Horror stories about people's experience crossing the Gulf Stream are common. I too have had a rough crossing, and the experience made me think very carefully about how to do it better.
My advice comes in two forms. First, a few pieces of broad advice. Second, a more detailed mathematical analysis of the best way to cross a current, and how to deal with various scenarios.
You can play with the mathematical model now if you like, and you can read about the mathematics behind what appears here, although it may be easier to understand these after you've read what appears below.
Some of the points made below are self-evident, at least in hindsight, but they bear repeating. Also, my reading indicates that various sources of advice do not state these points with the strength or directness they deserve.
This advice is given from the perspective of crossing between Florida and the Bahamas, which is the most common reason to cross the Gulf Stream. Also, it is aimed primarily at sailors, who have slower boats. If you have a fast power boat, then this is still good advice, but you'll have a bit more wiggle room if you must violate it.
As a mathematician, I couldn't resist a deeper look into the possibilities. I was surprised to learn that the question of how to optimally cross a current is difficult to answer in the general case. Suffice to say that Ernst Zermelo, a famous mathematician, whose work in the early 1900s forms the foundation of modern set theory, found the problem interesting enough to study the topic.
One might object that this kind of mathematical optimization is a complicated waste of time. If you are always able to follow the first bit of "Broad Advice" above (get far enough south), and if nothing unexpected happens (a huge assumption), then it's true: this is pointless wheel-spinning. But, if it is necessary to go upstream for some reason, or if conditions in the Stream are not as expected, then it's helpful to understand the trade-offs. When waves are crashing over the bow, this kind of analysis doesn't seem so "dry."
In any case, it's crucial to bear in mind that every boat responds differently and that the scenarios considered here are idealized. Perhaps the biggest shortcoming of what is done here is that wind and wave action are not considered at all, nor are the idiosyncrasies of any particular boat. A small change in a boat's heading relative to the wind or waves can make a huge difference in how it behaves. Finally, even though this was written primarily for sailboats, the boat is assumed to be motoring; if the sails are being used, it is assumed that this use doesn't restrict the possible heading or affect the speed of the boat.
The discussion begins with a couple of "dumb ideas" about how to cross the Stream and gets increasingly more realistic. Every example is presented as though the boat is traveling from west to east (i.e., from Florida to the Bahamas) since the Bahamas is a much smaller target. There are links at the top of the page where you can read more about the mathematics or modify the input scenarios.
To begin with, assume that you are always traveling in the Stream, and that the current is constant over the entire width. Later, more realistic scenarios are considered, but this simpler case helps to get a feel for the situation. Assume that the stream is 40 miles wide, that the current is a constant 2.5 knots, and that the destination is directly across the Stream at the same latitude. So, from the moment of departure to the moment of arrival, the boat is subject to a current of 2.5 knots flowing to the north.
The boat is assumed to travel at 5 knots. If there were no current, then it would take 8 hours at 5 knots to travel a distance of 40 miles.
To start off in seeing how things might go, suppose that your heading is always set to point to the destination. If a dog wants to fetch a stick that's been thrown to the far bank across a river, then the dog will continually swim in the direction of the stick, even as he is swept downstream — unless he's a very smart dog. If you keep your eyes on the chartplotter and always steer so that the bow points directly at the destination, then you're doing the same thing. I hope nobody tries this, but it's a place to begin the analysis, and it demonstrates what may happen.
The graph below shows the result. Think of the current as flowing up in the graph, from smaller y-values to larger y-values. As the boat travels across the Stream, the heading begins by pointing directly east (positive x-direction). As the current sweeps the boat further downstream, the heading gradually turns from east to south. At the very end of the journey, the heading will point almost directly south as the boat is fighting the current almost head-on, and the amount of time taken rises steeply.
The postion is graphed relative to the left y-axis, and when the boat reaches a point about 27 miles across the Stream, it has been swept downstream by a bit more than 7.50 miles. The cumulative time required is graphed relative to the right y-axis. So, the Dog Paddle strategy takes 10.67 hours to make the crossing, compared with 8 hours if there were no current.
