You can judge the possibility of a collision course with a simple method. Certainly you can "fly by the seat of your pants" but when out on open water or crossing a busy channel you can apply this simple "formula".
In this first scenario you, the kayaker, are crossing a channel, and a tugboat is coming down the channel, at 90 degrees. You are not sure how fast the vessel is going, or exactly how far away it is. These things are hard to judge when on the water, particularly from the seat of a kayak. You do not have to know your speed or his, but for the sake of example let us say that you are going at 3 knots and the tugboat is going at 5 knots. (This works with MPH too, so use that if it is better for you. 1 knot = 1.15 MPH.)
The first thing to do is to maintain your course and heading. (We can assume the captain of the tug will too.) Take note of the angle his boat is at in comparison to yours. Use an "O'clock", like 2 O'clock, or 11 O'clock with your bow being "noon". At your first check the larger boat is at 2 O'clock, or 60 degrees.
Paddle a way more, maintaining your course and heading. (Chances are you have not been spotted by the captain, and he is too.) After a minute or so you take a second check. While the distance between you and the powerboat has closed, the tug is still at 2 O'clock.
Keep your course and check again after a minute or so. That boat is still at 2 O'clock! What this means is that as the space closes between the two boats, and assuming that each boat keeps it heading and speed the two will collide at the intersection of their course lines.
So in this scenario you had better wait at the 3rd check with a full stop or turn to a different heading and or speed.
In this second scenario I will demonstrate a "miss". Once again you, the kayaker, are crossing a channel, and a pleasure boat is coming down the channel, at 90 degrees. You do not need to know any speeds, but lets say that you paddle at 3 knots, and the pleasure boat is traveling at 15 knots, both boats holding a straight course.
At your first check you note that the pleasure boat is between 1 and 2 O'clock, let's call it 45 degrees. The next check, after a couple minutes, it is about 1 O'clock, 35 degrees. You decide to take a 3rd check after a couple more minutes and the boat is at 20 degrees.
A pattern of steady decrease of the angle is indicating that the pleasure boat will pass in front of you, assuming that both vessels maintain their speed and heading. You can maintain your course with out breaking stride, knowing that a collision will not happen.
If a larger boat were coming from the left, spotted first at 9 O'clock, then 10 O'clock, and at 11 O'clock, the angle would again be decreasing, or moving towards noon, indicating a pass in front of the kayaker.
If the powerboat had been spotted at 1 O'clock on the first check, 2 O'clock on the 2nd check and then at 3 O'clock at the last check that will indicate a pass behind the kayaker. The angle is increasing and moving away from "noon".
If the angle does not change then trouble is likely brewing.
This formula also works when the paths of the vessels are not at 90 degrees. In fact it can work at any angle, theoretically, but the closer to 90 degrees the more applicable this formula is and more likely to be needed and useful.
This 3rd scenario is a likely encounter in open water. A larger, faster boat, say a freighter heading to a harbor mouth, is approaching you, the kayaker, from the right, at an angle.
need to know any speeds, but lets say that you paddle at 3 knots, and
the freighter is traveling at 12 knots, both of you holding a straight
course and maintaining your speed.
On your first look the freighter is at 63 degrees. On your 2nd look the freighter is at 56 degrees. The 3rd look is 48, 4th is 36 and so on. This steady decrease in angle, or movement to "noon" indicates that the freighter will pass in front of the kayaker.
Sometimes the judgment is hard to make. It can be difficult to determine if a collision is immanent. In this final scenario you are once again in an open water situation. A sailboat is approaching from the right at an angle, and you are paddling at 3 knots while they are sailing along at 9 knots. Lets also assume that it seems unlikely the sailboat will change tack.
The diagram indicates that the first 3 checks of the angle are all about the same, between 1 and 2 O'clock. The wise thing to do once you realize this is to wait, or change course and/or speed.
If we are to follow this out to the end, "play chicken" so to speak, we see that eventually the angle decreases with the sailboat passing in front of the kayak, but far too close for comfort. If it had been a much larger vessel you are likely to get a rocking on the wake, maybe even a horn blast from an angry captain!
You can see here how this formula is harder to use when the paths are less than square with each other, but still can be useful in making a judgment call even if erred to the side of caution.
For the most part what I have described here is all "common sense", but when you are new to kayaking, or paddling an unfamiliar area with the distractions of a busy harbor or channel you can loose sight of your common sense.
Practice and familiarity with your chart(s) and regular use of the "collision course formula" will help you apply these nuggets of nautical wisdom and increase your over all seamanship.
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