Wednesday, December 10, 2014

Sydney-Hobart Climatic Winds

The Rolex Sydney-Hobart Race is notorious for not just strong wind, but strong wind that changes rapidly. We in the Northern Hemisphere are not used to fronts and Lows that move as fast as they do along this route.

You can see the variability in the climatic wind patters at the wonderful COGOW site, from which we have captured the samples below. The COGOW data replace everything in the past as the best source of climatic average winds. They are actual winds measured by the Quikscat satellite. There are 9 years of data, with a pass over a particular region about once a day.  Then the folks at Oregon State University compiled the data and made this super nice presentation.  They have ended up with about 150 observations at each grid point. You can compare this to similar data in the Pilot Charts (much from 19th century logbook data) or other Navy Wind Atlases from the past, but the COGOW data are the best available and the best way to plan a sailing route…  when you might have some option on when and where you sail.

When you must sail on a given date at a specific place, this does not help much. We can then only look at the 5 day forecast at the start compared with latest satellite winds, and then keep updating the knowledge every 6 hr or so.  We get new maps every 6 hr, but we only get new forecasts every 12h.

The Race is on Dec 26th, Boxing Day, and the COGOW winds provide averages for the first and last 2 weeks of each month. Below we show Jan 1-15 and Dec 16 to 31. There is not much difference in these two periods.

COGOW winds overzoomed to compare the change with time.

The compiled picture below showing wind roses are from the Jan 1-15, primarily because it showed  the shear line about 37S, but it turns out we do not see much of this in the individual statistics. At the COGOW site you have several options on how to present the wind statistics. These wind roses are just one option.

You can vary the views on COGOW and get somewhat more precise data by selecting different regions to zoom in on from the base map…. but the general behavior is more or less as indicated in the wind diagrams shown, which are of course just averages.

Look closely at some regions and we do see interesting statistical details, for example how the wind changes near the coast in some regions.  This race is much influenced by strong currents just off shore. I will try to find some good links to these. I believe there is HF radar measurements available.

There are two ends to the wind pole.  The climatic averages of what has taken place at one end (shown below) and the winds at the very moment at the other end (see Sydney-Hobart scatterometer data). In this latter link we have compiled a very convenient way to look at all of the satellite wind data that are available, which is updated each time you look at it. The satellite data are not forecasts or model predictions, they are actual measurements of the wind. With 3 satellites ascending and descending, we end up with 2 or 3 looks per day at the real winds.  These satellite data are used to seed the numerical models, which are consequently pretty good at their zeroth hour report, but we still very often see details in the satellite data that get averaged out by the modeling.

COGOW data. The numbers are the percentage for the direction. The length of the line segments is the percentage wind speeds.  You can get this data in tablular form at the COGOW site. Other than west wind in Bass Strait, there is a lot of variability.  Click this pic to get a better view.

NOTE: sometimes it is tricky at the COGOW site to get to the popup that lets you change between wind rose and table data.  In principle you just left click on the main map and you should see the option, but once you select a choice that window dives to the bottom of all open windows and after that click away and nothing happens.  So if you can't get it, move all the windows around and look underneath for the popup.

Monday, December 8, 2014

Don't Blame eCharts for Anything

The grounding of Vestas Wind reminds us of basic issues in modern navigation.

We have long taught at Starpath that we should never blame echarts for anything that goes wrong. This is a fundamentally important rule that we see violated over and over again. Granted, there is much not to love about vector echarts—the ones called ENC (electronic navigation charts), as opposed to RNC (raster navigation charts), which are identical to their paper counterparts. Unlike the ENC, the RNC are updated weekly in print and echart at no charge. The rule applies to RNC as well, but they are not as often the brunt of criticism as are the ENC.

Vector charts are easy targets for blame. First, for general use in what is called ECS (electronic charting systems) there are no real standards in functionality and chart symbols, as opposed to ECDIS use (electronic chart display and information system, pronounced ek-dis) the professional system sanctioned by the International Hydrographic Organization. Sailors and other recreational mariners, however, do not often use official ECDIS software or charts.  We use mostly ECS, which means simply any combination of echarts and software we might have.  Some ECS strives for the ECDIS standards; others do not. The latest edition of the  Chart No 1 booklet now includes many of the ECDIS symbols, which is a valuable free download to have. The full range of ECDIS standards, however, is immense, as it also includes how the various aids and landmarks should be described, coded, and indexed for display in various layers. There are also standards on the ECDIS software functionality, which is often not as convenient as some ECS programs, which is in part why manufacturers do not use it.

A big difference between RNC and ENC chart symbols is the legends explaining the symbols are all in print on the RNC, whereas in ENC we usually need to right click it or highlight it and press Info to learn what it means. This has lead to several incidents. I recall a racing yacht grounding on the West Coast that blamed echart symbols, as well as a tanker hitting a bridge in San Francisco Bay because light symbols were misunderstood.

And of course there is the appearance of the land that differs between these two chart formats, sometimes tremendously.  All ENC start out as RNC that someone (or some software) manually (or electronically) digitizes. Eventually these might all be tested by satellite images, which is done to some level now.  Certainly at some point the ENC will be better than the RNC, and I would venture that someday all charts will be ENC. It is the logical direction to go, just as print on demand was a logical direction for paper chart production. But for now, we will find more errors in the ENC charts than in the RNC, and more of them blamed for navigation shortcomings.  ENC include all errors that might be in the RNC (from incorrect or outdated surveys) plus any new errors that come from the digitizing.

On the other hand, like any working database, the ENC will just get better over time as the errors are found and removed and new meta data describing the features are added. The attraction of the ENC comes from this great potential of including so much information, plus the fact that they are individually small files. Entire sections of an ocean basin can be included in one large file, including every harbor chart as well. Furthermore, we can have ENC charts for remote parts of the world where there are not many alternatives.

This last point came to mind immediately upon learning of the grounding of the Volvo Race boat Vestas Wind on a reef at the SW tip of Cargados Carajos Shoals on the 29th November at 1510 UTC. All crew are safe, which is quite a blessing in that the GPS track of the vessel shows 17 to 19 kts of speed within seconds of 0 kts. The grounding was just off Coco Island, meaning they were 5 miles off course to miss the hazard and at least 10 off for a safe passing at night.

This reef is in the quintessential middle of nowhere, about halfway through the 5,000-nmi leg two of the race, in the middle of the Indian Ocean, about 216 nmi NNE of Mauritius. But even though this is a remote location and a small group of reefs, islets, and shoals, it is not at all a secret place. In fact, the entire middle segment of the Indian Ocean has the Cargados Carajos Shoal’s name written across it in large capital letters in the graphic index to the US International Sailing Directions, Pub 171. It is Section 9. The Sailing Directions are the ocean counterparts of the Coast Pilots, and they have the same goal, namely to provide crucial navigation information that is not on the charts. For any long voyage it is fundamental that we check the Coast Pilots and Sailing Directions. In this specific case, however, we do not learn enough from the two paragraphs about this reef in the latest edition of Pub 171. In fact, the only chart of the area it refers to is DMA No. 61551, which has been out of print for about 5 years. It also has the confusing information that the SW tip might be 3 mi SW of where it is charted, then later says you can pass the SW tip within 1 nmi—presumably meaning from wherever it is.

Thus when planning a trip near this region we have to work harder. The natural next place to look is the BA Pilots, which are the British equivalent of the US Sailing Directions, though famously more thorough and famously more expensive. Vol 39, South Indian Ocean, is only $60 but other volumes are twice that. They are in good libraries, however.  Here we learn that  BA chart No. 1881 has pretty good detail, and No. 4702 is a smaller scale showing the extensive gamut the yachts must face headed north across the Indian Ocean. The BA Pilot devotes two full pages to these Shoals.

