Sextant tutorial by Frank Sarfati

Transcription

Frank Sarfati - 071006
Ilan Papini’s
VIRTUAL SAILOR 7©
TUTORIAL
USING THE VIRTUAL SEXTANT WITH VS7
By
Frankie the Funky Sailor
[email protected]
1.
Introduction
1.1
Purpose of this tutorial: The purpose of this tutorial is to give some information about using
the virtual sextant (the “Virtual Sextant”) designed by Ilan Papini for his Virtual Sailor 7 (“VS7”),
and how to use the information obtained with the Virtual Sextant.
This tutorial will endeavour to be practical. The theory of celestial navigation and sextants will
not be dealt with here. I will write a more exhaustive and comprehensive tutorial on that subject
later.
1.2
why use a sextant: It may sound weird nowadays with GPS’ and satnav to want to learn how
to use a sextant. The reason is very simple: the system can breakdown, there’s no power or a
nasty wave floods the electric system. What do you do in such a case? If you can’t determine
your position, you have a problem, and probably a big one. So, although Virtual Sextant will not
teach how to use, in practice, a sextant, it may help and facilitate the learning process with an
actual sextant!!!
1.3
how does it work: the Virtual Sextant and any actual sextant work according to the same
principle: it measures the elevation of sun (or any other celestial body) above the horizon,
such an elevation being expressed in degrees.
Practically speaking, Virtual Sextant and an actual sextant will “bring” the sun down to the
horizon. If you take a good note of the time at which you measure that angle (also call the
“elevation”), you can derive extremely useful information about where you are at a certain time.
1.4
1.5
Notice: Users of the Virtual sextant and readers of this tutorial should bear in mind the
following:
(a)
this tutorial will only deal with virtual sightings of the sun in VS7; other celestial bodies
such as the stars, planets or the Moon will not be dealt with: it is much more
complicated; it’s also customary to begin with the sun, which is a lot simpler to use in
celestial navigation;
(b)
learning how to use the Virtual Sextant may facilitate learning celestial navigation or at
least some of its theoretical aspects. However, one should not go at sea on the basis
of the information contained or derived from this tutorial, but should satisfy
him/herself that he/she has sufficient, proper and adequate training,
instrumentation and equipment before and when going at sea, all in accordance
with applicable laws and regulations;
(c)
I am in no way an expert in this area and everything I know, I have learned it by myself,
through my readings and personal experience (e.g. spending hours on the beach
training and people looking at me thinking “what a weirdo: is he that lost to use a
sextant ON a beach ???”). Therefore, there may be some mistakes or inaccuracies or
my approach may be unconventional. Please feel free to comment, criticise, discuss
etc…by contacting me at [email protected]. Or by putting your
questions on any good VS fori (once you get the authorisation og the webmaster !!!); let
me know by e-mail and I’ll have look and try to answer.
Structure of the tutorial: So without further ado, let’s see, with a Virtual Sextant, what one
can do!!!! The tutorial will be divided in two main sections:
•
How do I use Virtual Sextant (section 2);
•
How do I use the information obtained with Virtual Sextant (section 3).
2.
How do I use Virtual Sextant?
2.1
Description of the Virtual Sextant
Screenshot 1
Most of you are familiar with Ilan’s VS7. You can see that there is a new icon: it represents a
sextant. Double click on it or press shift + T.
Some of the Virtual Sextant’s functions are similar to those of the Telescope:
Most of you are also familiar with the presentation below (see Screenshot 2): the Virtual
Sextant window is very similar, at least in terms of presentation, to the virtual telescope. It has
similar functions:
•
Azimut indicator: on top you can see the Azimut indicator: you operate it exactly as you
do with the virtual telescope: right click and drag. You can also use the keypad (just like
for the telescope function);
•
Zoom: on the right hand side, you can see the zoom function. Again, this works exactly
as the zoom of the telescope function;
•
Vertical angle: You can also vary the vertical angle by right clicking and dragging the
mouse (without clicking on any other functions)
These are the only similarities. The differences are huge because a sextant is designed to
measure the elevation of a celestial body over the horizon.
