Dead Reckoning

In this series of posts, I deal with assessing motion.

To a large extent, most navigation on foot or by kayak proceeds just by comparing objects you see while traveling to objects marked on charts.   Every so often an object is incorrectly mapped on a chart, of course, and this can cause some confusion.   Trails shift to avoid erosion problems, buoys are moved around, and every so often a map-maker can just plain make a blunder.   It's important to keep that in mind.   GPS users are not immune from this problem either, as the information accessible to a GPS database can have the same errors that persist on chart.   By-and-large, however, mistakes are relatively uncommon.

The step from simply inspecting a map to pulling out a compass can be somewhat rare.   If I look back over the last year of travels, there were few instances when I had to pull out the compass, and it's worth listing them.

1.) An off-trail hike in the snow in the Sandwich Mountains.   We planned to hike up a drainage of a creek and then up over a saddle to a nearby lake.   The shape of the land didn't seem to match up with where I thought we were.   My friend Brad Holmes pointed out that we couldn't possibly be where I thought we were.   I was perplexed.   I finally took out the compass and took a sighting on a mountain peak, and used the back bearing from the peak and its elevation to locate us.   It turns out that the map incorrectly showed the path of the creek.    I continued to use the compass at that point to make sure I knew where we were heading.

2.) I was out kayaking with Dan Carr near Stonington, Maine.   There are a large number of islands off the coast there, and it's easy to get confused.   As we were pulling out after a lunch break, I used the compass to get my bearings to an island and find the way back to our campground.

Other than those two occasions, I don't recall having to use my compass, although I always had it with me.    In seven days of hiking in the Alps, I didn't once have to use a compass, but we were largely traveling on marked trails.

Now, there is another navigational skill which can be a life-saver, but can be even rarer than compass use: dead reckoning.    A sea kayaker should be relatively proficient in dead reckoning for one big reason: fog.

All of the discussion so far on these posts was predicated on the assumption that you can see landmarks, and objects in the distance.   When a thick fog descends, that all goes out the window and you have to estimate your position and progress toward a goal with dead reckoning.   Many people carry a GPS with them in case of fog, but one has to be wary, too.   GPS receivers can fail for any number of reasons - lack of satellite reception, dead batteries, or the actual receiver itself fails (which has happened to me).

In dead reckoning you use a history of travels from a starting point - called a point of departure to figure a position.     By way of analogy, consider private pilot licenses.  The first license people typically get is called VFR - or Visual Flight Rules.   The idea is that pilots who have a VFR license can only fly when the weather conditions allow for visible references in the distance.  The next step up the ladder is an instrument rating.   This is for pilots who want to be able to fly in conditions where visibility is significantly impaired.    For a kayaker paddling when a fog bank descends, he or she is in a similar situation as a pilot who has to rely on instruments.

It's often helpful to carry a grease pencil with you to mark up maps or charts with information or course bearings.   In a recent post, I noted how to move in a straight line by taking a sight and lining up objects in the distance along a heading.   If you're fogged in, you obviously can't do this, but there are some fallbacks.   First, if you have a compass, you need to monitor your heading on a regular basis, as it can be easy to walk or paddle in circles without a visual reference.

The figure below shows a typical deck-mounted compass for a kayak.  It's free to swivel around in all dimensions, so it remains horizontal even in wavy conditions.   The compass should be mounted so that the main axis of the kayak is parallel with lines on the compass called lubber's lines, which give you the heading of the kayak.

Figure 1 - Typical deck-mounted compass on a kayak.

In addition to the compass, there are a number of natural signs that allow a person to maintain a heading in the fog - wind direction tends to be reliable, at least over period of many minutes, although I have seen it shift.   Waves also act as markers, as they're pushed by the wind, but remember that waves can refract due to changes in underwater bathymetry.   Sounds can help a person maintain he or her orientation, providing they're coming from a known and fixed source, such as the bell on a buoy, or the sound of traffic on a highway in the distance.  