We do learn from both the US and BA sailing directions that the Cargados Carajos Shoals should not be approached from the east (breaking waves obscure the location of the reef, which itself is only poorly known) and that the Shoals should not be approached from any direction at night. The four boats that passed the Shoals well to the west some 5 hours earlier did so in daylight, and at least one may have been close enough to see them, which are described as clearly visible with some hills to 70 feet with vegetation and a few low-lying buildings. This can be seen on Google Earth (GE). There are even some permanent residents there, including two Coast Guard personnel—very isolated, but in a very pretty place.  Vestas Wind unfortunately came in from the east at night.

One other yacht passed well below 1 mile of the reef tip in daylight (too close for a navigation instructor, but not a racing tactician), and could have been lucky in light of the NGA warning about the SW tip.  Figure 1 shows the boat tracks. In daylight the closest may have seen the reef and its limits as they passed.

Figure 1.  Boat positions just after the time of the Vestas Wind grounding (blue track). The white boat is 111 miles ahead of this Vestas Wind position.  The yellow boat and white boat are 4.5 miles apart on this scale.

BA charts are available from all BA outlets worldwide (there are a dozen in the US), and remote  charts are probably in stock at many of them as it is part of a BA distributor requirement. The chart 1881 is the one of most interest here, being the basis of all other charts of this area, and the navigation charting story begins with it.

This chart is essentially the same as it was in 1941, based on a survey taken in 1894, with periodic updates over the years, but no real surveying improvements. There is the discussion mentioned in the sailing directions and much online chatter about whether or not the shoals are where they are plotted, but we can compare with GE to see that it is indeed very close (Figure 2). This is not an issue.  There is always the issue of having your GPS set to the chart datum of the chart, but that should be standard knowledge these days, and could account for hundreds of yards and rarely a mile. The out of print US chart 61551 is essentially identical to the BA chart 1881 (upon which it was based), but there is one important difference.

Figure 2. A Google Earth image overlaid onto chart 61551, showing good agreement. The approximate location of the grounding is shown with a red X. The segment shown is about 5 nmi across. The light showing on this outdated chart does not now exist. Soundings in meters.

If you compare 61551 with a paper version of 1881 purchased from an authorized BA distributor, you will notice one main difference in the vicinity of the grounding. The BA chart will have the notable light on Coco Island crossed out by hand in ink (Figure 3). All BA distributors are obligated to update the charts with pen and ink by hand, and this light was no longer functional after a BA notice to mariners in 2012. This light (nominally visible for 12 miles) is just  a few miles from where Vestas Wind went aground.

Figure 3. Section of the latest printed edition of BA chart 1881, hand corrected by Captains Nautical in Seattle, an official BA chart distributor. The correction is dated in the bottom left with the notice number. The BA RNC of this chart, on the other hand, has the light removed, which shows the value of official RNC. Soundings in fathoms

Which brings us around to the echarts. Unless you are purchasing official BA ENC or RNC (called ARC), which are very expensive, then you are buying from companies that do not necessarily have the same BA standards for keeping their charts up to date—and I must add NOAA standards as well these days, as all NOAA charts are updated weekly now. You can’t buy US litho charts anymore that may have been sitting in drawers for years. They are print on demand, and the masters, print and electronic, are updated weekly. 

But we are considering foreign charts, or charts of foreign waters made by commercial companies of the US or elsewhere. In the case of these shoals some of the electronic charts in use at the time of this grounding were not up to date in that they did indeed still show this navigation light, which could in fact (if there) have saved the day in this case. Hopefully it did not mislead any navigator.

Even worse than that, some of the ECS chart packages did not layer the scales of this region very well, and in fact this point was brought up in the chatter about this region by several sailors on the race on several boats. Namely on one scale the Shoals did not appear at all and on the next scale up they filled the screen (see Figure 4).  Thus if you did not zoom in at very near the right place, you would not see them at all­—that is of course if you did not know ahead of time that they were there from your homework, and that this was indeed the primary issue of the navigation for at least a day or so, and as such have all sorts of back up contingency navigation in place, including radar and depth watch, besides GPS waypoints and tracks. In short, we are back to our rule.

Figure 4. Example of one echart defect. This is a full screen view.  The top view (A) alerts us with the white patches that there are large scale charts available in that region. (B) shows zoomed into that region with multiple zoom-in steps, (C) is the very next scale step in from the view above it, which does show the light. (D) is next zoom in, and now the light is gone from all further zooms. (E) next zoom in.  (F) shows slightly different zoom from a different start that does show the light. The presence of the light and which zooms show it depends on where you start from the white region and how you move the screen before the next zoom.  But there is no way to watch your vessel approach this reef on a view that actually shows the reef. This is from an iPad app with poor  chart presentation. It might look different in computer software or GPS units running these same echarts.

No matter how bad the echarts and echart display might be, we cannot and should not blame them for anything. It is frankly our job as navigator to know such limits and work around them. When all is going well, echarts are an invaluable aid to navigation and racing tactics, but when the navigation is crucial, we need to back these up with other info. Figure 5, for example, shows a section of another commercial echart brand used on one of the race boats that also shows this light—I think.

Figure 5. Another commercial brand of echart used on some of the boats. It does show the light—or something on Coco Is (called South Is); it is not clear what that symbol means without right clicking it! We always have two issues: did the company up date the chart, and then did the navigator update from the company. Often the update option is a paid subscription.  It appears that this navigator had defined a custom boundary around the reef, which often has the virtue of scaling more nicely so it stays in view, as well as offering danger bearings and ranges. This chart shows much better sounding data than the BA chart. We assume the navigator highlighted the depth contour IDs (meters), again good practice underway.  We do not know which boats used which brands of echarts. Some I would assume have several.

Another flaw of at least one echart program in use at this time was when right clicking and getting the data for this (non-existent) light it gave us all the information except how high it was. This height is crucial for predicting visible ranges of lights, so I would consider that a major charting error. Its official Light List number was also missing.

But suppose this is the situation: You have this echart on shore before the race as you plan your route, and you look at the light and find the height is missing. You know how important this light might be, so you must find this height somewhere. A first place to look is the NGA Pub 122, List of Lights. It covers all lights worldwide and it is free.  In the latest 2014 edition of that book on page 566, sure enough you find that light. It is US No. 32892, International No. D6681.6. It is listed as Fl(3) W, 30s, 27 ft above MHW, with a nominal range of 12 nmi. All this info is on the echart except the height 27 ft.  That would mean standing on deck at 9 ft height of eye, you would see this light from about SQRT(9) + SQRT(27), or about 8 or 9 miles off. The 12-mi nominal range means it would show bright at that distance when it first comes over the horizon, and you might even “bob the light” by standing on the boom.

So you are better prepared... or so you would think. But not at all. This official reference book happens to be wrong. That light is not there; gone since 2012 as best I can tell.  It is an error in the 2014 Pub 122. So we are back to our rule.  This false confidence came from overlooking the main issue. The echart itself.  When things are crucial, and you are using echarts from a commercial company that are not certified by the Hydrographic Office of that country, then the first step is check the echart with a printed chart or an official echart.

At this stage, just a few days after the incident, we have no idea what led to the error. I have not heard of anyone directly involved with the boat blaming any echart, or in fact blaming anything.  We are all human, and humans make mistakes. The extensive online chatter from distant observers, however, went straight to the charts. 

