Tuesday, May 20, 2014

Tricky Terms in Navigation

Good navigation calls for clear communications. We would like to think, then, that the terms we use have precise meanings. Most do, but there are common exceptions that we should know about. This is especially important when learning navigation. We go over here a few important terms that require special attention, either because their meaning changes with context or the definition is more subtle than might be guessed. Significance is hard to rate, so we default to alphabetical order.

Aspect. This describes the heading of another vessel from your perspective. It is a crucial concept in collision avoidance, especially at night as it directly reflects what lights you should see. It is defined as the relative bearing (R) of your vessel as seen from the other vessel. It is measured from 0° to 180° and labeled Red when we are on the port side of the vessel or Green when we are on the starboard side. Thus a vessel with aspect Red 270 means you are looking at its port side. Green 45 means you are looking broad onto its starboard bow. (I did promise tricky—045R is the definition of broad on the starboard bow.)  

Allision. When two vessels underway run into each other it is called a collision. When a vessel runs into a dock (assumed above the water) then that is an allision. Allision is damage causing impact between a vessel underway and something not moving, such as an anchored vessel. This would seem just Admiralty Court jargon—there is, for example, an official “Oregon Rule” that presumes the fault lies with the moving vessel—but there are more subtle implications to this concept that I have always considered fundamental to basic navigation.

The word allision is not in the Navigation Rules. In fact, the only reference in the Rules at all that refers to collisions with anything other than another vessel is in Rule 6 (b) ii, on the things we must take into account when choosing a safe speed when using radar: “the possibility that small vessels, ice and other floating objects may not be detected by radar at an adequate range.” [emphasis added]. Though never stated specifically, clearly the authors of the Rules intended this document to be the guide to not running into anything. And it remains true. If you know and obey the Rules, you will avoid not just collisions but also allisions, which can be even more embarrassing.

Course made good (CMG). This is our average course over a specific distance or time period relative to the fixed earth. It is the direction from an earlier position to a later position, regardless of the track between these two positions. It can be something we have already done, such as our track of past positions shown on echart plotter, or it can be something we plan in the future by anticipating the course we will achieve in the presence of current or leeway. It should not be confused with COG.

Course over ground (COG). This term is known to everyone who uses GPS. It originated as one of the first important derived values we learned from LORAN units. It has, however, been generalized in modern times to a point where it risks distracting from effective communication. It is best thought of as the instantaneous value of our CMG relative to the fixed earth that we read from GPS. Past or future courses are best described as CMG, not COG. The predictor line on our vessel icon in echarting points in the direction of our COG. The trail of dots behind the icon shows our CMG. When we solve a vector problem to account for current we are finding or using our CMG, not COG.

The same distinction should be made between speed over ground (SOG) and speed made good (SMG).

Declination. To a land navigator declination is the difference between magnetic north and true north. To a marine navigator this difference is called variation. In marine work, we reserve declination to mean the latitude on earth directly below a star or other celestial body. We further distinguish declination from latitude by placing the label N or S in front of declinations and after latitudes.

Dead reckoning (DR). This most fundamental of all navigation terms has two different definitions in modern times, both of which refer to a position determined for your vessel without the aid of any piloting data. (1) Position by log and compass alone and (2) your best estimate of your position taking into account everything you know about your boat, the wind, and the waters you sail. The former is found by plotting distance run on each logged course, with no further corrections; the latter accounts for current, leeway, helm bias and sea state.

This distinction is not crucial. A practical implementation is to plot the DR position by definition (1) and then apply all corrections you know about. The distinction lies only in what you call this final position, the estimated position or the DR position. We prefer the latter definition (DR is everything) as there is no real need for a second named position, and it is difficult to coordinate the plotting in a logical manner—correction for current and correction for leeway are plotted differently.
 
From a Dictionary of the English Language by Samuel Johnson, 1755.

Drift. Used alone, this means the speed of the current, which can be measured in knots or nautical miles per day. Wind drift is sometimes used to refer to the wind-driven current, but in other contexts, wind drift is used to describe leeway speed and sometimes used as a vector to include speed and direction. Spindrift, on the other hand, is the foam blown off the tops of waves. Its first appearance is a good Beaufort Scale benchmark for about 30 kts of wind.

