From The Deck Of The SS Northing & Easting

Earlier this morning I let the dogs out to do their business and stepped out onto my deck to have a look around.  Although it was a bit cloudy out I noticed that the Moon was hanging brightly about 8 degrees above my roof line.  Dawn was just starting to break and I figured it would be a good time for this pseudo-mariner to get some practice sights in with the sextant.  The moon is entering its last quarter here in Georgia and there was still enough of the orb available for a good upper or lower limb shot.

I grabbed my old Astra IIIB sextant, screwed on the artificial bubble horizon and spent about 10 minutes practicing 'pulling down the sight', focusing more on technique than accuracy.  With a bubble horizon you have a lot of room for error because the horizon indicator (the bubble) is so large when viewed through the sight tube.  Don't worry - around 0720 EST the Moon was hanging at about 40 degrees 4.8 minutes, right where it should be.  The clockwork heavens are still ticking along just fine.

Astra IIIB Sextant

As I was fiddling with the sextant the winds started pushing the low clouds around and the Moon began darting in and out of view, sometimes partially obscured, sometimes fully obscured.  This made for an interesting practice session as I was forced to time the approach and departure of the heavier cloud patches and practice pulling down the sight quickly before the Moon became too indistinct for a good shot.   This is a common problem in celestial navigation - the navigator is at the mercy of the weather.  That's why so much emphasis was placed on grabbing a celestial shot whenever the heavens and the weather cooperated.  It is also why so much emphasis was placed on accurate dead reckoning - estimating your current location based on distance and direction traveled from your last known location.  Since you were never sure when you'd be able to get your next celestial fix an accurate running estimate of your position was absolutely crucial.

I was reminded of the particular problem celestial navigation posed for our submarine crews in WWII.  More than any other arm of the Navy, the Submarine Service operated far into enemy waters in search of victims, and they traveled alone.  Accurate navigation was absolutely essential and the navigators assigned to our submarines were some of the best the Navy produced.

WWII submarines were extremely vulnerable when caught in the wrong combination of circumstances.  Our subs like the Gato-class boats were really highly modified surface ships that could spend limited amounts of time under water on battery power.

US Gato-class submarine

The lower spaces of these subs were filled with giant lead acid batteries that allowed the boat to remain submerged for up to 48 hours and maneuver slowly (9 knots).  Eventually, however, the sub had to surface to charge her batteries, refill her air tanks and get a navigational fix.  For a boat operating alone in enemy waters this was a hazardous activity.  A submarine was never more vulnerable than when on the surface with low batteries.  It was common practice for the subs to surface in the dark of night and make a high speed dash to a new hunting area while replenishing her batteries.  The problem is that the middle of the night is generally a lousy time for a celestial fix.  Sure, the skies are filled with stars and planets, but the horizon is difficult to distinguish.  The best time for a fix is at nautical twilight, when the sun is 6 - 12 degrees below the horizon.  At this time the nautical horizon is still distinct and key navigational stars and planets are visible in the darkening sky.  But there's also enough light left to be spotted by an enemy aircraft or nearby surface ship.

This led to a unique 'navigator's dance' on American submarines.  At twilight the Captain would bring the boat to periscope depth to check for enemy ships and aircraft and to check weather conditions.  If the skies were clear of enemy and clouds he'd give the heads up to the navigator, who was usually the boat's executive officer.  The navigator would have already checked his navigational tables and picked one or more likely celestial objects to try to use for a fix.  This could be a planet or bright star or, if he was really lucky the Moon was already up and far enough above the horizon to provide a good fix.  The navigator would often wear goggles with red lenses to get his eyes adapted to dark conditions.