Now suppose that you follow a straight line from start-point to end-point. This requires steering somewhat into the current so as to go in a straight line. If you blindly punch your destination into an autopilot, then forget about any further navigation, then this scenario is likely to be what occurs (depending on your autopilot).
Because both the position and the time taken follow a straight line, there's no need to show a graph in this case. The total time taken is 9.24 hours, which is much better than the 10.67 hours needed by the Dog Paddle strategy. In the constant current scenario being considered, this is the optimal strategy. So, it's not a "dumb idea" in this unrealistic scenario, but as the situation is taken to be more realistic it will become less attractive.
When considering the Straight Line strategy, it is important to bear in mind that this strategy is not always possible. To stay on the line, the boat must fight the current, and if the current is too fast, then it can't be done. If the best a boat can do is five knots, but the current is flowing at six knots, then maintaining a straight line course perpendicular to the current is impossible.
The graph below shows what happens when following a Straight Line course directly across a 10 mile wide current which flows at 4 knots over the entire width. The center of the Gulf Stream is not so different from this.
A boat that can make 5 knots takes 3.33 hours to cross the current in a straight line, and a 10 knot boat can cross the current in 1.09 hours. For the 10 knot boat, that's almost as good as if there were no current at all. However, as the boat's speed decreases, the time taken to cross rises dramatically. If the boat loses only half a knot so that the best it can do is 4.5 knots, then it takes 4.85 hours instead of 3.33, and it only gets worse from there. At some point, as a boat's speed decreases, fighting the current to stay on a predetermined course is a huge mistake.
Assume that the far edge of the stream has no current. That is, once you're reached the far edge, you can travel directly up or down to the destination at full speed. This "edge" is taken to have zero width; the current has an effect for the entire width, but as soon as you've travelled as far east as necessary, you can go directly north or south with no effect from the current. This small modification bears some similarity to reality since the last few miles near the Bahamas often have minimal current, and it's easy to understand.
The Dog Paddle and Straight Line strategies considered above result in the same outcome in this scenario. Both the dog and a boat travelling in a straight line reach the destination at the moment when the current changes to zero. So there's no need to discuss those strategies any further for this scenario.
Take the boat straight across the current, getting swept downstream, then travel to the destination along the edge, where the current has no effect. This is easy to analyze. It takes 8 hours to cross the Stream (distance of 40 miles at 5 knots), but the boat is swept downstream by 20 miles (8 hours at 2.5 knots). It takes 4 hours to travel these 20 miles along the edge to the destination, for a total of 12 hours.
This scenario assumes something physically impossible: that the current instantaneously disappears as the reaches the far edge. But it brings out the important trade-off. To what extent does it make sense to allow the boat to be swept downstream? In the extreme case of a boat which is slower than the current, there is no choice but to be swept downstream. For a faster boat, the question is how much to allow. Both the Dog Paddle strategy and the Straight Across strategy accept being swept downstream by quite a lot — too much in most cases — and the Straight Line strategy avoids being swept downstream at all. Maybe the best strategy is somewhere in between.
Under the Intermediate Heading strategy, follow a straight line course across the current to a point of your own choosing, then reach the destination by traveling along the edge, out of the current. Choose the point where the boat emerges on the edge so that the total time taken is at a minimum.
To make the trade-off more apparent, change the scenario so that the destination is now 20 miles upstream. Up to now, the destination has been taken to be at the same latutude as the starting point. Continue to assume that the current is 2.5 knots over a 40 mile width and that the boat travels at 5 knots. With the destination 20 miles upstream, the graph below shows the total time taken versus the point at which the boat emerges from the current.
This shows that to reach a point 20 miles upstream, the optimal strategy is to steer for a point that is only 8.90 miles upstream, then travel the remaining distance on the edge, outside the current. That is, don't fight the current too much. This strategy takes 12.94 hours, while taking a straight line direct to the destination takes 13.33 hours. The difference is not large, amounting to only about 3% of the total time, but it becomes larger as the current grows (or the boat gets slower). Also, it is interesting to note that the curve is relatively flat at the minimum. That is, although it is fastest to emerge 8.90 miles upstream, a couple of miles either way makes very little difference.
