Tag: Gulf stream

We are in Stuart, FL and will move down to Lake Worth tomorrow to stage for crossing the Gulf Stream on Friday, headed to the Bahamas. This will be crossing number ten or so, but I really do not feel I have a tactic to make the best of the Stream’s current.

(edit: I first released this on 9 Nov. just after the crossing. Then realized maybe doing math after no sleep is not a good idea. So if you read this yesterday and had some issues with the math, I apologize. Hopefully my edits have corrected the math errors)

On the sailboat we were usually between New England and the Caribbean and the Stream was just a small distraction on a 1500 mile trip. Our tactic was to cross at right angles to the current and just maintain our general heading. The current would set us twenty miles or so, one way or the other. By the time we exited, we would just adjust our heading by a degree or two and keep on sailing. The word was, do not crab into the stream.

But sitting here in Florida, and wanting to go to Bimini, for example, the problem is a little different. I don’t really want to get set twenty miles north on a sixty mile trip. And I don’t want to run all the way down to the Keys, just to get a better angle. So I have been wondering just what is the most efficient method of crossing the Stream.

In central and southern Florida the Stream is about forty miles wide and has current from 2-4 knots, averaging 2.5 knots for the forty miles. A little internet searching will bring up as many tactics as there are sailors, but one can winnow those tactics down to just a few.

The first approach is to go south on the Florida coast in order to improve the angle, say Angelfish Creek to Bimini. This approach does provide a relatively quick, day hop, and if your goal is shortest possible time on the passage, this works. But proponents of this approach tend to forget about the days spent moving down the Florida coast, not to mention the pain of all the bridges if you do the trip inside on the ICW.

For the other approaches, lets use a trip from Lake Worth inlet to West End, Bahamas. About fifty-five miles on a bearing of 95 degrees. The Explorer Charts recommend the classic navigation technique of calculating the required offset for the current and then setting a heading to accommodate that offset. See below.

Assuming one holds a constant heading, this tactic will generate a ground track roughly “S” shaped as the current first increases then decreases during the trip. Not sure why they say, “Dont angle into the current” because that is just what you are doing here.

This approach has lead to some folks suggesting sailing a purposefull “S” track. Proponents of this tactic suggest leaving Lake Worth and turning SE even further than necessary to hold the rhumb line. Getting ahead of the current, so to speak.

Waterway Guide provides headings for various boat speeds and destinations, essentially the same as the Explorer chart Again, holding a constant heading to counteract the average current will produce an “s” curve track.

Then there is what the old salts told me way back in my sailing days. And that was to take up a heading perpendicular to the stream and let the stream set you. Then angle back to your destination once clear. This does have the advantage of getting you out of the stream the fastest, even if it does drop you off fifteen miles north of your desired track.

Finally, there is the approach of letting the autopilot carry you across the stream exactly on the rhumb line. This approach will get you across the stream in the shortest distance, as compared to the previous, shortest time approach.

As an aside, think about what would happen if boat speed were four knots and if the Stream were four knots. If you let the autopilot drive, you will stand still, with speed through the water of four knots and speed made good of ZERO! On the other hand, if you took the perpendicular heading approach, you would still get across the stream, albeit far from your intended destination.

So what is the modern mariner to do! Time for a little math. Using a speed through the water of 8 knots and a current of 2.5 knots for a distance of 40 miles, I would estimate about 12 miles of drift north. That would require an 11 degree offset and reduce my velocity made good (VMG) by one knot. That would increase my time by 45 minutes or so.

Alternatively, I could cross at 8 knots by not crabbing, then come back south 12 miles, which would increase my time by 1.5 hrs.

In the final analysis, all of the options fall in between those two options; the “S” curve approach is a compromise between the shortest time and shortest distance approach.

I plotted a course across the Gulf Stream and estimated the speed of the current every 5 miles. Here is my slice across the Stream, crossing from Lake Worth to West End

And then I built a table of headings and speeds for each 5 mile segment of the trip.

NM		0	5	10	15	20	25	30	35	40
Leg		0	5	5	5	5	5	5	5	5
Knots		1	2	2.5	3	2	2	2	1.5	1
Course		95	95	95	95	95	95	95	95	95
STW		8	8	8	8	8	8	8	8	8
HDG		102	109	113	117	109	109	109	106	102
Corr.		7	14	18	22	14	14	14	11	7
SOG		7.7	7.5	7	7	7.5	7.5	7.5	7.5	7.7
Hrs1		0	0.6	0.6	0.6	0.6	0.6	0.6	0.6	0.6
Hrs2		0	0.7	0.7	0.7	0.7	0.7	0.7	0.7	0.6
Set (NM)		0	1.3	1.6	1.9	1.3	1.3	1.3	0.9	0.6

If this is accurate, it should take me 5 hours, 45 minutes to cross, versus the 5 hrs with no current. Frankly, I doubt we will do this well.

My plan is to capture our actual headings and ground speeds every 5 miles and compare them to the calculated values.

My hypothesis is that the fastest way to get from point A to point B, in the presence of current is the shortest distance route, not the shortest time route. And that means running the rhumb line. The easiest way to run the rhumb line is to let the autopilot drive the boat, so that is what I will do.