The Captain would give the command to surface the boat and once the conning tower was clear of the water the hatch would be opened and the watch personnel would scramble up with binoculars, climb the periscope shears and scan the skies and the horizon for any signs of the enemy.  Once the all-clear was given the navigator would come up with the sextant hanging from his neck by a lanyard.  He would take a series of quick shots on the available celestial bodies and call the sextant readings down to the navigation team in the control room.  The navigation team would note the time of the observations against the boat's chronometers and begin the process of using the sight readings to establish a line of position.  A quick shot on Polaris gave the navigator an accurate and easily determined latitude, but the shots on the stars and planets to determine longitude took a bit more number crunching.  Things like the height of the navigator above the surface of the water, the time difference from GMT, the uncorrected error built into the sextant and other factors all had to be calculated.  This process was called 'sight reduction'.  It was (and still is) straight forward but somewhat tedious math.

In the end the navigation team (usually consisting of the executive officer, an enlisted navigator known as a quartermaster and another pair of trained eyes, often those of the Captain) would come up with intersecting lines of position, one for latitude and one for longitude, that provided the boat's true position at the time the sights were taken.

Here's an interesting description of the process taken from the book 'The Underwater War 1939 - 1945' by Richard Compton-Hall:

Away from land every opportunity for taking sun, moon, planet and star sights had to be snatched. Sight-taking with a sextant was treated as an evolution; if surfacing primarily for that purpose it was combined when possible with ditching (trash) — which made matters no easier for the navigator competing in the conning tower and on the crowded bridge with a hustling (trash) party, the lookouts and the sea itself. The smallest drop of water on the sextant mirror made sight-taking impossible and the instrument had to be wrapped tenderly in a towel when not actually bringing the observed body down on to the lurching, irregular horizon which, with so low a height-of-eye, made the task doubly difficult. The 'exec' was primarily responsible for navigation in American boats (assisted by excellent quartermasters) but German commanders relied upon the equivalent of a specially trained warrant officer to take sights. Most British captains thought sight-taking far too important to entrust to Vasco (the navigator) and did the sextant work themselves; but they were quite happy to delegate the long and boring working-out of the sights when they were taken! It could easily take an hour to plod through the spherical trigonometry (which actually amounted to no more than straight forward arithmetic) before arriving at a solution which almost invariably produced a large cocked hat; this led to thinly veiled hints from Vasco to the effect that the captain was incapable of reading sextant angles, and to more direct accusations from the captain that the navigator was incapable of simple addition and subtraction. Some boats carried rapid reduction tables derived from air navigation manuals which greatly shortened the time required to produce a fix: but the Royal Navy and most other services clung doggedly to Inman's Nautical Tables with their long columns of five-figure logarithms.

Today we are spoiled.  Want to know where you are on the face of the earth to within a few hundred feet?  Just turn on your smartphone or GPS receiver.  Within seconds you'll get a position fix that is far more accurate than any experienced navigator could have calculated using celestial navigation.

Yet I believe it is important we continue to practice the old techniques.  First, it is great mental exercise.  To be a good celestial navigator you need to be at least proficient in basic astronomy and mathematics.  You need to know how to evaluate and calculate error.  You need to be a good problem solver.  Celestial navigation is like golf - it takes just a few months to learn but a lifetime to master.  It sure beats playing another round of World of Warcraft.

Next, celestial navigation gives one a greater appreciation for the technology we have available today, and that appreciation and the resulting awareness of the GPS system's capabilities and limitations will make you a better navigator overall.

And last, the celestial navigation techniques and tools we use today are exactly the same as those used by history's great explorers and navigators - Capt. James Cook, Lewis and Clark, Robert Peary, Roald Amundsen, Earnest Shackleton, Robert Scott, Capt. William Bligh (yes that Capt. Bligh) and many others. Anyone interested in the history of exploration can make a direct and relevant connection to their heroes and better appreciate their achievements by dabbling in celestial navigation.

So that's today's report from the deck of the SS Northing & Easting.  I'll keep the spyglass and blunderbuss handy in case the pirates try to board.