For comparison, the graphs below show the Dog Paddle, Straight Line and Intermediate Heading strategies under the scenario where the destination is 20 miles upstream with calm water on the far edge (and the current remains at 2.5 knots over a 40 mile distance with a 5 knot boat). If there were no current, the journey would take 8.94 hours since the total distance is 44.72 miles (\( \sqrt{40^2 + 20^2} \)). The Straight Across strategy is not shown since the boat is swept so far downstream that it would make the graph hard to read; it would take 8 hours to cross the stream, getting swept down by 20 miles, then another 8 hours to travel 40 miles up the calm edge for a total of 16 hours.
The Intermediate Heading Strategy follows a course that is (mostly) in between the Dog Paddle course, which gets swept far down stream, and the Straight Line course, which is never swept down stream. The graph below compares the time required for each strategy. The best is the Intermediate Heading strategy, which takes 12.94 hours, followed by the Straight Line strategy, at 13.33 hours, and the Dog Paddle takes 14.59 hours. As noted above, the Straight Across strategy takes 16 hours, and if there were no current, then the trip would take 8.94 hours.
It's time to consider a more realistic scenario. Assume that the current is as shown below. This is roughly similar to the situation one would face if crossing from Lake Worth or Fort Lauderdale to West End on Grand Bahama. As one departs, there would be 5 miles without any current, then 10 miles with a two knot current, 10 miles with a three knot current, etc. The actual situation could be entirely different, but this is a reasonable approximation to the average.
Each of the strategies considered above may be applied in this more realistic scenario, with one change. The Intermediate Heading strategy no longer makes sense since there is no "calm edge." Instead, use the next strategy.
Under this strategy, choose a heading to bring the boat directly to the destination. This is the most commonly given advice for crossing the Gulf Stream. The idea is to choose a single heading, after adjusting it for the expected total amount you will be swept downstream by the current, taking into account your boat's speed and the average magnitude of the current. Typically, the advice is to assume 2.0 to 2.5 knots of current, on average, over a distance of 40 to 60 miles. As we will see, this is good advice. If your destination is significantly downstream, then this course is optimal or nearly optimal. If the destination is slightly upstream, or slightly downstream, then it's still good advice, although it becomes an increasingly bad strategy the further upstream you need to go (or the slower your boat).
Another new strategy is to follow a Dynamic Heading. Under this strategy, the course is allowed to vary throughout the journey to be optimal. Assuming perfect knowledge of the current and your boat's behavior, this is the best that one can do. Because the scenario being considered divides the Stream into strips, with a fixed current in any given strip, the Dynamic Heading will be one in which each of these strips is crossed in a straight line. The angle of these lines will vary as the boat moves from strip to strip, but each leg will be a straight line.
In practice, attaining a fully optimal solution is impossible. As the boat moves along, there's no easy way to know exactly what the current is at any time, it may not set exactly north/south, and you can't know exactly how the current will behave for the remainder of the crossing until you've done it. But it's worth examining how much this unattainable optimum is from something like the Constant Heading strategy. Moreover, when traveling under the Constant Heading strategy, this examination helps to see how one might tweak the heading as the trip proceeds.
If the strategies considered are applied to this more realistic scenario, then we have the following. The boat is still assumed to travel at 5 knots and the destination is at the same latitude as the starting point.
The graph above shows the boat's position, and the graph below shows the cumulative time taken.
Although the four strategies vary a great deal in the path taken by the boat, the variation in time taken is not as large as a comparison of these paths might indicate. The Straight Line is the worst, at 14.54 hours, followed by the Dog Paddle, at 13.72 hours. The Constant Heading and Dynamic Heading strategies take almost the same amount of time: 13.20 hours for the Constant Heading, and 13.18 hours for the Dynamic Heading. The spread from the best strategy to the worst is about an hour and twenty minutes, or roughly 10%.
