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From: Peter Rathmann <prathman_at_comcast.net>
subject: Re: [Paddlewise] GPS
Date: Sat, 28 Aug 2004 22:34:37 -0700
>>However, we did receive feedback that GPS could be quite badly in
>>error when satellites were low on the horizon and cliffs affected the
>>signal. I'ld be interested to know if anyone has experienced this?
>>    
>>
>
>GPS normally displays its range of precision, which depends on the number of
>satellites that can provide a good signal at given conditions, i.e.
>geographical position, obstructions etc.  I don't remember what is the
>lowest precision of my Garmin Legend (when it still gives some location),
>but must be better than 900m error of dead reckoning.  I've heard of
>possible fog-induced distortion of signal, but haven't had a chance to check
>it personally, so don't know whether it is just "honest" weakening of signal
>(= honest lower displayed precision), or really distortion of data beyond
>stated range of precision (this would be much worse).
>
I've used my GPS receiver on a daily basis for the last 6 years and have 
had a chance to see a number
of anomalous indications - none of which made themselves known through 
exceptionally high EPE
(estimated position error) or accuracy indications.  These included my 
all-time high indicated speed of
4032.3 mph achieved while pedaling my bike in a canyon area near a 
medical complex.  The tracklog indicated
a sudden jump in position shortly followed by a loss of signal lock.  I 
believe the hills were blocking most
of the satellites and I was probably getting a momentary multi-path 
reflection off the medical buildings
which the unit interpreted as my having rapidly moved to a new 
position.   There was also the 5-minute
period when the GPS indicated that I was at an elevation of 1500' over 
the north Pacific approaching
Seattle at 734 mph while my other navigational tools (eyes) indicated 
that I was on a
residential bike path in the SF Bay area and heading south at about 15 
mph.  The satellite page showed
a lock on just 3 satellites (i.e. a 2D lock) and I suspect that this was 
a case where with only 3 signals the
unit couldn't properly resolve between possible solutions of the pvt 
equations and picked the wrong one.
Turning it off and back on quickly resolved the problem.

But despite these and a few other momentary glitches, I've found GPS to 
be a highly reliable tool,
especially if care is taken to check the indications on the satellite 
page showing the number and
positions of the satellites being tracked.  I have never had a problem 
with reception due to weather
conditions and that includes thick fog and intense thunderstorms.  But 
there can be a problem due
to any film of water forming over the antenna - so condensation on the 
unit as a result of fog should
be wiped off.

Although I always have my GPS turned on when kayaking, I rarely use it 
for navigation.  The
main uses are to keep a record of the trip, incl. speeds and distances 
traveled, give an immediate
indication of actual speed and track including the effects of wind and 
currents, and to show me where
on shore appropriate restaurants, parks, restrooms, etc. may be located 
to help in deciding on
landing spots.  It's rarely used for navigation since I normally know 
where I am just by looking around.
But under unusual conditions, such as the fog coming in unexpectedly, 
the GPS can be a valuable
addition to other navigational aids.
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From: Bruce Grubbs <mail_at_brucegrubbs.com>
subject: Re: [Paddlewise] GPS
Date: Sun, 29 Aug 2004 07:02:23 -0700
I've had saved GPS waypoints be off as much as several miles. I suspect I had 
a 3 satellite (2D) fix at the time. I've never had such errors with 4 or more 
satellites, but it certainly is wise to cross check GPS against other means 
of navigation. I'm a pilot as well as paddler, and I never trust any single 
means of navigation in the air.

That said, GPS is wonderful for a pilot. It let's me go directly to my 
destination with a lot less work.

Bruce
Flagstaff, AZ
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From: PeterO <rebyl_kayak_at_iprimus.com.au>
subject: [Paddlewise] GPS Errors Summary
Date: Thu, 2 Sep 2004 19:12:18 +1000
G'Day,

Thought it would be worth summarising those posts in the GPS thread which
discussed GPS and coastal navigation errors. This is not to argue against
GPS which most contributors considered a very useful tool. Nevertheless the
comments seemed to be useful in describing how occasionally errors might
occur. Hope I don't misinterpret people: -

1. Peter Rathmann, during six years daily experience of using a GPS in a
variety of activities, occasionally observed errors so large as to be
obviously wrong, even though they did not show up as exceptionally high
estimated position error or accuracy indications. He ascribed these either
to momentary multi-path reflections off buildings or to the GPS receiving
signal from only three satellites.

2. Mike Daly reported that his GPS frequently shows an EPE of less that 15m
and he would ignore errors at that low level though larger errors he would
take notice of. Mike also mentioned that if only three satellites were
visible, then the receiver would assume the current altitude based on the
most recent determination. This gave rise to a discussion on how changes in
altitude could give rise to errors when moving from land to sea or paddling
in lakes.

6. Bruce Grubbs reported errors of several miles in saved way points when he
had a three point fix only (Bruce is a pilot and didn't say whether the
error was while flying or paddling).

