The "Making Trees" fallacy appears again...

[Ronny170]

Originally Posted by requiem

I do think getting into the various other methods (e.g. radar) distract somewhat from the original question about the basic geometry of the "making trees" topic.

For me, all the mentioned videos reflect a failure to understand the mechanics of the "making trees" concept. The original video selects a background reference that is far too close. The rebuttal videos get a little closer by recognizing distance as a factor, but then go astray due to not understanding why it's a factor.

Only a few days ago I saw some Reddit comments mentioning the method in the context of maneuvering within a marina. Thus, I think properly understanding the method is critical to avoid using it in inappropriate cases.

Agreed, at least except for the distance part. So I took your last diagram as a basic starting point, with some small adjustments for ease. You had also previously given an example of an observing vessel moving at 6 knots, so I used that too. In the diagram, you set the target boat speed at around 45% faster, which would be about 8.7 knots for the target boat, all reasonable variables. Just trying to stay as close to the set-up scenario you originally asked about. So that's shown in Fig 1

E is observing vessel moving at 6 knots and parallel to shoreline, which roughly to your scale is about 0.4+ nm from the shore.
M is target vessel, on a collision course with E, and traveling at 8.7, with a converging angle of 15 degrees (didn't use 16 degrees, sorry)
E-0 and M-0 are the respective starting positions of both vessels, and at each minute (your example), a line is sighted to the landmark behind the target boat M, and this is repeated each minute over a 5 minute period for the purposes of this exercise to see how trees are made. E and in this case M both have a travel time of 5 minutes, and the distance traveled by E is 0.5 nm. Boats therefore are starting .27 or a little over a quarter of 1 nm apart from each other. All of this was taken from your diagram. Some will suggest these starting distances are a little close, and that's fine, you can pick a new scenario for further out from shore, 4, 6, 8 miles out if you like.

The circle around the dot at E5 is the intersection point of the route lines of E and M, and in Fig 1 both boats are set to arrive there at the same time (collide).

There's a few ways to go about manipulating variables to see what happens. You could choose the same starting point but different starting speeds for M and maintain a collision course to see the differences that way. I decided to maintain the heading of M but change it's speed, so this way you can see what would happen if a boat on a specific heading or course line is set to collide with you, or is going to pass through the intersection point either just before or just after you arrive there, and what the 'trees' look like in each case. Fig 2 and Fig 3 show what happens when all other parameters and starting variables are the same, except that M runs a little faster, or a little slower, than E.

So in Fig 1 you note the point on the land directly behind M at T=0, which here is L1. You travel 1 minute and note the new landmark behind M at T=1, which is now L2 You now measure the distance between the two, as mentioned, with a ruler, the length of your finger, whatever. You just need to hold that out at arm's length each time you take a measure. What you'll find on a collision course is that this distance will be the same measure per unit of time, or in other words at each minute that length will be the same.

You can get a 'quick' idea without waiting a minute between readings, which you would need to do with a compass to check bearing changes, perhaps even longer than a minute. You can see that the target boat has an apparent movement across the shore that equals E's boat speed at any given time. M will 'make trees' at the same rate that E travels. This will be true on a collision course when E is running parallel or thereabouts to the shoreline. This not the same as the measure you will take by hand, but will be directly proportional to it.
Also notice that the small angle changes aren't a limitation for measurement, as they would be using a compass, because you're looking at that angle projected onto land, not the angle per se. Our eyes can't detect angle differences very well, but displacement of objects and relative motion are quite easy for us. So there's that advantage.

You also asked about the landmarks not being in a straight line. This is important, but becomes less so as the shoreline gets further from the E boat, and if it's behind the line vs in front of it. Look at the reading at E-4, you're looking at the difference between the new L-5 landmark and the previous one at L-4a. L-4b is set back about .15 nm from L4a in the sight line. Not a large amount of distance, but in the small scale of this scenario, not a trivial amount either. Look at the red lines, this represents the distances you'd be measuring between the current landmark and the one sighted on the previous minute. Not the real distance by any means of course, but a representative proportion. The double red is a comparison of what the measurements would be if you used L4a vs L4b, and it's not much. The smaller the proportion of variance off the line of landmarks to the distance to shore from E, the less it matters. If it's closer than the shore, it matters more, so stick with landmarks, and don't suddenly use a close buoy or marker as landmark.

