Friday, August 14, 2020


The value of mean high water (MWH) at a specific location on a chart can be a crucial number in marine navigation. We need it to figure how far we can see a light at night, and we need it to figure what a bridge clearance will be. It is also needed to know whether certain rocks will be visible or not at various stages of the tide. These are all basic safety considerations we face in routine navigation.

MHW plays these roles because MHW is the height datum used on US nautical charts, which is the zero point for light heights and bridge clearances. Note this is not the same as the elevation datum used for elevation contours and spot elevations shown on charts. The elevation datum is mean sea level (MSL), which for most  practical purposes can be considered equal to the mean tide level, halfway between MLW and MHW.

Strangely enough, the important values of MHW are not listed in the standard NOAA Tide Tables (see endnote), but they are listed on every printed nautical chart and their RNC counterparts. The data appear in a table called Tidal Information. There are generally several values listed for points across the chart.

As we transition into ENC, however, we notice the MHW data are not so readily apparent. In fact, we get MHW from an ENC in a rather subtle manner. Namely the green foreshore shown on a chart is a specified depth area (DEPARE) object whose two bounding contours are the sounding datum (tide = 0) on the water side, and the height datum (tide = MHW) on the land side. The latter is effectively the drying height of the land at tide = 0, thus it is presented as a negative contour height equal to MHW.  See Introduction to Electronic Chart Navigation, for details of this process.

That is the way it works, and it is certainly no harder, if not easier, to learn MHW from an ENC than it is from an RNC.

The nuance to this process comes about because the ENC uses only one value of height datum (MHW) for the full range of the chart. This is not an issue for larger scale charts covering smaller regions as then the MHW does not vary much, but on small scale charts, even just at 1:80,000 we can have MWH from one part to another vary by as much as 3 feet. When this occurs, NOAA chooses just one value to represent all values on the chart, and that one value is chosen with safety in mind, which I emphasize as that is the topic at hand.

Here is an example from the same region referred to in the Tidal Information table above that was captured from an RNC near Port Townsend, WA. First we look at two ENC chart scales, then the MHW on each.

We see that on a large scale chart, the ENC values change very little over the chart and the single value selected is a good representation of the actual values that we can read in the RNC table above. Oak Bay value is on the south side of the channel; the Port Townsend value is on the north side of the channel.

When we look at this same area on a much smaller chart scale, we now see that the ENC has chosen to use 10.5 ft to represent MHW on all areas on this chart, which does indeed span a much wider range of MHW values.

The question at hand is what does "safety in mind" mean in this choice.  If we have a range of MHW values, would the safest choice be the lowest of all of them, or the highest of all of them, or the average of the known values?  

Bridge Clearance.
Bridge clearance is maybe the most direct example. As I approach a bridge to pass under and my mast is right near the max that might get through, I know that I count on favorable tide to help me, so I have to reckon the clearance I have.  The charted bridge clearance is 58 ft, which means that when the tide height equals MHW then the distance from water to bridge is 58 ft. When the tide is lower than MHW I have more clearance.

Actual clearance = charted clearance + (MHW - Tide).  When the Tide is exactly MHW,  then I get the charted clearance,  and when the Tide is lower than MHW I get extra clearance, but if the Tide is higher than MHW there is less actual clearance than charted.  With a MHW of 8 ft and a Tide of 3 ft, I would expect a clearance of 58 + 8 - 3 = 63 ft. 

If this computation is to be wrong because the MHW value is wrong, most would agree you would want the clearance to err in the direction of predicting too little clearance, not too much clearance. If it erred being too big, I might try to go though and not make it. If the err makes it too low, I would not try…..or at least I would sneak up on it dead slow, hoping the tide itself was wrong and might sneak under. So with regard to bridge clearances, if my MHW is to be wrong, it is safest to have it be too small, meaning if we have a range of them over a specific ENC, but we can only choose one to use, the safest would be to use the smallest for all parts of the chart.

