Velocity Made Good – Trading off course against speed

In sailing it’s not unusual to find that changing course a little away from the direct line to your destination can give you more boat speed, as can sailing a little free of close hauled when you’re working to windward. Sometimes this can work to your advantage with the extra distance sailed being more than made up for by better boat speed, on other occasions the gain in speed isn’t enough and you end up taking longer than you needed. This article puts some hard numbers on the gains and losses and introduces a simple table that can be used in practical sailing situations to help to decide on the best course to steer.

The ideas that are described here apply to both off wind and close hauled sailing and can help out when you’re faced with a nasty motor sail into a head sea. We start off looking at the theory then introduce the table, look at tactics and finish off with some practical examples.

Some Definitions

Let’s start by defining what we’re talking about.

Rhumb Line is the straight line from our starting point to our destination, this is the shortest distance to our destination (strictly speeking this is the great circle line but for the sort of distances that we're interested in this is a straight line on the chart). Our starting point is wherever we are when we decide to sail a course that takes us off the rhumb line.

VMG stands for Velocity Made Good , which is the progress that we’re actually making towards our destination, that is our speed along the rhumb line. We want to make this as large as possible.

Boat Speed is the speed that the boat is making over the ground along its current course.

Course Offset is the angle between our course and the rhumb line, which is the amount we’ve decided to sail away from the most direct course to gain some extra boat speed.

Finally Cross Track Error (often abbreviated to XTE ) is how far we are away from the rhumb line at any time.

To start with we’re going to ignore the effects of tidal streams and leeway so that we can concentrate on the basics, we’ll look at including these factors later on. So at this stage speed through the water and over the ground is the same.

An Example – Downwind Sailing

Let's look at an example situation to clarify what’s going on. If our destination is dead downwind then we can, of course, sail straight to it along the rhumb line. We could be running with a poled out genoa or perhaps with a spinnaker or cruising chute. If there’s any sort of following sea then this is an uncomfortable point of sail, and if we’ve not rigged a preventer then there’s the risk of an accidental gybe.

By turning away from the rhumb line a bit we can bring the wind around onto the quarter. This is a much better wind angle, giving us airflow over both sides of the sails, so the boat will sail faster as well as feeling much more comfortable. If we can sail fast enough on the new heading to make the same VMG as we were making dead downwind then, provided that we gybe part way down track, we will get to the destination in the same time as we would have on a dead run, but we will have had a much more enjoyable sail in the process. Of course if turning off the rhumb line gives us a better VMG then we’ll get there sooner as well has having more fun!

This is what asymmetric dinghies do. They are much faster on a broad reach than a dead run so they sail downwind in a series of gybes. If we can pick up sufficient speed broad reaching in a sailing yacht then we can do the same thing.

The question we need to be able to answer is: “If I turn away from the rhumb line by x degrees what boat speed gives the same VMG?”, that gives us the minimum speed that we need to make on the new course to be winning.

VMG Table

Here is a table that that works out the boat speed needed to achieve a given VMG for a range of Course Offsets at the speeds that are likely to be encountered by a typical cruising yacht.

There’s a printer friendly version of the VMG table to take sailing.

Each row in the table is for a particular Course Offset. For each speed column the top row gives a VMG and the row for a particular Course Offset shows the boat speed needed on that course to achieve the VMG. There’s also a column showing this difference as a percentage, which we’ll use to draw some useful observations later.

Let's say you’re making 6 knots towards your destination (sailing along the rhumb line), if you alter course by 30degrees away from the rhumb line what boat speed is needed to maintain 6 knots VMG?

Look along the 30 degrees row of the table to the 6 knot VMG column. The boat speed needed to make 6 knots VMG is 6.9 knots.

A Few Observations

Looking at the percentage column of the table we can see that for course offsets of  up to 15 degrees we only need a speed increase of less than 4% to maintain VMG, and even at 25 degrees away from the rhumb line course we need to gain just over 10%. A course change of 15 or 20 degrees can make quite a difference in the way a boat sails, so small alterations of course are well worth trying.