3. My own experience with a GPS during a coastal navigation exercise
comparing a GPS against dead reckoning and non GPS pilotage. Almost
certainly the GPS error was negligible, and our non GPS measurements had an
average 10% error i.e 900metres over about 10km.

4. A second hand report from a yacht in Jervis Bay of a GPS reading that
computed their position to be on a reef, which they were nowhere near. The
explanation given was a possibility of interference by a cliff in the signal
transmission path because the satelites were near the horizon.

5. A report back channel that if the chart co-ordinates were supplied in a
different datum to the GPS then significant errors could occur. I don't
completely understand this but it seems as if it could easily be checked
before going on a trip.

The most common source of errors seemed to be when only three satellites
could be received. Those who reported occasional errors nevertheless felt
the GPS to be a very useful tool.

Hope this is helpful,

All the best, PeterO
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From: Michael Daly <mikedaly_at_magma.ca>
subject: Re: [Paddlewise] GPS Errors Summary
Date: Thu, 02 Sep 2004 11:58:53 -0400
On 2 Sep 2004 at 19:12, PeterO wrote:

> 2. Mike Daly reported that his GPS frequently shows an EPE of less
> that 15m and he would ignore errors at that low level though larger
> errors he would take notice of.

Just to clarify.  A low EPE means that the GPS thinks everything is 
fine even though those estimates are less than what is possible with 
the technology.  It isn't the errors that I ignore, it's the EPE.
Higher EPE means that there are real errors creeping into the 
position readings and I make sure that I consider that when looking 
at the reported position.

Even at SA levels of error (<100m, 95% of the time), that's still a 
lot better than what you can do with a sextant, so error 
interpretation is relative.

Mike
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From: Michael Neverdosky <mikenever_at_earthlink.net>
subject: Re: [Paddlewise] GPS Errors Summary
Date: Thu, 02 Sep 2004 12:11:35 -0400
Michael Daly wrote:
> 
> Even at SA levels of error (<100m, 95% of the time), that's still a
> lot better than what you can do with a sextant, so error
> interpretation is relative.


When I was practicing daily and using a $1000 sextant and artificial
horizon I could get to about 1/4 mile radius. 

Using normal gear on a sailboat I was more than happy if my 'triangle'
was only 2 miles across.

These days, with GPS in use I am more concerned about errors on my
charts as most have not been updated in many years and when they were
done much of the better position fixing systems did not exist.

I was on RV Hero in 1984-85 and we found Chiloe Island to be almost
3 miles from the charted position.
The charts of the Antarctic Peninsula were really interesting. Lots
of hand drawn updates and corrections, mostly from our own observations.

Remember, that there at least two positions that are important, yours,
and
that of land and obstacles on the chart. Both are subject to error.

michael (still more of a sailor)
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From: Michael Daly <mikedaly_at_magma.ca>
subject: Re: [Paddlewise] GPS Errors Summary
Date: Thu, 02 Sep 2004 17:44:55 -0400
On 2 Sep 2004 at 12:11, Michael Neverdosky wrote:

> When I was practicing daily and using a $1000 sextant and artificial
> horizon I could get to about 1/4 mile radius. 

That's twice as accurate as what most mariners consider very good.  I 
assume that's on land.
 
> Using normal gear on a sailboat I was more than happy if my 'triangle'
> was only 2 miles across.

That's a little more like it :-).  GPS users who complain about 
errors or insufficient accuracy are just whiners IMNSHO.  When you 
sail and are glad you can find a bay, worrying about a few meters 
seems excessive.

Mike
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From: <cholst_at_bitstream.net>
subject: Re: [Paddlewise] GPS Errors Summary
Date: Thu, 2 Sep 2004 12:10:46 -0500
Another observation about GPS: it can serve as a backup for a compass!

I'm usually careful about storing metal items near my deck compass, but at the 
beginning of our last trip, my wife handed me a food bag that I put into the 
bow hatch without thinking. As it happened, it contained a can of chicken meat. 
We had not been on the water long when I noticed a discrepancy between my 
compass heading and the map. The compass said I was heading SSE. Observation 
and the map said I was heading east. My wife's compass also said we were 
heading east, so after that I ignored the compass and just used the map and the 
GPS until we made camp.

We should have compared compasses when we put in, but we were so busy I forgot.

Chuck Holst
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From: John Fereira <jaf30_at_cornell.edu>
subject: Re: [Paddlewise] GPS Errors Summary
Date: Thu, 02 Sep 2004 13:53:02 -0400
This thread about errors using navigation instruments reminded me of 
something I was reading yesterday.  On a long train ride home yesterday I 
was reading Bill Brysons books "A Short History of Nearly Everything" and 
he was writing about carbon dating.  Apparently a couple of years after 
carbon dating was first used to determine the age of historical objects it 
was discovered that the numbers used for the half-life of carbon-14 were a 
not completely accurate. When the corrected number was used it resulted in 
a 3% difference in the age of an object (younger) than when the original 
half-life value was used.  However, because the method had been used for a 
couple of years and a lot of object had been carbon dated, rather than 
recalculate the age of all of them, all future calculations are made with 
the original incorrect value for carbon-14 half life.  As a result, any 
object that has been carbon dated is actually 3% older than published.
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From: Rafael Mier-Maza <silidriel_at_prodigy.net.mx>
subject: RE: [Paddlewise] GPS Errors Summary
Date: Thu, 02 Sep 2004 14:11:51 -0500
It is very interesting, mostly academically since 3% in thousands and
millions of years, still is thousands and millions of years. Error there
is of no significance, while 3% on a moon landing could be catastrophic.

