Introduction

In this module we are going to learn how to get from A to B and to keep a track of where we are when there is nothing to fix with. Nothing to see but sea! Navigating.

Topics covered in this module are

• Dead Reckoning.
• Estimated Position.
• Course to Steer.
• The Running fix.
• GPS fixing techniques

Including leeway drift and errors.

There are a few terms and standard notation to revise first:

Water track  is the course through the water a vessel makes.

Leeway  is the angle between the vessels course steered and its water track.

On some courses, particularly when the wind is on the beam or forward of it, our water track is governed by two forces:
Our forward speed and the wind pushing us sideways. This angle is hard to judge and accuracy comes with practice and experience. Take a bearing of the wake of your boat, then compare it to the reciprocal of your course steered (reduced to magnetic). The difference is your boat's leeway. Different types of vessel have varying amounts of Leeway, just like a high-sided truck might be blown over on the motorway, but your car will not.

Dead Reckoning

This method is used to work out our position when we cannot see any marks, or we cannot positively identify the marks we can see.

Here is an 8 step guide for plotting a Dead Reckoned position:

1. From a known position (Fix), note your log reading and time. (4 M at 0900UT)
2. Then steer a course. e.g. 100° Magnetic.
3. After some time, perhaps an hour on a passage, take a further note of the log. (8M at 1000UT).
4. Take the first log reading from the second and you have the distance run in the hour since you took your fix.(4M)
5. Next reduce your course steered to a True course...  eg, 100º Compass. No deviation. 5° west variation becomes 095° T.
6. Plot this bearing from your fix.
7. Open your dividers to measure 4 miles on the latitude scale.
8. Place the dividers on the fix and mark off 4 miles along the course. This is your DR position.

Dead reckoned positions are useful when you need a quick idea of where you are or when there is no tidal stream. After the last module though, you know the tide might be going somewhere other than where you’re going and faster!

So we need a better method……

This method takes account of both tide and leeway.

Here’s a four step guide to working out your Estimated Position.

1. Plot a DR, but include leeway.
2. Find out the tide experienced in your area between your fix and the time of the EP.
3. From your plotted DR position, plot the tide
4. The end of the tide is your EP

Let’s work through an example.
You need Chart 1.

We are crossing the channel from France and luckily sight EC’A’ Buoy

(50º 01’.0 N 005º 10’.6 W). The time is 0300 BST and the log reads 20 miles. We are heading for Fowey. Our course is 320º Magnetic. (I am keeping this simple at present and not dealing with compass Deviation). Let’s plot that lot.

At the buoy draw a circle and put the time and log reading next to it.
From the buoy, plot (draw a line) the course in True.
Yes, we have to work out the variation first. You can see the nearest compass rose showing Variation of 7º W.
True to Magnetic add west. Magnetic to True minus west. Take 7º from the course steered.
i.e. we are steering a course of 313º True.

We also have a northeasterly wind blowing and we estimate our leeway at 5º. In other words, because the wind is coming from the east, over our starboard bow, the boat will be blown to the west. So, although we are steering 313º True, (the pecked line) we are actually being pushed off our course by a further 5º. This is the leeway we are making. Therefore, the actual course is 308º True – this is known as the water track.

If that is a bit difficult to understand, try to remember: -

"Wind on starboard side reduce for EP";
320º – 7º (Variation) – 5º (leeway) = 308ºT
308ºT is the bearing to plot from your fix to take
account of magnetic variation and leeway suffered.

At 0400 our log reads 28 miles. We have covered 8 miles in one hour.

With the dividers measure 8 miles (minutes of lat) opposite your position and mark that off along your water track including leeway, to produce a DR.

So far, we have completed Step 1 of the Estimated Position

By using either the Tidal Diamond on the chart or the Tidal Stream Atlas, we find that the tide over the LAST hour in our area has been 230ºT at 1.2 Knots.

From your DR position, plot a line at 230º T for 1.2 miles.

At that point draw a triangle and write down the time and log reading. That is your new position and your vessel has travelled between the circle and triangle, not along the two lines!

The line which joins the circle to the triangle is called the Ground track. If you measure the distance between the two, you will see your vessel’s speed made good or Speed over the ground.

In the above example we have done a one hour EP. If you only travel for half an hour then use half an hour of tide. (half the speed of tide in knots)

Exercise 18

Or if you are on a longer trip or just haven't had time to do an hourly EP, you can just add up your distance run, plot it then plot all the different tidal rates and streams on the end. As you can see, the result will be the same. 

If you had to alter course for some reason eg tacking to windward, then you simply plot your water tracks including the leeway, then plot the tide on the end.

