Northbeach,Perhaps one of the things that is confusing you relates to terminology. For example, we never actually sail a "magnetic" course. Everything you said is correct except you refer to sailing a "magnetic" course when you should be referring to a "compass" course. The only time we can sail a "magnetic" course is when deviation is zero. Otherwise, we have no instrument that actually tells us our "magnetic" course, it's only a mathematical computation along the way. Feel free to disregard the following if it sheds no light.
When discussing compass correction we must be rigorous in the usage of our terminology. In this case we have three co-ordinate systems that we can relate to each other.
The first is the well known terrestial system. This consists of parallels of latitude and meridians. All meridians, at all times, point towards Polar North, or True North. All parallels point, at all times, east and west. This is true on all chart projections, with the most common being the Mercator. The confusing part arises when, if the chart scale is small enough, that is it covers a large area, the parallels and meridians will not intersect at a 90 degree angle. This can best be explained by the fact that the most accurate representation of the earth, is a globe. But a globe is rather inconvenient to navigate upon. So, in one way or another, we slice the surface off the globe and flatten it out so we can go to work. In the case of the Mercator chart, we end up with meridians that do not converge towards the poles, but always point north, and parallels that always run east and west. This results in the distortion of landmass that makes Greenland appear larger than the North American continent. But it works admirably for navigating at sea.
So our terrestial system gives us True, or Polar North. We often work out these problems using a "spider" diagram, which resembles a clock face when sketched out. We label True North as "Pn" for Polar North on it, and it is always pointing straight up on our diagram. Any angular measurements made from it, in a clockwise direction, are considered True Courses, and are labeled with the degrees clockwise from Pn and the letter "T".
Our next co-ordinate system is the Magnetic Co-ordinate system. We use the same global sphere for it, but our reference points are different. In this case our north is Magnetic North, or "Mn", and it is the magnetic north pole. The magnetic meridians we use from it are similar to terrestial meridians but subject to variations due to the effects of land masses and other inequalities in the earth's composition. Our various compasses are attempting to point towards Magnetic North, "Mn". In reality, our compasses will rarely point towards Mn accurately, unless perhaps we are in a liferaft with no metal objects about us. Our compasses will have the strongest pull or tendency to point towards Mn at the magnetic equator. This directive force will become weaker the closer we get to the magnetic pole. Specially balanced compasses are necessary for navigation in high latitudes as a result. The difference between True North and Magnetic North is called Variation. Due to the anomolies described above, variation is not a consistent number or ratio. Local charts will list variation, while sailing or oceanic charts will show lines of equal variation, known as isomagnetic lines.
Our third co-ordinate system is our compass system. The compass points towards Compass North, or "Cn". Compass North is where our individual compass thinks Magnetic North is located. We commonly label the courses derived for this by the name of the compass used, the most common being the standard or steering compass, hence the abbreviation "pSC" for per Steering Compass. The difference between Mn and Cn is Deviation. Deviation has many components, but for purposes of simplicity we will say that it is the error induced on our compass by the magnetic field(s) of our boat. Deviation varies with the heading of the boat, hence the need for a deviation card. Deviation also varies with the loading condition of the boat. If you rig a SSB antenna on a halyard you will change the deviation of the boat from the deviation it had un-rigged. If you modify the boat, running battery cables forward to a new windlass, you will change the deviation. Lastly, deviation varies with the magnetic heading of the vessel and not the true heading; the forces being operative are the isomagnetic lines of force-not the boats true heading. (and if that ain't confusin', nothin' is!)
True Virgins Make Dull Companions
You can work this formula forwards or backwards. On our spider diagram the line pointing up is Pn and is the same as the meridian on our chart, it points to True North. All of our labellings on the chart will be "true" courses, although we may add sub-labellings for magnetic or compass courses, with only the latter really being used. For example: we would label a DR track showing a course of 045 True as 045T on the top of the DR track drawn, and, say 038pSC under the DR track drawn. This then gives us our true course intended, which equates in an angularly true fashion with our meridians and parallels on the chart. The pSC for the same course is merely the conversion of 045T to that which we wish to steer at the helm. It should be endeavored to never label the course laid down with only compass or magnetic headings, always including the true heading or course. The compass, and most certainly the magnetic, course has no relevance whatsoever to what we are plotting on the chart, UNLESS. "Unless" will be explained below. Let's ignore it for now.
It is best to only consider variation in east or west terms. In my experience, labelling it plus or minus ends up confusing in the end. If we have 10 West variation we can draw another radial line on our spider diagram 10 degrees counterclockwise from Pn, and label it Mn. If we now look at the diagram we can, by inspection alone, determine that our 045T course would be 055M, or magnetic. But this does us no good as we do not have a "magnetic compass" we only have our Steering Compass which is subject to Deviation as well as Variation. Let's say our deviation card says that, on a course of 055M, our deviation is 2 East. We now go back to our spider diagram, and can draw in another radial line, this one two degrees clockwise from our Mn line, and label it "Cn" for Compass North. We commonly scribe arcs with the angular measuements between all of these on our diagram. It ends up looking somewhat like a portion of a spider web, hence the name. Note that, while doing this, our Pn line and our TC line, 045T, never change. The variables are variation and deviation, and the diagram allows us to relate them to one another and our true course so we can derive what to steer.
Now the reason I said not to assign pluses or minuses is that if we envision this spider diagram we will be able to properly place Mn to either the west or east of Pn, and then Cn to either the west or east of Mn.
Without the spider diagram, we can do this mathematically, and then we will use a plus or minus, remembering to ALWAYS apply the formula in the order written. You can work it backwards, but must then reverse the corrections. For example: 045T, 10 West Variation, 2 East Deviation Using TVMDC and "West is Best", "East is Least". We take our desired 045 True Course and add (best) 10 to it for a 055 Magnetic Course (NOT COMPASS!) and then subtract (least) 2 from it for our 053pSC course.
Conversely: We're steering 053pSC. What is our True Course? Working TVMDC backwards, with the rules reversed, we proceed; 053 plus 2 gives us 055M. 055M minus 10 gives us 045T.
It is best to learn the TVMDC, west-best, east-least, very well and then rely on your ability to transpose for working backwards.
The "unless" comes in with the use of the compass rose on the chart. The inner circle shows us "magnetic north". If our deviation is zero, or insignificant, we can use that compass circle to convert our true course to magnetic, which will be the same as compass.
The procedure would involve laying down a course unkown between two points. We then either walk our parallel rule or triangles over to the compass rose until centered on the rose. The outer ring, where we cross it, yields our true course, the inner ring our magnetic. I find it a hassle and, using triangles, I walk the triangle over to the nearest meridian and read my true course off of it. I then just apply the variation intuitively for the magnetic course. The advantage of triangles or the aviation parallel rule with protractor is that you do not have to slowly traverse the entire chart over to the compass rose, just the nearest meridian.
Now if that does not muddy the waters.... I gotta find a bored twelve year old to show me how to scan and post sketches.
“Scientists are people who build the Brooklyn Bridge and then buy it.”
Wm. F. Buckley, Jr.