The discussion here has been just one scenario. As it turns out some commercial echarts of this region are based on charts from the Indian Hydrographic Office, which happens to have an excellent chart of this area No. 2503 (Figure 6). Though much the same as BA 1881, they do they the light removed so users of this brand of echart would not be confused by this issue. Chart 2503 also has improved soundings data from their own surveys. I have not been able to test any echarts based on 2503 and what meta data appear in these echarts. I am trying to get samples of other brands for comparison. Also we have to assume that whoever makes the echarts (regardless of source) do keep them up to date. Chart 2503 was new in Mar, 2014.  Print on demand nautical charts from all nations are available online from EastView Geospatial.

Figure 6. Section of Indian Chart 2503, showing improved soundings over BA 1881.
With special thanks to the Hydrographic Office of India

Remember too that of the half-dozen or so commercial companies that make worldwide echarts, some are known to be better for some regions than for others.  We cannot learn which is best where from advertising; we have to check with experienced users.

The Volvo boats had been in difficult conditions for a couple days negotiating a tropical disturbance with winds up to 30 kts. Approaching the Shoals the wind direction was changing rapidly along the fringe of this Low (with clockwise winds in the Southern Hemisphere).  The grounding took place about 2 hours after sunset, which at this low latitude was well past nautical twilight, meaning dark enough that the horizon was most likely not visible.  Even in clear weather, you cannot see the reef downwind with waves breaking over it. There was a half moon about halfway up the sky to the east, which may have offered some light, but that near the Low this was likely hidden by clouds. I would have to guess that current was not a factor.  Both the OSCAR 5-day average and the latest RTOFS models gave current flowing to the west at about 0.5 kts at that time.  They were off to the east so this current would have helped, if anything.

I want to stress that vector echarts certainly have much virtue and not just limits. Besides the unique values mentioned, they offer custom displays and features that can indeed enhance safety not threaten it. Furthermore, all of the limits can and will eventually be removed.

For now we have the issues above in at least some systems, but these might not appear the same in all platforms—that is, in a computer versus in a tablet app, or integrated into the GPS display. On the other hand, it could be that even the best echart navigation software has limits on this that are inherent to the specific echart package. There is also the question of how this might vary between ECDIS standard ENC and commercial vector echart products. Though in use now for quite a long time, there is still a lot to learn and a long way to go.

PS. There is some discussion online, in print and audio, regarding work on the boat at high and low tide etc. But we must remember we are in the middle of the ocean here, so tide is not much of a factor. See Figure 7.

Figure 7. Tidal data near the grounding site. S=spring, N=neap.

A version of this note will appear in the Jan, 2015 issue of Blue Water Sailing Magazine, an issue that includes other topics of electronic navigation.

Thursday, December 4, 2014

How a big, well-run, high-tech race boat, can go aground... almost

In light of all the speculation about how Team Vestas Wind could go aground by error, I would like to offer one distantly related scenario that helps remind us of our fallibility and the fate of circumstance. This was on a race boat having left Seattle on the way to Hawaii on a delivery to a race there. It was in fact a bigger boat than the VOR boats, and the skipper and several of the crew were as qualified as many VOR sailors. It had all the latest technology of the mid 90s.

We had rounded Pt. Wilson after dark under power, and had about 70 miles to reach the ocean in the Strait of Juan de Fuca. I had set way points for the route out, which was very basic. We travel along in the inshore zone, just out of the shipping lanes, facing inbound traffic on our right. Then I crawled into the bunk to get some rest so I would be fresh when we reached the ocean, which often has much converging traffic and usually new current and wind to deal with. Unfortunately (as it turned out) it was a beautiful, clear night, in perfect conditions, on an easy route, with nothing to worry about.

Sometimes it is hard to go to sleep early, so there was tossing and turning, in and out of sleep. But from my bunk I could hear conversation in the cockpit very clearly. Somewhere in the half sleep I over heard someone say “I didn't realize Smith Island Light would be so bright from here,” which bounced around in the mind for a few moments before i realized Smith Island Light is actually not bright from where we are at all!

I scurried on deck to learn that the crew were looking at Dungeness Light, essentially right next to us. We were inside of Dungeness Spit headed for the beach. There were just minutes to spin around and head back out.

So now we get to say just what we read in the news today: How could this happen with such a trained crew on such a high tech boat? In this case, the base cause was the regular navigator had sat down at some point earlier with good intentions to review the waypoints, and to make a personal preference change to let the waypoints automatically advance to the next when within some set range. Although I strongly disagree with that approach (I think they should always be advanced manually) that was not the cause. Some how in this process the crucial waypoint WP33 got deleted or skipped in the active route. We were essentially headed from WP32 to WP34 on a straight line.

But now we have to fold in all the special circumstances that let this type of error get by without being caught. Like many of the VOR boats we had an international crew, with some of the best sailors from around the world, and more to the point like many big boats with a crew of 9 to 11, most of the crew was not involved with the navigation at all. They assume this is a matter taken care of by 2 or 3 other members of the team, and they concentrate on their specialties. Of this crew we had several local folks who had been this route many times and would never have made this error, regardless of waypoints. But you can get at times combinations on watch or at the change of watch that might not include local knowledge. I do not recall these details, but at least one person on deck knew the light, but they might have just come on watch. In any event, that is what happened.

Our target was a gently sloping sand beach, so chances are we would not have suffered serious damage, but a grounding there could have caused enough damage to cause us to miss the race, and cost all the investment of time and money that went into the preparation. The incident had been out of my mind for many years, but this recent grounding brought back the memory quickly.

So one answer to how such things happen is this: one fundamental error that would normally be caught, does not get caught, because of a series of peripheral factors that sadly come together at the same time. There is sometimes a fine line between bad judgement and bad luck.

Tuesday, December 2, 2014

Sydney-Hobart Scatterometer Winds

We have set up a convenient way to look at scatterometer winds over the Rolex Sydney-Hobart Yacht Race course that will automatically update on each view.  Unfortunately, the four panels of data available all meet right in the center of the race course, so we had to combine 4 images... otherwise you could just look at the source data we use at the Ocean Surface Wind Team web site.  These data are originally analyzed at the  Royal Netherlands Meteorological Institute (KMNI).

Please have look at compilations we have made. We show ASCAT A and B, both ascending and descending, as well as the WindSat data, and the brand new Rapid SCAT data from the International Space Station.

These are large images that you can drag around for best viewing.

To get ship reports in this region, send an email to with the subject line reading:  39.0S, 150.0E. Send one now.

In preparing this, we realized we needed a bit more instruction on how to figure valid times.  So here are some notes on this, but you can also download a pdf of the information below, which is just captured from that document.

See also Predicting Times of ASCAT Passes.
and Tactical use of Scatterometer Data.

.... or if you want to see the other end of the wind pole, ie not what it is doing now, but what it has done in the past, then see our discussion of the Sydney-Hobart Climatic winds.  (If you do not know what COGOW stands for, then it is even more important to check that link.)

Sunday, November 30, 2014

Taylor 1328PJ Sling Psychrometer — a Review

Relative humidity (RH) is a tricky measurement, primarily because it is so sensitive to the air temperature. One of the most basic measurements of RH is also one of the least expensive, namely a sling psychrometer. It has two identical thermometers one that remains dry (dry bulb) and the other covered by a clean cotton wick that is made wet with clean fresh water.  Both are mounted on a swivel that can be swung about for the purpose of increasing the rate of evaporation of water on the wick.

Since the process of evaporation takes energy it cools the water, wick, and the thermometer inside it as the water evaporates; the more the evaporation, the more the cooling.  But there is a limit, and that limit depends on the evaporation rate and that rate depends on the relative humidity of the air that is being evaporated into.  Thus the suppression of the wet bulb thermometer temperature compared to that of the dry bulb thermometer is a measure of the relative humidity of the air at the dry bulb air temperature.

