Need help explaining river-boat problems

[EricL]

Hello everyone. I'm a new member with a question about a topic that is probably way too simple to be of interest to most of you, but I would really appreciate some help.

Please excuse the fact that I don't use the proper jargon. I've only taken introductory physics (the kinds of classes that my engineer brother haughtily refers to as "physics for poets"), and that was about 40 years ago. Also, please bear with me while I set the stage for my question, because I think it makes a difference that I do.

I'm an avid canoe paddler, and there's a paddling message board where several of us have been talking about something that we paddlers call "ferrying". Ferrying is basically the process of trying to travel straight across a river by pointing the boat at an upstream angle that's somewhere between zero and 90 degrees to the alignment of the current, and paddling forward, so that the actual direction of travel is directly toward the opposite shore.

Ferrying can be done two ways, depending on the situation.

Method #1
If your boat is floating in a sheltered eddy and you vigorously propel it out into a zone of very swift current, the boat's inertia will initially prevent it from drifting with the current, and so for a few seconds, the water rushes past the hull, which means that by controlling the boat's angle to the current you can steer it rapidly across the flow. It's great fun. This method of using the interaction of flowing water with an initially-stationary hull to propel the boat in what appears at first glance to be a diagonal direction works in the same way that a kite immediately flies upward in a strong wind when released at ground level (in this instance, the boat's inertia provides the same kind of force as the does the string of a kite). This type of ferrying can't last long, as eventually the boat's inertia is overcome, and after that it's just "along for the ride" within the stream of current, and that brings us to ferrying method #2.

Method #2
When the boat is at equilibrium with the current, such as when crossing a broad river, ferrying is a simple matter of paddling the boat in a direction such that when you balance out the velocity of the boat as it moves through the water against the velocity of the current, the boat's actual direction of travel (relative to the river bottom) is straight across the river.

Method #2 is simple, right? Wrong. There is not a single person involved with this discussion who understands that in Method #2, the boat is moving in a straight line through the water that supports it. Everyone says that as soon as you start paddling, the current "pushes on one side of the boat" and that's the reason that the actual direction of motion is diagonally away from the direction it is pointed. According to their reasoning, all ferrying situations are just as explained in Method #1 above (though their understanding of Method #1 is often still not quite accurate). According to their beliefs, you could perceive the direction of the current while paddling across a large river simply by watching or feeling the effect of it as it "hits the side of the hull".

I tried to make the case that if one were paddling a boat among a pattern of free-drifting, floating markers, the boat's progress among those markers would be the same whether the water was stationary or part of a large, uniform, moving stream. No one believes that that is true. According to their belief system, the floating markers would float along and crash into the upstream side of the boat, as if the boat were somehow independent of the water which supports it.

It just boggles my mind how something so incredibly simple is totally beyond comprehension to these folks, so the question is how best to explain the situation.

I know there are illustrated "riverboat" problems online, but they never seem to deal with a boat who's true direction of travel is straight across a river. More to the point, for people who are already convinced that extremely complex hydrodynamic forces are at work propelling the boat diagonally away from its heading, typical river-boat examples using vector addition are seen as totally missing the point. Even examples of everyday experiences (like walking across the center isle of a bus as it cruises down the highway) are not seen as relevant by these folks.

Now, all of them understand that your boat's speed relative to fixed objects is faster when paddling downstream than when paddling upstream, and they seem to know why, but it's very clear that none of them understand that exactly the same principle applies when traveling at other orientations to the current. This principle is perfectly clear when working with examples of adding vectors, but as mentioned, the real problem is helping folks see that vector addition isn't a case of "missing the point".

I've given up on similar discussions in the past, but this time I want to take the next step if I can. What I'd really like to find, is a pair of animated videos that illustrate a boat crossing a river, with one frame of reference being fixed (relative to the river bottom), and a second frame of reference being the water itself as it moves downstream. That would show how, relative to the water that supports it, the boat moves in a straight line through the water in all situations. Other than this ideal video (which may not exist), a second-best option would be if some talented explainer of such things who enjoys a challenge were to join-in with the discussion! Otherwise, I'm all ears regarding ideas about how to make this more clear.

 

[jbriggs444]

That's a nice and entertaining exposition. I wish I knew a way of explaining things better than you have already done. The [false but intuitively appealing] cartoon physics picture seems to be that a canoe is like a little car that tries to go in the direction it is pointed, even while the current tries to push it otherwise.

 

[bahamagreen]

The problem with a video demonstration (cartoon posing as a simulation) is that the maker can cause it do whatever they think is the solution (a lot of relativity videos fall into this).