Brian

The NGS Does the IAGS

My blog post last year about the Inter-American Geodetic Survey (IAGS) has has proven to be my most popular post, both in the number of pageviews and the number of comments.  Although I'm not burning up the internet, it is interesting to track where visitor's interests lie.  Surprisingly, my blog post is also the #2 return on Google searches against the term 'inter american geodetic survey' (it seems that the acronym IAGS is in use by several completely unrelated organizations that generate a lot of traffic, so searches against that term won't put my post anywhere near the top of the list).

I'm both elated and just a bit saddened by this outcome.  Elated that I seem to have hit on poorly covered yet important subject that I can contribute significantly to, yet saddened that the Army Corps of Engineers continues to ignore the very crucial contributions their topographic services and personnel made to the professions of mapping, surveying and geodesy.

When I wrote the blog about the IAGS I noted that there's very little available information about the organization on the web and I tried to provide links to as much relevant info as I could find.  One of the sources I completely ignored was the excellent article about the IAGS that appeared in the March 1956 edition of the National Geographic Magazine.

March 1956 National Geographic article on the
IAGS.  Click here to read it.

Before the National Geographic gave up serious scholarly writing for feel good stories about baby seals and the therapeutic effects of tree hugging it actually published some darned good stories about geography, exploration, and adventure.  All three of these elements come together in this great story about the IAGS.  It is probably the best, and perhaps the only, popular account of the agency's activities.  So, follow this link and read about the Men Who Measure the Earth.

Whence The Meridian?

It seems that most folks' awareness of history reaches back only 20 or 30 years.  Few today can conceive of a world without laptop computers, cable TV, cell phones and Dancing With The Stars.  Oh how dark and disordered life must have been before the internet!  How did man survive?

Old farts like me realize that history is a cumulative progression of events, and the things we take for granted today had an origin in the murky mists of time long past.

So it is with the concept of longitude and the meridian.  Today we take for granted that the zero line of longitude, the international meridian, runs through Greenwich, England.  It seems just so natural.  Most people today don't realize that getting the meridian at Greenwich accepted as the world-wide standard was a long, drawn out process that spanned over a hundred years and involved most of the major world powers.  What we take for granted today is actually the result of some pretty intense diplomatic and scientific battles.

Man has realized since the time of the ancient Greeks that the Earth is round(ish) and that one of the best ways to refer to one's position on this big ball is to use angular measurements - degrees, minutes and seconds.

On land this convention wasn't really important - the common man was content relating his location as distance and direction traveled from known points.  There was always a track, trail or road that led to where he wanted to go.  The history of the march of civilization is the history of road building.  It's coded into our DNA.

But as soon as man started sailing out of sight of land things changed.  There are no roads in the middle of the Atlantic.  All sailors had to fall back on was positioning by latitude and longitude.  With the explosion of maritime trade in the 18th and 19th centuries most of the big navigation problems were quickly worked out.  By the late 1700s we had reliable navigation instruments (sextants and chronometers), most of the important places of the world had been charted and sea captains could reliably and safely make their way to the other side of the world and back carrying cargoes that made the ship's owners immensely wealthy.

But there was one last international navigation issue that was was still hanging out there in the late 1800s that needed to be addressed.  The issue of a common meridian.

Latitude and longitude are calculated from an accepted reference line, or zero line.  For latitude the solution was simple.  The equator is the natural zero line of reference.  When calculating latitude you are measuring your location north or south of the equator - the zero line of latitude.  Simply measure the angular distance from your location to the North Star - Polaris - and you have your latitude in degrees, minutes and seconds.  Mariners around the world have been doing this since before recorded history.  (If you are south of the equator it's a little trickier since there is no star that hovers directly over the south pole.  However, there are nearby stars such as those that make up the Southern Cross that permit similar measurements.)