Geographic range of lights.
In clear weather, the visible range of a light is the smaller of the charted nominal range of the light and its geographic range in nmi, which is 1.17 x SQRT (Height of the Light in feet) plus a fixed term based on your height of eye.  The Height of the Light is given on the chart or in the Light List. These tabulated heights are all relative to MHW, which is the height datum of the charts. Thus a light with tabulated height of 20 ft would be that high above the water when the tide equals MHW. If the tide is less than MHW then the light is higher above the same water we are floating in, so we can see it from farther away. 

Similar to the bridge clearance, actual Light height above the water = Tabulated height + (MHW - Tide). So then what is "safest" or most conservative if the MHW is to be off a bit? Do we want it too big, which would make the light higher than correct and thus visible from slightly farther than the truth, or do we want the visible range slightly under estimated with a low end MHW?  In other words, if the actual visible range to a light is 8 nmi, am I safer thinking it is 7 nmi or 9 nmi if it has to be one or the other.

My thought would be that it is safer to have the smaller range when planning an approach at night, and then when I see it earlier I know what to do, whereas if I think I should see it 9 nmi and do not, then I am not sure what is wrong with my navigation. So again in this case, the "safer" way to error on MHW is to take the lower limit.

Visibility of rocks.
On paper charts we have 3 kinds of rock symbols: a "plus-sign rock," which is a rock that is underwater for all tide heights greater than 0; an "asterisk rock,"  which is one that covers and uncovers when the tide is in the range of 0 to MHW (the height datum); and a "plus sign with 4 dots rock" that is awash when the tide is exactly or very near 0.  

ENC has one rock object called UWTROC (Underwater/awash rock), which has an attribute WATLEV (Water level effect), which in turn can have values:

1. partly submerged at high water: partially covered and partially dry at high water.

2. always dry: not covered at high water under average meteorological conditions. [ This is an islet, not a rock. ]

3. always under water/submerged: remains covered by water at all times under average meteorological conditions. [ This is analogous to plus-sign rock. ]

4. covers and uncovers: expression intended to indicate an area of a reef or other projection from the bottom of a body of water which periodically extends above and is submerged below the surface. Also referred to as dries or uncovers. (IHO Dictionary, S-32, 5th Edition, 1111). [ This is analogous to the asterisk rock. ]

5. awash: flush with, or washed by the waves at low water under average meteorological conditions. (adapted from IHO Dictionary, S-32, 5th Edition, 308) [ This is the plus-sign with 4 dots rock. ]

6. subject to inundation or flooding: an area periodically covered by flood water, excluding tidal waters. (Digital Geographic Information Standard - DIGEST 1.2)

7. floating: Resting or moving on the surface of a liquid without sinking (Concise oxford Dictionary)

Here we confront several distinctions between RNC rocks and ENC rocks. First a simple terminology distinction. Paper charts refer to rocks awash as those that cover and uncover as the tide changes from the sounding datum (0 tide) to the height datum (MHW). We can confirm that in the IHO document S-4, where this K11 rock is listed as B-421.2.  This rock has a symbol of a simple asterisk on both RNC and ENC. On ENC it has a WATLEV = 4. 

Here is the Bowditch definition, which is consistent with IHO S-4:

rock awash. A rock that becomes exposed, or nearly so, between chart sounding datum and mean high water.

In contrast, S-57 defines "rock awash" as one that is awash at or near the sounding datum, tide height = 0.  The ENC uses an asterisk for this rock as well, but assigns a WATLEV = 4.  Note that we must know the ENC definition of "awash" when reading this cursor pick.

The other distinction, which has effect on the present discussion, is the S-57 ENC definition of WATLEV 4, which is covers and uncovers—without any reference at all to the height datum, MHW. The quick conclusion from that is, the ENC choice of MHW therefore cannot have any influence on rock navigation, safe or unsafe, be it too high or too low. We could end it there, but for at least four more years we will navigate with both ENC and RNC, so we should still have a look at the consequences of an ENC error in MHW. 

Right now if we have a rock that dries at 6 ft, with an actual MHW of 6 ft in that area, then this rock would be awash at tide = 6 ft, and for any tide height lower than this we would expect to see that rock.  If  the ENC reported MHW were 4 ft, then we would expect this asterisk symbol rock to be underwater or just at the surface at tide = 4 ft, but in fact when we got there it would be 2 ft above the surface. On the other hand, if the ENC reported the MHW at 8 ft, then we would expect to see this rock for any tide height less than 8 ft, but if we got there at tide 7 ft we would not see the rock.  