Estimated position (EP). If one chooses to define a DR position as that found from compass and log alone, then anything you do to that position to improve it changes it to what is then called an estimated position. This is common training, though it does deviate from the historical meaning of DR and may add some ambiguity to the plotting. On the other hand, if DR is defined as including all you know about your navigation in the first place (short of piloting), then a DR position and an estimated position are the same.

The term estimated position requires more care when it is expanded to include piloting data, such as a single line of position (LOP) or a depth contour. If you have a single measured LOP, then in its broadest sense, one can define EP as your best estimate of your position taking everything into account, including this one LOP. This is indisputably a sound definition, and indeed the proper guide to position evaluation underway.

The required care comes into play whenever a specific prescription is given on how to do this. This type of EP, for example, is frequently defined as the point on the single LOP that is nearest to the “DR position” at the corresponding time—which immediately drives us back to the terminology. This use of “DR position” cannot mean DR by log and compass alone, because known corrections can take you away from the nearest point on the LOP. Thus this prescription must be worded: the estimated position is the point on the LOP nearest to the estimated position without the LOP.

Even then we must be careful. When you measure an LOP by any means (compass bearing to a lighthouse or sextant sight of the sun) and this LOP does not cross through your corresponding DR position, you know only two things: one, you are on the LOP somewhere, and two, your DR is wrong. We can project that point onto the LOP and call it the estimated position—as you must do on any navigation exam!—but underway, we should remember this is largely wishful thinking. If the single LOP crosses right through the DR position, then you can add to your knowledge that the DR might be right.

Log. This term has several meanings, all related. Verb: Make an entry into the log book (“I logged our mark rounding.”). Verb: Travel a distance (“We logged 130 miles today.”). Noun: Another name for logbook. Noun. Device for measuring distance traveled through the water (knotmeter log, taffrail log, chip log, etc).

True wind. Every meteorologist in the world, and I would hope every navigator in the world, agrees on the definition of true wind. It is the wind speed and direction relative to the fixed earth. For some aspects of sailing performance analysis, however, it can be useful to know what the wind is relative to the water, which in turn can be moving. Periodically we see this later wind referred to as “true wind,” and that should be avoided. We should not even say “true wind relative to the water,” which only muddies the matter. Ben Ellison of pandbo.com has suggested calling the latter the “water wind,” which seems a good solution. Google the phrase “true wind versus water wind” to find extended discussion of this terminology.

Range. This is an important term in navigation with several distinct meanings. It can be used to refer to a specific distance between two points on a chart (“range and bearing from A to B”), also used as distance from vessel to radar target (range rings, etc), but it is also used to mean the maximum effective distance a light shows, or a radio or radar beam reaches (nominal range, luminous range, VHF range, etc). Likewise we refer to the maximum range we can achieve under power without refueling. And of course there can be a mountain range along the coast. Thus there are a whole range of extents using this term. 
 
Extend a given extent on a chart and you get what the British call a transit, namely the line on a chart between two landmarks or aids, which in US parlance is called a range. A navigational range is between two aids put in place for that purpose; a natural range is any two objects you choose for navigation, charted or not. All navigational ranges show the nearest mark or light lower than the farther one, and a similar convention on ship's masthead lights (forward lower than aft) has led to the nick name “range lights” for the two white masthead lights on a ship that tell us which way it is headed. By watching the space between them we can tell if and how it is turning.

Less often used is the verb to range along a coast, meaning to travel at a fixed distance off.

Sea mile. A nautical mile is defined as 1852 meters, exactly. A sea mile is a distance of 1' of latitude. We tend to use these interchangeably, which is rarely an issue... unless you are hiding treasures by GPS coordinates in both Alaska and the Galapagos, where the latter has a sea mile that is 50 ft shorter.

Set. Set is the true direction a current flows toward, but it is also used as a verb (to be set by the current), and also used to refer to the magnitude of the offset. “The set of the current is 200 T, which is causing me to be set off course. The GPS shows my set is 30º to port.”

Tide. Vertical motion of the water is the tide; horizontal motion of the water is the current. We are better off to not ask what the tide is doing when what we want to know what the current is doing.

Velocity made good (VMG). This is a derived term that actually predates LORAN. It began as a sailing performance term, which means your speed projected onto the direction of the true wind, either upwind or downwind. It takes a simple processor chip to compute; no position data are needed. It is still used that way, and in a sense this is the preferred meaning of the term. But with the advent of LORAN and later GPS, this term began to be used as the projection of your SOG onto the direction of your desired course. (Recall speed is just a number, but velocity is a vector, meaning a number and a direction.) Thus we get some integrated instrument systems reporting both VMG Wind and VMG Waypoint, which is tidy enough, we just need to be careful when discussing VMG on the boat. Our main concern arises when we have instruments reporting just VMG. Then we have to look up what it means.