Note that our ultimate destination is Palm Cay on New Providence. So the full question gets a bit more complex. The route we will take, crossing the stream at right angles, results in a total distance to our destination of 201 nm. If we were to go by the most direct route, the course would cross the stream on a course of about 125 degrees, angling into the stream. So the bigger question becomes: is it better to cross at right angles to the stream, even if that takes you out of your way. In this case, 10 miles out of your way.

I will update the blog after our crossing. We will do the 40 mile test run, then turn south and run overnight to Palm Cay marina, so give me a few days to do the data analysis.

Part 2 Trip complete:

Good news is, the trip was great. Stream was smooth and for the rest of the trip the water was like glass. And a 3/4 moon to boot. So how did all the calculations work out? Below is a table that shows the calculated GS current and the actual current derived mathematically from my actual headings and SOG. (speed over ground). (Best I can do to get all the numbers on the chart)

Miles		0.0	5.0	10.0	15.0	20.0	25.0	30.0	35.0	40.0
Leg		0.0	5.0	5.0	5.0	5.0	5.0	5.0	5.0	5.0
Estimated current		1.0	2.0	2.5	3.0	2.0	2.0	2.0	1.5	1.0
Course		95.0	95.0	95.0	95.0	95.0	95.0	95.0	95.0	95.0
Speed Through Water		8.0	8.0	8.0	8.0	8.0	8.0	8.0	8.0	8.0
Estimated Heading		102.0	109.0	113.0	117.0	109.0	109.0	109.0	106.0	102.0
Estimated Speed Over Ground		7.7	7.5	7.0	7.0	7.5	7.5	7.5	7.5	7.7
Set		0.0	1.3	1.6	1.9	1.3	1.3	1.3	0.9	0.6
Actual Heading		110.0	116.0	115.0	116.0	109.0	103.0	102.0	101.0	100.0
Actual Speed Over Ground		7.7	7.5	7.5	7.5	7.7	7.8	7.8	7.9	7.9
Actual Current		2.0	2.7	2.6	2.7	2.0	1.5	1.0	1.0	1.0

As you can see, the actual current in the Stream was a bit less than calculated, so our speeds were better than planned. With a no-current crossing time of 5 hours, and an estimated crossing time of 5hours, 45 minutes with the calculated current, our crossing time was 5 hours, 25 minutes. Our total time for the 201 mile trip was 25.5 hours, exactly as predicted, which means we were slower than 8 knots for the portion of the trip once we exited the stream.

Now lets compare this to the direct route. The no-current total time for the 191 miles at 8 knots would be 23.9 hours. At a 125 degree heading across the stream we would be in the Stream for 50 miles at an average speed of 6 knots. At that speed and distance it would take us 8.33 hours to cross the stream. We would complete the remaining 141 miles at 8 knots in 17.6 hrs for a total time of 26 hrs, all that using the original calculated estimate of Gulf Stream current.

However!! The stream was not as strong as estimated. If we use the actual stream data calculated from our actual trip, then the direct route crossing would not have taken 8.33 hours but just 7.8 hours. And that would result in a total trip time of 25.5 hours. Exactly the same!

A brief note on geometry here. As angle A, in this case the angle between a route perpendicular to the current and one angling into the current, increases, the hypotenuse, in this case, the time/distance in the Stream, increases rapidly (geometrically, actually). So in our case, with a direct route angle of 122 degrees and the estimated current of 2.5 knots, it is better to take the perpendicular/shortest distance route. At the actual current of about 2.2 knots, the two trips are identical in time. At this angle, slower current favors the direct route and stronger current favors the perpendicular route. With lesser currents a larger angle of attack can be taken. With stronger current, say the more typical 3 knots, then the perpendicular route will be favored.

And a last note about boat speed. The slower the boat, the more favored the perpendicular route will be – up to a point. If your boat only goes 4 knots, and the current is 4 knots, take a plane. Just kidding, but in this whole experiment we used a constant 8 knots and variable angles of attack and current level. Varying boat speed leads to the same conclusion, the more time you spend in the stream, the larger the penalty.

With all this, my conclusion is: the fastest way to cross the Gulf Stream at typical current levels is to cross at right angles and crab into the current sufficiently to maintain a course perpendicular to the current. And the best way to accomplish that is to use a capable autopilot.

I understand the “S” curve idea, but I believe it is a hold over from when autopilots just held a course. Using old fashioned navigation skills to calculate a heading to counteract set and drift, a constant heading would result in an “S” curve track with the Gulf Stream current. But that does not make an “S” course efficient.

Of course this over-simplifies the problem. If you are trying to make a day hop of it, and want to check in at Bimini or West End, then you might need to pick and choose your departure point. Lake Worth works well for West End, Fort Lauderdale or Miami for Bimini. And the slower your boat the more you might need a lift from the stream to improve your ground speed. And finally, if the weather stinks in the stream, moving south in the meantime might improve things. But I wouldn’t waste time going to Miami for the angle if the weather was decent when I was still in Lake Worth.

Finally, a note on calculating speeds, angles and distances. The easiest and quickest way is with an old fashioned E6B flight computer, nowadays available on a computer or as a phone app. Using the tool you can quickly and easily test various alternatives and choose the best combination of launch point, course, etc. So, try this experiment yourself and see what you find.