Screenshot 2
Other functions are very different:
Elevation Knob:
This knob is used to “bring” the sun down to the horizon. In section 2.2, I‘ll explain how to do
this.
As you turn the knob (and consequently “bring” the sun down to the horizon), the window
called “elevation” shows…the elevation of the sun (or whatever celestial body you may be
sighting).
Elevation is measured in degrees, minutes of arc and seconds of arc. Here the elevation is
also indicated in degrees and decimal degrees. We’ll see later on that this will avoid stupid
(and fatal) errors.
Filter:
The filter is also a very important function of the sextant. On an actual sextant, the filter is used
to protect your eye when sighting the sun and to reduce the glare: in order to do a proper
sighting of the sun, you must see a perfectly neat circular disk and its edges without any glare.
Digital Watch:
Last but not least, the digital watch. You always have to note precisely, by the second, the time
at which you do your sighting: one second of time can make a material difference in your
result. Be precise !!!
It is extremely important to note the Greenwich Mean Time (“GMT”) when you do your sighting:
in celestial navigation, you must never take note of the time in the time zone you are but only
according to GMT. In future tutorials, we’ll see how we can determine local time with a sextant,
but for know just think “GMT” !!!!
GMT is given in hours, minutes and seconds and also in decimal. This will avoid a number of
silly but fatal mistakes.
2.2
2.2.1
Using the Virtual Sextant
Step One – Click on the Virtual Sextant Icon – (See Screenshot 1 above and 3 below).
Set the time and date at approximately 9:00 a.m. or 15 p.m. (around March or September of
any given year, say 2006). For the first time, set the weather with 100% visibility, no clouds,
no waves, no wind.
This will be explained in more detail in the next tutorial. All you need to know at this stage is
that you don’t want the sun to be too high or too low for your first virtual sighting of the sun.
Screenshot 3
2.2.2
Step Two – Turn the filter knob and set it to 60/65% approx - See Screenshot 4.
Screenshot 4
2.2.3
Step Three – Set the zoom to 3 and turn the elevation knob to approximately 30 degrees (30
in this example only, depending on your position and time) - See Screenshot 5.
Screenshot 5
2.2.4
Step Four – use the keypad (4 or 6) or right click and slowly “turn” the Virtual Sextant visor
until you see the sun appear - See Screenshot 6.
In the (virtual) morning, you should look towards E or ESE (approx 120/130), in the (virtual)
afternoon, WSW (approx 220/230). You should see the sun near the horizon slightly above (if
in the morning) or below (if in the afternoon), “in the sea”.
Screenshot 6
2.2.5
Step Five – centre the cross of the Virtual Sextant on the sun so the horizontal red line
coincides with the horizon; set the horizontal angle to zero – See Screenshot 7
Screenshot 7
The sun’s lower limb should be like “one hair” (i) below the horizon, if you’re sighting in the
virtual morning (don’t forget, in the morning, the sun is going up towards the zenith); or (ii)
above horizon if you’re sighting in the afternoon (when it’s going towards the nadir).
2.2.6
Step Six – tangent the sun on the horizon – see Screenshot 8
Screenshot 8
Right click and “move” the sextant in this “arc” like motion from left to right, not too fast and
have your finger of your free hand ready to press F10. – press F10 as soon as the lower limb
perfectly tangent the horizon.
On a piece of paper take a note of the elevation in both degrees and decimal and the time of
the sighting (IN GMT !!!!) in hours and decimals.
Here, the elevation is 35:50:32 at 15:47:00 Hours GMT; in decimals, 35.8424 and 15,7857
Hours GMT.
(you may find a slightly different result than me, that’s because I wrote the tutorial over
several days and I couldn’t remember which day I referred to initially)
2.3
Making it “more real”
Once you have a little practice, you can set things in a more real mode:
•
•
•
•
Increase the wave height;
Don’t lock the simulation with F10 when you do you’re sighting;
Keep on sailing, don’t dock or anchor the ship;
Use a real watch (just make sure it’s set exactly on the same time as the clock of the
Virtual Sextant i.e. GMT of Virtual Sextant)
3.
