too difficult for me. I apologize and sign off. No bets, not boasts about paddling skills, no nothing. I'm not into winning at the cost of offending and I apologize if I crossed that line.

Good bye

John

[jason]

John,

You can see by the time of this post that I couldn’t sleep. What kept me up all night is your inability to understand the simple operation of the GPS that Lisa and I have been describing over and over, ad nauseam. The path is a straight line (testing has proved it).

Allow me to give it another try (hopefully the last). Pretend you are a GPS sitting on a kayak. Because of the satellite signals, etc. you know as a function of time the following items: 1. The fixed position of the waypoint chosen. 2. The position of the kayak. 3. The velocity vector of the kayak (which is the vector addition of the kayaks forward speed vector and any movement vector of the kayak due to wind and current). With this information, it should be easy to calculate the heading angle that the kayak should move along in order to be consistent with the ferry-angle that would move the kayak along the track-over-ground from the kayak’s current position to the target. Even a lowly retired mathematician like me can do the simple math. This doesn’t prove that I’m right about how the GPS works, but at least it proves the plausibility.

Answering another question, I am using the course pointer which results in a straight line to the target as long as you keep the arrow pointed to the top of the screen. Why in the world would I want to go on a pursuit curve to waste energy.

So what's your problem guys. My GPS was purchased last year for about $100 and that's how it works. Lisa's GPS was purchased more than 4 years ago and that's how her's works. If you guys want to argue that there are crummy GPSs that don't work that way then so what? There are obsolete cars on the road too, but would you buy one? Just go out and buy a good GPS (one for kayak use).

So, I guess you now admit that Lisa and I have been right all along. You can always (think) that you've won an argument by basing it on false premises. I think that Lisa is owed an apology and I'd appreciate it if you thank her for the free GPS lessons.

Quod erat demonstrandum

Leon

Leon,

I think that you have steep over the line on this one.. As for GPS's I have a number of them and would be glad to provide lessons if John needed one. The issue is he knows how they work and is correct. My newest one is a fairly fancy 3 month old model, that I tend to keep in my boat. It's great, but can't deal with current.

Your going to a point works great with a GPS but it really doesn't deal with current. To see this in action I think that your going to have to go some place with current that's faster that what you can paddle try it with the GPS then do the same thing setting ferry angle with Ranges.

If you would like to go some place with fast current I would be glad to do an on the water demo with you, but I don't think that we are making ANY progress with this on the message board. I think that I too will be sigin off the topic. If you would like to call or e-mail me I would be glad to work out a date/time to try this on the water. (660-960-0070 or jason at kates dot org).

-Jason

BTW a rule of thumb is about 17deg for each knot of current.

[djlewis]

Here's a page from a Garmin manual which, I think, illustrates my understanding well.

Whoops, forgot to answer Lisa's question:

• Using bearing pointer ==> #3 -- pointing straight at the tree
• Using course pointer ==> #1 -- pointing left of the tree

--David

[lhunt]

From what's been said so far, I would have thought that the arrow is directing you back to your original, A to B (A = where you started, B = the tree) straight line course, and that means correcting for your rightward drift, so #1 -- left of the tree.

But your statement below about resetting A to your current location would lead me to say #3 -- directly at the tree.

OK, David, you got me there. I was wrong when I said A is your current location (sorry). A is the location you were in one second ago. You don't have to set A, because the GPS continually re-computes your direction.

Remember, it doesn't know which direction you are pointing in (it has no compass). It records a one-dimensional point where you are, and one second later it takes another point. The difference in location between these two establishes a direction of travel. When you are using a ferry angle, or when you are not using a ferry angle and should be, you are pointing in a direction other than your direction of travel. The GPS gives you its pointer based on the direction of travel, so the pointer is "off" by the ferry angle relative to the tree you actually look at on the shore.

if the GPS always sets a straight course from "here" to B, it is doing no more than mimic a visual "always paddle directly toward B" strategy

That is true if the GPS is using a compass. It confused the bejesus out of me when I began using it for paddling. I had the compass set to kick in below 3 mph. Imagine my confusion when, as I accelerated, the whole map swung around as soon as I reached 3 mph and seemed to be "off" by some mysterious angle. In fact, if you are using the GPS in a boat, an integral compass/GPS combination is a bad idea. If you want a compass, it should be a normal compass.