So the relative bearing of target and compass bearing to target would remain the equal throughout the short journey. Target would stay on EBL the entire time, or however you want to measure it or avoid the topic at hand, and M's relative position to E would not change while the range decreases. AND, contrary to what some have stated with certainty, M will 'make trees' forward against the shore on a collision course with E, and do so at a constant rate and as a proportion of E's speed, and in this particular case that will be 100%

Fig 2 shows the exact same set-up, except M is now traveling a bit faster than before. For ease of graphing, that turned out to be 1.3 knots faster at 10 vs 8.7 but that can be changed as well. You note the landmark at E-0, which is W1. I left the L landmarks in place for comparison. You then get your first measurement at E1 and note the apparent distance between W1 and W2. Now at your second reading at E2, you notice that the measured distance between W2 and W3 is more than a third (35%) larger than your last measurement. That difference is very easy to differentiate. And at your 3rd reading at E-3, the measurement is much much larger than the previous two. Measurement E-4 is just off the charts. The apparent movement or 'tree making' is forward but not at all constant, so M will beat you to the intersection point in this particular case.

Fig 3 shows the same except M is now going slower than it was before, about 1.3 knots slower at 7.4. I don't need to graph or explain what happens to the trees here, other than the initial forward "tree making" slows, then stops, then M starts losing trees. M arrives late to the intersection point of course, and the trees could have told you that in the first minute or so.

You don't need to wait this long between measurements in this scenario, like you would with using a compass trying to measure small changes in degree. A couple of measurements spaced 10 to 20 seconds apart would do it, and you could get a good current estimate of collision risk before you'd even have time to take a sound compass bearing reading.

Let's start there. Check my math too, it was a long night today.

[Ronny170]

Originally Posted by s/v Jedi

No you are twisting it again. You are making this a slapstick circus. When the EBL is pointing at the tree and the target remains on the EBL, then the target is NOT making trees. You say it IS making trees and being unable to grasp that is the problem only you seem to have… all the rest of us understand it.

Right...

[Lodesman]

Originally Posted by Ronny170

What was being discussed is what that forward motion or amount of "tree making" actually looks like when on collision courses, vs not on collision course.

Have you actually read any of the responses in your thread?

You're the only one having that discussion.

Jedi's right again. You don't understand how people use the "making trees" method.

[Ronny170]

Originally Posted by Lodesman

Have you actually read any of the responses in your thread?

You're the only one having that discussion.

Jedi's right again. You don't understand how people use the "making trees" method.

You may well be right about that, perhaps ‘everybody else’ uses the trees method only in a very limited circumstance where the background is functionally infinitely far away from the observing vessel, and you only need a couple of seconds to come to a conclusion. Although from the comments posted by others and how they have used the trees method, that generalization wouldn’t seem to be entirely justified.

The OP and the video referenced are not about that specific scenario anyway, so not sure how some seem determined to want to talk only about that one special case and no other. And no I'm not the only one having that discussion, Requiem was actually asking questions and bringing up some good points that we were discussing with respect to the many possible non-infinite scenarios.

Otherwise it wouldn’t have been much of a conversation anyway, as the “infinite” case is a simplified version of the general geometry, and isn’t especially interesting anyway. When the land is at any other distance, that’s when it gets interesting. It’s relevant because the rules for assessing collision risk with the trees method is significantly and consequentially different in each of these respective scenarios. For instance, the target boat remaining stationary against the land might indicate collision risk if the land is infinitely far away, but it actually means you’ll pass in front of the target ship in the many non-infinite cases. And forward apparent motion or 'making trees' of the target might mean the target will pass in front in the first case, but indicates a potential collision in all the other cases. That difference I would argue is important to know.


Discussions of these more common scenarios was all that the original post was about, including the videos mentioned, which is where the topic originated from in the first place. If I had wanted to limit the discussion to ONLY infinitely far away reference points instead of actual landmarks, I would have stated so in the OP. So I’ll continue to respond to posts about any and all of the other many common situations where the land isn’t infinitely far away from the observing vessel, and put aside any unnecessary tangential discussions of infinitely far away landmark situations.