Waypoint closing velocity (WCV). This is the NMEA term for VMG to a waypoint. It would be nice if manufacturers converged on common terminology, but they do not; we do not see this one used very often, maybe because it's harder to say.

With special thanks to Starpath instructor Larry Brandt for valuable suggestions.







Friday, May 9, 2014

Hawaii by Sextant — An Overview of Celestial Navigation

Most blue water sailors think about celestial navigation at some point. Many pursue it so they can  navigate on their own if they need to. They do, after all, have a boat that can proceed without power–nor any other communications with civilization–so why not learn how to navigate it in those conditions. It is not a challenge power boaters have to face.

Until recently, a sailor would learn cel nav from textbooks using carefully crafted examples of sextant sights, and thus learn how the process works. But the real world usually differs from the classroom, so we are left to learn the practical matters on the wing, when we really need it. A new book from Starpath Publications called Hawaii by Sextant (starpath.com/HBS) takes a unique step forward to changing the options we have for learning cel nav. It brings the real world into the classroom.





The book is a documentation of the ocean passage from Victoria, BC to Maui, HI carried out in 1982, when cel nav was the only means of navigation available, other than log and compass. The essence of the study is the logbook of course changes done between the celestial fixes, along with watch times and sextant readings to each of the bodies sighted. The work is unique in that even the classic early texts of Bowditch and others used manufactured data for their training voyages, whereas this book uses real data.

The boat was taking part in the Vic-Maui yacht race (vicmaui.org, even years), one of the three popular races to Hawaii from the West Coast, including Transpac (transpacyc.com, odd years) from Los Angeles to Honolulu, and the Pacific Cup (pacificcup.org, even years) from San Francisco to Kaneohe Bay, Oahu.

The study includes over 220 sextant sights making up 27 position fixes, over the 2,800 miles logged that lasted 17 days. It was a slow passage for a yacht race, but it was not uneventful, and in long retrospect offers us much to learn about navigation of a small boat across the ocean. There were dead calms (crew swimming in the ocean) and 40-kt squalls with rain so hard you could not see the bow of this 40-ft boat. That under-the-faucet experience of what is called violent rain remains one of striking memories of the trip.

Here are a few key points we are reminded of from this new study of practical celestial navigation.

What you need
The basics are: a sextant, a watch with known error and rate, sight reduction tables, a nautical almanac, and universal plotting sheets. With a metal sextant and standard books, this costs about $900. With a plastic sextant and minimalist books, it is about $100. The minimal approach takes more work and won’t be as accurate, but does reflect what a safe backup package would cost.

What accuracy can you achieve
With practiced use of a metal sextant, employing good procedures, in good conditions, you can find your position underway within an accuracy of 1 nmi. Pushing this to the limits might get you half of that, but never better, and indeed rarely that. More routinely a position within 2 to 5 nautical miles is more likely. Much worse than that, means something is not being done properly. The keys are good procedures and proper accounting for the motion of the boat during the time of sight taking.

When do you do it
Sun and moon sights can be taken at your convenience during the day. Star and planet sights are only available in morning or evening twilight when you can see both the bodies and the horizon–typically a 30-min window, depending on latitude. You have a long time in Alaska (assuming the sky is clear), but the “sun comes up like thunder on the road to Mandalay.”

When relying on cel nav exclusively, you try to get star sights either in the evening or morning, and one fix from the sun during the day. But this will not always be possible, either because of the sky or because of your schedule. In the summer the nights are short, so morning or evening plus one day session is usually enough. When the sky is overcast or cloudy, you have to take every sight you can, because you do not know when you won’t get anything.

How do you do it
With the sextant you measure the angular height of the body above the horizon, and carefully note the time to the second. The goal in star-planet sights is to do this 4 or 5 times for each of 3 bodies, roughly 120º apart in bearing. That is the ideal. In practice you take what you can get in the time you have. With these sights you can then figure where you were at the time of the sight taking. But clearly if you are moving at 7 kts and it takes 30 minutes to do the sights, you have to choose a time, and adjust all sights to that time.