Once we get above 30 degrees away from the rhumb line the required boat speed starts to build up rapidly, by 60 degrees we need a boat speed of twice the VMG and beyond that it’s unlikely that we’d gain enough boat speed to give any advantage.

It’s important to remember that the course offset angle is relative to the rhumb line from our start point to our destination. If the destination lies to windward then we’re already sailing with a course offset when we’re close hauled. In this case any change of course away from the wind is an increase in the course offset we’ve already got, not from zero, so the gain in speed required to keep the VMG will be higher. Usually the best option is to make your best course to windward when close hauled, though there are occasions where freeing off a little can help.

The Real World – Making use of GPS

Out in the real world our water track is rarely the same as our ground track. There’s the effect of tidal streams to consider, and if we’re sailing to windward we’ll be making some leeway. We can predict the effect that tides are going to have, this is a basic part of coastal navigation (but remember that it is a prediction, the current and recent weather conditions can change things). We can also make allowances for leeway, but in practice it’s difficult to come up with an accurate estimate. Trying to work this out at the chart table isn’t easy and I’d rather be up in the cockpit sailing the boat, so lets look at using the GPS to do the hard work for us.

For VMG calculations what we’re looking at is progress towards the destination, that is progress over the ground. Even the most basic GPS receiver is able to read out speed over the ground (SOG) and course over the ground (COG). That’s all the information that we need.

We can work in either true of magnetic bearings, but to avoid lots of arithmetic it’s best to either use true or magnetic for all courses. A GPS will generally be set to use one or the other format but take care that you use the appropriate format (true or magnetic) for courses taken from the chart.

The rhumb line course is the course from start to destination taken from the chart. If, as is usually the case, your passage is not a single straight course then treat each leg individually. In any case optimising VMG is a short term process because it depends on the current wind conditions.

The course offset is the difference between course over ground (COG) and the rhumb line course. Just subtract the smaller value from the larger one, it doesn’t matter which side of the rhumb line you are (at least for working out VMG).

Current boat speed is speed over the ground (SOG). So with a course on the chart, a couple of numbers from the GPS and a little bit of arithmetic we’ve got all of the information that we need.

If you have a waypoint set for your destination then your GPS may well be able to work out VMG for you, in which case you don’t even need the table. As with any other GPS navigation its sensible to check that the waypoint really is the right one in the right place and that the course to it is safe. Personally I don’t always have a waypoint set up for every turning point on a passage, and I may decide to change from the pre-planned route, or be forced away from it for some reason, but I can always get SOG and COG from the GPS and use the table for a quick VMG calculation.

In the rest of the examples we’ll work in terms of COG and SOG, so all of the examples relate to using the GPS.

Making the best Progress

Here’s the basic process for making the best VMG.

On your current course with the boat properly trimmed work out what your VMG is. If your ground track is the rhumb line (probably the case if you’re off the wind and, of course, going the right way) then this is the boat speed, if you’re off the rhumb line then work out the course offset, round this to the nearest 5 degrees and look up the nearest value to your boat speed in the table. Your current VMG is the value at the top of that column.

For example. Lets say you're on a course that's 23 degrees off the rhumb line and making 4.5 knots over the ground. Rounding up to the nearest 5 degrees gives a course offset of 25 degrees, looking along this row the closest entry to our boat speed is 4.4 knots, which tells you that your VMG is 4 knots.

Now change course to one that should give you better boat speed, trim the boat for the new course, let her settle on a new boat speed then work out your new VMG on this course offset (again by rounding the course offset to the nearest 5 degrees, finding the nearest boat speed in this row and getting the VMG from the top of the row).

If your new VMG is better than your old one then you’re winning, it’s worth trying a further course change to see if you can improve things further. Try small steps at a time, 5 or 10 degrees. When you find that VMG is falling off then go back to the course that gave the best VMG.

If your new VMG is less than your old one then the course change has made things worse so you should go back to your original course. If it looks like turning the other way is worth a go then give it a try, otherwise stick with the original course.