[requiem]

Your diagrams look generally correct for these scenarios. I've pulled two brief quotes since they are particularly critical here...

Originally Posted by Ronny170

The smaller the proportion of variance off the line of landmarks to the distance to shore from E, the less it matters. If it's closer than the shore, it matters more, so stick with landmarks, and don't suddenly use a close buoy or marker as landmark.

...

You don't need to wait this long between measurements in this scenario, like you would with using a compass trying to measure small changes in degree. A couple of measurements spaced 10 to 20 seconds apart would do it, and you could get a good current estimate of collision risk before you'd even have time to take a sound compass bearing reading.

The first part is important because it changes the angles, and you can see why suddenly using a much closer buoy has a greater impact. And of course the goal is to be able to make a very quick assessment, though my goal is closer to 2-3 seconds at most.

So, let's consider your first diagram.

In the first one, assuming that the E0-L1 line and the E1-L2 lines are parallel, then angle L1 is identical to the angle between E1-L1 and E1-L2 (i.e. that subtended by the first of your red lines). That angle also indicates how much the landmark has "fallen behind" the target boat as the target progressed from M0 to M1, yes?

Keeping that in mind, consider the E0-L1-E1 triangle. We can use the law of sines to relate four things:

1. initial bearing to landmark and target (angle E0)
2. distance from observer to landmark (side E1-L1)
3. change in the relative bearing of the landmark (angle L1)
4. distance run by the observer in that time (side E0-E1)

It looks like the initial bearing is about 137°, so what happens when the landmark is about 5 miles away, and the observer is moving at 6 knots? To simplify things, round up 5 miles to 10,000 meters, and 6 knots to 3 m/s. Over 5 seconds the boat will have moved 15 meters. So, we have sin(137°) / 10000 = sin(L1) / 15. Rearranging that you have sin(L1) = (15 * 0.68)/10000, or L1 = arcsin(0.001) = 0.059°. That's a pretty small number!

If we consider each square on your graph paper to be 3 meters on a side (i.e. side E0-E1 is still 15 meters), then landmark L1 is only 105 meters from the observer at E1. Doing a similar calculation as before, sin(L1) = (15 * 0.68)/105, we get L1 to be 5.6°. I think if you drop a protractor over the sketch you'll get something reasonably close.

What does this mean? On the scale of your sketch, the landmark will have fallen behind by about 3 fingers whilst the target remains on a fixed bearing. If you observed for 10 seconds, or even 20, the change would be quite obvious: the target would clearly be making trees. The problem here is that 105 meters is really, really close, and a standard sheet of graph paper isn't going to be large enough to draw a decent triangle when one side is 1000x the length of another.

[Ronny170]

Originally Posted by requiem

Your diagrams look generally correct for these scenarios. I've pulled two brief quotes since they are particularly critical here...

If we consider each square on your graph paper to be 3 meters on a side (i.e. side E0-E1 is still 15 meters), then landmark L1 is only 105 meters from the observer at E1. Doing a similar calculation as before, sin(L1) = (15 * 0.68)/105, we get L1 to be 5.6°. I think if you drop a protractor over the sketch you'll get something reasonably close.

What does this mean? On the scale of your sketch, the landmark will have fallen behind by about 3 fingers whilst the target remains on a fixed bearing. If you observed for 10 seconds, or even 20, the change would be quite obvious: the target would clearly be making trees. The problem here is that 105 meters is really, really close, and a standard sheet of graph paper isn't going to be large enough to draw a decent triangle when one side is 1000x the length of another.

Thanks for taking the time. I'll have to look over your points more carefully tomorrow and get back on it, but this set-up was based on your overall motion diagram from earlier.

Something's not right with those distances you mentioned though. Each individual cell is 37 meters square, and the block of 5 cells (such as E-0 to E-1) is 185 meters, not 3m and 15m, if I recall correctly. That would put landmark L1 at 1,300 meters from the observer at E1, not 105m, or a little under 3/4 of a nm. Again this set-up was lifted from your original diagram based on the numbers/speeds selected from elsewhere in your previous comments. We can talk about any other set-up you'd like, just provide the desired numbers.