Best Regards,

Rafael
Mexico 
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From: alex <al.m_at_3web.net>
subject: Re: [Paddlewise] GPS Errors Summary
Date: Thu, 2 Sep 2004 11:19:09 -0700
GPS frequently shows an EPE of less
> > that 15m and he would ignore errors at that low level though larger
> > errors he would take notice of.
>
> Just to clarify.  A low EPE means that the GPS thinks everything is
> fine even though those estimates are less than what is possible with
> the technology.

I think (have to turn it on, and wait for a while) that my Garmin can show
15 ft accuracy, which is 4.5m. There are additional (or different)
satellites to achieve such increased accuracy, called WAAS. But not in all
areas.  I've seen such accuracy displayed quite often, and didn't notice it
to be incorrect, though such accuracy exceeded that of the built-in map :-).

And, yes - GPS can be used as a subsitute for compass (but it should be a
supplement, - there is no excuse not to carry at least $5 around-the-neck
compass).  Even GPS without a compass can display a bearing to some map
point or waypoint.
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From: Michael Daly <mikedaly_at_magma.ca>
subject: Re: [Paddlewise] GPS Errors Summary
Date: Thu, 02 Sep 2004 17:44:54 -0400
On 2 Sep 2004 at 11:19, alex wrote:

> I think (have to turn it on, and wait for a while) that my Garmin can
> show 15 ft accuracy, which is 4.5m. There are additional (or
> different) satellites to achieve such increased accuracy, called WAAS.
> But not in all areas.  I've seen such accuracy displayed quite often,
> and didn't notice it to be incorrect, though such accuracy exceeded
> that of the built-in map :-).

Sorry, my GPS is pre-WAAS so I never consider those things.  

You're correct - with extras like WAAS or DGPS, you can get increased 
accuracy.  You also have to consider that some GPS units will do 
averaging of a position over time - taking lots of readings to cancel 
out the errors.  My comments should be considered in terms of basic 
GPS functionality when the unit is just turned on.  Under those 
conditions, the basic position error is <15m, 95% of the time.

The latter pretty much describes how I use my GPS.  It's off almost 
all the time, but I may turn it on, take a reading and turn it back 
off.  In fact, I only bring my GPS for a long trip or in an 
unfamiliar area.  

> And, yes - GPS can be used as a subsitute for compass (but it should
> be a supplement, - there is no excuse not to carry at least $5
> around-the-neck compass).  Even GPS without a compass can display a
> bearing to some map point or waypoint.

If you're picking up a GPS for the first time, make sure you know the 
difference between a GPS with an electronic compass and a GPS that 
figures out direction based on motion.  If you don't have an 
electronic compass, the compass direction indicated by the GPS relies 
on the GPS moving at a significant speed to interpret compass 
directions based on relative locations of adjacent position readings. 
If you're sitting still or moving very slowly, the apparent compass 
orientation may be meaningless.  A lot of paddlers I know stop 
paddling to confirm locations with map and compass.

Mike
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From: alex <al.m_at_3web.net>
subject: Re: [Paddlewise] GPS Errors Summary
Date: Thu, 2 Sep 2004 21:04:05 -0700
> If you're picking up a GPS for the first time, make sure you know the
> difference between a GPS with an electronic compass and a GPS that
> figures out direction based on motion.  If you don't have an
> electronic compass, the compass direction indicated by the GPS relies
> on the GPS moving at a significant speed to interpret compass
> directions based on relative locations of adjacent position readings.
> If you're sitting still or moving very slowly, the apparent compass
> orientation may be meaningless.  A lot of paddlers I know stop
> paddling to confirm locations with map and compass.


This expalins why I sometimes noticed a significant discrepancy between the
direction shown by my non-compass GPS and actual direction to waypoint when
paddling.  I thought GPS calculated the direction using calculated location
of the kayak and known location of the waypoint.
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From: Michael Daly <mikedaly_at_magma.ca>
subject: Re: [Paddlewise] GPS Errors Summary
Date: Fri, 03 Sep 2004 01:48:32 -0400
On 2 Sep 2004 at 21:04, alex wrote:

> This expalins why I sometimes noticed a significant discrepancy
> between the direction shown by my non-compass GPS and actual direction
> to waypoint when paddling.  I thought GPS calculated the direction
> using calculated location of the kayak and known location of the
> waypoint.