How do I use the information obtained with Virtual Sextant?
3.1
General
This is where it all begins. Section 2 was the easy part !!! Let’s get into the nitty gritty !!!
The information obtained from a sighting - elevation and time of the sighting - will be used
create a “line of position”.
There’s nothing mysterious or complicated behind this apparently esoteric term. What we will
try to do is to find out “how wrong our assumed position is”. We can do this with the “line of
position”.
In order to use that information and create a line of position, we need to do 4 things:
•
Create a (simple) cruise in order determine our assumed position after cruising
according to the parameters of that cruise (section 3.2);
•
Determine the coordinates of our assumed position “AP” (3.3);
•
Carry out a sighting of the sun at AP, at or around the time we reach AP, with Virtual
Sextant (section 3.4);
•
Carry out certain calculations by using the information obtained with the Virtual Sextant
(section 3.5);
•
Draw the line of position (section 3.6);
•
Do another cruise from AP to AP1, reproduce all the steps from section 3.3 to 3.6 but
with a new sighting and find the intersection between our 2 lines of position but that will
be the subject matter of the next tutorial.
Simple, a piece of cake !!!
3.2
Creating a simple cruise
Let’s start a cruise, let’s say we’re in the middle of the Atlantic Ocean. So set your boat to carry
out the cruise. DON’T put any waypoints. You can use auto pilot if you want.
First Leg of the Cruise
Initial Point or “IP”
Date of Cruise:
Course (on the compass)
Speed
Cruise starts at :
Cruise ends at:
45:00:00N 025:00:00W
31st March 2006
225 degrees
Whatever you want (in my
example I’ll use 7 Knots)
07:46 am local time
9:16 am local time
Avoid using the GPS or map function during the learning process. Just use it to position
yourself at IP and then turn them both off.
Set the time on weather with 100% visibility, no clouds, no waves, no wind, no current (we’ll
deal with current in the next tutorial).
If you’re using a sail boat, use the engine, not the sail: we’ll make this as simple as possible;
later on, you can add one or more layers of complexity. During the cruise, click on panel to
monitor and control speed and course. Try to stick to the parameters of the cruise. Accelerate
the simulation rate if you don’t want to wait that long.
3.3
Determining the coordinates of our assumed position “AP”
3.3.1 Step One - Distance
.
The distance sailed from IP to AP since 7:46 is calculated as follows: we sailed for one hour
and a half at the speed of 7 knots. As 1 knot is 1 nautical mile an hour, the distance is 1.5 x 7 =
10.5 nautical miles
3.3.2 Step 2 – drawing the relevant portion of the map
Picture 1
•
Take an A3 sheet of paper (if you don’t have one, just take two A4 sheets and stick
them;
•
Indicate N-E-S-W as shown of the Picture 1;
•
As we are going WSW, place IP on upper right hand side corner of the sheet of paper by
drawing a horizontal line (latitude) about 3cm away from the top of the page and a
vertical line (longitude) 3 cm away from the right hand side of the sheet;
•
the intersection of these two lines is IP – write as shown on Picture 1 the coordinates of
IP and the time at which you left;
•
determine the scale of your portion of map: you must divided 1 by COSINE 45 which
equal 1.4142. This means that 1 nautical mile on your chart is equal to 1.4142 cm. This
also means that on your chart, a distance of 10.5 nm will be equal to10.5 x 1.4142 cm =
14.84 cm. To calculate COSINE 45 you can use any scientific calculator: enter the 45,
press “COSINE”. The reason you choose COSINE 45 is because you must take the
closest round latitude: if for example your position was 57: 48: 32 N (or S, it makes no
difference), you would choose 58 because it’s the closest round latitude to yours;

On the latitude line you drew, mark the longitude divisions: start on IP and divide that
line by going East to West (or right to left) and mark one division every centimetre. I
centimetre on your chart is one minute of arc of LATITUDE. So your portion of chart will
indicate 25:00, 25:01, 25:02, 25:03 etc.. until you reach the left hand side of the sheet of
paper;
– see Picture 2;
•

On the longitude line you drew, mark the latitude divisions: start on IP and divided that
line by going North to South and mark one division EVERY 1.4142 CM: this is extremely
important otherwise your chart will be wrong and give you wrong coordinates. So your
portion of chart will indicate: 45:00, 44:59, 44:58 etc.. until you reach the bottom of the
page – see Picture 3.