A better method might be a physical model that demonstrates the principle. Since your antagonists are on a message board, you might need a very simple model that they could construct using simple available materials...

Off hand, I'm thinking of two transparent pages overlaid on a tabletop (the ground), the two pages marked as like Cartesian coordinates, one moving along the table top to represent the river flow, and the other overlaid with a brad fixing a little rotatable "canoe" at its origin to indicate orientation angle. Few minutes sliding these over each other with due respect to the canoe's orientation should make for a convincing demonstration.

I say, try this yourself and then write up the thing as an experiment (materials, procedure) ... for your message board friends to do themselves and report (observations, conclusions).

 

[sophiecentaur]

The problem with a video demonstration (cartoon posing as a simulation) is that the maker can cause it do whatever they think is the solution (a lot of relativity videos fall into this).

Yes yes yes! A cartoon can show anything happening, however daft and unreal. I have a similar view of simulations in general, when the models used are incomplete (which is much more common than beginners seems to think.) A dodgy video could be used in this particular context to 'prove' anyone's crackpot idea about what's going on. (As with Tom and Jerry' antics in a boat)
The concept of Vectors was introduced to deal with problems like this one. Trying to explain things without the term 'Vector' is so much harder. Eric's one advantage is that these guys will have experience and a memory of what it's like in a 'ferry glide' and other situations.
Until the basics of the equilibrium situation are dealt with, there is no point in discussing Method #1; far too many variables are involved in that situation so the steady state is the one to go for.
@Eric: Your free floating markers could be a good starting idea. If these guys have ever paddled in the open sea they could perhaps imagine dropping breadcrumbs regularly behind them as they go. When you are on open water (no wind, of course) and the tide is flowing, you have no idea of your progress over the ground. Your breadcrumbs would lay in a straight line, equally spaced behind you and they would all be drifting with you, in the direction that the tide is running, at the same rate. They would be in a straight line behind you (dead astern) - just where you left them (as far as you, in your floating frame of reference can tell) so that indicates that you are traveling in a straight line through the water (relative to the water). The river situation is the same - even when the flow is very fast - only you can see the bank close enough to be aware of relative speed (and to interfere with people's intuition). This could all be described with the help of a simple static diagram. No need for a possibly confusing animation.

 

[A.T.]

A cartoon can show anything happening, however daft and unreal.

Since this here seems purely about understanding kinematics (vector geometry), an animation could definitely help. One could also build a model, like a toy car crossing a slowly running treadmill.

 

[NTW]

Instead of an animation, I'd suggest a 'mental experiment'. Tell those skeptical canoe paddlers to imagine that the river is a solid moving surface, like a conveyor belt, and that their canoes are small cars. After a little reflection, sure all of them shall agree that crossing that 'river' is a simple matter of direction and velocity, the path of the car along the solid moving surface being a straight line, with the cars moving smoothly, with no 'hull-hitting forces' at all...

 

[sophiecentaur]

Since this here seems purely about understanding kinematics (vector geometry), an animation could definitely help. One could also build a model, like a toy car crossing a slowly running treadmill.

It's true that animations have their place and I am over-sensitive (possibly) about this matter. The problem is always when the person they are aimed at, takes things too literally and extends the analogy too far. It would be important, for instance, to emphasise the common aspects and differences of the flowing (liquid) water and the rigid surface of the treadmill.
That is the great strength of mathematical explanations - that they are so clearly abstract and carry their own caveats intrinsically. I appreciate that the canoeists discussed in this thread are not likely to grasp Vectors with open arms.

 

[sophiecentaur]

no 'hull-hitting forces' at all

'tyre hitting forces' instead, perhaps?

 

[A.T.]

I appreciate that the canoeists discussed in this thread are not likely to grasp Vectors with open arms.

Yes, and animations can visualize the motion without vectors. A real life demo on a river would be tricky, because a real river doesn't have a uniform flow speed.

 

[A.T.]

According to their beliefs, you could perceive the direction of the current while paddling across a large river simply by watching or feeling the effect of it as it "hits the side of the hull".

This could be wave propagation, which is not necessarily indicative of the flow direction.

 

[jbriggs444]

This could be wave propagation, which is not necessarily indicative of the flow direction.

All things being equal, the waves on a river will tend to propagate upstream (relative to the current flow), not down. The vee-shaped waves from submerged or partially submerged obstacles are standing waves and most certainly propagate upstream. Waves from wind will generally propagate upstream because, all things being equal, the wind will generally be upstream.