The GPS does calculate that way and that bearing's accuracy is 
directly related to the accuracy of the kayak position measurement.  
However, it has to calculate the direction to north (N) from the 
motion of the kayak.  Since slow speed means short distances between 
position determinations and each position can be in error by up to 
15m, the line between two positions can point all over the place.


         x1 <--- 10m ---> y1


      y2 <--6m--> x2

For example, assume your kayak moves from point x1 to point x2.  If 
the error in determination of the first point is right 10m giving y1 
and the error for the second is left 6m giving y2, you can see that 
the apparent direction of motion y1->y2 is very different than true 
direction x1->x2.  If this angular error is used to determine N, 
you'll be way off.  

If you're moving very quickly, the distance from point 1 to point 2 
is larger and the angular error is reduced even if the linear error 
is the same.

Note that the GPS is reading every second or so, so averaging out 
tends to reduce the errors.  The error in estimating N is still 
velocity dependent as is the estimated speed (in the above diagram, 
estimated distance y1-y2 is somewhat larger than true distance x1-x2, 
so the speed will be overestimated).   

Sitting still is the best way to ensure that the estimated position 
of N is bad.  If I turn on the GPS and don't move, the direction that 
my GPS reports it's traveling is usually way off.  The reported speed 
also wanders a lot, rarely stating 0.

Mike

PS - above assumes my usual worst case limits - no WAAS or DGPS and 
GPS turned on briefly.  With WAAS and leaving the GPS running, things 
improve due to smaller errors in position determination and more 
averaging.
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From: Bruce Grubbs <mail_at_brucegrubbs.com>
subject: Re: [Paddlewise] GPS Errors Summary
Date: Thu, 9 Sep 2004 09:30:55 -0700
Just a note- the position averaging feature works only when the GPS receiver 
is not moving.

Bruce
Flagstaff, AZ
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From: Dave Kruger <kdruger_at_pacifier.com>
subject: Re: [Paddlewise] GPS Errors Summary
Date: Thu, 2 Sep 2004 12:24:10 -0700
Alex's point is well-taken:  If the chart indeed was not accurate enough to
check the 15 ft "accuracy" then there is no way to establish the accuracy
limit is that size or smaller.

I have noticed errors in placement of waypoints (established in the field,
not from a chart), on a subsequent revisit of a marker (not a buoy), of about
200 feet in one case and 400 feet in another case ... which I took as an
indication of the limits of the system --- and as a piece of knowledge
important if/when I need to REALLY trust the dang GPS.

--
Dave Kruger
Astoria, OR
----- Original Message ----- 
From: "alex" <al.m_at_3web.net>

> I think (have to turn it on, and wait for a while) that my Garmin can show
> 15 ft accuracy, which is 4.5m. There are additional (or different)
> satellites to achieve such increased accuracy, called WAAS. But not in all
> areas.  I've seen such accuracy displayed quite often, and didn't notice it
> to be incorrect, though such accuracy exceeded that of the built-in map
:-).
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From: Michael Daly <mikedaly_at_magma.ca>
subject: Re: [Paddlewise] GPS Errors Summary
Date: Thu, 02 Sep 2004 17:44:54 -0400
On 2 Sep 2004 at 12:24, Dave Kruger wrote:

> Alex's point is well-taken:  If the chart indeed was not accurate
> enough to check the 15 ft "accuracy" then there is no way to establish
> the accuracy limit is that size or smaller.

That's a good point.  Canadian 1:50k topo maps are not stated as 
being more accurate than 25 or 50m (can't remember which).  GPS is 
better than that most of the time.

Mike
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From: Michael Daly <mikedaly_at_magma.ca>
subject: Re: [Paddlewise] GPS Errors Summary
Date: Thu, 02 Sep 2004 19:20:07 -0400
On 2 Sep 2004 at 17:44, Michael Daly wrote:

> Canadian 1:50k topo maps are not stated as being
> more accurate than 25 or 50m (can't remember which).

In English, that's "stated as not being more accurate...".  

Sorry.

Mike
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From: Jens Viggo Moesmand <jensviggo_at_moesmand.dk>
subject: RE: [Paddlewise] GPS Errors Summary
Date: Fri, 3 Sep 2004 09:57:16 +0200
"This expalins why I sometimes noticed a significant discrepancy between
the
direction shown by my non-compass GPS and actual direction to waypoint
when
paddling.  I thought GPS calculated the direction using calculated
location
of the kayak and known location of the waypoint."

Alex

You must read the manual. Some GPS (Magellan e.g.) gives you a choice
between a magnetic compas and a satelitecomputed compas. But the
precision of the magnetic measurement is limited, recalibration (easy to
do when on land) necessary and battery consumption increases a bit.

Jens Viggo
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From: PeterO <rebyl_kayak_at_iprimus.com.au>
subject: Re: [Paddlewise] GPS Errors Summary
Date: Fri, 3 Sep 2004 19:09:07 +1000
Michael Neverdosky wrote:
>Using normal gear on a sailboat I was more than
>happy if my 'triangle'was only 2 miles across.

Michael Daly replied:
>That's a little more like it :-).