With a heading, you can extend from your point of departure what is effectively a line of position that is a bearing identical to your heading.   This can be drawn on the map with the grease pencil.   The other piece of information that you need to assess your position is the distance of travel on that heading.   This can be found in a number of ways.   The easiest is from the time of travel, assuming some uniform speed.   Obviously this involves having some kind of time-keeping instrument, or at the very least an ability to assess elapsed time - something people aren't terribly good at.   I have a robust watch that I wear, and am in the habit of always checking it when I launch my kayak or start out on a leg of a hike.   

How fast do you travel?   That depends on a number of factors.  

Hiking and walking speeds

This can vary from individual to individual.   When I'm left on my own, I walk very fast compared to most of my usual companions, so I find that I usually have to slow down when I'm walking with other people.    I estimate my walking speed is about 4 miles per hour when on level terrain without any weight on my back.   If I have a backpack on with any amount of weight, this slows me down to about 2.5 miles per hour.   If I walk uphill, I might slow down to 2 miles an hour.   I rarely speed up significantly when walking downhill however.   This is mainly because I tend to 'brake' myself on downhills to avoid injury by tripping over something.   

If I'm walking with others, I find that the pace is more like 2 miles an hour.   Factor in rest breaks and maybe a pack on the back, then the typical pace is 1 to 1.5 miles per hour.    

Distance equals speed times time.  When I was hiking in the Alps recently, all the trail signs were marked with destinations in time.   So, a sign might say "Col de Clapier 1.25" - meaning that the Col de Clapier would be 1 hour and 25 minutes away.   After seeing enough of these signs, I figured that whoever made them was using a walking speed of about 1.5 miles per hour ( 2.4 kph).   

The unit of a league was based on how far one could travel in an hour.   In this case, a league is 3 miles.

Another way of assessing distances when walking is from the number of paces.   The word mile is derived from the Latin phrase mille pacem - a thousand paces.   A pace is two steps, so every time one foot (pick right or left) touches the ground, it's a pace.   In testing students, I found that 1000 paces per mile is very close to the average over large sample sizes.   This number will, of course, vary from one individual to the next, and will also depend on whether he or she is walking uphill, downhill, with weight on the back, or any number of factors.   The best way to do this is to just measure your paces over a known distance, although people will rarely spend the time doing this.   In a pinch, 1000 paces per mile is a pretty good approximation on flat terrain. 

Kayak paddling speed

Again, this varies from individual to individual, and with conditions.   Let me remind you that on the water, people talk about speeds in knots, or nautical miles per hour, where one nautical mile is 1.15 statute miles (a bit over 6000 feet).   When I sprint, I can hit about 6 knots or a bit more.   The top speed of kayaks (and other vessels) is limited by the length.   

When I'm just paddling in a touring mode, I typically make about 3 to 3.5 knots.   This speed will drop going into the wind.   I find that heading into a 20 knot wind, my speed will go down to about 1 to 1.5 knots.   Going downwind, I'll definitely speed-up.   Still, wave conditions can affect my speed.  The most annoying seas are when I have waves quartering me from behind.   In these conditions, my boat will tend to yaw, which forces me to make some kind of rudder stroke to get back on path, and slows me down considerably.     With a quartering sea, I will sometimes just surf downwind, and then paddle back with the sea on the beam to regain my heading.   Unfortunately, I can't play this game in the fog, because I would lose my sense of location rapidly. 

Again, distance = speed times time, so keeping track of elapsed time with an educated guess at speed will help assess position.   

Like counting paces, a person can count paddle strokes.   Each time one of the paddles (left or right) dips in the water, count this as one stroke.   The number of strokes per mile will vary from one individual to the next, and also will depend on the kind of paddle.   Longer paddles take more effort to draw them through the water, but may get the same speed as a shorter paddle. 

I will average 420 strokes per nautical mile on flat water with no wind.   Into a head-wind, I'll average 520 strokes per mile, and with a tail wind, I will typically take 320 strokes per mile.   