[Cloroxbottle]

Simple solution: mandate everyone have AIS installed and operating when operating in port and in coastal waters.

https://www.youtube.com/watch?v=XoyQ...xpc2lvbg%3D%3D

That's what this industry did with Transponders, Mode-C, and ADS-B.

[thinwater]

Originally Posted by Cloroxbottle

Simple solution: mandate everyone have AIS installed and operating when operating in port and in coastal waters.

That's what this industry did with Transponders, Mode-C, and ADS-B.

Mmmm. Off the point. Look at the little windows. In nearly all aviation cases they didn't see each other. This thread is all about cases where they do sea each other. (Fog and night are different cases, not under discussion here--in that case AIS is a big help.)



With boats, more often either no one is on watch (so AIS would not help), they wait too long to maneuver, or turn in the wrong direction.


The constant bearing solution is so simple I do not understand the thread. I understand the math (engineer). I just don't understand the confusion (7th grade geometry).


I rather dislike electronics for this sort of problem. The solution is to get your head out of the cockpit, not to stare at screens. My bicycle doesn't have AIS, I don't hit people, and I don't think AIS would help, particularly where it is congested. You keep your head on a swivel.

[s/v Jedi]

Originally Posted by thinwater

Mmmm. Off the point. Look at the little windows. In nearly all aviation cases they didn't see each other. This thread is all about cases where they do sea each other. (Fog and night are different cases, not under discussion here--in that case AIS is a big help.)



With boats, more often either no one is on watch (so AIS would not help), they wait too long to maneuver, or turn in the wrong direction.


The constant bearing solution is so simple I do not understand the thread. I understand the math (engineer). I just don't understand the confusion (7th grade geometry).


I rather dislike electronics for this sort of problem. The solution is to get your head out of the cockpit, not to stare at screens. My bicycle doesn't have AIS, I don't hit people, and I don't think AIS would help, particularly where it is congested. You keep your head on a swivel.

AIS is much like ARPA except it is a cooperative model while ARPA is fully controlled by one party.

Formal education used to be taking a bearing from bearing compass or compass-equipped binoculars and radar with EBL and VRM, plus ARPA.
There was no AIS when I did these exams but I understand that AIS is now a required instrument for watch keeping as well. I believe audible alarms on ARPA and AIS are mandatory.

When I see a target at constant bearing I always get curious enough to switch on radar, set an EBL, then use binoculars and find which one is more precise. It is hard to believe anything can beat the EBL but I never once experienced the binoculars being wrong either.

For using shoreside markers I never had trouble either. This is the primary method during dinghy competition sailing. I did have a compass but it was only used to find the next marker (this was a Laser so very wet and no free hands)

[requiem]

Originally Posted by Ronny170

Each individual cell is 37 meters square, and the block of 5 cells (such as E-0 to E-1) is 185 meters, not 3m and 15m, if I recall correctly. That would put landmark L1 at 1,300 meters from the observer at E1, not 105m, or a little under 3/4 of a nm.

The numbers themselves matter less than the various ratios. Using 185 m for the block of 5 cells means that at 6 knots the time between the observations is about 1 minute. To keep that distance from shore and diagram the effect of observations at 10 seconds you'd need the E0 to E1 length to be about 0.8 cells long, making for a much narrower triangle. Which gives me another idea...

[Ronny170]

Originally Posted by requiem

Your diagrams look generally correct for these scenarios. I've pulled two brief quotes since they are particularly critical here...

>>The first part is important because it changes the angles, and you can see why suddenly using a much closer buoy has a greater impact.

Yes, I would imagine it need not be stated that using a crab pot float or buoy located just off the passing target vessel’s port side in the diagram would not be a wise choice. These should be onshore landmarks. The more a landmark is ‘in line’ with the others, the more accurate the measurements. The point mentioned was that landmarks situated ‘behind’ the line of other landmarks affects the angle less than points ‘in front of’ that line of the same distance. Or, as with L4a and L4b, which are about .13nm or the lengths of 2 footballs fields apart, the angle difference is minimally affected when measured from E4. If L4b were instead in front of L4a in line of sight by that same amount, it would affect the angle more. So landmarks inline or behind the overall landmarks line are better than those closer to the observing vessel, presumably those reference points that are in the water, and so these should be avoided with the 'trees' method.


>>And of course the goal is to be able to make a very quick assessment, though my goal is closer to 2-3 seconds at most.