The GPS knows where the tree is, and it knows where you are, but it doesn't know what direction you are pointing in. Pointing the GPS at the tree doesn't help. You have to actually move toward the tree before the GPS tells you everything is OK. So, yes, the answer is #1.

Looks like I shouldn't have gone to bed last night! More after I read John's stuff more carefully.

[lhunt]

Leon -

Here's where I think the nut of the problem is:. My old Garmin Etrex Vista *only* pointed to a waypoint with no calculation whatsoever that factors in additional motion. So, the idea that my GPS device *only* points to a waypoint is what obscured the conversation. Now, I'm perfectly willing to be taught that a new GPS device factors in additional things that can be calculated, like current. But, the way it was phrased was to say "you just don't understand how GPS works", as opposed to "you may not realize that current GPS devices have the following features..."

At least the way I was approaching the problem was based on the experience with my old device, which was probably less sophisticated, being older.

I'm assuming that everyone, however, agrees with the assertion that the 'continually heading along the bearing that points directly across' is longer than factoring the ferry angle. Right?

I certainly apologize for not appreciating the capabilities of your GPS device.

I for one will not be contributing to NSPN website for some time to come, however, as the tone of the dialog on here is just too difficult for me. I apologize and sign off. No bets, not boasts about paddling skills, no nothing. I'm not into winning at the cost of offending and I apologize if I crossed that line.

Good bye

John

C'mon, John, don't desert us now! At least read through this and let me know what you think and that will be the end of it.

Your old GPS is not less sophisticated than mine or Leon's, it's more sophisticated. You have the compass enabled. If you disable the compass you'll be there, I promise. Do one more thought experiment with me:

Take your tree and put it in a field. You are hiking and can see the tree. Here are some questions (and answers).

#1: Stand completely still and point the GPS at the tree. Which way is the pointer pointing? Answer: It's a trick question, because the pointer is random. Maybe it's stuck where it was the last time you moved (that is, if it was pointing to the left of the screen it's still there), or maybe it's swinging wildly around as it gets little errors from the satellites. Point is, it doesn't know which way you are pointing because you are standing still.

#2: Start walking toward the tree. The GPS pointer swings to the top of the screen. It's happy because you're moving toward the tree. You're happy because the pointer is pointing at the tree. Good. Now, while walking toward the tree, pivot the GPS 45 degrees to the left. Which way is the pointer pointing? Answer: It's pointing 45 degrees to the left. That is, it's happy, because you're walking toward the tree, so the pointer is at the top of the screen. The fact that you're pointing the top of the screen to the left is unknown to it. You can hold the device at any angle and the pointer will always be at the top of the screen as long as you walk toward the tree.

#3: This is the same as #2, but is more obviously a metaphor for a drifting kayak. While pointing your face and the GPS at the tree, walk with a sidelong gait 45 degrees to the left of the tree. Which way is the pointer pointing? Answer: It is pointing to the right of the tree. Why? The GPS is unhappy because you are not moving toward the tree. It tells you to bear right by moving the pointer 45 degrees to the right of the screen. You are (seemingly arbitrarily) pointing the top of the screen towards the tree, so the pointer is pointing to the right of the tree. To your perception, the whole map is pivoted "off" the real world by 45 degrees, but that's only because you are holding the GPS 45 degrees "off" your direction of travel.

Continuing with #3, now, continuing to use the same sidelong gait, turn your body and the GPS right (traveling more to the right) until the GPS pointer is straight to the top of the screen. Your face and the GPS are pointing to the right of the tree, but you are sidling to the left towards the tree. Now the GPS is happy because you are moving toward the tree. The pointer still seems to be pointing to the right of the tree, because you are holding the GPS to the right of your direction of travel. This is a metaphor for the kayaker using the correct ferry angle.

David, I'll read up more on the "course" pointer. I've never used it, but I think it isn't what you want. It would, as you say, give you the whole "A" to "B" thing, but would stick you with a particular course. If you drifted off that course for any reason, it would want you to get back on the original line. I would rather have a new line which is straight to my destination.

-Lisa

[leong]

John,

You go to war with the army you have not the army someone else has. We told you countless times how our GPS’s work. I’m not familiar with yours so I can’t speak for it.