We have tested several of the these Taylor units. They are well made and a nice compromise in price, size, and accuracy. The list price is about $180 these days, but generally you can find them notably less... and I have seen then on eBay called new for well under $100.

Range 20°F to 120°F
9" Permacolor™ filled thermometers
Temperature accuracy ± 0.2°
Folding swivel handle
Hard plastic protective case (about a 12 " wide)
6 replacement wicks

The instrument is used by wetting the clean wick with distilled water, then swirling it around for about 30 seconds or more (rather vigorously) and then reading the wet bulb and dry bulb temperatures. With these values you can look in tables (included with the device) to learn the dew point of the air and its relative humidity.  Or go to this link to find both RH and dew point from the two temperatures:  Dew point is of more interest to navigators as it tells us how far we are from fog, whereas RH is of more interest to human comfort and how other things like violins and cigars interact with the atmosphere. Also for optimum espresso you have to change your grind number by 1 or 2 with RH changes between say 40 and 70.

By plotting dew point and temperature as a function of time you can often predict when fog will form. Accurate sling psychrometers like these can also be used to calibrate hygrometers that read the relative humidity directly on a dial. 

Here is a quick test of 4 Taylor units showing the dependability of the thermometers. The wet and dry bulb temperatures should be identical for all units on a given time when sitting side-by-side at rest, out of breezes, and on a uniform temperature base. Also keep in mind looking at the dial, that tenths of a degree must be estimated. These were read using a magnifying glass, being careful to avoid parallax errors, and being careful to not get so close to the thermometer that radiant heat from your own body does not change the reading, which is a real concern, because  the result is sensitive to tenths of a degree. Clearly they are all well within the specs given by Taylor. This is a crucial condition, because the accuracy of the humidity and dew point results are a direct computation from the temperature data. (Unit 4 was sold on Day 2.) 

 We only have these data at this temperature, but from this the instruments look good, and we have used our in-house model for several years.

A few related, random notes:

(1) There are devices like this that have reservoirs for the wick water and fans that blow on the dial (ie do not have to swing them) and some have even more accurate thermometers.  These are called Assmann aspiration psychrometers. Good ones cost $1000 to $1500.  These units can get RH to about 2%.

(2) RH can be measured directly, either electronically or mechanically (based on the fact that how much human hair stretches depends on the RH). 

(3) Electronic units that read RH directly and cost less than $100 or so, probably do not work.... ie compare 5 or 6 side by side and they will differ by 20 to 40%.  Even ones that cost $1,000 have to be calibrated every year or so.

(3) Hair hygrometers can be human hair (works all temperatures) or synthetic hair, works above freezing.  The Fischer Precision Instrument Company that is famous for high quality barometers receives the same high esteem worldwide for their hair hygrometers.  Synthetic hair takes less maintenance. Always get a matching thermometer to sit beside it as you must know both numbers to do anything with the results.  ie, to say the RH is 40% does not tell you much about the conditions of your atmosphere without knowing what temperature that was.  Fisher hair hygrometers (model 122.01) cost about $60 and yield about 3-5% accuracy... all such instruments must be calibrated at some point. Matching thermometer (model 117.01) costs about $40.

(5) I must also add that we have not tested less expensive sling psychrometers. It could be that some that cost much less will also do the job.  They key issue is are the thermometers identical and how accurate can you read them.  In principle you could make your own from two thermometers and just blow a fan on them.  We have done that with our Taylor and that works fine.... if not better than slinging it around. The wicks are easy to find online. You might call that one a half-Assmann model.

In short, a device like the Taylor model above is a good solution to many needs for accurate RH... or as a way to calibrate a good hair hygrometer.

Friday, November 7, 2014

Barometer for Wind Warning

There are numerous tactical uses of barometric pressure for safe efficient navigation, but here we take a quick look at just the basic one of using the barometer to anticipate strong winds.

In the picture below we see a classic case of wind rising with a pressure drop. We show this on the very nice combined display of wind and pressure shown on the NDBC websites, in this case for West Point Lighthouse (WPOW1), which is 1.6 nmi to the SW of Starpath HQ.

Top is wind and pressure from NDBC reports for West Point Lighthouse in Seattle. Bottom is the pressure tendency (mb change over the past 3h) measured with a Mintaka Duo at Starpath HQ, 1.6 nmi away.
We see wind going from 5 kts to 32 kts  in 9h... and in the first 6h of that it only went up to 15 kt, so really this is 15 to 32 in about 3h.  This is something we would like to be prepared for as soon as possible. That 6h of watching the wind go from 5 to 15 is all wasted when we do not have a good barometer that could warn us that this wind increase could keep going on.

But even with a good barometer we still need a guideline to interpret what we observe.  Our guideline is "4-5-6," meaning a drop of 4 or 5 mb in 6h is the sign to pay attention. This implies an average tendency (change in last 3h) of  -2.0 or more.

In this example, we see a drop from 1025  at  12z on 5th to 1008 at 15z on the 6th, or 17 mb in 28h = 0.68 mb/h = 2.0 mb/3h. So the average drop rate in this example is plenty for a good warning, but once it starts down at this rate we still have to see this for 6 hours before the flag goes up.

Shown below the NDBC data, we have plotted the pressure tendency measured here at Starpath with a Mintaka Duo instrument (discussed more at the end of this note).  The scale on the left is pressure change in mb over the previous 3h.  Looking above that to the pressure data, we see a drop from Point A (where the tendency first crossed 0.0) to Point B, marking 4 mb drop. This has dropped enough to keep an eye on, but not enough to conclusively trigger our 4-5-6 guideline because this took about 9h.  After this point, however, you see an average tendency that is close enough to the 2.0 we need for a solid warning.

In other words, by the time of Point B, we should be fairly warned of strong wind potential.  Thus we have (from B to C) about 18h warning that the wind we have watched increase to 15 is likely to increase notably more. Once we get to a tendency near 3.0 for a couple reports, we are beyond the forecasting zone; the strong wind is likely either imminent or present.

Mintaka Duo wind warning arrows

To help mariners take advantage of the accurate pressure measurements using the Mintaka Duo instrument, we show pressure trend arrows next to the digital value of the pressure. These offer a quick graphic view of the trend, which are scaled to match our strong wind warning guideline (4-5-6). The definitions are shown below.

 With these definitions, keeping in mind our 4-5-6 guideline, we can make a shorter summary.

These arrows are updated continuously on the dial face after the unit has been running for 1h, and with these we can anticipate the drop over the next 3h based on a projection of what we learned over the past 1h. (The actual tendency value that is stored in the device with each pressure record is rigorously defined by the WMO and NWS as the pressure difference between now and 3h ago, so this value cannot be stored until the unit has been running for 3h or more.)

The drawing below shows how these arrows would have shown up as the pressure dropped.

Notice that the arrows would change during the short periods when the pressure flattened off during the drop, but the Fast Drop indicating real warning would dominate in this pattern.

Another point to stress is the pressure warning guideline assumes the wind is starting from light air. When the ambient wind is over 15 kt or so, as in the case to the left of this time period (3 days earlier) the guideline is not useful.  In the open ocean, when the wind is above 15 to 20 kts to begin with, a rise in pressure often brings with it an increase of wind—most famously in the "sting of the scorpion's tail," which is the poetic description of a back bent occlusion.  We see this behavior in the left-hand data for completely different reasons, but we are on inland waters here, effectively between two mountain ranges, so any standard pressure-wind forecasting can vary notably.  Our guidelines were developed for the open ocean, but they are nevertheless a good guideline anywhere.  As it turns out, the behavior seen here for this larger pressure drop is a fairly good example of what we might experience at sea.

