Here are a few pictures of the sun taken over a 3 or 4 minute period. Before this it was all grey; after this is was again all grey.
With a standard 4x40 scope with standard sun shade you would be able to get sights of this sun at the times of the best views below, providing you were standing there waiting and ready to go. You might just have a few seconds, but as long as you can see the outline of the disk you can get a sun line. It might not be your best work, but it will be usable if that is all you have.
This is a point that came up several times in the voyage documented in Hawaii by Sextant. At the end here we show that it can't be too far off, even in these cases.
To get a feeling for how far off a sight like this could be, we take a look at the scale of things.
When we take a sun sight, the bottom edge of the sun should just touch the horizon. Our job in all sights is to be sure this is aligned as precise as possible. But how far can we be wrong? The semi-diamter of the sun is about 16'. The sun above is not aligned properly; that is very easy to see. This one is off by 2'. Even half of this would be very easy to see. In short, we should be able to line up the sun in even just reasonable conditions to well within a mile (1' or so). The sun can be very sharp in a scope behind a filter, even when it is very fuzzy or not even discernible without these aids.
Tuesday, March 25, 2014
Monday, March 24, 2014
Piloting Practice with Geocaching — You Can Do It Online
The hobby of geocaching has been popular for many years now. In its simplest form, you hide a small container with a logbook in it, then post the GPS coordinates of the cache where interested parties can see them. They then go and find it using their handheld GPSs along with whatever hints or riddles you provide, sign their name in the logbook, put the cache back where they found it, and then post that they have found it. There are many nuances and variations to the process; it is a much more dynamic and engaging activity than that simple description might imply.
It turns out that the world
headquarters for this activity (www.geocaching.com) is just a couple
miles from Starpath HQ. Their office overlooks Lake Union in the
Fremont area of Seattle. This is a successful business; there are over 6 million geocachers worldwide, many of whom pay $30/yr
for special access and features online, and many must want
their excellent $10 app to facilitate the searching and recording.
There are numerous other apps from other companies to facilitate the sport. There are more than 2 million registered caches worldwide to be found and logged. The reason
the business is so successful is the participants get their money's
worth and more. Even those who just do it for a while and quit, do
not mind the fees. They have had fun and they learned something. Most
members are devoted to the hobby and get much enjoyment from it. For
many it is a key part of their social life.
It is also a fine example of American
entrepreneurship in that the company was started from scratch by a couple
young friends with an idea, along with the skill and determination to
organize, promote, and manage the operation so it could achieve the
outstanding success it has. Now with such good resources, they have
topnotch software and services and they have established a set of
rules that can preserve their image of the process in light of many
challenges.
In the Age of GPS, this seems a natural
pastime. You cannot do it without learning how to optimize your GPS
work. We often get to remind even seasoned navigators about the
conversions shown in Tables 1 and 2. You won't get far in caching
without knowing that 0.001' of Latitude is about 6 ft, and likewise
that this is not true for Lon––that is, assuming you do not have
an app that does all the computations for you, which is bound to
hamper the will to learn the basics.
Table 1. Latitude Increments
|
|
Latitude Minutes
|
Approx. Feet
|
1.0'
|
6000 ft
|
0.1'
|
600 ft
|
0.01'
|
60 ft
|
0.001'
|
6 ft
|
Latitude Seconds
|
Approx. Feet
|
30”
|
3000 ft
|
20”
|
2000 ft
|
10”
|
1000 ft
|
5”
|
500 ft
|
1”
|
100 ft
|
Table 2. Longitude Increments
|
|
Latitude N or S
|
Feet per 0.1' of Longitude
|
0º
|
608 ft
|
10º
|
600 ft
|
20º
|
572 ft
|
30º
|
528 ft
|
40º
|
467 ft
|
50º
|
392 ft
|
60º
|
305 ft
|
70º
|
209 ft
|
Furthermore, a commonly reported GPS
uncertainty is 5 m (16.4 ft), which also teaches us something: the
uncertainty is not necessarily the error. More often than not, you
can home in on a target well within the reported uncertainty. GPS
positions will scatter about the indicated position with some
standard deviation. A good way to study this is just park your GPS
linked to an echart tracking program and let it sit overnight. You
will get something like what is shown in Fig. 1. Modern handheld
units include an option to average the position, even reporting back
to you when they have a good fix. It typically takes just a few
minutes.