The wind is never constant and tidal streams are going to change both with time and your location, so from time to time it's worth experimenting with course changes to see what effect they have. How often you do this depends on how much you like to mess about with sail trim and the like, it depends on your sailing style.

One final point, do pay attention to sail trim with each course change. Any speed gains are going to come from getting a more favourable wind angle, if you change the wind angle you need to re-trim the boat to make the best of it otherwise you’ll not be comparing the boat’s best progress on each course.

Windward Sailing

It’s important to remember that the course offset angle is relative to the rhumb line from our start point to our destination. If the destination lies to windward then we’re already sailing with a course offset when we’re close hauled, so a 10 or 15 degree course change away from the wind isn’t the same as a 10 or 15 degree change away from the rhumb line. In some conditions it may be worth sailing a little freer to keep the boat speed on, but a big move away from the wind incurs a big loss in VMG. Here’s an example:

Remember that the VMG table works with courses over the ground, so we need to think about our course over the ground not our angle to the apparent wind. Even if the wind instrument shows an angle of 30 or 35 degrees in reality our ground track is more like 40 or 45 degrees to the true wind.

With the destination dead to windward and a ground track 40 degrees off the true wind our course offset is 40 degrees. If we’re making 5.2 knots through the water our VMG is 4 knots. Now if we bear away by just 5 degrees the boat speed we need to maintain VMG becomes 5.7 knots, that’s almost a 10% increase. In some conditions, like working into a big sea, paying off a little to get more power from the rig can give a good speed advantage so it is still something to consider, just remember that you’re increasing an existing course offset not putting in a small offset from zero so make sure that you work from the proper rows in the table.

Something else to remember is that when sailing to windward an increase in boat speed moves the apparent wind forwards, so a change of 5 degrees in ground track to increase speed will give us less than a 5 degree change in wind angle. Looking at this another way a 5 degree increase on the apparent wind gauge is probably more that a 5 degree increase in course offset.

This isn’t an argument to start pinching. If you sail too high then as well as losing boat speed the keel will lose grip and you’ll make more leeway so you may find that the course offset actually increases! Combine this with less boat speed and you’ll put a big dent in your VMG.

Which Way to Turn?

If we decide to try turning away from the rhumb line we need to decide which way we’re going to turn. Sometimes this will be decided by navigational constraints, we don’t want to turn into a sand bank or a shipping channel for example, in which case we chose the safest direction. Often we will be free to chose either direction, here are some things to consider:

A good rule is to pick the direction that keeps us closest to the rhumb line. Not straying too far from the rhumb line means  that we shouldn’t lose out too much if we get an unhelpful wind shift. You’ll also find that picking the direction that keeps you closest to the rhumb line gives the best VMG for a given boat speed because the course offset angle is smaller.

The wind rarely blows exactly along the rhumb line, which is why one direction will keep us closer to the rhumb line than the other.

If you’re running then turn towards the wind (i.e. if the wind is over the starboard quarter then turn to starboard, over the port quarter then turn to port). Turning towards the wind gives a better wind angle on a run and so should give better boat speed. If the wind is already slightly off to one side of the boat then effectively we’re already turned a little towards it so we make our turn towards the wind to improve the wind angle further. If we decide to turn away from the wind then we’ll have to go through a dead run and out the other side before things start to improve, in this situation if the wind is 5 degrees off to port of the rhumb line then if we turn 10 degrees to starboard we’ve only moved the wind to 5 degrees on the other side but we’ve already increased the course offset to 10 degrees so we’ll be getting exactly the same drive as we had before but be 10 degrees off course. Conversely if we turn just 5 degrees to port we get a true wind angle of 10 degrees off our stern and the increased drive will increase our boat speed which will bring the apparent wind a bit further around in our favour, and we’ve got this for just a 5 degree course offset.

When we’re beating things are the other way around. Here if the wind isn’t dead on the rhumb line it’s best to chose the tack that’s on the opposite side to the wind because turning away from the wind on a beat gives a better wind angle so we chose the tack that gives us the wind angle we need while keeping closest to the rhumb line.