Mintaka Duo data compared to NDBC data

In the pictures below we compare what we measured at Starpath with the Mintaka Duo instrument compared to what we downloaded from the WPOW1 website.  The agreement is very good. We actually have much more data in finer steps stored in the Duo, since we can only get data hourly from the website.  Thus even with Internet access to this excellent data from the NDBC websites around the country, we still gain more resolution and earlier warning with our own precision instrument in hand. 

In a later article I will discuss how this instrument can be used underway for sailboat racing or cruising to predict wind changes on inland waterways. Then the precision and fine steps stored are especially valuable.

The red curve is from the Mintaka Duo. The blue from WPOW1. If has been randomly offset to show the comparison.  The Starpath instruments are located 5.8 mb above sea level. We see every small variation reproduced, which shows that such fine structure is indeed being created by subtle changes in the atmosphere, that at least cover a 1.6 mi radius, as that is the separation of the two instruments shown above.

We see even more interesting agreement on the tendency measurements at both locations.  Again the red data is from a Mintaka Duo; the blue from WPOW1.

In this case the elevation difference does not matter. Here the scales and measured values are identical. This type of measurement provided by the Mintaka Duo is valuable to ships who must report the pressure tendency with their regular weather reports back to the NWS.  The detailed agreement and reproduced structure of the plot is even better testimony to the precision of the Mintaka Duo.

Wednesday, September 3, 2014

Barometric Pressure During Squall Passage

Last year we posted a note here about an unexpected small rise in barometric pressure as a severe squall passed over a boat in the Caribbean (Local Pressure as a Squall Goes By). The article served two purposes, it documented that unexpected behavior and in doing so demonstrated the value of a high quality barometer, such as the Starpath Mintaka Duo.Today, we get to carry on with that story, but with more data.

It started with a bike ride home from work, with just enough drizzle to put on rain pants. Ten minutes later however, the wind was at least 25 kts, gusting to 30, with rain heavy enough to reduce visibility to about 200 yards for a short time... not to mention an excellent test of good rain gear. This was an honest to goodness tropical squall, which I have seen many times underway... actually it was not at all a "tropical squall;" it just behaved like one.  See Cliff Mass explanation of the system.

After dinner and much banter about the unusual likelihood of such a squall here in Seattle, I happen to notice the trace on one of our Mintaka Duos hanging on the wall. Screen captures are shown below.

Shown on a 6 hr trace, the bump is at about -2.5h
Same data, zoomed to past 3 hr, but captured at a different time.
We can look at real times since the Mintaka Duo has an accurate clock.

The cursor is the close dotted line showing the pressure was 1008.4 at 1802 or so, just before the event.

The peak pressure of 1009.2 occurred at 1813 (PDT).
The pressure continued its pre-bump rise by about 1825.

Thus we see that at about 1813 the pressure rose by about 0.8 mb above its trend over a period of 10 to 15 min.  This instrument was roughly 25 ft above sea level, in a room with open windows, about a mile  or two from the West Point Lighthouse (WPOW1), which recorded hourly (MSL) pressures of 1009.0 and 1009.7 at 1800 and 1900 PDT.

The new data here is some documentation of the squall as it also passed over the Atmospheric Sciences Building at UW, which has several fine instruments on the roof, as well as a precision barograph inside the building.

In the earlier note, linked above, we speculated that maybe there was some brief pressurization of the cabin on the boat where the barometer was located, but now there is clear question about that interpretation. Namely the environment of this instrument was rather different from the boat, and also we now have the UW data (below), from an entirely different environment.

High precision barograph at UW Atmospheric Sciences.

They see the same bump about 5 min later, and about half the intensity, rising about 0.4 mb.  For what it might be worth, my guess is the squall was less severe when it got to UW, which is about 5 mi east of here. I say this because we have the data (below) from their measurements, and I was right in the middle of this one, on a bike, and have some experience in the observations.

Unless their meter is blocked on some level, I know for certain we had much stronger winds at our location.

 But they did indeed have a lot of rain, but this is much harder to gauge by eye to make comparisons. I would guess what we had here for a brief time was violent rain.

They recorded about a quarter inch of rain in a few minutes.

This record of rain gauge bucket tips shows the downpour even more clearly.

And as you would expect with a big squall, there was a fast and notable air temperature drop.
Likewise as we would expect in a fast moving squall, the wind direction was all over the place.

So in conclusion, we have clear proof of a squall and some estimate of its severity (there is likely other data on this as it was an unusual event) and we have two independent measurements of the pressure bump, in rather different measurement environments.

Now we just have to figure out what caused this... though there is no doubt that with a good barometer you learn things you would not otherwise.  For example, we can see very nicely on the Mintaka Duo the local pressure variations that lead to the sea breeze in Puget Sound on a warm clear day. Later I will write up how racing sailors can use this information to predict the wind while underway in a race on Puget Sound.

PS... it is a bit difficult to tell what took place at West Point Lighthouse because they only record data hourly... but there was definitely some larger scale system in place over the region, which we will have to look up.  The Lighthouse data is shown below, with the corresponding pressure trace from a Duo.

Wind and pressure at West Point. Recall wind in kts is about 2 x wind in m/s. Notice that they had more wind here than at UW, and I would guess somewhat less then I experienced for a short period.

This is the corresponding pressure trace from the Duo. We clearly cannot see the details discussed above on this scale.

Follow up from the next day, Wed Sept 3.

At the office we have many of these instruments running, so I took one to see if we still had detail enough to see the bump, and sure enough in the 3 min data file we see this just fine in all of them, as shown below.

This illustrates three  points.  One is we have still another completely different environment of the instrument during the measurement, so this seems to imply this might not be the factor. 

And second, it seems we may have a real meteorological effect here to understand. We need to rig up our Gill Pressure port, and have this set up outside for the next squall to remove all such influences.... unfortunately (in this regard) Seattle has only some 4 or 5 squall days per year.

The other important point to observe is the great value of the data export function of the Mintaka Duo.  At 24 h ago, this bump was just barely visible on the instrument screen, but we could just connect it to a computer with a USB cable, export the data to a spread sheet and plot it. The whole process took just a few minutes.

These types of details are much easier to see with a good plot. The above picture is from the 3-min table.  I had missed seeing it in the 750 data points of the 1.5 min table and what would have been better  still the 15 second table.

Monday, September 1, 2014

Rotary Currents

Most tidal currents we deal with on inland waters are reversing currents. That is, from slack water the current builds in the ebb direction to a peak value, on average about 3 hours later, then it starts to diminish in speed back to another slack—and over this full ebb cycle the current is flowing in more or less the same direction, tabulated as the ebb direction.

Then the current reverses, and carries out the same pattern in the tabulated flood direction. Usually in a reversing current, the ebb and flood directions are nearly opposite to each other, but it is not uncommon to be out of alignment by 10º or so, and in extreme cases as much as 45º—but even when misaligned there are these two unique directions that define the set in a reversing current.
In stark contrast, there are some locations in open inland waters, and in essentially all coastal waters, where tidal current behavior is quite different. These currents are called rotating currents. A pure rotating current rotates its direction of flow over the tidal cycle without changing speed. In a pure rotating current there is no peak current speed and no ebb or flow direction.

A pure rotating current, however, is rare. In most cases the current speed does change somewhat as the current rotates, and thus the pattern of the flow is not a circle, but an ellipse, in which case the long axis of the ellipse can be thought of as defining the ebb and flood directions, as well as the peak values to be expected.