( For those new to echart software, we have a list of free viewers to check out. You can then connect your GPS to one of them for such tests. )
Then do the exercise at home with the GPS facing a window with limited view of the sky. The pattern will be different, and larger, and take longer to home in. The significance of that observation is when you are outside you may still have part of the sky blocked off. Just standing next to a big tree could matter, or in a valley, or boaters in a deep fjord. There are a lot of satellites and the units are better and better every year, but this is still something to have in mind at all times.
( For those new to echart software, we have a list of free viewers to check out. You can then connect your GPS to one of them for such tests. )
Then do the exercise at home with the GPS facing a window with limited view of the sky. The pattern will be different, and larger, and take longer to home in. The significance of that observation is when you are outside you may still have part of the sky blocked off. Just standing next to a big tree could matter, or in a valley, or boaters in a deep fjord. There are a lot of satellites and the units are better and better every year, but this is still something to have in mind at all times.
In some circumstances, however, the
center of the distribution is not the true location, althrough the
true position is usually within range of the displayed accuracy if it
is stable long enough. I will come back to such nuances of precise
navigation with consumer-grade GPS units in a later article.
When tracking down caches you also very
quickly learn the limitations of the compass apps in mobile devices.
These are still very sensitive to horizontal alignment as there are
fixed coils in them that measure the strength of the magnetic field
components, and this field is not parallel to the surface because of
the dip angle. But with practice we can learn how to use them. Most
mobile-device compasses have self-correcting procedures to adjust for
local disturbances, but this does not address the alignment issue.
True versus magnetic is not an issue,
because they are sitting right next to a GPS. They know where they
are so they can compute the magnetic variation very accurately. They
all use a program called geomag, which you can download and put into
your own computer if you like, which is a nice back-up if you get
stuck with old charts at high latitudes (www.ngdc.noaa.gov/geomag).
From what I have learned of geocaching,
it seems to me this is an ideal way to practice marine piloting.
First to fine-tune the use of GPS, which might include learning more
about what satellites you are using, and when to expect better fixes
when the present ones are not so good (66-ft uncertainty vs 16-ft,
for example). Are you next to a bluff in your boat, or between
skyscrapers downtown? It will show the value of having a display of
the satellites in view and how to interpret it (figure 2), and how to
anticipate when this will change. If you are in a real bind, ie
traversing a narrow fjord with just a sliver of sky, there are handy
free apps that predict satellite passes for your location, with the
altitude and bearing of each as they pass. These apps are also useful
for predicting the next Metop-A pass for satellite wind data. Check
your AppStore for a slick free one called Satellite Tracker by
MacCon.
You can also get practice sending
yourself gpx files. This format is the best way to transmit
waypoints, routes, and tracks from one device to another, or to
Google Earth. There is a neat utility online to help with this at
www.gpsvisualizer.com. (We have discussed this utility earlier here and also here.)
The main geocaching goal for mariners,
however, would be to go on and practice the more sophisticated
piloting skills we teach in the classroom. These days, it is only the
conscientious navigator––we would say prudent––that takes the
time to learn the old methods of navigation, so they are not
dependent on the GPS, but there is plenty of evidence that this is
worthwhile.
Beyond the basics like crossed compass
bearings and the use of natural ranges, we can really home in on our
position using a simple plastic sextant that costs less than $50. Few
navigators and geocachers realize that you can pinpoint a
position on a chart much more accurately with a sextant (essentially
the same as used in the 1700s) as you can with the latest handheld
GPS. There is a detailed explanation of the methods in the book
Your accurate position is
determined by the two horizontal angles A-B and B-C between three
objects (A, B, and C) on the near horizon. These two angles are
essentially the differences in the bearings to the objects, but the
sextant angles will be far more accurate than bearing differences.
Once you have these measurements, you need a large-scale chart that
shows the three objects on it, and then there are several ways to
solve for your position.
