Your log and compass readings are the starting points, but then there are many corrections and adjustments to make, not the least of which are tied to the strength and direction of the wind.
Strong persistent head winds bring a new twist to navigation that has a serious effect on DR if not accounted for. Three factors that don’t matter much in light air now matter a lot. These are wind-driven current, helm bias, and leeway. They are each fairly small effects, even in strong winds, but they all cause error in the same direction, so their sum is not small. They cause navigational error because they are invisible—they take us off course and we have no way of knowing it (without GPS) until the next position fix. In short, we must simply make an educated guess of their individual sets and drifts and correct our DR accordingly.
Figure 1. On a reach or in moderate wind, the wake is straight aft indicating no leeway. When sailing to weather in stronger winds leeway sets in and the wake appears to shift to windward as the boat slips to leeward. Schematic drawing adopted from the Starpath Online course on Inland and Coastal Navigation (www.starpath.com/courses). In the golden age of sailing when sailing ships slipped very much more than today it was common advice to new helmsmen to “Keep your wake right astern.”
To read one treatment of this from that era see Lecky’s, Wrinkles in Practical Navigation, page 664. We have made this link to get you a free copy of this great book: www.tinyurl.com/1918Lecky.
Leeway
Leeway is how much a boat slips to leeward on a windward course. It is a function of the boat’s draft, the point of sail, and the wind speed. It’s only a navigational factor when going to weather close hauled in strong winds—or very light wind, but that is not the subject here. The effect is distinctly different from current set because we can measure leeway underway (without electronics in some cases), so it is not strictly invisible as implied above. A typical keel boat of 6-foot draft might slip as much as 10° to leeward in a solid 15 knots of true wind. Yacht design specs might have this number as just a few degrees, but here we are discussing the reality of navigation, not a design parameter that may have a more complex interpretation.
Leeway can be discerned in your GPS derived data in special cases. For example, if the wind has just started to blow (so it has not had time to generate any surface current (discussed below), and there are no other sources of current in the waterway, then when close hauled you will find your average COG to be some degrees to leeward of your average compass heading when steering a steady course on the wind, whereas your average SOG will match your average knotmeter speed. When this happens symmetrically on both tacks, you have a nice snapshot of your leeway. Sometimes you can actually see your wake bent to windward, which is the same effect. Yacht designers have developed underwater gimbaled vanes that measure the angle of motion through the water relative to the centerline for an accurate measurement of leeway vs wind speed and heeling angle.
With differential or WAAS enabled GPS, leeway shows up very nicely on units that directly compute current based on SOG and COG compared with accurate inputs of knotmeter speed and compass course. Going to weather in still water, you will have current on your windward beam regardless of your tack.
From a practical point of view, you can ignore leeway as soon as you fall off the wind. Above some 45° apparent you can forget it unless you are still well heeled over or have other evidence that you might be slipping. Remember that leeway, unlike current, adds uncertainty only to your course direction, not your speed. In slack water, your knotmeter speed is your SOG even as you are slipping with leeway.
Leeway depends on wind speed. If your optimum wind speed is 10 knots true, then leeway increases going both up and down from there. In one sense, this is how optimum wind speeds are defined for sailing vessels. If it is, say 6° at optimum, then by the time you get to 20 knots it might be as high as 15°. In practice, however, it doesn’t get much higher than this in normal operations because by then you start to fall off—except in some well designed race boats, it just doesn’t pay to pound into the waves in very strong winds. And once you fall off, the slipping stops. Likewise at very low winds (a knot or two) you will also slip a lot, but again at some point you fall off and it goes away.
Leeway also depends on keel depth—the depth is much more important than the shape. Sailing a kayak, for example, just a paddle down in the water makes a world of difference. Likewise, to first approximation, a high tech racing keel and a full length cruising keel are about the same in this regard for a given depth. The high tech fin keel, however, can make up a lot by the actual lift it adds as water flows over it as wind does on airplane wings.
Some performance programs compute leeway based on knotmeter speed (S) and the measured heel angle (Heel) according to:
Leeway = K x Heel /(S x S),
where K is between 10 and 13 and has to be determined for your vessel. See discussion in Modern Marine Weather. A digital value of the heel angle can be found from a phone app!
See also this article Navigation with Leeway.
Wind-Driven Current
Leeway occurs in all waters, regardless of actual current flow. In strong winds, however, no water (ocean or lake) will stay still for long. When the wind blows steadily for half a day or longer it generates a surface current in any body of water. This new current must be added vectorially to the prevailing ocean or tidal current, or treated as a new issue in areas with no natural currents.