If your reference point is or can be considered infinitely far away, then you can get a quick visual estimate of collision risk. This is a simplified scenario in the overall geometry, so not much to talk about there anyway. For now let’s stick with general scenario of all the other non-infinite cases.
And here’s where the problem arises if you want to have that type of quick single assessment in non-infinite cases. A single assessment won’t tell you very much about collision risk, because it’s just a single data point. If the target boat is stationary against the land or losing trees, you can be relatively certain in non-infinite cases that you will pass ahead of the target vessel if your courses lines cross. However if the target boat is ‘making trees’ against the land, this in and of itself tells you absolutely nothing. Zero. Whether the ‘making trees’ occurs for 2 seconds, 30 seconds, or a minute, this tells you literally nothing. That boat can make trees and still pass behind you, collide with you, cross in front of you, cross way in front of you, or cross way way in front of you, when it eventually crosses your course line.
So not unlike taking a compass bearing or calculating a relative bearing, a single measurement to the target is essentially useless. In the infinite case, the math simplifies and you can thus gain some useful info from a single observation time span, even just a couple of seconds, especially if the target vessel is also relatively close. But keep in mind the visual 'rules' for predicting collision risk are quite different between the two cases, and I THINK that may have been the source of some of the confusion on here earlier.
But for all other non-infinite cases, you need at least two observation periods or ‘data points’ to compare, the same way as with compass bearings in CBDR. With the compass you’re looking at and comparing bearing measures, while with the trees method your assessing apparent rate of travel against the land, at least that what was originally posted and discussed in the videos in the OP. We can convert that ‘rate’ into just a simple distance measure if we keep the time span equal in both assessments. But it can’t be done with just a single observation period, whether it’s 2-3 seconds, 10 second, 60 seconds or 5 minutes. You need TWO separate measurements to compare, much the same way you would need to take two separate compass bearings to compare using that method. So the trees method may not fit your needs, at least not in the non-infinite cases, if that’s your criteria of a single assessment of short duration.

>>In the first one, assuming that the E0-L1 line and the E1-L2 lines are parallel, then angle L1 is identical to the angle between E1-L1 and E1-L2 (i.e. that subtended by the first of your red lines). That angle also indicates how much the landmark has "fallen behind" the target boat as the target progressed from M0 to M1, yes?

So lines E0-L1 and E1-L2 are parallel only because M and E are set to collide, but yes.
I think if what you are saying is that angle E0-L1-E1 is congruent to angle L1-E1-L2, then yes.
Yes that angle ‘represents’ that distance traveled, but keep in mind it’s an angle not a distance. The red line distances are not equivalent to the amount of land or distances ‘made’ by the target boat in that given time span, but are proportional to it. The amount of land 'made' by the target is of course from the perspective of the observing vessel.


>>Keeping that in mind, consider the E0-L1-E1 triangle. We can use the law of sines to relate four things:

• initial bearing to landmark and target (angle E0)
• distance from observer to landmark (side E1-L1)
• change in the relative bearing of the landmark (angle L1)
• distance run by the observer in that time (side E0-E1)

You can, but not yet sure I see the point of the exercise in doing so. What are you trying to find here?

>>It looks like the initial bearing is about 137°
No idea where this number comes from, or why an absolute bearing measure is needed or relevant. You had actually set the heading of E at 000 and M at 0016 I believe in your original diagram, so I tried to follow that closely, and the bearing difference here I think is 15 degrees, but even that isn’t really relevant unless you want to calc some number specific to this scenario.

>>so what happens when the landmark is about 5 miles away, and the observer is moving at 6 knots? To simplify things, round up 5 miles to 10,000 meters, and 6 knots to 3 m/s. Over 5 seconds the boat will have moved 15 meters. So, we have sin(137°) / 10000 = sin(L1) / 15. Rearranging that you have sin(L1) = (15 * 0.68)/10000, or L1 = arcsin(0.001) = 0.059°. That's a pretty small number!