G'Day,

Well if thats what is achievable with a $1000 sextant it makes our student
efforts with deck compass, thumbs or sticks and string look quite cost
effective. (900m error over a 10km distance). But I'm guessing the two
Mike's error estimates were for navigation rather than pilotage, i.e not
using landmarks by Mike's earlier explanation. Would that be the case? In
fact I would have thought a kayaker more experienced in pilotage would have
made less than half the error we did.

By the way has anyone actually tried to use a sextant in a kayak? I tried
once with a very cheap plastic sextant. My friends refused to paddle with me
until I put it away. They made a number of extremely impolite remarks:~)

All the best, PeterO
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From: Michael Neverdosky <mikenever_at_earthlink.net>
subject: Re: [Paddlewise] GPS Errors Summary
Date: Fri, 03 Sep 2004 09:29:34 -0400
PeterO wrote:
> 
> Michael Neverdosky wrote:
> >Using normal gear on a sailboat I was more than
> >happy if my 'triangle'was only 2 miles across.
> 
> Michael Daly replied:
> >That's a little more like it :-).
> 
> G'Day,
> 
> Well if thats what is achievable with a $1000 sextant it makes our student
> efforts with deck compass, thumbs or sticks and string look quite cost
> effective. (900m error over a 10km distance). But I'm guessing the two
> Mike's error estimates were for navigation rather than pilotage, i.e not
> using landmarks by Mike's earlier explanation. Would that be the case? In
> fact I would have thought a kayaker more experienced in pilotage would have
> made less than half the error we did.

If you want to compare using a GPS to using compass bearings on
landmarks
then you need to use a DGPS.
Try using your compass, thumbs and sticks and string to fix your
position
on a large sheet of ice with no identifiable features.

The big reason for pilotage when along a coast is because it references
to
the LAND and that is what you care about. When you are out of sight of
land
you use celestial nav because you need to. In celestial you have to be 
concerned about the position error of the charts because you are fixing
your 
position relative to the sun and stars. In coastal pilotage you have
removed
the chart position error because your reference is to features on land
that
are shown on the chart.


> 
> By the way has anyone actually tried to use a sextant in a kayak? I tried
> once with a very cheap plastic sextant. My friends refused to paddle with me
> until I put it away. They made a number of extremely impolite remarks:~)
> 

There are a number of problems with using a sextant on a kayak. First is 
staying upright while taking the sight. Second is the height of eye, as
it
is very low and keeps changing. Third is the difficulty of plotting the
LOPs found onto your chart.

The smallest boat that I *used* celestial nav on was a 24 foot monohull 
sailboat and it was not very easy.
Doing celestial on my 28 foot trimaran was downright easy because of the
stability.

The GPS is always more accurate and easier than celestial as long as
long as it is working. OTOH celestial only requires your tables and
watch with a sextant. 

michael
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From: PeterO <rebyl_kayak_at_iprimus.com.au>
subject: RE: [Paddlewise] GPS Errors Summary
Date: Sat, 4 Sep 2004 17:45:50 +1000
Michael wrote:
>If you want to compare using a GPS to using compass
>bearings on landmarks then you need to use a DGPS.
SNIP
>Try using your compass, thumbs and sticks and string
>to fix your position on a large sheet of ice with no
>identifiable features.

G'Day

Thanks for that Michael. I realised from reading your post: that the error
in "pilotage" would vary enormously depending on amongst other things the
quality of landmark; that it would probably not be possible to have a
general idea of error for pilotage as compared with the range of error you
and Mike Daly were able to describe for celestial navigation.

Three questions if you have time. i) What is GPSD compared with GPS ii) Is
it possible to determine longitude without a time reference (Greenwich)
using celestial navigation. iii) With your measurements on the trimaran is
the sextant gimballed in any way to help with stability or is that a
ludicrous concept?

By the way I still have a problem using the word pilotage or piloting for
finding ones way along the coast in a kayak. My friends in the Australian
Navy tell me its a bit inappropriate considering the sophistication and
skill required to bring a modern large ship into harbour. Is the phrase
"coastal navigation" generally considered an acceptable alternative these
days?

All the best, PeterO
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From: Michael Daly <mikedaly_at_magma.ca>
subject: RE: [Paddlewise] GPS Errors Summary
Date: Sat, 04 Sep 2004 13:22:31 -0400
On 4 Sep 2004 at 17:45, PeterO wrote:

> Three questions if you have time. i) What is GPSD compared with GPS

Differential GPS (DGPS) uses a special second receiver to pick up a 
radio signal from a ground station (usually obtained by paying a fee 
to the operator of the ground station). This signal transmits 
information that indicates accurate position information (IIRC, the 
info is more precise satellite positions).  It can be used to produce 
a position estimate with much higher accuracy.

> ii) Is it possible to determine longitude without a time reference
> (Greenwich) using celestial navigation. 

Determining longitude depends on two things - finding your local time 
and knowing Greenwich time.  The difference in these two times, 
taking into account that the Earth rotates once every 23h56m (24h 
sidereal time), allows you to determine longitude.  