For the sun navigation you choose a time, take 3 or 4 measurements, about a minute or so apart, then wait for the bearing to the sun to change 30 or 40º and do it again.  Then using your dead reckoning (DR) between sights, you advance the first sights to the second for what is called a running fix.  It is just as good as star sights if you have good DR between the sights.

A daylight sun-moon fix is a bonus available a couple weeks each month. A prominent moon at twilight is usually more trouble than it is worth; it distorts the horizon. The bright planets Venus and Jupiter are always a bonus as they can be seen in the daylight phase of twilight, when the horizon is sharp.

Then comes the paper-work, called sight reduction.  With a programmed calculator or computer program you can do everything you need in a matter of 20 minutes or so to find a position. Doing it all by hand with tables and plotting, it will take about an hour to get a fix, or twice that to do the best you can. We have to accept that this is more work in a moving nav station than it is at the kitchen table where we learned to do it…. but not so much as it might seem, because everything we do at sea is harder than on land, and at some point we simply adapt to this moving world. At home you would get mad if someone jerked the chair out from under you every few minutes as you tried to concentrate, but after a few days at sea, you just get up and keep working… or figure out a way to stay in your chair.
Plot of three fixes and the DR between them.


The importance of ocean DR
Besides having a record of actual sights and logbook records in all manner of conditions, with multiple examples of having to pull a fix out of limited data, we see in practice the main reason we do celestial navigation. It is not so much just finding out where we are; the main goal is to learn how well we can navigate without it. In other words, we use it to test our DR.

It is precisely the same goal we should have today crossing the ocean using GPS. Each time we get a fix, we compare that fix with where we think we should be based on our log and compass records, adjusted as needed by how we think the current, waves, and wind have affected our progress.

No matter how we navigate routinely (cel nav or GPS) the main goal of prudent navigation is to learn how well you can navigate without it, with no electronics and with the sky socked in or no usable horizon. A lack of clear horizon is as often a show stopper to cel nav as is an overcast sky.

The question addressed is how accurately can we expect to navigate by DR alone? The proposal we have used for years is you must think of this in two ways. First, consider a position uncertainty that is growing at the rate of 7% of your distance run, and at the same time assume you are in a current of 0.7 kts in a direction you do not know. After logging 100 miles with good records of all course changes (assuming calibrated instruments) and accounting for leeway and any known or predicted currents we must assume our position is uncertain by 7 nmi. If this run takes us 24hr, then we have an additional position uncertainty of 17 mi (0.7 x 24). These combine as the square root of the sum of the squares for an uncertainty of about 18 miles.

In that example the time dominated. Traveling at 10 kts for the 100 mi, the error current adds only 7 mi to the uncertainty.  This does not mean you are wrong that much, it just means that is the uncertainty you must use when making decisions on your route based on DR alone. The larger will dominate in this statistical addition.

Mesocale current eddies
A day to day study of this comparison and what you can learn from it is covered in this book, and one of the things that stands out is a week-long shift of the DR to the east, in what was effectively an error current of about 1 kt.  This observation was not fully appreciated at the time of the voyage, though it was indeed recognized.  Since that time (1982) oceanographers have learned a lot about ocean currents. That shift of the DR to the east was almost certainly the work of an unforeseen mesoscale current eddy. The speed and size are consistent. The DR before and after that was normal.

These are loose canon circulations of the ocean surface that form and migrate and dissipate in seemingly random fashion, though indeed there is a complex theory behind each one, just as there is to the  water surface in a washing machine. It is just difficult to predict. Modern ocean models are getting much better at this, but they have a long way to go for routine application to navigation. We have extensive notes on this at starpth.com/currents.


The images below are explained in the text. We cannot count on climatic values from Pilot Charts to be pertinent when underway.  The colored squares mark the same location.









The main message is ocean currents can be larger and quite different from those predicted on Pilot Charts and we should be on the alert for their effect.

Tropical storm forecasting
Another reminder we get from that 1982 voyage is the value of modern tropical storm guidelines we get from the National Hurricane Center (www.nhc.noaa.gov/prepare/marine.php). One is the 34-kt Rule telling us to avoid the forecasted region around the storm that has winds stronger than 34 kts. This region is included in the forecasts and reports. The second is the Mariner’s 1-2-3 Rule that tells us how the uncertainty in the predicted storm location increases with the forecast days: 100 miles for 1 day, 200 miles for 2 days, and 300 miles for 3 days.