The simplest is to use a three-arm
protractor, which is designed to solve this problem. Inexpensive
plastic ones are available. Set the two angles on the protractor and
move it around the chart until the three index lines cross your three
targets, and you are located at the hub of the arms. Alternatively,
you can draw the two adjacent angles emanating from a single point on
a piece of clear plastic (overhead projector sheets, if you remember
such things). Then slide that plastic around on the chart until the
three lines defining the two angles each cross one of your targets.
The Plastic Sextants book also describes plotting procedures
that can be used without the need for three-arm protractors or
transparencies, which can enhance the accuracy.
Line of Soundings Navigation
Another advanced skill of marine
navigation that you can practice on land is depth-contour navigation.
In the fog with no GPS, you sail on a steady heading and record the
depth at several log readings. Then on your chart highlight a few of
the depth contours in your approximate region. Then plot a line on a
piece of transparency and using the same distance scale as your
chart, mark off the logged runs between measured contour depths,
corrected for tide and draft. Then slide that sheet over the chart
keeping the line oriented in the heading you were sailing until you
find the place where you cross the contours at the right rate. In
many cases you can get by with a roller plotter and dividers, without
the transparency. If the bottom is not flat, nor water too deep,
this will often locate your position.
To practice on land you can use
elevation contours, replacing the depth sounder with a good digital
barometer. You do need an actual barometer, however, because GPS
elevations reported are not accurate enough for this. Some GPS units
and some smart phones have barometers in them, which should do the
job. You must always normalize the pressure reading at some known
elevation to account for the atmospheric pressure.
Both of these exercises can be
practiced online, without getting up from the desk! Google Earth
shows both precise locations as well as digital elevations (but no
contours). You can also drop a pin at locations of interest so they
will show up when you print the screen to make your chart.
For the depth-contour exercises, it is
best to use the USGS National Topo Viewer
(viewer.nationalmap.gov/viewer), again zooming in on what you need
and plotting out a chart. Check out all the tools options for
measuring distances, spot elevations, and so on. It will help ID the
contours and distances between them. Google Maps has a terrain view
that shows some contours, but nowhere near as good as the USGS
Viewer.
Practice with Horizontal Sextant Angles
(1) Just west of Newport, RI, start at
41º 33.516’ N, 71º 26.852’ W. What have you found? Are there
more of these (whatever they are) to the south? (Note this is a very precise starting point.)
When you are standing at the cache, the
angle between this one (#1) and the next one to the south (#2) will
be 30º 36.0’, and the angle between that #2 and the next one to
the south (#3) will be 24º 18.0’. Use the base of the objects for
the target. Where is the cache?
(2) Now with same targets, use 1 to 2 =
22º 16.8’ and 2 to 3 = 24º 24.0’. Now where are you?
(3) Finally, use 1 to 2 = 21º 47.4’
and 2 to 3 = 25º 41.4’. Again where are you?
In these last two examples you are
finding locations that are less than 10 ft apart, and these angles
viewed through a sextant are huge differences. A handheld GPS
would rarely be able to pin point a location to this precision.
Practice with Line of Soundings Navigation
(1) Here is an example of depth-contour
navigation. You are walking (sailing) somewhere in Central Park in
NYC, and you measure the following elevation (depth) records on
heading 298T on a leg that is 0.436 nmi long. Where are you located
when your barometer (depth sounder) reads 88 ft?
Log (nmi)
|
Run (nmi)
|
Run (ft)
|
Elevation (ft)
|
0.000
|
0.000
|
0
|
80
|
0.172
|
0.172
|
1045
|
70
|
0.211
|
0.039
|
237
|
70
|
0.267
|
0.056
|
340
|
80
|
0.376
|
0.109
|
663
|
90
|
0.417
|
0.041
|
248
|
90
|
0.436
|
0.019
|
115
|
88
|
As with marine navigation, step one is
identify the contours. You know the answer is just downhill of 90 ft
and you were at 90 ft for a distance of 248 ft. Find where there is
0.267 nmi between 80-ft contours on heading 298, or use other
patterns.