Picture 3
•
then draw a line with a ruler and protractor or with a marine protractor that goes from IP
down towards, roughly the lower left corner of the sheet (don’t forget, we go WSW) with
an angle of 225 if you’re using the marine protractor or 45 degrees if you’re using the
ordinary protractor;
•
Once you have the angle, draw a line (your course) with that angle from IP going WSW;
the length of that line is equal to the value of I mile on your chart (1.4142 cm) times your
distance; this means that on your chart, 10.5 nautical miles represent 14.84 cm – make
that line a little longer than 14.84cm, say, 17 cm - see picture 4;
Picture 4
•
Draw a line parallel to the longitude line, across the sheet in such way that it crosses
your course – see picture 5; this will give you your assumed latitude: 44:51:30
Picture 5
•
Draw another line perpendicular to the one you just drew starting from the intersection of
your course and the line you drew as per the above bullet point – see picture 6;
Picture 6
•
The intersection of these 3 lines give you your assumed position AP and you should find
the following coordinates approximately: 44:51:30 N 025:10:30 W.
IMPORTANT: DON’T FORGET THAT WHEN YOU DETERMINE YOUR SCALE, YOU MUST
DIVIDE THE UNIT OF LONGITUDE (E.G. 1 IN THIS EXAMPLE, OR ANY OTHER UNIT YOU
PREFER, DEPENDING ON THE SIZE OF YOUR SHEET AND THE DISTANCE INVOLVED) BY
THE COSINE OF THE NEAREST ROUND LATITUDE OF YOUR ASSUMED POSITION. THE
RESULT OF THAT DIVISION WILL TELL YOU IN CM (INCHES WHATEVER YOU CHOOSE)
THE VALUE OF 1 MINUTE OF LATITUDE WHICH IS EQUAL TO ONE NAUTICAL MILE. If you
don’t get that, drop me an e-mail.
•
You can also calculate your assumed position with the formulae below. Let’s try it and
see what result we get. Please note that this formula only works for distances less
than 300 nautical miles.
Please open the Excel Spreadsheet – Assumed Position Tab.
Before I give the formulae, let me briefly explain what they will allow to achieve: we need
to know by how much our latitude and longitude will vary as we navigate. Prima facie,
this exercise may seem simple but, as you all know, the earth is not flat (if you have any
doubts about that, well...what can I say...buy a trip to space and find out for yourself). So
we need to take into account the fact the earth is a sphere.
There are 2 formulae: one to calculate the variation in longitude and one for the variation
in latitude.
Variation in Latitude:
l = (m/60) x COS course where “l” is the variation in latitude we are looking for, “m” i the
distance in nautical miles and “COScourse” is the cosine of our course.
In our example m = 10.5 nm, our course is 225 so COSINE of 225 = minus 0.7071
l = (10.5/60) x minus 0.7071 = 0.175 x minus 0.7071 = minus 0.1237
Our Latitude when we left was 45, we travelled minus 0.1237 degrees in latitude
towards south west (225), so our assumed latitude is 45 + (minus 0.1237) = 45 – 0.1237
= 44.8763 or 44:52:34N which is very close to what we get by using the chart method
(44:51:30N). Don’t worry about the difference: (i) it’s less than a nautical mile so this is
very good for an assumed position; (ii) both methods give in essence approximate
results. PLEASE NOTE THAT AS WE ARE GOING SOUTH, THE LATITUDE
DECREASES. DON’T GET THIS WRONG OTHERWISE YOUR RESULTS WILL BE
WRONG. IF YOU DON’T GET IT, DROP ME AN E-MAIL.
Variation in Longitude:
g = (m x Sin course) divided by ( 60 x COS delta latitude), where “g” is the variation in
longitude we are lookng for, “m” is the same as above i.e. distance travelled, “SIN
course” is the sine of our course and “COS delta latitude” is the cosine of of “l” we found
above.