Local time can be determined from observing time of transit of the 
sun (hence the importance in the days of sailing ships of measuring 
noon), the moon, planets or stars. With a sextant, you can determine 
this indirectly without resort to actually observing a transit.  

(Transit is when a celestial body passes your meridian or is at it's 
highest point in the sky.)

Regardless of how the maths are done, the process is equivalent to 
the above.  Hence, the clock is critical.

> iii) With your measurements on
> the trimaran is the sextant gimballed in any way to help with
> stability or is that a ludicrous concept?

If you swing a sextant side to side, the apparent angle changes and 
the minimum angle is the correct one.  The quality of the navigator 
is indicated by their ability to get the angle correct regardless of 
how the ship is moving.

At one time, there were experiments with gimballed chairs to steady 
the observer.  They were largely futile.  This was in the days of the 
lunar distance method.  The latter was a process of measuring the 
angular distance between the moon and several stars to detemine the 
moon's true position.  Once this is known, the time at Greenwich can 
be determined.  It was an unweildy method and was largly ignored once 
marine chronometers were perfected.  Lunar distance tables were still 
published up to the first world war, however (aah, naval tradition!).
What made the method unpopular was not the measurement, but the many 
hours of computation required to produce the time.  It was the lunar 
distance method that gave us the sextant.  The octant was sufficient 
for measuring the altitude of stars, but too narrow in range to 
measure the lunar distances.  Hence the larger sextant was developed.

There are many excellent books that cover the history of this stuff - 
notably Dava Sobel's "Longitude".  It was also made into a superb 
made-for-TV movie starring Jeremy Irons and Michael Gambon.  Check it 
out of the video store!  

(In the film, Irons plays the role of Rupert T. Gould, an amateur 
chronometer enthusiast who rebuilt the original Harrison chronometers 
and got them working.  Gould's book "The Marine Chronometer" is out 
of print (both editions) and is quite valuable.  I spend untold 
numbers of hours in used bookstores when traveling to other cities in 
the hopes of finding a copy - it's on Amie's list of things to look 
for at garage sales).

Another book I like is David Landes' "Revolution in Time", but it 
focusses almost exclusively on the development of the chronometer 
rather than the other aspects of navigation.  

The root of modern astronomy and much of physical science arises from 
the problem of determining longitude.  All of the significant 
observatories were set up to determine the star positions with great 
accuracy.  All the great scientists were involved and many theories 
and discoveries in physical science resulted.  Galileo proposed using 
the moons of Jupiter as an accurate timepiece (they were used to 
establish longitude on land for many years).  Robert Hooke's 
experiments on springs (to power timepieces) resulted in the 
foundations of the theory of elasticity.  Newton invented the 
Calculus of Variations to explain the characteristics of a perfect 
pendulum to govern a clock. The concept of open scientific 
publication was also debatably enhanced as a result of the constant 
communication between seventeenth and eighteenth century scientists 
trying to solve the problem - all this in spite of frequent wars.  
Economists can point to the collapse of the guild system and the 
development of the free market in Britain as a reason why the 
technology of navigation blossomed in Britain and was stifled in the 
rest of Europe.  Fascinating stuff!

But I digress...

Mike
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From: PeterO <rebyl_kayak_at_iprimus.com.au>
subject: [Paddlewise] Longitude was GPS Errors Summary
Date: Sun, 5 Sep 2004 17:14:00 +1000
Michael Daly wrote: -
>Determining longitude depends on two things finding
>your local time and knowing Greenwich time.
SNIP
Local time can be determined from observing time of
transit of the sun (hence the importance in the days
of sailing ships of measuring noon), the moon, planets
or stars. With a sextant, you can determine this
indirectly without resort to actually observing a
transit. (Transit is when a celestial body passes your
meridian or is at it's highest point in the sky.)
Regardless of how the maths are done, the process is
equivalent to the above.  Hence, the clock is critical.
SNIP
>but I digress.

G'Day Mike,

Wonderful digression, very much enjoyed it, as far as I'm concerned you can
digress as much as you like!

The book "Longitude" was the source of my question on measuring longitude
without a Greenwich time reference. I realise navigators need a means of
measuring time at their location but still wonder if there are ways of
calculating longitude without the need for a time reference at another point
on the earths surface. I'm thinking in particular of the lunar distance
method.

A sub plot in the Longitude book is the dispute between the Astronomer
Royal, Nevil Maskelyne and John Harrison, the inspired clockmaker. Maskelyne
claimed to be able to measure longitude using the "Lunar Distance" method,
which I think precluded the need for measuring the difference in time
between two points on the earth's surface, however the method required such
careful and prolongued calculation as to be considered impractical. Thats if
it worked at all? The Nautical Almanac, which Maskelyne first wrote,
continues to be updated and published to this day, hence my question. If the
lunar distance method did work, albeit clumsily, then I wondered if nowadays
it would be more practical given the availability of more accurate celestial
tables and computers.