In summary, if the above arguments are correct, then it seems that given a range of MHW values from which just one must be selected to encode into an ENC, then the "safest" value would be to choose the lowest one on the chart.

It seems to me that in at least some ENC this is not the guideline being used; it seems the higher end of the range is chosen.  So now I need to reach out to the professionals to learn more of the policy on this detail, and when I learn more, I will return here to correct the above as needed and fill in the rest of the answer.

Note that although MHW is not directly included in NOAA Tide tables, there are two other parameters given for each station from which we can compute MHW:

Mean Range = MR = MHW - MLW

Mean Tide = MT = (MHW + MLW)/2, which, in passing,  is a good approximation to MSL

Thus we can rearrange these terms to solve for MHW = MT + MR/2

In Port Townsend, for example, MR = 5.34 and MT = 5.17, so MHW = 5.17 + 5.34/2 = 7.84


Wednesday, August 5, 2020

Correcting Add East—An Overview of Compass Conversions

A true direction is the bearing of a target from your location measured relative to true north (000 T). True north is the direction on the horizon that is directly below the pole of the sky that all stars rotate about. It is the direction from any point on earth toward the North Pole, the one point on earth that is at latitude 90º exactly. Standing at this point, the true pole of the sky is overhead and every direction from there is south! True north is always placed at the top of standard nautical charts, which are made on a Mercator projection. Due east true is on the right side; due south on the bottom; and due west on the left side.

(Note that true north is not the direction to the North Star, Polaris. Polaris is overhead on latitude 89º 20' N, so it is about 40 nmi south of the true pole at any time. This makes its actual bearing vary from about 359 T to 001T depending on the date and time of night.)

A magnetic direction is the direction of a target from your location relative to a special direction  called "magnetic north" at your location. This direction is not unique, like true north is, but instead varies continuously across the surface of the earth. It is the direction of the strongest horizontal component of the magnetic field at the earth's surface. In short, it is the direction that any compass needle would point at that location.

Also unlike true north, magnetic north is not the direction to any specific point on earth. If we take a simple hiker's compass and look at the needle, it is aligning with the earth's magnetic force lines at this location, pointing to our local value of magnetic north.

(Note that magnetic north is specifically not pointing to the geomagnetic north pole of the earth; nor is it pointing to the magnetic north pole, which is actually a completely different concept, which we leave for now to the Wikipedia. When most of us say magnetic north pole, we actually mean geomagnetic north pole—as Trump says when he learns something for the first time "Not many people know that."

Since mariners rely on compass bearings to find their way across a chart, we must know for each point on earth what the difference is between magnetic north and true north.  Then we can read a magnetic direction from the compass and correct it to get the true direction that we can plot on the chart relative to the top or sides of the sheet.

The difference between true north and magnetic north is called variation or magnetic variation. Its ENC object name is MAGVAR. Magnetic variation is a well known number for all points on earth, but there are rare isolated regions, usually small, of anomalous values.

The numerical value of the variation varies from 0º to about 25º for most navigable waters below latitude 70º N. Variation is labeled East if magnetic north is to the east of true north. For example, if magnetic north is located at a direction of 016T, then this is to the east of true north at 000T so this would be var = 16 E, which is typical of the Pacific Northwest. In Northeast US waters, on the other hand, magnetic north is in the direction of about 348 T, which is 12º west of 000T, so this is var = 12º W.

To see how this works with variation of 16º E, if we are told that a target is at bearing 050 Magnetic, we know that means it is located 50º to the right of 000 Magnetic,  the direction of the local magnetic north. We know from the variation that magnetic north is 16º to the east of true north (000T), so this bearing of 050 M is pointing in the direction 050 + 16 = 066T. In short, regardless of the bearing around the compass card, the way to get true bearing from magnetic bearing will always be:

True direction = Magnetic direction + Variation East.  