Dealing with Tide

If there is a tidal stream running more or less parallel to the rhumb line then it’s either going to improve our progress or slow us down depending on which direction it’s flowing. We can’t do anything about it (other than picking a time for the passage that gives the most favourable tides of course).

Things are more complicated if there is a cross tide. If the wind is close to the rhumb line and there is significant cross tide then it’s generally best to chose the tack or gybe that puts the tide on the lee bow. In other words if the tide is coming from our port side then go onto starboard tack/gybe so that we’re sailing partly into the tide. The tide will push us back towards the rhumb line so it will make our ground track nearer to the rhumb line than our water track. This means that when we come to tack or gybe back to the rhumb line we’re closer to it so we have less distance to travel and we get to the destination sooner.

Turning to put a cross tide on the windward side is going to increase the course offset so should generally be avoided (of course providing that there’s not a navigational or safety reason to chose that course), but if the wind is some way off the rhumb line and the tide is week then it may be the better choice. The way to check is to try each tack/gybe, see what the ground track and speed are on each and use the VMG table to pick the one with the best VMG.

If we’re beating then “lee bowing” the tide also gives us a lift which helps. If we’re running then lee bowing the tide also lifts us, but we actually want a header to improve the wind angle so we loseout a little, though staying closer to the rhumb line is normally worth the loss in wind angle.

When to Tack or Gybe

As soon as we alter course away from the rhumb line we start accumulating a cross track error so as well as making progress down track we’re also moving off to the side. At some point we’re going to have to tack (if we’re beating) or gybe (if we’re running) back towards the rhumb line. Lets look at some things to consider.

To make an accurate decision about when to change course we need to be able to predict what boat speed we’ll have on any new proposed course. Top racing teams collect data on how their boat sails in different conditions with different sail plans and wind angles, this is built up into polar diagrams that show what the boat speed will be for any given wind speed and wind angle. Cruising sailors don’t have this sort of detailed information (well I’ve never met one that does) so we’re not able to make such accurate predictions, we need a rule of thumb to help out.

Lets assume that the boat will make the same speed with the same wind angle on either tack (that’s not always the case with all boats in all conditions but it’s a reasonable guess). If we’re in a situation where changing course off the rhumb line is worth trying then the wind will be reasonably close to the rhumb line, so a wind angle that gives us the best VMG on one tack/gybe should be fairly good on the other tack/gybe. We’ll assume that we’re going to chose to sail on the same wind angle when we head back to the rhumb line.

To work out the course that gives us the same wind angle on the other tack we need to know what our angle is to the true wind , most wind instruments can show this. The reason we want the true wind in this case is because the boat’s speed is affecting the apparent wind direction, moving it forwards relative to the boat’s heading, on the opposite tack with the same boat speed it will be moved forward by the same amount but be on the opposite side. This means that the compass bearing of the apparent wind will be different on each tack which means we can’t easily use it to work out our ground track on the new tack. The true wind is not affected by our course or speed and if we make the same boat speed and wind angle on the new tack our angle to the true wind will be the same (just on the other side).

To work out the ground track that gives us the same wind angle and boat speed on the opposite tack (or gybe) start by reading the current true wind angle. Changing course through twice this angle will bring the true wind to the same angle on the other side of the boat so should give the same sailing conditions on the other tack. The new ground track will be the current ground track plus or minus twice the true wind angle. Use the wind angle from the bow if you’re beating and the wind angle from the stern if you’re reaching.

Some examples. If we’re beating with the true wind 42 degrees off the port bow then we need to tack through 84 degrees to port to get to the same wind angle on starboard tack. With a current ground track of 270 degrees the new ground track should be 270 – 42 = 228 degrees. If we’re reaching with the true wind 160 degrees off the port bow then we can also say that the true wind is 20 degrees off the stern. To put it 20 degrees off the stern on the starboard side we need to turn 40 degrees to starboard. If our current ground track is 149 degrees our new ground track should be 149 + 40 = 189 degrees.