You can come up with any scenario you like, but again you’re going to need to have separate measurements of apparent distance traveled over the same time span or length of time to compare anything in these cases. A single measurement of any time span isn’t helpful for non-infinite cases. 5 miles is not anywhere close to functionally infinite, unless you’re not moving at all. And if that time span you do select is very small, like 5 seconds, it’s not going to work in most non-infinite cases. That would be like taking two compass bearings on the target only 5 seconds apart. It’s not likely going to be helpful.
What I will say is that if that displacement angle, such as L1-E1-L2, gets below around 0.9 degrees or so, it’s not really practical to measure the apparent distance anymore. You’d need to have a greater time span between measurements, or drive faster, so the angle gets above that level to get a measured ‘distance travelled’ measurement above a centimeter at arm’s length. In fig 1 I think that angle was 5.3 degrees if I remember right, which is more than enough.

>>If we consider each square on your graph paper to be 3 meters on a side (i.e. side E0-E1 is still 15 meters), then landmark L1 is only 105 meters from the observer at E1. Doing a similar calculation as before, sin(L1) = (15 * 0.68)/105, we get L1 to be 5.6°. I think if you drop a protractor over the sketch you'll get something reasonably close.
What does this mean? On the scale of your sketch, the landmark will have fallen behind by about 3 fingers whilst the target remains on a fixed bearing. If you observed for 10 seconds, or even 20, the change would be quite obvious: the target would clearly be making trees. The problem here is that 105 meters is really, really close, and a standard sheet of graph paper isn't going to be large enough to draw a decent triangle when one side is 1000x the length of another.

Definitely not correct on the distances here as mentioned in the last response, they are way off. So I can’t speak to the rest of those calcs.

[Ronny170]

Originally Posted by requiem

Using 185 m for the block of 5 cells means that at 6 knots the time between the observations is about 1 minute.

Yes, and that was also taken from your original diagram and initial conditions that you set. My diagram was merely a close rendition of the conditions you had originally asked about in yours.

[smarquis]

Originally Posted by danstanford

This is what I have always done. Done before one can take any other steps to get started.

Pilots are trained to do the same thing in their planes, and there are generally no trees behind the planes that may be on a collision course. Pretty easy to see the other plane is at 3:00, and note whether it stays at 3:00. Might be slightly easier if your boat has vertical components to help determine if the other boat stays at 3:00, but it is hardly necessary. It is often far more difficult to see the other airplane to begin with (even with radar), and it is sometimes difficult to find the other plane a second time, but it is not hard to tell whether you are close enough to being on a collision course that you should change some aspect of your speed, course or altitude.

It seems to me that all of this talk about trees misses the point, and could cause confusion on a relatively simple analysis. If the other boat stays at the same clock reference (or anywhere close to it), then slow down, speed up, or make a minor change in course. Fortunately, boats are not generally required to maintain specific vectors, so you don't need to fight with air traffic control to make a change to ensure you are in no danger of collision.

[thinwater]

[QUOTE=smarquis;3797044... If the other boat stays at the same clock reference (or anywhere close to it), then slow down, speed up, or make a minor change in course....[/QUOTE]


The other thing worth mentioning is that the course change should be ...

• Early. Should be well outside the minimum collision avoidance zone.
• Significant. A large enough change that the other sailor can see it and not mistake it for a momentary wind shift adjustment.
• Consistent with COLREGS. Preferable, you are the give way boat giving way in the expected manner. For example, if you are the stand on boat in a crossing and decide turn to starboard, this is confusing to the other boat if their give way turn is to port (your turn combined with their turn will put you head-to-head, not avoiding).

[s/v Jedi]

Commercial shipping all use collision alarms and have company-wide instructions for the settings. When you observe AIS you can see this. Example: Carnival cruise liners have a 1.7nm range setting for generating an alarm. When you are on a collision course at 2nm range they do nothing but at soon as it is 1.7nm you see a minor correction to stay out of their allowed CPA.

I have seen others (freighters) have the range set at only 1nm.

When coming from opposite directions like in a channel or around a point etc. I always like to acknowledge a port-to-port correction from the other (like a 5 degree course change to starboard) with my own 5 degree course change to starboard. You can count on the other side noticing this.

One thing that can confuse them is when your speed or course changes due to wind conditions. I have had cases where we slow down when the wind comes down and a ship needs to correct more and more to cross our stern. I could imagine they wished to have chosen to cross our bow instead but in the cases where ai called them they were just delighted to see us and talk with us