>>Now, I'm perfectly willing to be taught that a new GPS device factors in additional things that can be calculated, like current.

Again, I say the GPS that Lisa and I use doesn’t factor in current. It factors in how the kayak is moving. Whether, current, wind or my son-in-law pushing the kayak sideways, it doesn’t know.

>>I'm assuming that everyone, however, agrees with the assertion that the 'continually heading along the bearing that points directly across' is longer than factoring the ferry angle. Right?

Yes, of course. I’d hope everyone reading this is smart enough to know that a straight line is the shortest path.

The bet idea came from David Lewis on another thread (strangely on a trip report). Let’s call what I want just an experiment to see what the curve is. No one likes my experiment because they think that they’re not good enough at navigation to compete against me. So, someone please design a better experiment. Let’s find out how good a manual way stacks up against my GPS. I’m quite flexible … anything you want.

>>I'm not into winning at the cost of offending and I apologize if I crossed that line.

You didn’t offend and you didn’t cross any lines. My friend, you frustrated me by continually restating the “opposite” of what Lisa and I said over and over and over again. You never responded when I said no to some of your erroneous assertions. You just came back and restated over and over an erroneous idea of how my GPS works. I can’t help it if you were using the wrong mental construct for my GPS. Lisa and I were trying our best to educate you on how our GPS’s work. Lisa was the good cop. I was the bad cop, because I was trying to force you to understand. Neither of our methods worked. The Garmin manual apparently worked.

David,

I’ve read two books and countless articles about ferry crossings. All of the literature discusses only two methods for such. Both methods estimate of the ferry-angle. The first method is to look back and estimate the set angle as I discussed earlier. The other method is to estimate the cross drift speed and the paddling speed. Then the (obvious) trig formula is employed to compute the ferry-angle. Could you please point to some write-up that discusses the approach that you’re pushing. I can’t figure out what your approach is from any of what you said.

Jason,

You’re missing the whole point of the argument. Both Lisa and I agree that there are situations where not using a GPS is better. The point in contention is that our GPS’s don’t keep pointing you to some waypoint or arbitrary fixed point. Instead, my GPS gives me the direction to head to which is exactly consistent with the proper ferry-angle. If the current or wind are not constant (and it never is) then the direction to head towards changes in accordance with the latest ferry-angle.

I’ve not stepped over any line. I like David and I think that John and I would enjoy each other’s company. Arguments get heated when one person (John in this case) continually restates an erroneous conclusion about someone GPS that he’s never used or seen.

Peace to all. I soon have to leave to push Lisa as fast as I possibly can over the water in preparation for the July 14’th Blackburn. I have no time to proof this.

Respectfully,

Leon

[EEL]

I for one will not be contributing to NSPN website for some time to come

John:

I sincerely hope you will reconsider this decision. I, and I believe many others, have greatly benefitted from you presentations, downloads, and comments posted on the NSPN website.

I understand the basis for your decision, but please reconsider in a few days.

Perhaps a good time to remember the first line of "Ten Thousand Men of Harvard".

Ed Lawson

[lhunt]

Just to give myself a sense of finishing the practical part of this discussion, here are 2 drawings of a GPS pointer in a cross current. In the first one, the paddler is using a ferry angle to get a straight direction of travel. In the second one, the paddler has spaced out and is just using a set heading.

If you find these difficult to see on your monitor, I also have them uploaded here - use full screen mode to view.

Here is the case of a paddler just going stupidly straight ahead without looking down at the GPS:

I'm not much of an artist, so forgive me for that :-) Hopefully this helps a little to explain how a pointer based on the direction of travel gives you a ferry angle that changes with conditions.

-Lisa

[PeterB]

Lisa,

You diagram looks ... not right... to me. For "Case # 2: Using a Good Ferry Angle" it says "GPS is happy because its pointing at the waypoint") , but its not pointing at the waypoint; Its pointed in the direction the bow is pointed . I don't know much about GPS, but I believe you set a waypoint and the arrow points to it. not in the direction your bow is pointed. While ferrying your boat is essential crabbing sideways, so arrow pointed in direction that bow is pointed would not the same as the waypoint.

