My boat can make 10 knots through the water. The current set and drift are 030T and 2.5 kn. My desired true course to my next waypoint is 075T. What course should I steer in order to offset the current and travel the desired course?
Bonus question. My next waypoint is 20 NM away (bearing 075T as has been said above). How long will it take me to get there?
This can be easily resolved graphically. I draw a line from a, my present position to d, my destination. This represents the course I want to make good over ground (and, as has been said, in this example is 075).
I select any convenient arbitrary unit of length and draw a vector with origin in a, direction equal to the current set (030) and magnitude equal to the current drift (2.5). I call the tip of this vector b. This is where my boat would be due solely to the effect of the current if it did not make any way through the water.
(The units of distance and time are irrelevant as long as we keep them consistent).
I now take a compass and set it with a radius distance equal to my boat's speed through the water (10 in this case). With center in b I draw an arc (r=10) that intersects ad at a point I call c.
Segment bc represents the course to be steered to obtain the desired COG (course over ground). In this particular problem it is 085T. It is easy to see that ab + bc = bc + ab = ac
To answer the bonus question: the boat's speed over ground is ac measured in the same arbitrary units we used for ab and bc. In this example we can see the speed made good over ground is 11.6 knots which is greater than the 10 knots the boat is doing through the water because the current is in our favor. In real life it seems we are always going against wind and tide. The time required to cover 20 NM at a speed of 11.6 knots is... Do I really have to do this for you?
Click here to download an Excel spreadsheet that does the calculations.
The previous problem assumes the current is constant in set and drift. Let us complicate the problem slightly. Let us suppose I need to cross a channel and the tide current flows in one direction and then in the opposite direction. What course should I steer?
The problem can be easily resolved using the same method as before except that vector ab now represents the integral of the current flow over the time of navigation.