Longitude however has always been the problem child of navigation.  Part of the problem is that there is no natural zero line of longitude - the earth does not have a natural vertical equator.  The other problem is that there are no fixed or unmoving celestial bodies - stars or planets - that could offer an easy reference for longitude measurements like Polaris does for latitude measurements.  All the useful celestial bodies are in constant motion overhead.  What was needed was first a fixed reference line - a meridian - and then in reference to that line the minute-by-minute locations of all useful stars and planets as they marched across the sky.  The designation of the meridian also drove the publication of accurate nautical charts for use by merchantmen and navies.  This was a monumental task that only governments could support.

The realization that establishing a meridian and charting the night skies was a national necessity coincided with the scientific revolution of the 1700s.  Nations were willing - even eager - to put their money and their best minds to the task; it became an issue of national pride among the major seafaring nations.  Most also saw it as a national security issue.  These efforts were some of the earliest examples of directed research - scientific investigation not for the sake of enlightenment but to meet a specific economic or military goal.

As a result everybody who fancied themselves a bigshot on the global stage established their own meridian and published navigational charts and celestial almanacs referenced to their meridians.  Most also required their navies and merchant fleets to use their meridian.  Countries such as England (Greenwich), Spain (Madrid), France (Paris), United States (Washington D.C. and Philadelphia), Portugal (Lisbon), Norway (Oslow), Russia (St. Petersburg) and Japan (Kyoto) all developed their own meridians.  Even non-seafaring nations like Switzerland and Romania tried to get in on the act.

By the mid 1800s the worldwide nautical charting community had become a seafaring Tower of Babble; not everybody spoke the same positional language.  At the same time the development of reliable steam power was driving an explosion of commercial shipping activity.  As merchant marine activities became more globalized ship captains, owners and insurance companies began demanding standardized navigational charts and nautical almanacs.  A ship captain sailing from Boston needed to know that when he got to Lisbon and needed a new chart he could walk into a chandler and purchase a chart that uses to the same meridian he was trained to use and was comfortable with.  Seafaring nations realized that a single universally recognized meridian was a good thing.  But whose meridian would be the winner?

In 1884 the President of the United States, Chester A. Arthur, got representatives from all the key nations together in a big room at the State Department in Washington D.C. and told them to figure it out.  By this time the US really didn't have a dog in the fight; although we were willing to accept Greenwich, England as our standard Prime Meridian we were open to switching and were not going to push a US-based solution.  My guess is that most of the attendees saw the US as something of a neutral party in this argument, which is why they agreed to show up and work things out.

The 'International Conference For the Purpose of Fixing a Prime Meridian and a Universal Day' was convened on October 1st 1884 and ran for the full month.  The proceedings can be found on the Project Gutenberg website.  The proceedings are an interesting read from a historical, scientific and political perspective.  The delegates from France did a lot of talking, extolling the glories of the Empire and the primacy of the observatory in Paris.  In the end however Greenwich in England won out, in large part, I suspect, because at the time over 72% of the world's shipping used nautical charts based on the Greenwich meridian.  The Greenwich solution had the weight of numbers behind it and came without a lot of Gallic preening and posturing.

And so we have the Final Act:

Note who decided to take a pass on the final vote.  Sore losers I guess.

The conference addressed and adopted a number of other issues including the designation of a 'universal day'.  This is why we have Greenwich Mean Time, or GMT (also referred to as UTC) and the standard solar day starts, and ends, at Greenwich.

After the conference the US Congress moved quickly to adopt Greenwich as the standard prime meridian for all US-based mapping and charting.  The US Navy and the Royal Navy began working jointly on the development and maintenance of nautical almanacs for celestial navigation and the sharing of nautical charts.  This is a collaboration that continues to today.

So there you have it.  Something a seemingly mundane as the starting point for all longitudinal measurements around the world actually has a history that impacts us today.