Once we know the optimum ground track for the other tack we can draw a line on the chart at this angle through our destination. This is the lay line, that is it’s the line that we should sail along to reach (lay) our destination in the optimum time (well more or less the optimum time, remember that we’ve made a few assumptions to allow us to approximate without a full set of polar diagrams). In reality sailing off on a long leg hitting the lay line then sailing back to the destination is not a wise thing to do, it leaves us open to falling foul of bad wind shifts. The lay line does put a limit on the chart, we should be heading back to the rhumb line before we get to it, unless we're nice and close to our destination where we can get onto the lay line for the final tack/gybe.

As we’ve just seen it’s not a good idea to stray too far from the rhumb line. How far too far is depends on the distance to the destination. In open water a good technique is to draw a triangle on the chart with its point on the destination and each side a set angle from the rhumb line (something like 10 or 20 degrees works well). The aim is then to keep inside the triangle so when we’re some way off the destination we can make long legs between tacks or gybes and as we get closer we shorten the length of the legs.

Sailing in the swatchways of the Thames Estuary we don’t have so much space to play with. Here we tend to chose contours on either side of the rhumb line and tack/gybe on these, being careful not to sail past the lay line at the end.

VMG after a Gybe or Tack

Having sailed off away from the rhumb line we reach a point where we decide to tack or gybe to bring us back towards the rhumb line (and maybe over to the other side if we’re planning to do a series of tacks or gybes to get to the destination). How do we decide what the best course is on the new tack?

Having made the tack or gybe we’re now setting up on a new course. We’re some way off the original rhumb line so this won’t give completely accurate results if we use it to calculate the course offset. For example if we chose to sail on a course parallel to the rhumb line we’ll calculate that our VMG is the same as our boat speed, where as there is actually a component of the boat speed that’s not towards the destination so our VMG is less than calculated.

To accurately work out the new VMG take the position of the tack/gybe as a new start point and draw a new rhumb line to the destination and optimise your VMG along this new rhumb line.

On a short leg, unless you really enjoy chart work, it’s not worth working out a new rhumb line at each course change. A simpler solution is to continue using the original rhumb line heading to work out our course offset and optimise VMG along this line just like we did at the start (picking the course that gives the best VMG on the new tack). Be aware that this may not take you exactly to the destination, so towards the end of the leg you may need to pick a slightly different course to get you to the destination (assuming that you absolutely have to get there of course).

Example 1 - Downwind Sailing

Your destination lies more or less downwind so the simplest thing to do is point at it and set the boat up to sail on a run. This way you’ll sail the shortest route to your destination.

A run, especially with a following sea, can be a really uncomfortable point of sail. The boat will be rolling, unless you rig a preventer there’s the risk of an accidental gybe, if you’ve got the kit you can poll out the headsail or fly a spinnaker or cruising chute but any of the sails in your wardrobe will be much happier with clean airflow over both sides rather than just being bags to catch the wind.

This is a good time to try turning away from the rhumb line. Head up far enough to get your sails setting properly, exactly how far will depend on the sails you have, a traditional spinnaker can be flown properly closer to a run than a cruising chute or genoa.

As you bear away the increased boat speed will bring the apparent wind forward a little, so you’ll find that the apparent wind will come round more than the course change. For example, with 10 knots of true wind (top of a force 3) reaching on a course 20 degrees away from dead downwind at 4 knots brings the apparent wind round to 32 degrees off the stern, and if the boat speed picks up to 5 knots the apparent wind comes round another 6 degrees. This is good news because the wind angle, and hence power from the rig, improve more quickly than the course change away from the rhumb line.

Turning across the wind a little also means that the apparent wind, which is what’s driving the boat, doesn’t fall off as quickly as boat speed increases. Taking the 10 knot true wind case again, at 20 degrees away from the downwind course a boat speed of 5 knots gives an apparent wind of 5.6 knots (rather than 5 that it would be on a dead run). Heading up to 30 degrees away from downwind 5 knots boat speed gives 6.2 knots of apparent wind 54 degrees off the stern. Of course as we turn away from the rhumb line we need more boat speed to maintain the VMG so there is a limit to how far it’s worth going, you need to experiment with the conditions on the day to find the best compromise.

