How To Calculate Course Over Ground (Illustrated Guide)
With a modern GPS and chart plotter, reading a Course Over Ground (COG) number tells you what the COG is. As the name suggests, it's the direction the boat is traveling over the bottom, including any side slipping, current and drifting. It can differ from your compass heading, and it's important to know why.
How do you calculate course over ground? If you have an estimated course and you're doing dead reckoning, you add the known effects of currents to your projected course to derive the COG. With a known start and ending position, COG is measured from a chart.
Dead reckoning? Adding currents? We'll cover the basics for you and make it crystal clear.
COG - A Complete Definition
At its simplest level, imagine your sailboat dragged a chain on the bottom as you sailed, leaving a line through the mud and sand. It doesn't matter what your compass heading was or your angle of sail off the wind, your "Course Over Ground" is literally that line you drew on the bottom. It is the path the boat travels relative to the bottom, no matter which way you're sailing.
COG is not Heading. The heading is the compass direction your boat is pointing, and it may not match COG if you have current and tidal effects. Heading is instantaneous, we derive COG from your boat's motion over time.
If you know where you are now, and you know where you were five minutes ago, describing your COG is just a straight line back to where you were. Your GPS can calculate this because it knows where you were five seconds or five minutes ago, and it displays the number on the fly from the known start and ends.
Calculating COG between two fixed points is easy, it's just plotting points and measuring. On a chart, its primary use is to document what happened since you already have a fix, so you which way you traveled despite the direction the boat was pointed.
Figuring COG when you're doing dead reckoning plots is different - it gives you an estimate of your position and is useful for navigation without a GPS.
Calculating COG - Fix to Fix
If you're not comfortable plotting a point on a chart and measuring a line, start with this guide to be sure you understand dead reckoning and how to plot a point and measure a line. Those skills are important to figuring your COG by either method.
To calculate COG from point A to point B with a chart is simple if you understand the basics of plotting and measuring.
- Plot Point A and Point B on your chart.
- Draw a straight line from A to B.
- With a parallel rule, measure the compass angle of the line and record it.
- Adjust the number for magnetic variation, adding West variation and subtracting East.
The final number was your COG between the points.
Calculating COG - Dead Reckoning
This is where the calculations get useful and much more interesting. When you are navigating with dead reckoning and paper charts, you estimate your position based on information about your course and heading. But a current can move you miles off course, and you'll never feel it. Accounting for it and estimating it is how we calculate our Course Over Ground.
To do this, you will need a dead reckoning plot - this will be a series of estimated fixes and recordings of speed lines. If you are sailing in an area with known current effects, make the COG adjustment after each DR plot.
For this calculation you will need to know an estimate of the strength and direction of currents affecting the boat - sometimes referred to as set (direction) and drift (speed). This will be a speed in knots and a compass heading.
The steps, including the dead reckoning plot:
- From your last fix, calculate how much time has lapsed. We will use an hour, because most DR plots are done on the hour.
- Get your compass heading for the last hour and boat speed.
- Draw a line from the last fix equal to your boat speed for the measured hour on your heading.
- Starting at the end of the line you just drift, draw a line representing the set and drift of the current. This will be the length of the drift on the compass direction of the set.
- With your straight edge, draw a line from the last fix to the end of the set/drift line.
- Measure the angle of this line against the compass rose to get the Course Over Ground. The Speed over Ground is also the length of the line, if the measured time was an hour.
Other Error Factors
The other major error factor which makes your COG and estimated position inaccurate. The first is leeway, or sideslip. Because the wind is blowing from the side of the boat, the boat is pushed sideways. This effect is most pronounced when sailing to windward and reduces as the wind moves aft and disappears running downwind.
The amount of leeway varies with boat speed, wind speed, and sailing conditions. A boat moving slowly has more leeway, and higher wind speed causes more leeway with more sideways force. Rough conditions, especially when a boat is sailing into waves which slap it backwards, can increase leeway.
Unfortunately, you can't plot a course ahead of time to account for leeway, since it varies with the conditions and you won't know them until you set sail. But you can estimate it once you start sailing, though it's better to adjust your last Course to Steer than it is to plot leeway on your chart, especially if it's upwind to your destination.
Without hard data for leeway (which rarely exists), the best you can do is estimate. Five degrees isn't a terrible estimate to start with for many boats going upwind, but as you sail your boat, you can try to figure a better estimate. Once you have a Course to Steer, add the leeway to your heading to sail a few more degrees upwind, then it will be factored into your COG calculation when you plot it.
Course Over Ground - Why Bother?
Since you have a COG function on your GPS, why take the time to learn how to calculate a less precise number on paper? And what can you do with the COG once you have it?
The answer to "why bother" is the same one for why learn Dead Reckoning navigation - if you lose your instruments or there's a problem with the GPS system you still can get to a safe harbor or home. Understanding basic navigation, even if you never use it, will make your electronic navigation more efficient and safe, and give you a good fallback in case you lose power or your instruments.
But what else can you use COG for?
With electronic navigation, I find it useful as my first clue there are currents at play that I don't know about. It happens more than you expect; most coastal waters have some tidal effects and it's not always obvious what they are doing.
In parts of the world where current plays an enormous factor in navigation, are are often published sets of current data. But those often apply to very specific locations like the entrance of a harbor or canal. Their accuracy is a prediction, not a statement of fact, and your COG can be your first clue you're being swept in a different direction than you're pointing the boat.
Check your COG against your heading when you're sailing. In theory, they should be close together. If they aren't, you've got current, leeway, or both. It gives you a chance to adjust your heading to compensate for the current and stay near the course you plotted. With practice, you can learn enough about your boat to estimate current set and drift from checking the COG against your heading.
If you're a hundred miles from land, a mile or two isn't a big deal. But if you're sailing near the Middle Ground Shoals in Vineyard Sound - a notorious area for fast and shifty tides and currents - that side slippage or push from the current can be the difference between smooth sailing in deep water and bumping a sand bar.
When you're navigating with Dead Reckoning, calculating the COG is a critical step to getting a more accurate DR position in areas with a lot of current. No matter the current set, you want your best position possible. If you know about currents in the area you're sailing, you can account for them before you sail with the Course to Steer - refer to our guide on that topic.
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