Brian

A False Sense of Confidence

For Christmas my lovely wife gave me a new GPS receiver.  At work I'm surrounded by some of the most expensive and precise GPS surveying technology available today - devices that can reliably locate you to within a few centimeters of your true position.  What I didn't have was a consumer grade GPS device that I could take out hiking or fishing.  It seems Roberta read my Dear Santa letter and got me a DeLorme PN-60 receiver.

Many of you are probably asking, "why not just use your iPhone?"  Good question.  While I love my iPhone experience has taught me that it makes a lousy GPS receiver.  It may locate you good enough to allow accurate vehicle navigation while cruising up the interstate and it may provide good enough locations to allow you to update your Facebook status, but as a dedicated GPS tool it just doesn't cut it.  To be fair, the iPhone does excel is as an integrated device for wayfinding.  Apple's integration of hardware and mapping software makes the iPhone a wonderful and reliable urban navigation tool.  However, most of this functionality is dependent on a wi-fi or 3G signal, making the device unreliable for use in the backwoods.

What I wanted was a dedicated GPS that is rugged, water resistant, accurate and allows me to upload maps and aerial photos.  The PN-60 seems to fit that bill just fine.

Of course the first thing I had to do is take it out and play with it!  A few days after Christmas I loaded the dogs into the old Volvo wagon and we headed out to one of my favorite parks with walking trails.  This park, Lake Horton, is located in Fayette County and has a number of walking trails that skirt the lake.  Once we got there I leashed up the dogs and set the PN-60 to generate a track file (basically recording my location every 10 feet).  The trail we walked is a 1.8 mile long trace that moves through a mix of topography - some open ground, some heavy canopy cover, some areas where the canopy obscures just half the sky.  It is a good test environment for a GPS receiver.

Let's pause for a minute to review just how GPS works.  The GPS receiver establishes a position by a triangulation process that uses signals from the GPS satellites in orbit around the Earth.  A GPS receiver needs good signals from at least three GPS satellites to calculate a useable position in 2 dimensions (horizontal).  Note that the key word here is useable, not accurate.  To get a useable 3 dimensional position (throwing elevation into the mix) the receiver needs good signals from at least four satellites.  The accuracy of the position your receiver calculates is highly dependent on a number of factors such as satellite geometry (where they are in the sky overhead), how healthy the satellites are (yes, there are 'healthy' and 'unhealthy' GPS satellites), the amount of overhead interference (things like heavy tree cover, tall buildings, etc.) and the overall sensitivity and accuracy of the receiver itself.  All of these factors have a vote in how accurate or inaccurate you GPS location will be.  The only fixed variable in this equation is the capability of your GPS receiver; all other factors can vary from minute-to-minute and location to location.

Just how accurate can a GPS receiver be?  The US Air Force, which operates the GPS system, states that civilian users can expect the GPS system to provide position fixes to within 100 meters 95% of the time.  That's pretty darned conservative and assumes a very basic early generation receiver that is not applying any modern GPS correction signals from systems like the WAAS satellites (Wide Area Augmentation System).  

The civilian GPS industry tosses around the number 15, as in 15 meters.  A modern consumer grade GPS receiver operating under open sky and in the static mode (not moving) should provide a fix to within 15 meters (49 feet).  If the receiver is WAAS-capable (and most are) then that potential accuracy should drop to about 3 meters (10 feet). This is about the best a modern consumer grade GPS unit can be expected to do.

This big improvement in accuracy has come through improved receiver hardware and software.  GPS receiver manufacturers have gotten pretty good at this business over the past 20 years and they've developed some nifty tricks to greatly improve overall accuracy and satellite signal acquisition speed and lock.  A modern GPS receiver, even a relatively inexpensive recreational unit like the PN-60, is a marvel of modern hardware and software design.

Now back to our regularly scheduled blog post...

So the dogs and I walked the 1.8 mile trail and then rushed home to upload the GPS track file to the DeLorme Topo North America desktop software to see what was recorded.

Zoomed out it looked sort of OK; at least I was on the right part of the world.