When the variation is west, we subtract it from the magnetic bearing to get true bearing.  These rules are summarized below.

compass direction is the bearing of a target (or the bow of the boat) from your location read directly from a compass. These are bearings relative to 000 on the compass card. Ideally this would be identical to the magnetic direction, which is afterall defined as the direction a compass needle would point. But that is assuming the needle is feeling just the earth's magnetic field. We assume the compass is not being disturbed by any external magnetic fields.

If you have a compass sitting in a clean position, not near any magnetic materials, then 000 on the card will point in the direction of the earth's magnetic field, and indeed bearings read from this compass will be the same as magnetic bearings.  But set a magnetic screwdriver near that compass and you will see the needle move to a new direction, which is not the correct magnetic direction.

The difference between magnetic north and compass north at any time, on any vessel heading, is called the deviation of that compass on that heading. Deviation is labeled E if the compass bearing is east of the correct magnet bearing. Thus if a compass bearing is 050 C when the correct magnetic bearing is 045 M, then this deviation is 5º E. The conversion is the same as with variation:

Magnetic direction = Compass direction + Deviation East.  

When the deviation is west, we subtract it from the compass bearing to get magnetic bearing.  These rules are summarized below.

Here are the rules

True heading = Magnetic heading + Var E
True heading = Magnetic heading – Var W

Magnetic heading = compass heading + Dev E
Magnetic heading = compass heading – Dev W

Magnetic heading = True heading – Var E
Magnetic heading = True heading + Var W

Compass heading = Magnetic heading – Dev E
Compass heading = Magnetic heading + Dev W

Maritime training has traditionally called going from Magnetic to True or going from Compass to Magnetic as "correcting" and going the other way as "uncorrecting." Neither are very tidy terms, but we feel it is best to not generate new terminology in this arena.

On the other hand, individual mariners are welcome to create whatever rules work for them.

I have always used the one rule "correcting add east." From this I understand that "uncorrecting" would call for adding west, and if the variation or deviation is west and not east, then the adding goes to subtracting—but I do not say this in my mind or on paper.  One short rule goes into the mind: "correcting add east"—then if anything changes, the add goes to subtract.

With all that said, on a long trip where you are likely to be tired when navigating and the local variation is say 17º E, it pays to just write somewhere prominent in the nav station that
Then you are less likely to make a mistake when tired, and others at the nav station can see this to keep it in mind as well. This is especially true on a long trip that covers new waters for you, where you will not know the variation by heart. This saves looking it up every time you need it. Then just update your note as the variation changes. We learned this trick well on a trip from Long Island Sound, NY to San Juan Islands, WA down through the Canal.

If you have failed to do that and end up really tired and maybe a bit seasick on top of that, and the conditions are terrible and it is hard to think, then just look at a compass rose and draw a line across it to get the conversion done for you.

Doing a compass conversion with the compass rose for variation 17ºE

We tend to concentrate on variation, but the deviation is handled the same way. On a non-steel boat we should be able to adjust all of the deviation out of our compasses.  Below we work a generic example with both variation and deviation.

As a minor point with regard to these conversions, in our course we do not use the term "compass error." The official US maritime definition (Bowditch, Dutton, etc, and see Note 1 below) of "compass error" is the algebraic sum of the deviation and variation. To me this is a muddy concept, which is to be avoided. First and foremost, variation is not an error in any sense. It is the deviation alone that is an error.

Secondly, it combines two completely different effects. Variation is a well-defined physical property of the planet earth at that location and date that applies to all compasses, everywhere on the vessel. We can look variation up very easily from numerous sources beside the chart, including phone apps.

Deviation, on the other hand, is a totally nebulous quantity, difficult to measure, unique to a specific compass, different on every vessel heading, and likely to change over a single long voyage. In short, we recommend keeping these two concepts completely separated and not to ever combine them into a single "compass error."

One way to remember the terms if you are new to the subject is to ponder the thought that "God makes Variation; Man makes Deviation."

We propose trying the one simple rule (correcting add east) for all conversions, which I will illustrate in a moment, but many mariners have found a form solution useful. They typically look like:

True           ___________
var              ___________
Magnetic    ___________
dev             ___________
Compass    ___________

You put in what you know and go up or down the form to find the missing values. In this form the var and the dev will have labels E or W. Going up this form is correcting, going down is uncorrecting.