The rotation is created by the interaction of two tidal waves moving in different directions. Either one of these waves on its own would create a simple revering current, but where these waves cross the resulting current shows a rotation pattern at that location. The shape of the rotation pattern depends on the relative amplitudes, times, and directions of the crossing tidal waves. In the Northern Hemisphere the rotation is usually clockwise. Running farther into a large open estuary with various channels, the same tidal waves will later create reversing currents.

A key point for navigators is to know and expect this different behavior of the current once sailing into large open bays or into coastal waters. Sometimes the official NOAA Tidal Current Tables alerts us to this with reference in the list of secondary stations to special tables or diagrams for rotating current stations, but in other parts of the world there is no warning. We just have to know it happens and search through the references for the data. On some Canadian charts, rotary current diagrams are printed right on the chart at the pertinent locations, but we do not see this often on US charts.
Once we know the current rotates where we care about, and we find the data describing it, we are faced with how to use this information. The procedure for figuring time, set, and drift of a rotary current is different and more involved than is the same process for a reversing current. 

For a reversing current, we go to the Tidal Current Tables, find the nearest station, and look up the peak and slack times and speeds. Then use the interpolation table from the book to figure speeds at other times or use a shortcut like the Starpath 50-90 Rule. Or much easier, go online to and look up the data already corrected for secondary stations. Or easier still, open an echart program that includes a tides and currents utility, and click the place on the chart you want, set the calendar and clock, and read off the current for that specific time, or print a plot of current versus time for a day or so. This feature of electronic charting is one of its strong selling points for those who sail tidal waters.

For rotary currents, however, none of these easy methods work. Furthermore, you must have the official NOAA Tidal Current Tables at hand. Abbreviated versions rarely have the needed information, and it is not online, and it is not included with echart current utilities. Rotary current predictions are too complex to be tabulated, so we are left with approximations.
To show the process, we look just SW of Cuttyhunk Island in Rhode Island Sound (Current station #749). A section of Table 5 from the Current Tables shows how this current rotates at this location. The currents are not strong at this location, but other places rotating current can be quite strong. On Nantucket Shoals or the entrance to Strait of Juan de Fuca, or many places in Alaska rotating currents can routinely be well over 2 kts.

Also note that within just 3 to 6 miles of this rotating current there are 3 stations with purely reversing currents. One just inside Buzzard’s Bay (#773) and two just inside Vineyard Sound (#747 and #745). There are numerous examples around the country where pure reversing switches to rotating in just a few miles.

The main reference to using the data are the Instructions to Table 5 in the Tidal Current Tables, but I venture to guess that not all navigators who might benefit from the information have seen them, so we offer a brief summary here till they get a chance.

The current speeds shown in Table 5 are the monthly averages. The times of each current are relative to the time of max flood at Poll0ck Rip Channel, which is a primary reference station in this area. Thus that one time sets the times for the currents at each hour after that. If for example the max flood at Pollock Rip occurred at 0551, then the average Cuttyhunk current at 0951 (4h later) would be 0.5 kts, setting toward 146 T. Since we know the current each hour, if we knew the time period we expected to be in this current we could figure the net tidal vector and from this figure our CMG and SMG as we transited the area.

But we are not done. These are average speeds, and just as with reversing currents, the speeds are stronger at spring tides (new moon and full moon) and weaker at neap tides (quarter moons, which appear in the sky as half-moons). As a rough rule, spring tides give rise to currents about 20% larger than the average, and neap tides yield currents about 20% lower than the average at any particular location. And this can be fine tuned even farther taking into account the location of the moon in its orbit at these phases. When the moon is closest to the earth (perigee) at the springs, the x 1.2 factor increases to x 1.4, and when the moon is farthest from the earth (apogee) at the neaps, the  x 0.83 factor (1/1.2) is reduced to x 0.71 (1/1.4).

With reversing currents we do not have to worry about this. The astronomical influences are built into the current table predictions. But for rotating currents we get only the averages and have to apply the astronomical corrections ourselves. The needed astro data are on the inside back cover of the current tables and also online. This year, for example, July 12 is full moon and July 13 is perigee, so we expect currents throughout the region to be some 40% larger than average on these days, which you can see in the current tables for all reference stations in the region. On these two days, however, we would need to increase the tabulated rotary currents by this factor ourselves.

Sailing in rotary currents takes extra work, but knowing how to figure them and how to account for their influence on neighboring reversing current helps you make good predictions ahead of time that in turn helps you interpret what you see on the GPS.

Excerpt from Table 5,  NOAA Tidal Current Tables

Section of chart 13218 showing four current stations, three are reversing, one is rotating (#749, Cuttyhunk Is, 3.25 mi SW). The average speeds at the stations are shown to scale, with the average ebb at #747 being 2.0 kts. The current predictions are for the precise location of the station dots, not along the arrows. Away from the precise station locations we must infer the currents from neighboring predictions.

We might expect the converging max ebb currents near point B to be near southerly, with some element of rotation. The current NW of #773 is similar to that at #773, but we can expect the peak flood current near point A to be curving to NE with some element of rotation.  An echart program with a range and bearing tool is an easy way to make a rotary diagram as shown above. The vectors correspond to the ones shown in Table 5.

We have exercises on rotary currents in our new Navigation Workbook 1210 Tr, which are discussed in more detail in our text Inland and Coastal Navigation.

Tuesday, July 29, 2014

Lobster foot.

Original reports that the whale watcher was caught in a lobster pot sounded so absurd that a quick check shows what really happened, which is again another good reason to study navigation.

After multiple descriptions of the location in the public media, the USCG finally reported the location as 13 mi East of Nahant, MA. As shown below.

Zoomed in to see the region below shows how this area is charted.

Now we come to our classroom preaching... always read the chart! Below is Note J.

And next comes the power of the Internet.  We just google 33CFR 150.940 and read what the regulation really says, just part of which is below.

Then we decided to take another look to the Boston District 1 USCG to see if they had any other news, which they did...

"...Initial attempts by the divers to clear the line from the propeller were unsuccessful. Original reports indicated a lobster pot line was caught in the propeller, but further analysis revealed it was a cable from Northeast Gateway's offshore facility which required additional dive resources and heavy duty equipment for removal.

Considering the dangers of an at-sea night operation, a passenger transfer was deemed unsafe until morning. Meanwhile, Boston Harbor Cruises provided additional water, food and blankets to the passengers."

In other words, someone else has now looked at a chart!

To repeat the message, if you do not want your passengers spending the night at sea when they planned on just a 3-hr outing, then read the chart.

Tuesday, June 3, 2014

Finding Longitude by Lunar Distance using the Stark Tables

Steve Miller

The follow are instructions for using the Stark Tables for finding UT and Longitude with a work form that I have modified from the original Stark Tables form. This procedure requires a copy of the Stark Tables, which also have notes included related to this process.

After completing the [lettered steps] to get the data,
follow the numerical steps to fill out the form.

[A] Do an IC check using the Moon or Sun (3 on and 3 off). It has been found that using the Sun (with a special Baader Film filter) is preferable to using the horizon. The procedure for the IC sights and how to make the filter is explained in How to Use the Plastic Sextants.

[B] Time and measure a set of Lunar Distances (Try to do at least 6 sights).

[C] Do another IC check as above.

[D] Average your Lunar Distances and Times to obtain a single value of Time and Distance for your determination of your GMT and Longitude. A direct average can be used, or  better still use the Fit Slope method explained in detail in Hawaii by Sextant

[E] Obtaining the Body Altitudes

OPTION 1 - Take normal sights of both Bodies for their respective Hs if possible. This requires a  good sea horizon or an artificial horizon.