Given that the Constant Heading strategy differs from the Dynamic Heading by only a minute or two, and the fact that it's a much easier strategy to implement, it's clear that following a Constant Heading should be the default. Also, in practice, it would be impossible to pilot the boat with the level of precision demanded by the Dynamic Heading strategy, even if you had perfect knowledge of the boat and current speeds. The Constant Heading strategy steers 25.6° south of due east for the entire trip, and the dynamic heading varies from 20.4° to 29.2°. Consistently keeping course deviations below 5° is not easy. Incidentally, the headings used when following a straight line max out at 53° in the center of the Stream!
If your journey starts well upstream of the destination (20 miles or more, depending on your boat's speed), then there's not much you can do to improve the route if conditions worsen. You already made the smartest decision by starting upstream, and continuing on a directly east/west course remains the best choice. But people do often start from Lake Worth, headed to West End; or from Miami, headed to Bimini. Now, what if conditions worsen?
Obviously, things can "go wrong" in many ways, but one likely possibility is that conditions become increasingly rough and turbulent, slowing the boat down. You no longer have the 5 knot boat you planned for; instead, you're struggling to make 3 knots. Should you soldier on with the original plan, or change course?
Assume that you start out 5 miles north of the destination (as you would when going from Lake Worth to West End), and that you began the trip assuming a speed of 5 knots throughout. Using the Constant Heading strategy, and the "realistic" current assumptions above, the correct heading is 29.3° south of east, and the trip should take 13.76 hours, assuming that all goes well. Suppose that conditions become increasingly turbulent, slowing the boat down so that when you're 10 miles out, where the current speed increases to 3 knots, you realize that the boat is only making 4 knots. You don't expect things to get any better until you come out the other side, and you're willing to assume that the boat's speed will drop to 3 knots when the current is at 4 knots, then rise back up to 4 knots in the next strip, then return to 5 knots once the current is 2 knots or less. Since you're only 10 miles east of the departure point, it may be smartest to turn around, but what if you decide to continue?
After 2.29 hours, the boat's speed dropped to 4 knots when you're 10 miles across. Assuming that things went as expected up to this point, the boat would be 3.32 miles south of the departure point, or 1.68 miles north of the destination. If you continue with the same heading, even though the boat is slower, it will take an 14.14 additional hours, and you will emerge 12.87 miles north of the destination. So the trip would take 16.44 hours, plus the time necessary to get all the way south to your destination. If you "cut the corner" near the end, in the 10 mile wide strip of calm water, then the trip takes a total of 18.35 hours. That's what happens if you stick with the original plan.
Realizing that the boat has slowed down, and feeling some nervousness about the way the boat is being swept further north, you may think that changing the heading to point a bit more south is prudent. In other words, you want to follow a constant heading from your current position to the destination, taking into account that the boat is slower than originally expected. The correct heading, from a point 10 miles east and 3.32 miles south of the starting point is 40.7° south of due east, a difference of more than 10° relative to the prior heading. The entire trip would then take 18.56 hours, which is worse than continuing with the original plan. This is a bad idea. Once the boat is in the strongest part of the current, you should not turn more directly into it. Not only does it take longer, but you will spend more time in the roughest part of the Stream.
The theoretically optimal strategy would take an additional 15.26 hours from the point 10 miles across, for a total of 17.56 hours. The optimal headings are roughly 27° in the two strips with 3 knots of current (about the same as the original plan), but only 18° where the current is greatest, and the headings in the remaining strips increase to make up the distance lost, to 38°, 45° and 55°. The smart thing to do is to get across the current quickly. It takes less time overall, and you'll spend less time in the area of highest risk.
Obviously, this is only one scenario out of an infinite number, and it's been heavily idealized. If the Gulf Stream is not as assumed above, or the boat behaves differently, then the best course might be entirely different. All you can do is plan based on your best estimates, bearing in mind that they are estimates.