Occasionally you will need to use this technique (EP) to look forward in time to find out where you are going to end up. Your log will tell you how far you have gone, say in the last half an hour. So you assume that speed and can Estimate where you will end up in half an hours time by plotting your suspected water track and then the tide on the end. This method is a guide only as your speed may change over the period.
Exercise19

Using Estimated position has lots of error.

1. Your log will not always give you a true distance covered. See Module 1, Logs
2. Your course steered may well not be accurate, due to helmsman error or various compass errors. See Module 1, Magnetics
3. Leeway is hard to judge accurately, even with experience.

Because the boat does not go where we point it we need to be very careful. If there were a danger along the ground track then we would have hit it! Remember EP is finding out where we have been! not where we are going.

When the wind is against us we have no choice about our course. We steer as close to the wind as possible. Usually about 45º off. We have to EP.

Deck log
I keep going on about log readings and times and I feel I should mention this log. Not to be mixed up with the log (distance measuring device) 
This is the ships log. A legal record of the yachts activities. You must keep a log. There are two reasons for keeping it 

1. It's the law
2. It is impossible to navigate effectively without one.

In the log, you keep a note of all Times, log readings, courses, and positions Then you will have them when needed later. (remember that most of navigation is done retrospectively)
Also in a good ships log will be weather information, barometer readings, VHF calls (this is also a  regulation) A narrative is also helpful, telling the story of the day. For example, if you had a collision or a man overboard or any kind of notable incident, these must be logged.
Write in ink and in capitals as it is often tricky to read small case when it has been written in a storm!
I say write the log. What I mean is make sure it is written. You probably will not have time to keep it your self, but you have chaps to do that.

This is where we take control of our destiny and work out a course to make best use of wind and tide, rather than simply pointing the boat and suffering them!

To learn how to shape a Course to steer, we will use the same situation as in EP above.

Here is a 5 step guide.

1. Plot your desired Ground Track.
2. Find out the tidal rate and direction in your area for the next hour.
3. Work out your True Course to Steer, allowing for tide.
4. Counteract your leeway.
5. Convert to the Magnetic Course to Steer.

We have a fix at the EC’A’ buoy. It is 0300. The log reads 28 miles. Wind is northeast and we have found that the tide will set at 230ºT and its rate will be 1.2 knots over the next hour.

Rub out all traces of your EP. Draw in another circle with the time and log reading around the buoy. Now, this is where things change. Draw a line from the buoy to Fowey entrance and put two arrows on it (Ground track). Step 2. Mark off the 1.2 knots of tide on 230ºT FROM THE BUOY. Put three arrows on it
Step 3. Next we have to guess at our boat speed. As we sail along my eyes are usually glued to the speedo to make sure we are going faster than every one else. I’m sure you will be just the same! You will know the speed. Let’s assume 8 knots. Measure 8 Miles (minutes of Lat) on the lat scale. From the end of your pencilled in tide, scribe an arc across the ground track with the dividers set at 8 miles. Put a mark at this point in pencil. Draw a line from the end of the tide to this mark with your plotter. Now, find out what the bearing is from the end of the tide line to the mark. About 330º T? That is the True COURSE TO STEER, allowing for tide.
Before you ask – ‘scribing an arc’ in this case simply means; Take the dividers, set to the correct distance Place one point on to the end of the tide Place the other point onto the ground track, wherever this happens to cross. The most common mistake when working out Course to Steer is normally made at this point. You naturally look at where you want to end up overall (i.e. Fowey entrance), rather than where you can go in the next hour. So you might be tempted to draw a line straight to Fowey entrance from the end of the tide. You then use that as the True course to steer. This is wrong! – Remember to ‘scribe the arc’ instead!! Step 4. Now we have to counteract the leeway. We will be blown west by this Northeaster, so we must add on 5º to counter it. i.e. steer more to the East. "Wind on starboard side reduce for EP, add for Course to steer". So 330º + 5º =335º T Step 5. Then we have to convert to Magnetic. "True to Mag add west .Mag to true minus west". 335º plus 7º variation = 342º Magnetic is the COURSE TO STEER to stay on the Ground track. The boat will sail up the ground track but its heading will be somewhere else. At this point we would check our deviation card and apply any correction required. "Error West Compass Best. " ie compass is bigger than magnetic so add it on "Error East Compass least." ie compass is less than mag, so take it off       CALCULATING AN ETA
If you measure the distance from the fix to the scribed mark, it is also the ground speed. Measure it on the lat scale. Yes, the tide is slowing us down a bit. We are making good 7.8 Knots. How? It’s easy. Just measure your ground track (two arrows) as shown. From this we can work out our speed and therefore our time of arrival at a given point.

Using the simple formula. "Dinner Time Session" (I was taught this one by a Royal Marine Who was terrible at math’s, but loved going to the pub at dinner time!)

Distance, Time and Speed

To explain this, let’s see when we will leave the "area to be avoided" around our buoy?