To work this online, it is important to use the nationalmap viewer referenced above. It has many layers that let you measure specific elevations and the distance between them. There is a bit of a learning curve on their site, but well worth the effort. Or just find any detailed view of the contours and print them out and work it by hand.
If you do soundings exercise like this just once, you will forever be a better navigator. You may not have call for depth sounder navigation very often, but when you do need it can save the day and you will be prepared.
Below is another example of a GPS running overnight with positions stored. In this case the positions were from a Yellow Brick tracking GPS and the results were posted online automatically. The unit was left on by mistake on a hotel room deck in Snug Harbor, BC at the center of the distribution.
Wednesday, March 5, 2014
Wind Near Clouds
A topic has come up in our weather course that deserves extra information having to do with oscillating wind shifts. We will address this issue more specifically shortly, but for now we need to show a couple pictures and give some references.
It is a safe assumption to expect the wind to shift when a large cumulus cloud goes by, especially with relatively low base. We do not mean squalls. We have much written in our weather book and radar book on winds near actual squalls, before and after downburst.
The point we make now is this wind behavior on a smaller scale can also be seen under fair weather cumulus. It is especially important for sailors when there is a symmetric pattern of the clouds passing over, or a sequence of them in a line... and especially important in a yacht race, in the ocean or on a large inland lake.
A general rule easy to remember is the wind will shift when one of these clouds goes by. Predicting the shift is more involved, but a related pretty good rule is if the cloud is not raining, it is pulling the wind into it. That is, biasing the ambient flow toward the cloud. But the final surface wind is a vector combination of cloud wind and ambient wind, and thus the comlication.
For now let us just give a couple references, and we will add more discussion and more references as soon as possible.
See Chapter 8, Winds near Clouds, in High Performance Sailing by Frank Bethwaite. Below is a picture from that book.
Another good reference is from a similar book by C.A. Marchaj, called Sailing Theory and Practice and a couple sample images from Part IV, Wind and Water, section (3) Local Wind.
These are not books one might have turned to for weather tactics, as they are mostly concerned with yacht design, but they are both excellent texts on many aspects of sailing, and since the authors are engineers as well as sailors, they use real numbers, which are often missing in sailing books.
Again, I will return to this topic as time and student interest requires. But the above pictures are the hints, and then just imagine a row of these clouds going by that you have the option to choose a route though. Somewhere in our notes we have such a picture made and we will look for it.
I have seen such patterns in the ocean and it was quite remarkable how predictable the shifts were in direct correlation to what we could see over head.
It is a safe assumption to expect the wind to shift when a large cumulus cloud goes by, especially with relatively low base. We do not mean squalls. We have much written in our weather book and radar book on winds near actual squalls, before and after downburst.
The point we make now is this wind behavior on a smaller scale can also be seen under fair weather cumulus. It is especially important for sailors when there is a symmetric pattern of the clouds passing over, or a sequence of them in a line... and especially important in a yacht race, in the ocean or on a large inland lake.
A general rule easy to remember is the wind will shift when one of these clouds goes by. Predicting the shift is more involved, but a related pretty good rule is if the cloud is not raining, it is pulling the wind into it. That is, biasing the ambient flow toward the cloud. But the final surface wind is a vector combination of cloud wind and ambient wind, and thus the comlication.
For now let us just give a couple references, and we will add more discussion and more references as soon as possible.
See Chapter 8, Winds near Clouds, in High Performance Sailing by Frank Bethwaite. Below is a picture from that book.
Another good reference is from a similar book by C.A. Marchaj, called Sailing Theory and Practice and a couple sample images from Part IV, Wind and Water, section (3) Local Wind.
These are not books one might have turned to for weather tactics, as they are mostly concerned with yacht design, but they are both excellent texts on many aspects of sailing, and since the authors are engineers as well as sailors, they use real numbers, which are often missing in sailing books.
Again, I will return to this topic as time and student interest requires. But the above pictures are the hints, and then just imagine a row of these clouds going by that you have the option to choose a route though. Somewhere in our notes we have such a picture made and we will look for it.
I have seen such patterns in the ocean and it was quite remarkable how predictable the shifts were in direct correlation to what we could see over head.