By the way Dava Sobel and William Andrews wrote a second version of
Longitude called "The Illustrated Longitude" which includes a parallel story
of the development of 17th century navigational instruments in notes
attached to each picture. William Andrews has also written a book "The Quest
for Longitude". which is top of my Christmas list:~)

All the best, PeterO
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From: PeterO <rebyl_kayak_at_iprimus.com.au>
subject: RE: [Paddlewise] Longitude was GPS Errors Summary
Date: Sun, 5 Sep 2004 20:03:15 +1000
G'Day Michael,

Sorry I see now that you have already covered the Lunar Method, I must start
wearing spectacles :~).

All the best, PeterO
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From: Michael Daly <mikedaly_at_magma.ca>
subject: Re: [Paddlewise] Longitude was GPS Errors Summary
Date: Sun, 05 Sep 2004 12:01:36 -0400
On 5 Sep 2004 at 17:14, PeterO wrote:

> A sub plot in the Longitude book is the dispute between the Astronomer
> Royal, Nevil Maskelyne and John Harrison, the inspired clockmaker.

All due to his overly strong belief in Newton, who'd claimed that if 
the problem of longitude was to be solved, it would be by the 
astronomers and natural philosophers, not the mechanics 
(clockmakers).  Maskelyne wasn't the only one, which indicates the 
god-like status that Newton had attained.

> Maskelyne claimed to be able to measure longitude using the "Lunar
> Distance" method, which I think precluded the need for measuring the
> difference in time between two points on the earth's surface

The lunar distance method determines time, not longitude.  It's an 
astronomical clock, like Jupiter's moons.  Since the motion of the 
moon was well understood, its position among the stars could be 
predicted with high accuracy.  Tables listing position versus GMT 
were calculated and printed.  If the navigator used the sextant and 
tedious calculations to determine the moon's position, the time could 
then be looked up in the table.

> By the way Dava Sobel and William Andrews wrote a second version of
> Longitude called "The Illustrated Longitude" which includes a parallel
> story of the development of 17th century navigational instruments in
> notes attached to each picture.

This past spring at our kayak club's Spring Rendezvous, I gave a talk 
on the development of navigational instruments from ancient times to 
the sextant.  I made the instruments out of foamcore (cardboard-
laminated stiff foam) and held them together with spring clips.  That 
way I could show how if you move this and change that, the instrument 
changes from, say, a quadrant to a backstaff or a backstaff to a 
reflecting quadrant and thence an octant.  I also pointed out things 
like a kamal and a cross staff are two different forms of the same 
instrument.

> William Andrews has also written a
> book "The Quest for Longitude". which is top of my Christmas list:~)

Something to look for!  Thanks, Peter.

Mike
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From: Bob Carter <revkayak_at_aptalaska.net>
subject: Re: [Paddlewise] GPS Errors
Date: Sat, 4 Sep 2004 11:13:18 -0800
I use GPS primarily for checking milage. For navigation I use the old
fashion map and compass. Three reasons:
First, Map and compass do not rely on batteries.
Second maps are like a book to me that tell a story and give me a lot more
info than the tiny GPS screen does.
Third I can get lost just as easy with a GPS as I can a map. ("I have never
been lost...totally bewildered for a couple days but never lost" Davie
Crocket)
My problem with GPS (a Garmin 12) is the altitude reads are inaccurate. I
went down to the boat harbor when the tide level was at zero, held the GPS a
couple inches abobe the water and got a reading of 32 +feet. (No wonder
tourists ask how far we are above sea level!)
 Bob
Petersburg, Alaska
N 56  48  636
W132  57  265
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From: Dave Kruger <kdruger_at_pacifier.com>
subject: Re: [Paddlewise] GPS Errors
Date: Sat, 4 Sep 2004 12:41:31 -0700
Bob,

Could be your GPS uses a different datum for its altitude determination than
what is used for the tide book's "sea level."

The tide book uses MLLW (= Mean Lower Low Water) as its zero point, while
USGS topos use a National Geodetic Vertical Datum, usually the 1929 datum,
which uses MHHW, I think, as "zero altitude."

Around here, the difference is about 7 ft (2.1 meters).  If the tide range
where you are is 20 some-odd feet, that would account for most of the
discrepancy.

--
Dave Kruger
Astoria, OR

----- Original Message ----- 
From: "Bob Carter" <revkayak_at_aptalaska.net>

> My problem with GPS (a Garmin 12) is the altitude reads are inaccurate. I
> went down to the boat harbor when the tide level was at zero, held the GPS
a
> couple inches abobe the water and got a reading of 32 +feet. (No wonder
> tourists ask how far we are above sea level!)
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From: Michael Daly <mikedaly_at_magma.ca>
subject: Re: [Paddlewise] GPS Errors
Date: Sat, 04 Sep 2004 18:52:25 -0400
On 4 Sep 2004 at 12:41, Dave Kruger wrote:

> The tide book uses MLLW (= Mean Lower Low Water) as its zero point,
> while USGS topos use a National Geodetic Vertical Datum, usually the
> 1929 datum, which uses MHHW, I think, as "zero altitude."