DeLorme Topo North America 9.0 (click on image to enlarge)

But when I zoomed in to specific sections of the track I noticed some concerning issues with how the recorded GPS track was lining up with the portions of the trail visible in the image.

25 ft. offset between the walking trail and the GPS track
(click on image to enlarge)

Note the high tension lines running north-south across the image.  This is a potential source of interference.

Next:

38 ft. offset between the walking trail and the GPS track
(click on image to enlarge)

Note the heavy canopy coverage immediately south of the trail.  Heavy tree canopy can either block or interfere with GPS signal quality.

Next:

An average 10.2 ft. offset on a section of trail with light overhead canopy
(click on image to enlarge)

In an area with fairly open sky (and well away from powerlines) the average offset drops to just over 10 feet, perfectly acceptable accuracy for this receiver operating in the moving mode.

Next:

Offsets ranging from 14.5 ft. to almost 25 ft. in an area of completely open sky
(click on image to enlarge)

What's going on here?  This is an area of completely open sky - no trees or other obstructions.  Accuracy should be much better than what we are seeing here.  Well, if you look closely you can just make out the trace of the high tension power lines cutting across the lower right hand corner of the image.  My suspicion is that the powerlines are interfering with the GPS signals.

And last:

Two sample areas in close proximity - one showing a 60.7 ft. offset and
one showing almost negligible offset
(click on image to enlarge)

This example clearly illustrates the impact of heavy tree canopy cover.  The upper measurement, taken in an area of dense canopy cover, shows an almost 61 foot offset between the walking path and the GPS track.  However, just 55 feet to the south, under fairly open sky (and with no power line interference) the offset is so small as to be negligible.

So what can we learn from this simple example?  Let's review:

1. The manufacturer's stated GPS accuracies are for their products operating under the most ideal conditions - open sky, with good satellite geometry and no electromagnetic interference.  Your real world results can, and will, vary widely.

2. Overhead or adjacent obstructions like trees can have a dramatic effect on GPS accuracy.

3. Unseen influences like nearby powerlines can have significant impact on GPS accuracy.

4. In areas of little obstruction or interference consumer grade GPS receivers can achieve their claimed accuracy of +/- 3 meters (10 feet) in the moving (tracking) mode.

So what can you do to improve your GPS receiver's accuracy?  Here's a few tricks:

1. Make sure WAAS is turned on.  On most receivers sold in the US it is turned on by default, but you still need to check.

2. Make sure position averaging is turned on.  While this won't help when moving, when stopped to record a position (waypoint) if you let the receiver average your position for a few seconds before storing it your accuracy can improve dramatically.  When collecting waypoints I'll try to let the receiver average between 5 and 10 seconds before storing the point.

3. Hold or carry the receiver so that the antenna is fully and properly exposed to the sky.  Don't expect a GPS receiver buried deep inside a backpack or tucked inside a shirt pocket to return a good position.  Your receiver has to 'see' the GPS signals and anything you can do to improve it's view of the sky will result in more accurate positions.

Understand your potential sources of error!  Remember how the system works - radio signals from space.  If you understand what can interfere with those signals and you remain observant of your environment you can often work around these sources of error.

So many people I talk to about GPS have a false sense of confidence about GPS accuracy.  The vast majority think their receiver is far more accurate than it really is.  While the GPS satellite system and our modern receivers are true marvels of modern technology the system still has plenty of real world limitations.

Brian

Note: I do have to add that the measurements I show in the images above also have a lot of built-in but uncontrollable error.  The DigitalGlobe images I'm measuring against have an advertised resolution of 30 centimeters (roughly 1 foot).  Assuming these images were processed without a tight orthorectification their inherent positional error can range from 2 - 5 feet (my estimation).  In this blog post I'm not trying to establish absolute accuracies or inaccuracies for a given receiver.  I just want to give the reader as sense of what impact physical and electromagnetic interference can have on GPS accuracy.