Leon, you have continually addressed John personally, and those who have expressed differing views from your own. Can't you just state your position on its substance or merits, or challenge an opposing position on its merits rather than address its author in the way that you have?

[leong]

Leon, you have continually addressed John personally, and those who have expressed differing views from your own. Can't you just state your position on its substance or merits, or challenge an opposing position on its merits rather than address its author in the way that you have?

Yes, Peter, when you're right you're right. A PM to John is in process.

[lhunt]

Lisa,

You diagram looks ... not right... to me. For "Case # 2: Using a Good Ferry Angle" it says "GPS is happy because its pointing at the waypoint") , but its not pointing at the waypoint; Its pointed in the direction the bow is pointed . I don't know much about GOS, but I believe you set a waypoint and the arrow points to it. not in the direction your bow is pointed. While ferrying your boat is essential crabbing sideways, so arrow pointed in direction that bow is pointed would not the same as the waypoint.

Hi, Peter, yes, that is the point of the whole thing. But maybe it's hard for you to see? The example is Case #1, Using a good Ferry Angle", and it says "GPS is happy because direction of travel is towards the waypoint". It goes on to state: "GPS doesn't know that it isn't, itself, pointing at the waypoint". Wish I had something that would make a .pdf or something, that would help. I guess I could print it out then scan it in (ugh).

The arrow definitely does not point at the waypoint, if by that you mean the visible tree. If the GPS is happy (as it is if your boat is moving toward the waypoint), the arrow points to the top of the screen regardless of how you hold the GPS. When moving at a good ferry angle, if you have your GPS pointing toward your bow, then the arrow points towards your bow. As long as you keep the pointer at the top of the screen, your ferry angle is good. It's a little disconcerting when you look up and the tree is to your right, but that's the way it is supposed to be. You get used to it.

The simple reason it is this way is that the GPS, (when it doesn't use its internal compass (if any)), doesn't know in which direction it is pointing. It only knows in which direction it is moving. If you were in a tandem, and the stern paddler kept the ferry angle while the bow paddler held the GPS up and pointed it at the waypoint rather than at the bow, the arrow would still be at the top of the screen, and would now be pointing both in the direction of travel and at the waypoint. But it is unnecessary, obviously. The point is to keep the arrow at the top of the screen, period.

When using a GPS for hiking this isn't an issue, because one normally points the thing in front of one, which is also the direction of travel. Only in a boat (or a plane) is the direction of travel (course) frequently different from the direction you are pointing in (heading).

Lisa

[Katherine]

Hello all,

No worries, I am not about to join in this debate. From my perspective it seems as though opinions are stuck and people have been hurt and offended.

I am, however, going to ask that people consider the idea that perhaps it is past-time to "agree to disagree" and end this discussion on the message boards.

Please consider...

[leong]

Hello all,

No worries, I am not about to join in this debate. From my perspective it seems as though opinions are stuck and people have been hurt and offended.

I am, however, going to ask that people consider the idea that perhaps it is past-time to "agree to disagree" and end this discussion on the message boards.

Please consider...

Thanks Katherine. It's probably just me and I've taken some steps to amend the situation. My broken leg that you noticed the other day probably added to my frustration.

Nice paddling next to you.

Leon

[lhunt]

Hello all,

No worries, I am not about to join in this debate. From my perspective it seems as though opinions are stuck and people have been hurt and offended.

I am, however, going to ask that people consider the idea that perhaps it is past-time to "agree to disagree" and end this discussion on the message boards.

Please consider...

Hi, Katherine,

Yes, I see your point, but can you stand it just a little while longer? I think there is a thread within this thread which has stuck pretty well to the practical concept under discussion and I'd like to see it through if it can be done. It's an elusive concept; I've tried many ways to explain it in the past (and in this thread), and the last drawing has been the most successful summary so far. It's a little like getting a roll: It's not intuitive, but it's easy when you get it.

The topic of ferry angles is pretty apropos for a kayaking club - if it turns out a relatively high percentage of people don't know that there's a gadget you can use, that might be useful information. It won't necessarily drive people to use a GPS (there are many drawbacks, as everyone knows), but it does round out one's breadth of knowledge about a common subject, I would think.

Bear with us - we promise to be good :-)

Lisa