Further to that, remember that elevation errors in GPS are roughly 
50% greater than horizontal errors.  A good spread of satellites for 
horizontal determination is not necessarily a good spread for 
vertical.  For horizontal you can get satellites all around you, but 
for vertical, you never get satellites below you.

Also remember that as with vertical, there are several horizontal 
datum standards that can fool folks when they compare GPS to maps.  
If the GPS uses a different standard than the map, it won't show the 
same location as the map.  

GPS usage is not as simple as just turning it on.  Not everyone 
realizes that.  You don't just read the numbers, you have to 
interpret them sometimes.

Mike
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From: Bob Carter <revkayak_at_aptalaska.net>
subject: Re: [Paddlewise] GPS Errors
Date: Sat, 4 Sep 2004 12:09:30 -0800
>From: "Dave Kruger" <kdruger_at_pacifier.com>
> Could be your GPS uses a different datum for its altitude determination than
> what is used for the tide book's "sea level."
>
> The tide book uses MLLW (= Mean Lower Low Water) as its zero point, while
> USGS topos use a National Geodetic Vertical Datum, usually the 1929 datum,
> which uses MHHW, I think, as "zero altitude."

Thanks, mystery solved.
Bob
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From: Carey Parks <cparks_at_fuse.net>
subject: RE: [Paddlewise] GPS Errors
Date: Sun, 5 Sep 2004 19:10:52 -0400
>From: "Dave Kruger" <kdruger_at_pacifier.com>
> Could be your GPS uses a different datum for its altitude determination
than
> what is used for the tide book's "sea level."
>
> The tide book uses MLLW (= Mean Lower Low Water) as its zero point, while
> USGS topos use a National Geodetic Vertical Datum, usually the 1929 datum,
> which uses MHHW, I think, as "zero altitude."

Makes sense when you stop to think about it. Nautical types divide things
into "Water/Aint water" and land types divide things into "Land/Ain't land"
so that strip of stuff that spends some time as both land and water would be
considered out of play by both groups.

Thanks Dave!

Carey
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From: Michael Neverdosky <mikenever_at_earthlink.net>
subject: Re: [Paddlewise] GPS Errors Summary
Date: Tue, 07 Sep 2004 21:53:23 -0400
PeterO wrote:

> Three questions if you have time. i) What is GPSD compared with GPS 

Differential GPS uses a second signal from a land based reference to
correct for some of the errors in the signal. It makes a very accurate
system much more accurate.

The WAAS system is another version of the same idea.

> Is
> it possible to determine longitude without a time reference (Greenwich)
> using celestial navigation. 

Yes it is possible but not easy.
The lunar distance method was mentioned and has been used by a few
people. Joshua Slocum was one who used lunar distance, he had a clock
but it
had no minute or second hands.  :-) At least so goes the legends.


> With your measurements on the trimaran is
> the sextant gimballed in any way to help with stability or is that a
> ludicrous concept?

The only boat I know of that used a mounted sextant is a submarine. They
have the sextant function built into the periscope.
On a trimaran the boat rolls so much less than a monohull that it is
far easier to get a good sight and it is faster so that a navigator
might
shoot three rounds of stars in the time it would take to do one round on
a mono.
The better accuracy of each sight and the greater number of them to show 
you when one of them is not good you can be much more certain of the
fix.

In general, on a ocean crossing you don't need to be very accurate at
all.
You only need to be good enough to be sure of not missing the
destination
land mass. In many cases this can be pretty rough.

Most navigators make it a matter of pride to refine their ability to
produce an accurate fix and make a landfall at a desired spot at a 
predicted time.


> By the way I still have a problem using the word pilotage or piloting for
> finding ones way along the coast in a kayak. My friends in the Australian
> Navy tell me its a bit inappropriate considering the sophistication and
> skill required to bring a modern large ship into harbour. Is the phrase
> "coastal navigation" generally considered an acceptable alternative these
> days?

Yes, today most people, especially in the small boat world (rather than
ships)
would call it coastal navigation.

Just to note a "Pilot" is also a term used to refer to a book of
information
used to navigate and operate a vessel in a particular part of the world.
Much information is gathered together and kept for reference, some of it
dates
back centuries.  These books make interesting reading.

 
> All the best, PeterO

Thanks,
I'm rambling again so will stop here.

michael
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From: Chuck Holst <cholst_at_bitstream.net>
subject: RE: [Paddlewise] GPS Errors Summary
Date: Thu, 2 Sep 2004 21:19:49 -0500
That might explain why my GPS track from my last trip in Canada (Silver 
Islet to Rossport) doesn't always correlate with what the map shows. Most 
of the time it is a little south and east of where I remember us being, and 
so I thought it might be a matter of map calibration in OziExplorer -- 
except that in some places on the same map it is north of where I remember 
us being. 25 to 50 m mapping error would cover that discrepancy nicely.

Chuck Holst

-----Original Message-----
From:	Michael Daly [SMTP:mikedaly_at_magma.ca]

That's a good point.  Canadian 1:50k topo maps are not stated as
being more accurate than 25 or 50m (can't remember which).  GPS is
better than that most of the time.
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