Here is another more practical form of the form

In other words, "going up" is finding Magnetic from Compass so Dev E is +, and finding True from  Magnetic so Var E is +

The jingle used is Can Dead Men Vote Twice... at elections, which reminds of the correcting sequence with "at elections" reminding us to add east when correcting.

Here is a set of practice exercises from our Navigation Workbook: 18465Tr

This is 9 practice exercises in carrying out various compass conversions. In an extended career in navigation, you might actually run across any one of these, although it is more rare on non-steel boats. Again, on non-steel boats, we should be able to make all compasses free of deviation, but that does not mean they will stay that way.  A lightning strike, for example, is a rare event that can indeed disturb the compasses, as can loading the vessel in new ways, or installing equipment without thinking about the compasses.

In modern times, we tend to have a lot of compasses (electronic and magnetic), and it is rare to have them all agree, so we have to then track down which ones have deviation and what it is, and generally to do that we have to have complete control over these types of conversions.

Example (A) is pretty basic. We are at sea at a known Lat-Lon, time, and date and we want to check our compass for deviation. We point the vessel to a star and the compass reads 296 C. For this time and place, we then use celestial navigation to compute the true bearing to that star, which is 280 T. We know from our chart or software that the variation at this location is 16ºW. So what is our deviation?

Dev is the difference between compass and magnetic, so we have to compute the magnetic from known true and variation. This is called uncorrecting and the rule is uncorrecting add west, so magnetic is 280T + 16W = 296 M, which is the same as compass, so the deviation is 0.

Example (B) would be the case where I was told that the proper course to stay on the entrance range is 014 M, so i need the compass course to steer, knowing the compass has a deviation of 5E on that magnetic heading, and I want to check this information on the chart, but the only chart I have does not have a magnetic compass rose, so i need the true heading as well, in an area where the variation is 21E.

We want True from known Magnetic and var, so this is just correcting add east, or  T = 014M +21E = 035T. Getting the Compass from known Magnetic and dev is uncorrecting, so C = 014M -5E = 009C.

Example (C) We want to find the local variation, because we do not have a chart with it, nor the software to compute it. We point the boat toward an object we know the true bearing to (ie 007 T), which we could get from a chart in coastal waters or at sea from a cel nav computation.

We read our compass heading and we know the dev at this heading, so we can find the Magnetic heading by correcting 354C - 8W = 346M. The rule is correcting add east, but this one is west, so we subtract.

So now we know True = 007 and Magnetic is 346 M, and we know the difference is the var, which is 346 to 360, which is 14º and then on around by 7º more, so the total difference between Magnetic and True is 21º.  Then we choose the label of the variation by noting that 346 + 21 = 007, so since it is plus in the correcting direction it must be East. Ans 21E.

Since this one more involved, let's see if the form helps:

True    007
var      ___
Mag    ___
dev      8W
Comp  354

We get Magnetic going up, which is correcting, which is add east, subtract west, so we now have

True    007
var      ___
Mag    346
dev      8W
Comp  354

And we are back to figuring the difference between Magnetic and True as before, which we know is 21º, so the form now looks like

True    007
var       21 .... now is this E or W?
Mag    346
dev      8 W
Comp  354

And at this point, form or no form, we have to reason through the label E or W.  Thinking in terms of correcting, we have 346 ± 21 = 007.  This has to be +, so the label has to be E, based on the the rule "correcting add east."

In summary, we have to ask ourselves if a form helps with these conversions or can we do variation corrections and the deviation corrections independently and then combine these results when needed.

The question is, does the form help, or can we do it with just "correcting add east" and then knowing what we mean by correcting.

Here are the answers for more practice.

A related article: Compass Bearing Fix: An Overview

Note 1.  We have yet to find an "official" British Admiralty definition (The Admiralty Manual of Navigation, Vol 1 does not use the term "compass error."), but in the British book Self Instruction in the Practice and Theory of Navigation, Vol. 1 by the Earl of Dunraven (London, 1900) on page 66 he states: "Error is caused by Variation or by Deviation, or by both combined. We shall consider the effect of Error from whatever causes it to arise."