It is difficult to imagine a paddler who is paying attention to be unaware of this. Disturbances always arrive from the downstream side of the boat.

Edit: To be fair, the bulk of my paddling experience on rivers is in the context of paddling or floating downstream.

 

[A.T.]

To be fair, the bulk of my paddling experience on rivers is in the context of paddling or floating downstream.

Same with me. Which is maybe why I'm sceptical about the feasibility of real life demonstration. The river speed is non-uniform, the speed of a paddle propelled vessel is non-constant. This makes it difficult to reproduce the ideal case where the boat keeps a constant course, and any correction of the course will of course produce temporal side slip and the effects the paddlers claim to observe.

 

[NTW]

'tyre hitting forces' instead, perhaps?

Correct...

 

[NTW]

This may also be of some help:

 

[sophiecentaur]

This exercise is best carried out with a fairly large motor boat that has a tiller (rather than wheel steering) and a wide channel with a reasonably even current flowing. It is not hard to get a grasp of the angles and the lines involved. A good ferry glide is very impressive - even to the guy at the tiller! Paddling and turbulence tend to cloud the issue and the physical memory from having learned what, rather than why really does't help.

 

[bahamagreen]

I guess another example would be a visit to an airport on a windy day, watching the the landing planes "crab" their approaches (turning the plane into the wind so as to make their landing straight along the landing line but with the orientation of the plane at an angle to the landing line...)... the car on the treadmill is good.

 

[EricL]

All things being equal, the waves on a river will tend to propagate upstream (relative to the current flow), not down. The vee-shaped waves from submerged or partially submerged obstacles are standing waves and most certainly propagate upstream. Waves from wind will generally propagate upstream because, all things being equal, the wind will generally be upstream.

It is difficult to imagine a paddler who is paying attention to be unaware of this. Disturbances always arrive from the downstream side of the boat.

Edit: To be fair, the bulk of my paddling experience on rivers is in the context of paddling or floating downstream.

Thank you. I think the difficulty comes not from inaccurate observation, but from preconceived notions that automatically come to the forefront while paddling, and since those ideas seem to explain what's going on, that's as far as they get. Kind of like seeing that the world might as well be flat from our perspective, so since that explains all that we see in our immediate surroundings, that must be correct.

QUOTE="bahamagreen, post: 5534265, member: 353971"]I guess another example would be a visit to an airport on a windy day, watching the the landing planes "crab" their approaches (turning the plane into the wind so as to make their landing straight along the landing line but with the orientation of the plane at an angle to the landing line...)... the car on the treadmill is good.[/QUOTE]
Thank you. I've actually had those same ideas before when this came up a couple years ago (though with the example of a plane in a cross wind, I didn't think of suggesting that people watch them close up as they approach a runway). Anyway, I'm sure there were some folks who "got it", and some who do now as well, but the only ones replying believe "boats are different". It's preconceived notions that they can't even explain that are getting in the way. I am getting a few ideas from you guys, however.

This exercise is best carried out with a fairly large motor boat that has a tiller (rather than wheel steering) and a wide channel with a reasonably even current flowing. It is not hard to get a grasp of the angles and the lines involved. A good ferry glide is very impressive - even to the guy at the tiller! Paddling and turbulence tend to cloud the issue and the physical memory from having learned what, rather than why really does't help.

Thank you. I see I am making a mess of my replies because I don't yet understand the workings of the system here, but here's another reason the motorboat idea is good. You can look back at your wake and see that it's straight behind you, not trailing off diagonally (mainly by looking at the trail left by the prop itself). I might be more aware of this than most canoers because I also row canoe-like boats, and when rowing you face the rear, so I can constantly see that my wake describes straight-line travel of the boat through the water, even going cross-current (my own breadcrumb trail!)

 

[EricL]

Same with me. Which is maybe why I'm sceptical about the feasibility of real life demonstration. The river speed is non-uniform, the speed of a paddle propelled vessel is non-constant. This makes it difficult to reproduce the ideal case where the boat keeps a constant course, and any correction of the course will of course produce temporal side slip and the effects the paddlers claim to observe.

You are probably correct about this, that is, the way some paddlers are likely to misinterpret what's happening. However, for me, being able to envision what's actually happening, even those deviations make perfect sense. This is much less of an issue on a fairly large river, in any case.

 

[EricL]

This may also be of some help:

Wow, this is perfect. I've actually tried to describe that situation - a car on a conveyor belt - to these folks in previous attempts at explaining the situation (a year or two ago), but was met by claims that the example is not applicable. Well, of course it is applicable, and I think actually seeing it in action might make that more clear.

