In an earlier article I wrote, "It is important to remember that the DR position is only an approximate position, because it does not allow for the effect of leeway, current, or steering error."A visitor to SailNet recently sent me an e-mail regarding this statement, and I have included it here, since it is a good lead in for today's subject:
"I disagree strongly; I was brought up to include an estimate of both leeway and current in calculating DR. It is easy to include them; just do a graphical solution in a triangle on your chart. The DR position is still approximate, of course, but it's a lot better than if you ignore leeway and current."
Here is my response:
|"Thanks for the input on your method of navigation. I am not suggesting that leeway and current are to be ignored, and using them in your calculations is great if you know the set and drift ahead of time from a GPS and/or Loran (or use an estimated value), but the end result is an Estimated Position (EP) not a DR. A DR, by definition, does not include set and drift.After you plot a DR for the time of a fix, the vector between them is the set and drift that affected the boat over that period of time. It is very important to keep the two positions separate and to restart the DR only from a fix, not an EP. I would recommend that you continue to plot your EP, as you currently do, but to also plot a DR position."|
Using predicted set and drift to arrive at an EP is the art of adjusting your course and speed to counteract the effect of the current. For example, to cross a river you would need to point your bow upstream to offset the effect of the current pushing your boat downstream.
By definition, leeway is the leeward motion of a vessel, caused by the wind, and can be expressed as a distance, speed, or angle. Since the wind is constantly changing and can be difficult to predict, leeway is seldom used in calculating an EP in advance. However, when a fix is plotted, the vector between the DR position and the fix is the total effect of set and drift, leeway, and steering error since the last fix.
Now I don't know about you, but the only time I see my desired course on the compass is when I pass through it as I adjust for changing wind and sea conditions. And on some compasses the card only shows every five degrees, so holding a heading within plus or minus one degree becomes a challenging task of estimation. In other words, we will always have some steering error that is automatically included in the set and drift calculation. Even the best autopilots wander about the set heading as they compensate for changing conditions.
In order to understand all these forces affecting your boat, I need to define a few terms. To simplify them, I have also included a diagram.
When you plot your DR position, you will be using your Course (C) and Speed (S).
Course is the intended horizontal direction of travel measured from 000 degrees clockwise through 360 degrees. It is almost always plotted in relation to true north.
Speed is the velocity of the boat through the water and is always recorded in knots and tenths of knots (i.e. S 6.0).
Water in motion is called current. The direction in which the water is moving is called set and the speed of the current is called drift. They are almost always used together as Set and Drift.When the Set and Drift are estimated or predicted from the tide tables, you can apply them to the DR position to obtain a position known as an Estimated Position (EP). Draw a straight line from the DR in the direction of the set for a distance equal to drift times the amount of time in hours and tenths of hours since the last fix. Convert minutes to tenths of an hour. For example, one hour and 30 minutes would be 1.5 hours.
Estimated or predicted Set and Drift is taken from a current table at a reference station and then adjusted for your location.The direction of a straight line from the last fix to the plotted EP is the Track of the vessel (TR), and the length of this line divided by the time is the Speed of Advance (SOA).
When a fix is obtained, one assumes that the current has set from the DR position to the fix and that the drift is equal to the distance in nautical miles between these positions divided by the number of hours and tenths of hours since the last fix. This is true regardless of the number of changes of course and speed since the last fix.A straight line between fixes is known as the Course Made Good (CMG) or the Course Over Ground (COG). The length of this line divided by the time is the Speed Made Good (SMG) or the Speed Over Ground (SOG). You will see these terms used interchangeably in textbooks, but SOG and COG are used more often today, especially in GPS displays and manuals.
In the diagram below, the triangle with TR (track) and SOA (speed of advance) represents your estimated course and speed. The triangle with COG and SOG represents your actual course and speed. Course, Speed, and Set and Drift can be components of either triangle.
If a current is setting in the same direction as the course, or its reciprocal, the COG is the same through the water and the effect on speed can be found by simple arithmetic to obtain the SOG.Keeping a good DR and plotting an EP for the predicted set and drift allows you to properly evaluate your fixes, cross-check the accuracy of the GPS, and see the effects of leeway and steering error on your navigation.
I know how easy it is to enter the waypoints into the GPS, connect up the old autopilot, and allow the equipment to do all the navigation work. However, you should occasionally do the navigation manually so that when the equipment fails or isn't there, you can still apply your navigation skills and arrive home safely.