We know from measuring the ground Track, that our speed is 7.8 knots. I make the magenta limit line to be 0.7M from the buoy.

Put the numbers into the formula: -

Therefore, to find the time taken to leave the area, we use the formula as follows;

Time = Distance / Speed
Distance is 0.7 M
Speed is 7.8 knots (nautical miles per hour)
Time = 0.7M / 7.8Knots = 0.089 hours

To convert the time from hours to minutes, just multiply by 60 = 5.38 minutes.

5. 38 minutes to get out of the area that we should not have entered in the first place!!

Time equals Distance over Speed. (Multiply by 60 to convert hours to minutes)

Speed equals Distance over Time. (Change minutes to hours first - divide by 60)

Distance equals Time multiplied by Speed. (Change minutes to hours first - divide by 60)

If all else fails, there is a Time, Speed and Distance table in all almanacs, but I’m afraid you don’t have one in the Practice Navigation Tables.

Even if you are only using your course to steer for a few minutes, you still draw the tidal vector for an hour. All those lines and arrows are a vector diagram. If your chart covers such a small area that you cannot plot the boat speed and tide for an hour then  Mini vectors

If crossing the channel or your destination is more than one hour away, you could decide to compile a multiple tidal vector to stay on the fastest ground track over the whole passage. There are a few problems with this method. First you must be sure that the courses steered do not take your vessel over or too near to dangers. Second, for this method to work, your speed needs to be relatively constant throughout. (difficult on a sailing vessel!)

Here's how.
Using the tidal stream atlas (with the correct High water time pencilled in!) Guess at a speed that your vessel is likely to make. Then mark off dead reckoned positions in the tidal atlas for each hour. Make a note of rate and direction at the DR for each hour. Do this until you have reached your destination, then count up the hours.
Next plot the required ground track, from the start point to the destination. From the start point, plot all the tides as shown. From the end of all these tides, using your boat speed multiplied by the number of hours that you found it would take, scribe off an arc through the ground track to gain the course to steer.

Exercise 20a

The Running Fix
This is a method of fixing when there is only one point to fix on. For example, you are on passage across the channel for Plymouth and you sight the Eddystone lighthouse. This is all you can see as the visibility is down to three miles.
Take a bearing of the lighthouse and note the time and log reading and course steered. Wait until the bearing has changed by at least 40 degrees, then retake the bearing and note time and log again.
Plot fix like this.

On the chart, plot the first bearing to the lighthouse. Then from anywhere on that line draw out your course steered. Mark off the distance run along this line. (logged distance between the two bearings) On the end of your distance run, plot the tide for the time between the two bearings. Plot the second bearing.
Now "transpose" (keep it parallel) the first bearing through the end of the tide. this transposed bearing will also cut the second bearing and that is your fix.

Ok now a few words about cheating!

We all have GPS these days and here are a few methods to make good use of the machine

Waypoint webs
This is a method of quickly finding out where you are when you don't have time to plot a Lat Lon from the GPS. (which you might well interpret incorrectly anyway!)

Lets assume that we are tacking into Torbay in a westerly wind, in the dark. there are only two of you aboard so not much time for navigating!
Before you started you have prepared yourself a way point web to help free off the navigator as you get close. All he has to do is check the distance to go and the bearing to the waypoint at Paignton to be able to put his finger on the yachts position.
the GPS shows the bearing to waypoint as  277mag and the distance as 1.5M. because you have the web its easy to put your position on the chart. Don't forget to tell the GPS to give you a True or Mag display!

the trickiest bit with this stuff is simply working out how to enter a waypoint into the various GPS sets, but you soon get used to your own.

Cross track error ladders.

We are now on our way to Holcombe Bay. its still dark and we are two up, but at least the winds behind us for a change! Unfortunately the leading lights are obscured by bad vis. A cross track error ladder can show us quickly and easily where we are. Again with out plotting Lat lon.
just enter Holcombes front leading light as a waypoint then draw the ladder as shown. Just like the waypoint web, you can easily plot your position from the XTE readout (how far off the ground track you are to left or right) and the distance to the waypoint.

You cannot see the scale on this picture, but I hope you get the idea. the GPS says XTE 0.3M and the distance to go (to the waypoint) is 1.5M so that's where we are!

Exercise 20b

That’s all for this one.

I hope you know the meaning of a line with one, two, or three arrows on it.

You know that in navigation, the yacht’s position is not known exactly, there are lots of errors, but by keeping a good record and careful work you can reduce those errors sufficiently to make your EP usable.

If by some miracle the wind allows you to go where you want to, you can lay off a course to make the best use of the tide and you will know how long it will take to get there.

You are never going to forget that boats don’t go where you point them, they are always going somewhere else, and that somewhere else is governed somewhat by your course steered, but also by leeway and tidal stream.