As a rule of thumb the strength of the wind drift is some 2.5% of the wind strength, directed some 20° to the right of the wind in higher northern latitudes and to the left of the wind in higher southern latitudes. In central latitudes the set is more in line with the wind. In Puget Sound or Juan de Fuca Strait and similar confined waterways where the land constrains the wind to flow along the waterway, wind drift here can be figured as essentially parallel to the waterways—with or against the tidal flow. In any waters, though, a 25-knot steady wind for a day or so will generate a current flowing downwind of some 0.6 knots.
Figure 2. This graph assumes a maximum wind drift current of about 2.5% of the wind speed when fully developed. Shown on the left are the times required to develop this current.
The blue example marked shows a 30-knot wind producing a maximum of 0.75 knots, which would take some 19 hours to develop. When the wind has blown only 8 hours, the wind drift would be more like 0.4 knots.
Notice on the data that below about 30 kts, a required duration of half the wind speed is a good guess for maximum development, but at higher wind speeds it is more like hours = knots to get the water moving at max speed. Adapted from the Starpath Weather Trainer.
In long heavy rains the wind driven current tends to be larger, since the brackish surface layer slips more easily over the denser salt water below. In extreme cases you might expect surface wind drift of over 3% in long, strong winds with much rain.
Helm Bias
Helm bias is even more evasive in our navigation reckoning. Strong winds bring high seas (at least in the ocean) and with them the problem of steering over them. It is usually possible in these circumstances to detect a persistent course alteration at each wave. A common tendency going to weather is to fall off (turn downwind) or get pushed off slightly at each wave. The only way to gauge this effect on the average course manually is to stand and watch the helm and compass for some time. Then make a guess at an average offset.
Or simply look at the track of a GPS plot of positions, which is what one would do in a normal situation—although it would still be difficult to pull out the helm bias from leeway and wind-driven current in some cases.
We are discussing DR here, however, and that means we are assuming we don’t have these aids to look at. But it does bring up the important point that the best use of such wonderful nav aids is to use them to teach us about DR. In other words, when the waves start to build, confirm with the helmsman what course is being steered, and then watch the plot of positions to see what is being made good. There can of course be other influences (the subject at hand), but by noting what is being made good and then just standing there and watching the compass and the helm for a while, you can see what is taking place.
We are looking at going to weather here, which won’t happen much in strong winds unless you are racing or trying to claw off a coast after getting in too close, but this same helm bias occurs going downwind as well. The bias sailing downwind tends to be to leeward (the right way) in big waves and fresh air, but in light air it might tend to be upwind in big waves as you try to keep the boat moving. So the summary is sailing to weather helm bias will most likely be to leeward, but sailing downwind it could be either way.
Also if you are navigating a race boat there can be numerous types of helm bias to watch out for, and they might be personality driven. Some drivers like to go fast regardless of what the course is supposed to be. Others might choose a more conservative course than called for to not risk a round up.
Summary
Here’s an example to sum up these invisible problems. Going to weather across a 0.6 knot wind drift at 6 knots would set you off course some 5°, your leeway might be some 10°, and a helm bias account for another 5°. In this case the overall off-course set is about 20°. In the ocean, after 100 miles you would be some 30 to 40 miles off course to leeward if you did not figure these factors in your DR. Summarized another way, going to weather in a steady 20 to 25 kts of wind, will most likely cost you at least 20° of course made good.
When sailing to weather in strong winds, you will always be slipping down wind more than you might guess. While the GPS is still working, keep a record of what angles you actually tack through in big waves and strong winds—not compass headings, but the actual angle between the two track lines on the GPS plot. If you end up having to DR in these conditions without electronics, then it is usually a reasonable first guess to assume you did indeed cover the miles your log indicates, but then simply set the course made good some 20° to leeward.
Figure 3. Effect of slipping downwind. We have a fix at 1110 then sail to weather for 7 hours and get a noon sight latitude at 1820. These are plotted above showing the course and DR position at 1820. We know we are on the LAN line, but where. Near the DR might be good guess reaching in good conditions, but to weather we know we will be to leeward. So mark off the distance run and swing it down to the LOP and that is your most likely position with just this information.
When racing, there is an obvious advantage to tacking at the right time. If the electronics take a hike when you need them, these are the basics to fall back on. The compass headings alone won’t help. In the above example, it would mean overstanding the windward mark by 20°.
Accuracy evaluation and statistical errors in DR are covered in detail in the book Emergency Navigation, because in an emergency without the aid of our accustomed instrumentation we are left with little but DR to go by.
Figure 4. How to use electronic charting display of your track to choose the time to tack when you are not making good the course you are steering. Here the boat is steering 045 on port tack in a northerly wind, but only making good 055. On a starboard tack, steering 315, you only make good 305. Once you have your actual tracks established on the chart on both tacks, you can then draw a range and bearing line parallel to the CMG of the final starboard tack, and move it to the windward mark. Then where that line crosses your last port tack line (projected from your COG), is when you tack to lay the mark. This would be the same maneuver to make if it were tidal current setting you off course rather than just wind.
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