OPTION 2 - Compute the Hc for the Moon and Other Body. This is a bit circular as you must know your Lat and Lon, but you can use an approximate position.  These values are not super crucial. They are mainly used to compute a refraction correction.  For the computations you can use the standard trig functions, or use get the answer online from or

Fill in the main data for the sight: Date, Times (Local and GMT), Bodies, IC, Near or Far sides of the bodies used, HP for the Moon, and p (additional altitude correction if Venus or Mars). These go in the blue boxes 1 through 19 at the top of the Form. Box 1 is for your Sight Identification.

Note that the parallax of Venus or Mars, when applicable, is called "p" on page 259 of the Nautical Almanac, but it is called "Additional altitude correction" in Table A2. In our form it is labeled "p."

Figure 1

Using OPTION 1 from above. Using Stark's Table 1,  lookup values for your Bodies and enter them in boxes 20, 21 for your Other Body and 26, & 27 for the Moon. 

Unless otherwise noted, when entering the Stark Tables using a value that is in-between two values listed in the tables, always take the answer corresponding to the higher one. Do not interpolate.

Figure 2

Add your Bodies Hs degrees (box 14) and box 20 values to obtain Sa degrees and enter in box 30 repeat with boxes 15 & 21 to obtain Sa minutes and enter in box 31. Then add the Moon's Hs degrees (box 16) and box 26 values to obtain Ma degrees and enter in box 32,  repeat with boxes 17 & 27 to obtain Ma minutes and enter in box 33.

[7]  Using OPTION 2 from above.  Enter the your Hc values in boxes 14, 15, 16, & 17 on the Form

Figure 3

Enter Stark Tables with the Moon Hc to extract the WWP correction and enter in box 22 & 23, then got to the WWRef Table to get the parallax correction for both the Moon (enter value in box 28 & 29) and the other Body (enter value in box 24 & 25).

Add the values in boxes 16, 22, & 28 together for the Ma (Moon Apparent Altitude) degrees value  and enter in box 32  and  add the values in boxes 17, 23, & 29 together for the Ma (Moon Apparent Altitude) minutes value and enter it in box 33, then add the WWRef box 24 & 25 and HC box 14 & 15 together for the Sa (Body Apparent Altitude) enter results in boxes 30 & 31 (degrees & minutes in proper boxes)

Upon examining  the Ma (boxes 32 & 33) and Sa (boxes 30 & 31) values select the column where you can write the smaller value under the larger. If the Ma is less than Sa copy the value in box 32 into box 42 and copy the value in box 33 into box 43. Otherwise copy the value in box 30 into box 44 and the value in box 31 into box 45. Subtract the lesser value to get the Ma ~ Sa value either in boxes 46 & 47 or in boxes 48 & 49. You could now copy the Ma ~ Sa values thus found and recorded into boxes 73 (degrees) & 74 (minutes) in Section 2.

Figure 4

Enter Table 2 and extract the 2 values at the Ma (boxes 32 & 33) and HP (box 18) row/column intersection, insert these values on the Form in boxes 34 & 35, also extract and enter the values in the sidebar table for the additional HP remainder from the value in Table 2 in boxes 36 & 37.

Enter Table 3 for the same 2 values for the Other Body (Sun, Jupiter, Stars and Saturn columns are self explanatory, Venus and Mars have special columns based on their HP) Enter the Table 3 values in boxes 38 & 39.

Figure 5

Once these values are entered add the values in boxes 34, 36, & 38 together and enter in box 40. Next, add the values in boxes 35, 37, & 39 together and enter in box 41.

Round the value in box 40 to 1 decimal place and enter it under the Ma ~ Sa value obtained earlier (your rounded value will be entered in either box 50 or 51). You will be adding this value to Ma ~ Sa value if you Lunar Distance sight was to the Far side of the Moon or subtracting if it was to the Near side. This operation will result in the H ~ H value (depending on which column you are working in this H ~ H will be in box 52 & 53 or in box 54 & 55) .

You could now copy the H ~ H values thus found and recorded into boxes 84 (deg) & 85(min) in Section 2.

* * * 

You have now completed the Input section (Section 1) of the Form and are ready to compute your Cleared Lunar Distance (D) using the Green highlighted boxes 91 & 92 in the next section of the Form.

Add the values in boxes 34, 36, & 38 together and enter in box 40. Next, add the values in boxes 35, 37, & 39 together and enter in box 41.

Round the value in box 40 to 1 decimal place and enter it under the Ma ~ Sa value obtained earlier (your rounded value will be entered in either box 50 or 51). You will be adding this value to Ma ~ Sa value if you Lunar Distance sight was to the Far side of the Moon or subtracting if it was to the Near side. This operation will result in the H ~ H value (depending on which column you are working in this H ~ H will be in box 52 & 53 or in box 54 & 55).

You could now copy the H ~ H values thus found and recorded into boxes 84 (deg) & 85(min) in Section 2.

You have now completed the Input section (Section 1) of the Form and are ready to compute your Cleared Lunar Distance (D) — in the Green highlighted boxes 91 & 92 in the next section of the Form

Enter Table 4 to obtain the Moon's Augmented Semi-Diameter value using your Ma value (box 32 & 33)  and the Moon's HP (box 18) and enter that value in box 56 on the Form.

Next, go to Table 5 to obtain the Sun's Augmented Semi-Diameter value using your Sa value (box 30 & 31) and enter that value in box 57 on the Form.

Add box 56 and 57 together and enter the result in box 58. If you are dealing with Low Altitudes for the Sun or Moon enter the appropriate value from Table 6 in box 59.

Subtract the value in box 59 from the value in box 58 and enter the result in box 60. Round this result to 1 decimal place and enter it in the box that matches the column for Near (box 65) or Far (box 66) as appropriate for your sight. 

Figure 6

Enter your IC in box 61 (off) or 62 (on) and Instrument error in box 63 or 64 and combine with your Lunar Sextant Distance (Ds in boxes 67 & 68) and box 65 added as well resulting in your Da value (off - boxes 69 & 70 (copy to boxes 71 & 72) or on - boxes 71 & 72 with box 66 subtracted - see arrow on Form as a reminder)

Next bring down your Ma ~ Sa value, if you have not done so already, and subtract the Ma ~ Sa value in box 73 & 74 from the Da in box 71 & 72 entering the result in boxes 75 & 76.
Then add Da (boxes 71 & 72) and the  Ma ~ Sa (boxes 73 & 74) values together entering the result in boxes 77 & 78.
Figure 7

The next operation requires entering the K Table and extracting the K value for the Da/ Ma ~ Sa (boxes 75 & 76) difference and entering that K value in box 79 and the Da/ Ma ~ Sa (boxes 77 & 78) addition and entering that K lookup value in box 80. Add these two K values (boxes 79 & 80) together entering the result in box 81 and then divide that result (box 81) in half and enter that value in box 82.

Bring down the Q value (box 41) from Section 1 of the Form and copy it to box 83, next, add boxes 82 and 83 together and enter the result in box 84. Round the value in box 84 to 5 decimal places.

Figure 8

Enter the K Table again and extract the K value for the H ~ H (boxes 84 & 85) that you copied from Section 1 of the Form

Figure 9

Compare the Value in box 86 with the value in box 84a. If box 84a is less than box 86 copy the value in box 84a into box 87 and subtract box 87 from 86 and enter the result in box 88, otherwise copy the value in box 86 into box 89 and subtract box 89 from box 84a and enter the result into box 90.
Lookup this 'resulting value' (box 88 or 89 value) in the body of the Gaussians Table and extract the 3 digit value at the top of a column where your 'resulting value' is found and extract the 2 digit number next to your 'resulting value'. 