Uncertainties in dead reckoning

I hope the above discussion leads you to understand that dead reckoning is not 100% precise, but uncertainties creep into the assessment of position.   It's important to have roughly some sense of these uncertainties and how to cope with them.   

Roughly speaking, I cannot guarantee my heading to any better than +/- 5 degrees.   As a rule of thumb, this means that the uncertainty in my position perpendicular to my direction of travel is about 10% of the distance I've traveled through dead reckoning.   As above, with the speed or the number of strokes or paces per mile, varying conditions and uncertainties will also translate into an uncertainty of position.   

The figure below illustrates how the uncertainties in heading and speed translate into an increasing uncertainty of position with time, which can is represented as the ellipses in the figure. 

Figure 2  How uncertainties in heading and speed translate into uncertainties in position over the course of time. 

Let's put this together on a planned trip.  I highly recommend trying this exercise at least once, even if in clear weather.   The chart below shows the southern end of Mt. Desert Island in Maine, and islands just to the south, the Cranberries.   I had a planned paddle from Northeast Harbor to Islesford on Little Cranberry Island.   

Chart of the SE part of Mt. Desert Island (Maine) and parts of the Cranberry Islands.

The exercise, here, is to chart a course from Northeast Harbor to Isleford.  The first operation is to lay out the variation lines, as explained in this post.  This is shown below.   The magnetic variation is 18 degrees, and the lines are spaced one nautical mile apart. 

Prepared chart with lines of magnetic variation drawn in, spaced 1 nautical mile apart. 

In the figure below, I show my sketched out path from Northeast Harbor to Isleford.  I've removed the magnetic variation lines to simplify the figure.   Each leg of the planned route is given in terms of nautical miles and the true compass heading.  In order to convert to magnetic headings, you can remember the CADET rule (see this post), in which case you add the magnetic variation of 18 degrees to find each magnetic variation, so the first leg of 90 degrees true would be 108 degrees magnetic and so forth. 

Planned route from Northeast Harbor to Isleford in terms of true headings and distances in nautical miles (nm). 

I then converted the information on the legs of the trip and made myself a table that gives me the true heading, magnetic heading, distance, time anticipated, and number of strokes.  The conversion of distance to time assumed that I paddled at three knots, which is about right for me.   The number of strokes per leg was based on the assumption that I paddled 417 strokes per mile. 

Table of headings, distances, time, and number of strokes on the route laid out.

This is an actual table I had made for myself for this paddle, which I reckoned would take just a little over an hour.  When I reached Northeast Harbor, however, and got ready to put into the water, there was thick, pea-soup fog.   At this point, I had a couple of choices.   I could have tried to get my kayak onto the mailboat that ran from Northeast Harbor to Islesford, but unfortunately it was too long for them to accept.   I had no choice to make a go of it.  

View of Northeast Harbor and boats moored in the fog. 

I paddled the first two legs - basically heading due east or 108 degrees magnetic until I hit the other end of the harbor.   I then followed the second leg, which was 189 degrees magnetic.   These were both relatively easy.   Although the fog was thick, I could still stay within sight of land. At the end of the second leg, however, I reached a small headland that jutted out and there was nothing visible in front of me.   I could *not* see Bear Island.    Now if you refer to my original game-plan, I planned to paddle on a leg of 144 degrees true (163 magnetic), but if I did this, I was afraid that the uncertainties in the compass heading would take me too far to the west of Bear Island and I would miss my next turning point, which was the buoy to the south of Bear. 

The first two legs were easy, but then I was confronted with a wall of fog. 

In order to ensure that I didn't miss Bear Island, I changed my plans and decided to paddle somewhat more to the east of my originally planned heading.   I decided to subtract about 13 degrees from the plan so I would hit square in the middle of Bear Island, which should give me some margin of error.  Here, I paddled at 150 degrees magnetic (132 true) until I reached the shore of Bear.   