In 1982 we were on a collision course with Hurricane Daniel for about 10 days, after which the system degraded to a tropical storm and altered course to the south. As it turned out, we both got to Hawaii at the same time, and we did experience remarkable squalls likely associated with that system. Had we known these NHC rules then, we would have had more quantitative guidelines to consider. What was left mostly unsaid on the boat at the time was we never were out of a collision course with the system, because the statistical path of such storms is a curve poleward, straight at us.




Always old, always new
I encourage ocean sailors to have a look at this book for a modern review of the oldest way to navigate and to keep in mind our own guideline to prudent, efficient navigation: always old, always new.

Friday, April 25, 2014

Fit-Slope Method — A Shortcut to the Manual Solution from 1856

We are in the process of a much needed office clean up, and in the process today found a copy of our first text book on cel nav dated 1978—a loose-leaf set of pages that we photocopied (or maybe even mimeographed! for classes).  In that book we found a page related to the Fit-slope Method that we outlined in our new book Hawaii by Sextant.

It is not clear how relevant this is in light of other options, but it does show how we were discussing this a long time ago, and this discovery led to the thought of archiving some of these obscure materials that have moved in and out of our mainstream teaching.  Below is the related page... as it turns out there are rather a lot of these items.


Zoom for our 1978 description.
This table is from Wm Thom's 1856  text on navigation, a time without sight reduction tables (let alone electronic calculators), so this type of shortcut was much more valuable then.  It tells us simply how fast a body rises (the 'slope' part of fit-slope) as a function of latitude of observation and bearing to the body. (The 25 edition from 1902 is online.)

To use it you go down the left side to your latitude, then across to the azimuth angle (figured from actual Zn) and then go up to the top to get the slope in arc minutes of Hs per 1 minute of time. For example at lat 42 a body with Z = 64 and 81, rises respectively at 10' and 11' per minute. Note that this result does not matter what body it is, North or South Lat, and it could be to the left or right of North or South by Z.  If your actual sights had a Z of say 73, then the slope would be about 10.5' These are the conditions of Problem 3 from Hawaii by Sextant.  (Our iPhone app called InterpPlus gives fast accurate interpolations for any nav problem, in any units.)

If you have taken multiple sights of a body in these conditions, and you plot Hs vserus WT (sextant height vs watch time), then these sights should each fall on a line that has a slope of 10.9' per minute. You draw that slope on the graph and then move it up and down with parallel rulers to find the best fit to the data, often spotting outliers.

So that is a shortcut way to get the right slope, which could save time in some circumstances,  but we can also get this result manually direct from modern sight reduction tables by just doing the sight reduction of the first sight of the session to get Hc, then do one for the last sight of the session to get Hc, and the difference in Hc divided by the difference in times is the slope we want.

An example from Problem 3 in Hawaii by Sextant, which is a series of 5 sun sights starting at 0827 and ending at 835. From Pub 229 we find the Hc at each end and subtract go get a slope of 11.0' per min.  Recall that LHA increases at 15º per hour so every 4m of time is 1º of LHA.


Relative t=0m t=2x4m
WT 08h 27m 0s 08h 35m 0s
Lat 42 42
Dec 22 22
LHA 280 282
Hc 21º 44.1' 23º 11.9'
Z 79.4 80.6




dHc/dT = 10.975'


Back in the day when folks actually used cel nav for routine navigation, the Pub 214 Sight Reduction Tables actually listed the slope of Hc every hour of LHA, which then was presented as hour angle HA (0 to 90).  It is not clear that they anticipated this application; it was there primarily to allow plotting an LOP from a DR Lon on the assumed Lat line. 



Our start HA was 80, ie a body that has LHA 280 is 280 west of us, which puts it 80 east of us.  At the end of the sights this moved to 78 east of us.  The delta d is same as we now call d-value; the delta t is what we are after, which is change in Hc for each 1' of HA. Multiply that by 15 and you have the change in Hc for 1m of time.  BUT... we have to know that these values of delta d and t are given multiplied by 100.  That is the 73 we see should really be 0.73.  I would like to say it is strange they do not explain that in the book, but it is actually not so strange for early nav books to gloss over details that are crucial to their application—the mumbo-jumbo factor.




Thus we see that 0.73 x 15 = 10.95' is the slope we want, from just one multiplication.