Place these digits as a 5 digit number (first the 3 digits, then the 2 digits) in the empty box under the number you originally moved to the other column(if you entered the Gaussian table with box 88 enter the gaussian value in box 89 OR if you entered the Gaussian table with the box 89 value enter the gaussian value in box 87. (put a line through your 'resulting value' so you do not mistakenly use that value in the next step.

If your gaussian value was placed in box 89, subtract box 89 from box 84a and enter result in box 90, otherwise subtract box 87 from box 86 and enter the result in box 88.

Now enter the K Table again, but this time this latest result (box 88 or 89) will be found in the body of the K Table. You will be determining the degrees from the page and the minutes and tenths from the row and column in the K Table.
This resulting Value as found in the K Table is your Cleared Lunar Distance (D) and is now entered in Green highlighted boxes 91(deg) and 92 (min/tenths).

You have now computed your Cleared Lunar Distance (D) boxes 91 (deg) & 92 (min) and have completed Section 2.

Next, You will determine the Computed Lunar Distance for the Hour PRECEDING and Hour FOLOWING the TIME of your Lunar Distance Sight in order to determine the Computed Lunar Distances for those hours.

The next steps involve entering the Nautical Almanac and extracting the GHA and Declination for the Moon and the Other Body for the Hour PRECEEDING and FOLOWING the TIME of your Lunar Distance Sight. If the Other Body is the Sun or one of the Planets the GHA degrees and minutes are entered in the center column boxes 105 through 110. The Declinations are entered in the left column in boxes 111 through 119 (Preceding) and 149 through 157 (Following). Please make sure that you note the sign (N/S) in boxes 111 and 115 (Preceding) and 149 and 153 (Following). If your Other Body is a Star the computations required for determining the GHA of the Star are provided in the right hand column boxes 93 through 101 (Preceding) and 131 through 139 (Following). 

Figure 10
Once you have entered the GHA and Declination of your Bodies in the appropriate boxes, enter the difference between the GHAs in boxes 109 & 110 (Preceding) and 147 & 148 (Following)  and the difference between the Declinations in boxes 118 & 119 (Preceding) and 156 & 157 (Following). NOTE: make sure that you take into account the SIGN of the Declination when determining the difference - i.e. Same = subtract, Contrary = add.

The next step involves entering the K Table with the value of the GHA difference boxes 109 & 110 (Preceding) or 147 & 148 (Following) and entering that K value in box 120 (Preceding) or box 158 (Following).

Figure 11
Then, enter the log Dec Table with the Declination values and extract the log Dec for each Declination and enter those log Dec values in boxes 121 & 122 (Preceding) and 159 & 160 (Following). 

Add the values in boxes 120, 121 & 122 (Preceding), enter result in box 123 and in boxes 158, 159 & 160 (Following), enter result in box 161.

Enter the K Table once more with the difference between the Declinations Boxes 118 & 119 (Preceding) and boxes 156 & 157 (Following) and extract the K value and enter it in box 124 (Preceding) and box 162 (Following) in the center column of the Form as indicated.

The next step is to compare the values in boxes 123 & 124 (Preceding) and boxes 161 &  162 (Following). The accompanying Form shows how to handle the TWO POSSIBILITIES  resulting from the comparison. Either or both possibilities can occur in your solution.

Figure 12
In the PRECEEDING area the value in box 123 is lesser than the value in box 124, thus we will copy the value in box 123 into box 125. Then, subtract the value in box 125 from the value in box 124 and enter the result in box 127. You will now enter the Gaussian Table with the value in box 127 in the body of the Gaussians Table and extract the 3 digit value at the top of a column where your 'value' is found and extract the 2 digit number next to your 'value'. 

Place these digits as a 5 digit number (first the 3 digits, then the 2 digits) in box 126 (put a line through your 'value' in box 127 so you do not mistakenly use that value later. Next, subtract the value in box 126 from the value in box 123 and enter the result in box 128. 

Now enter the K Table again, with box 128 value which will be found in the body of the K Table. You will be determining the degrees from the page and the minutes and tenths from the row and column in the K Table. This resulting Value as found in the K Table is the Computed Lunar Distance (D1) and is now entered in Green highlighted boxes 129 (degrees) and 130 (minutes/tenths).


Figure 13

In the Following  area the value in box 162 is lesser than the value in box 161, thus we will copy the value in box 162 into box 164. Then, subtract the value in box 164 from the value in box 161 and enter the result in box 166. You will now enter the Gaussian Table with the value in box 166 in the body of the Gaussians Table and extract the 3 digit value at the top of a column where your 'value' is found and extract the 2 digit number next to your 'value'. 

Place these digits as a 5 digit number (first the 3 digits, then the 2 digits) in box 163 (put a line through your 'value' in box 166 so you do not mistakenly use that value later. Next, subtract the value in box 163 from the value in box 162 and enter the result in box 165. 

Now enter the K Table again, with box 165 value which will be found in the body of the K Table. You will be determining the degrees from the page and the minutes and tenths from the row and column in the K Table. This resulting Value as found in the K Table is the Computed Lunar Distance (D2) and is now entered in Green highlighted boxes 167 (degrees) and 168 (minutes/tenths).

NOTE.  Either possibility can occur in the PRECEEDING hour or FOLLOWING hour areas in your solution and not necessarily in the order or place that I have shown them.

You have now completed Section 3 and determined the Computed Lunar Distance for the Hour PRECEDING (D1) and Hour FOLOWING (D2) the TIME of your Lunar Distance Sight. Next you will determine the Computed GMT for your Cleared Lunar Distance in Section 4.

Compare your D value in boxes 91 & 92 with the D1 value in boxes 129 & 130 and enter the difference in box 169. Usually it will only be necessary to use the minutes/tenths values in boxes 92 & 130 as the degrees are generally the same. 

Figure 14

Next, compare your D1 value in boxes 129 & 130 with the D2 value in boxes 167 & 168 and enter the difference in box 170. Usually it will only be necessary to use the minutes/tenths values in boxes 130 & 168 as the degrees are generally the same. 

Now enter Table 7 with the values in boxes 169 & 170 and enter the respective values found into boxes 171 & 172.

Subtract the value in box 172 from the value in box 171 and enter the result in box 173.
Go to the Table 8 body with the value in box 173 and find the minutes and seconds corresponding to that value. Enter the resulting values in box 178 (minutes) and box 179 (seconds). Copy the value in box 103 (Preceding Hour) into box 177.

You now have the Computed GMT in boxes 177 (hr), 178 (min), & 179 (sec). Copy your GMT from box 7 into boxes 174 (hr), 175 (min), & 176 (sec). Once you have done this enter the difference between boxes 176 & 179 into box 180. Note: you may have to get the difference between the minutes found in boxes 175 & 178. If you do convert the result into seconds and add this result to the value in box 180.

The value in box 180 is your Error in Time. By dividing the value in box 180 by 4 (derived from 15' of arc movement in 60 seconds of time) and entering the result in box 183 you have determined your Longitude Error. Applying this error to your DR Longitude in box 4, you will calculate your Computed Longitude. Enter this value in box 184.

 * * *

You have now completed Section 4 and have determined your Computed GMT and corresponding Longitude for your Lunar Distance Sight.



Editor's note: A copy of the full Miller-Modified Stark Work Form is shown below, annotated with the box numbers referred to in the text along with some notes, colored boxes, and some arrows indicating where to place certain data values. You can here download the form in Excel format.

Figures 15 and 16