Deliberate compass offset to reach middle of north shore of Bear Island. 

This technique is called a deliberate compass offset and incorporates some sense of the uncertainty of holding a heading.   In this case, I reached the northern short of Bear Island.   I knew from my previous calculation that it would take about 13 minutes to reach there, so after 10, I was relieved to see the shoreline.   

At this point, I decided to handrail around Bear Island, which means paddle along the coast, always keeping the coastline in sight.   

Handrailing around Bear Island until reaching the number 10 buoy, which is the next jumping-off point. 

I hand-railed around Bear, and then could see (barely) the number 10 buoy, which you can see on the chart above.   The chart says R "10" Fl R 4s BELL.   This means that it's a red buoy with a number 10 painted on it.   It has a flashing red light on it that illuminates once every four seconds and has a bell that rings by the wave motion.   It was pretty unambiguous to me, but it illustrates that an understanding of the chart symbols and their meanings can be quite helpful.   This buoy was my jumping off point for the next leg, which I originally planned to reach the eastern end of Sutton Island before turning south.  

As before, if I headed to the eastern end of Sutton, which I couldn't see, there was a substantial chance that I could paddle to the east of it, and miss it completely in the fog, so I had to make another deliberate compass offset.  In this case, I had to adjust my heading to the west of my original planned leg. 

Deliberate compass offset in leg from buoy to north shore of Sutton Island. 

To reach Bear, I made a deliberate compass offset of 10 degrees.   I felt comfortable doing this as that leg was rather short.   I perhaps erred on the large side by making a deliberate compass offset of about 30 degrees from my original leg to the west.   Part of the rationale for this is that there is a lot of boat traffic between Sutton and Bear Island, and I wanted to spend as little time as possible on the water between those to islands in the fog and tried to find the fastest route that would also ensure that I reached to north end of Sutton.   So, while I'd planned on a 123 degree magnetic heading, I ended up with a 153 degree magnetic heading.   

Once I reached Sutton, I hand-railed along with north shore.   

Now, this raises an interesting question.   I needed to have a good position fix before starting off on my next leg.   The number 10 buoy off of Bear Island worked well for this as it was a well defined point on the chart.   On the other hand, the coast of Sutton is continuous - what can one choose as a good jumping off point?   

Here is where you can take a bearing along the coastline to see roughly which direction it's running.  As I approached the eastern end of Sutton Island, I noticed that the coastline was beginning to turn to the south - first it was running to the southeast.   At some point, I was off of a point of land, and beyond that point, the coast began to run to the southwest.   I decided that I was at the easternmost end of Sutton and this gave me a good position fix to use for my next take-off point to Little Cranberry Island. 

So, here I wanted to again intercept the shore of Little Cranberry Island.  My original course had me skirting the west side of Little Cranberry, so I wanted to adjust my course to the east.   While the original course was 170 degrees true, I adjusted it to 150 degrees true (or 168 degrees magnetic).  

Deliberate compass offset to the east of the originally planned course to make landfall on Little Cranberry. 

This off set is shown in the figure above.  If you look closely, you'll see a buoy a bit to the right of the "G" in Gilley Thoroughfare.   While I was paddling on my final leg, I could hear the buoy first to my right and a bit in front of me, and then to the side of me, and then a bit behind me, so it provided an auditory clue as I made my way across to Little Cranberry.   Once I reached Little Cranberry's northern shore, I again hand-railed until I reached the docks of Islesford and took out. 

Comments

I hope you can see from the above exercise how the originally planned route and breaking it down into legs helped me adapt to the conditions of fog and how I used three deliberate compass offsets to help me find my way.   In addition, there were issues like using the sound of a buoy as a way of reassuring me that I was on my path. 

Now, this kind of strategy is not limited to kayaking.   If you're walking through a relatively dense forest on an overcast day, you have the same issues of uncertainties in dead-reckoning to deal with, so a very similar set of strategies can be employed, providing, of course that you have a good map.  

In the next post, I introduce vectors.