 

[rcgldr]

If the boat is moving straight across a flowing river, then the boat's velocity with respect to the ground is perpendicular to the bank (assuming bank is perpendicular to the river), and the boats velocity with respect to the river will have an upstream component equal to the river's downstream component relative to the ground. Ignoring the air, the boat only interacts with the water. The boat will not hit any floating objects that are not directly ahead of the boats path with respect to the flowing river. To a ground based observer, the objects will have a downstream component relative to the boat, same as the downstream component of the water.

 

[NTW]

Wow, this is perfect. I've actually tried to describe that situation - a car on a conveyor belt - to these folks in previous attempts at explaining the situation (a year or two ago), but was met by claims that the example is not applicable. Well, of course it is applicable, and I think actually seeing it in action might make that more clear.

If any of them is familiar with flying, you can mention the frequent case of landing with a crosswind, when the heading and the course are at an angle that can be quite large for slow flight and strong winds. Of course, the plane is flying 'within the moving medium' ('Mobilis in mobili,' as captain Nemo put it) and there are simply no 'hull forces' to speak of. These things are, however, counter-intuitive, and many pilots don't understand them correctly...

 

[sophiecentaur]

upstream component

This is the pivotal word, of course. But, for these `Mathsphobic' canoeists, it could well be a step too far. There is a great problem trying to 'explain' stuff people for whom a massive shutter comes down as soon as they are required to think outside their box.

 

[A.T.]

These things are, however, counter-intuitive, and many pilots don't understand them correctly...

As the never ending discussions about downwind turns show.

 

[sophiecentaur]

These things are, however, counter-intuitive, and many pilots don't understand them correctly...

That's an interesting comment. The effect of tidal current (essentially the same situation) is a significant part of what you learn in boating courses. 'Everyone" knows that you should always make manoeuvres into the wind or current - whichever is the dominant factor at the time. Trying to pick up a mooring without doing this is sure to give you problems. The nearest boating equivalent to a vehicle handbrake is to balance motive power with external forces. That statement (forces) describes what helmsmen bear in mind although, as we have discussed in this thread, it is motion vectors that really count. But what you feel, when you get it wrong, is definitely a Force on the boat hook! So much for intuition (again).

 

[EricL]

Okay, I've been away for a while. I appreciate the replies, and I have come back to report that explaining this sort of thing to the average person is far more difficult than I imagined it could be. I worked at it for a few days, and then my job got overwhelming and I didn't go online at all for more than a week. However, because of the arguments I was faced with before I took some time off, I'm in no hurry to go back and continue trying to clarify anything. It seems that virtually no one was able to accept the fact that, relative to the water itself, the boat travels in a straight line. One person practically called the whole notion of relative motion bogus by referring to it as "so-called relative motion" as he was proposing some other idea. I was asked questions, posed to me for the purpose of proving that I was wrong, which simply side-stepped the basic facts as if they weren't even relevant (and to these folks, they are not relevant). Seriously, one person was trying to tell me that the Bernoulli effect plays a role in all this! Another said that it's simply not possible for a boat which is exerting no propulsive force of its own to drift at the same speed as the current, that it will always travel more slowly than the water that supports it, and that therefore friction with the water must somehow be accounted for in this particular problem. No one with an outlandish idea such as those two examples (or others) could offer the slightest logical basis for their belief. "Knowing it to be true" but without a shred of understanding of how the incorrect concept might actually be applied is clearly a comfortable position for them to be in, and of course, that makes them uniquely unwilling to consider evidence that actually supports what's really happening.

I'm sure some people "got it" but just didn't say much. I figure that to be true because some were able to quickly grasp the idea of how forces exerted by the water are unbalanced only when the boat first nudges out into the current, and again when it leaves the current and enters still water again (like stepping onto a conveyor belt and later stepping off again), and that's a basic start to understanding what goes on in-between.

 

[sophiecentaur]

Your objectors are clearly not able to cast aside their false memories. Very understandable actually. You could ask the 'drifters' how the amount of drift would be affected by boat size. Would breadcrumbs also lag behind the moving water too? They are probably thinking in terms of the transitional situation if you plonked the boat into already moving water. A heavier boat might take longer to get up to speed but the steady state would take only a few seconds for a rowing boat.

 

[sophiecentaur]

There are similar problems about simple circuit theory when people can't reconcile the steady state with what they imagine happens at switch on. You may get objections to the idea of waiting 'long enough' to reach steady state but it may start them thinking outside their box.