# Simple compromise

What is the best navigational approach to crossing an ocean current? This question is perhaps best asked of the most famous of ocean currents, the Gulf Stream. The stream’s high speed and predictable path in the Straits of Florida makes the Florida to Bahamas crossing a classic example of how to deal with current set and drift.

The problem, of course, is that the Gulf Stream, like other ocean currents, as well as rivers and tidal currents, does not allow a vessel to head for its destination but requires some offset in course to account for the current. If the velocity of the current remained constant as the vessel progressed, the optimum solution would be fairly simple. Unfortunately, the velocity of the current is very lowessentially zeroat each shore and increases to a maximum velocity more or less in the middle of the stream. This changing velocity in the ocean current is the crux of our problem.

Consider a passage from Miami to Ocean Cay located on the west side of the Great Bahamas Bank. The stream has a velocity of roughly zero at both the Florida shorethere might even be a southward-flowing countercurrentand at Ocean Cay. It reaches an average maximum of roughly 3.5 knots just west of the stream axisat maximum the stream can get up to five knots. That maximum is based on my observations during some 50 crossings made over 25 years.

Worst way to cross

Let’s take the case of the sailor who, on leaving Miami, plans to set his vessel on autopilot. The machine will sail a constant bearing to his destination. As we shall see, this is the worst way to cross the stream!

We’ll assume that his destination is Ocean Cay because that is a frequent mark for ocean racing. Let’s also assume that he will either sail or motor at 5.5 knots. Initially he will make good progress toward his destination (see figure 1 above), since close to the shore the current is very slight. But as the vessel proceeds eastward, the autopilot will require it to turn right more and more.

At the center of the stream the vessel will be wasting most of its speed just to “stem the current.” Indeed, if it were a slower boat that could only make five knots on a day when the stream reached five knots, then he could never cross the stream using this strategy. He would remain in the center of the stream, headed directly into the current in order to maintain constant bearing to his waypoint. Admittedly, the stream velocity does not always reach five knots, and most vessels are faster than that anyway, so we are not talking about an inability to cross the stream. What is important is finding the best way to cross in the minimum time.Best way to crossLet’s move from this worst strategy to better approaches. I learned how to cross the stream in a slow boat by racing the SORC for many years as navigator for one of the world’s best sailors, Lowell North. Actually we had a fast boatit’s just that all sailboats are slow in light air. Lowell liked to win, and to win it’s always best to sail the fastest course. My job was to calculate that fastest or optimum course. To do this, I developed a computer program that approximated the solution by brute force. This program changed the shape of the crossing curve in small increments until a minimum crossing time was found.As input to the analysis, I had data from my prior crossings of the stream. Of course, we had some expectation of what the wind would be and some knowledge of how our boat responded in various wind speeds and directions. This amounted to quite a few assumptions, but with these it was possible to calculate in advance the optimum course. It was always similar to the sinuous course shown in the accompanying diagram.

In the specific example given in figure 2, the sinuous course shortens the crossing compared with the worst way to cross (using destination as a waypoint). Compared with the simple compromise of setting a fixed heading (described in the next section) the savings amount to roughly 57 minutes.

Note that this best strategy is exactly the opposite of the worst strategy. Of course, while heading directly across the strongest current, the boat will be set far off course in this strong current. Therefore, to make up for this, a course into the current must be taken at each shore. The computer analysis and logic show that sharp changes in course are not fast; hence the resulting sinuous course.

I have observed maximum stream speeds of up to 5.4 knots. However, it seems that, over the years, although the distribution of speed with position changes, the total volume of water and the average stream velocity remain fairly stable. An average drift is 2.4 knots. While the principle of the best strategy is simple enough, it is apparent that its execution requires resources not available to most sailors. Therefore, we next come to the simple compromise.Simple compromise The simple compromise illustrated in figure 3 is merely what we all did anyway before the advent of electronic navigation. Estimate the average current of the stream and your average boat speed; then work out the vector diagram on paper. From this you get a fixed heading which will take you to the mark, provided that your assumptions of average current and boat speed are reasonably good. Forget the waypoints and realize that you are going to be far off the rhumb line for most of the passage, first to one side, then to the other side. Just do a good job of steering your fixed heading and you will come close enough to your destination for small corrections at the end.

To do this, you have to have confidence in your steering compass so that you can steer the fixed headingif not, then all bets are off, for an electronically derived course over ground (COG) is of no help.Seaman’s eye compromise

I like the simple compromise as a very great improvement over the worst way to cross. However, several of my sailing friends feel that they would prefer to approximate the best strategy by a “zee path.” This is sort of a seaman’s eye estimate in which the initial leg of the zee while near shore is headed fairly sharply into the direction of the current.

As the current begins to build as measured, for example, by the difference in COG and boat speed, the course is changed to head sharply across the stream. Heading perpendicular would be okay, but heading, say, 12° into the current makes, as we have seen, a faster crossing. As in the best and simple crossings, the boat will be swept downstream across the original rhumb line and beyond. Don’t worry; it has to be that way for a fast passage.

Finally, as the stream velocity begins to diminish, the navigator can begin to do what the skipper and crew probably wanted to do from the beginning: namely, look at the GPS bearing to the destination and begin steering for it.

Thus far we have been considering the problem of current crossing when the destination is approximately directly across the current or somewhat upstream of the origin. After all, that is the challenging situation because a slow boat, such as a sailing vessel in light air, might have difficulty getting across.

What if we were sailing from, say, Marathon, Fla., to Great Isaac, Great Bahamas Bank? In that case, we might think that the strategy would change, but it does not. It is true that, as the current will actually be assisting our passage, the objective is to get into the current as soon as possible and to stay there as long as possible. The optimum path is, however, still a sinuous curve. The initial and final courses are approximately perpendicular to shore, perhaps 12° downstream, so as to get out of the slow-moving water as soon as possible. Otherwise, the optimum or sinuous course appears very similar in shape to that of figure 2. The curve is simply rotated toward the downstream destination.

In crossing ocean currents, the rhumb line is not fast. Although, unfortunately, it is very hard to get everyone onboard to be happy when the boat is far from the rhumb lineand getting farther awaynevertheless, if the navigator sticks to the principles outlined here, the passage will be faster than any rhumb line passage.

Nils L. Muench, a former naval officer, has raced in the Sardinia Cup, the Admiral’s Cup, the Fastnet, the Maxi Boat World Championships and the Newport/Bermuda Race. He has raced his own one-tonner Moonraker in 22 Chicago/Mackinac Races.