With the boat now on a broad reach things will be much more comfortable. The boat will feel happier, be rolling less, and will be going faster through the water. If you’ve got a keen crew then they can enjoy trimming the sails, especially if you’re flying a spinnaker or cruising chute. Look up the VMG on the new course, if you’re at least matching the speed you managed on a run then you’re going to get there no more slowly, if you’re VMG has improved then you’re making better progress. See what effect turning a little further has on your VMG until you find the course that’s giving you the biggest gain.

As an aside, in this situation even if I’m not winning I’d be inclined to stick with the reach if I’ve got enough time in hand and the crew are enjoying themselves, after all we go sailing to enjoy ourselves. If I’ve got a decent distance to make and heading up doesn’t help then I’d go back to a run and make sure that the boat was properly set up (I’m a big fan of gybe preventers in this situation).

Example 2 – Motor Sailing into the Weather

Anyone who’s been sailing for any length of time will have been here. The weather hasn’t been listening to the forecast and that close reach in good winds has turned into a bash to windward into a head sea. The crew are cold, tired and turning green. You’re motor sailing to try to make some progress but the boat speed is getting knocked back by the waves, from time to time you’re close to losing steerage. You’ll safely get to harbour, but it’s not a pleasant experience.

Lets say you’re averaging 3 knots over the ground, motoring to harbour with the wind on the nose. There are 5 miles to go so it’s over and hour and a half to get home.

Try turning the boat away from the wind to the point where you start to get some drive from the mainsail. If the wind is strong then your boat speed is not going to have much effect on the apparent wind angle, a course change of 30 degrees or so will give close to a 30 degree wind angle, at this sort of angle you should start to get some power from the main. This will do all sorts of good things for you, the extra power will help to drive through the waves, and you’ll be taking the waves at an angle rather than on the bow, both of which will help to improve the boat speed. The boat will feel more like a sailing boat, helping the crew to perk up, and sailing the boat to keep the main driving will be easier and more rewarding than chugging along a compass course.

In our example, if the course gives us an average boat speed of more than 3.5 knots then we’re winning. It’s not unusual to be able to push the boat speed up over 5 knots with this sort of change, 5.2 knots gives a VMG of 4.5 knots, which takes 1/3rd off the time to go.

A word of caution. Whenever you’re motor-sailing be careful not to let the boat heel too far. Most marine engines have a maximum operating angle of something like 15 or 20 degrees (this can vary a bit depending on details of the installation as well as the type of engine). As the boat heels the engine oil runs to the side of the sump, eventually getting to the point where the oil pick-up starts to suck in air which is not at all good for the engine’s bearings. So if you are motor-sailing into heavy weather be prepared to travel the main down, sheet it out or head up in teh gusts to keep the angle of heel under control.

Closing Thoughts

In this article we’ve looked at topics affecting VMG in some detail. Of course it’s up to you how much or how little of this you chose to use.

These techniques will normally only give an advantage if the wind is blowing reasonably close to the rhumb line. If you’re lucky enough to have the wind on the beam then set the best course to your destination and enjoy the sail.

A lightweight approach is just to remember that for courses of up to 15 or 20 degrees away the rhumb line there’s very little loss in vmg. If you can get decent improvement boat speed from a small change in course like this then it’s worth while.

If you use the more detailed techniques that we’ve looked at you should make better gains, they’re worth considering on longer legs.

Remember that if you’re beating then it’s course changes relative to the rhumb line rather than to close hauled that count.

Effort spent improving your VMG can be effort well spent. Increasing average VMG from 5 knots to 5.5 knots can shave almost an hour and a half off the passage from Harwich to Oostende (roughly 80 miles), that’s plenty of time for a shower and a extra bottle of Belgian beer, well worth a little extra effort in my book.

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