In our example, we get the following result:
g = (10.5 x SIN 225) divided by (60 x COS minus 0.1237) = (10.5 x minus 0.7071)
divided by (60 x 0.99999) = (minus 7.42455) divided by (59.99) = minus 0.12376.
However WE ARE GOING WEST SO OUR LONGITUDE IS . DON’T GET THIS
WRONG OTHERWISE YOUR RESULTS WILL BE WRONG. IF YOU DON’T GET IT,
DROP ME AN E-MAIL.
Our longitude when we left was 25W, we travelled minus 0.12376 in longitude towards
south west (225) so our assumed longitude is 25 + 0.12376 = 25 + 0.12376 = 25.12376
or 25:07:25W which is very close to what we get by using the chart method (25:10:30W).
Don’t worry about the difference: (i) it’s about 3 nautical mile so this is very good for an
assumed position; (ii) both methods give in essence approximate results.
Use whichever method you like. I personally use the “chart” method when I’m actually
sailing becasue honestly, doing all these calculatin when you’re sailing, just makes me
seasick: the chart is quicker and faster, so no risk of vomitting all over the cabin !!!!
But this is not a problem, because our sighting , which will allow us to determine
our line of position, will tell us quite accurately how wrong our assumed position
is. This is the whole point of using a sextant !!!!
3.4
Sighting of the sun at AP
To do this, simply follow the procedure set out in section 2.2. For your first virtual sighting, I’d
recommend you stop the boat, put the anchor down and use the wheel of the mouse to “get
out of the boat” so the structure of the boat will not bother you when doing your sighting.
When the sun is tangenting the horizon as explained above, press F10 and take a note of the
elevation of the sun and the time of the sighting in GMT.
You should find approximately: Elevation: 30:55:17 degrees and 10 hours : 56 minutes : 40
seconds GMT.
30.91
Elevation: 30:55:17
GMT : 10:56:40
Screenshot 9
Now we will do a few calculations.
3.5
Carrying out certain calculations
We need to calculate 2 values: (i) the elevation we would get if we really are located at AP and
(ii) the azimuth of the sun.
The above elevation will be referred as to the Assumed Elevation (“ASE”), the one actually
measured, the Actual Elevation (“ACE”); the azimuth of the Sun, Az.
The idea is that if our Assumed Position is correct, in theory the difference between ASE and
ACE should be equal to zero (although, in practice this is never the case).
The smaller that difference is and the closer to AP your Line of Position will be. As you will be
somewhere on that Line of Position, the closer it is to AP and the more accurate is your
Assumed Position.
The tables below (from the French “Almanach du Marin Breton”) will allow to do the relevant
adjustments to the instrumental elevation.
Calculation of ASE and Az
To do this, we need to use the following formulae:
First formula: to calculate the ASE:
SinASE = (SinALAT × SinD ) + (CosALAT × CosD × CosGHA)
Second formula: to calculate Az or the Azimut of the sun or the direction in which we see the
sun when doing our sighting at AP at that particular GMT:
CosAz =
SinD − (SinALAT × SinASE )
CosALAT × CosASE
where “SinASE” means SINE of ASE, “SinALAT” means SINE of assumed latitude, “SinD”
means SINE of declination, “CosALAT” means COSINE of assumed latitude, “CosD” means
COSINE of Declination and “CosGHA” is the angle of rotation of the Earth from midnight GMT
until the GMT of the sighting; Cos
These formulae are not as “scary” or “complicated” as they seem: all you need to do, is to be
precise and follow the steps. You can calculate them “by hand” or use the small Excel
Spreadsheet I prepared. You can also download a whole bunch of freeware providing these
calculations. I usually do it by hand even at sea but for my next trip, I’ll bring my laptop: it
should be ok as I don’t need alot of power to run the calculation with the laptop. The important
point is to be able to do it by hand EVEN if instrumentation fails you !!!!
Please open the Excel Spreadsheet – Line of Position Tab.
Please note that in practice your “intercept” i.e. the difference between actual
elevation and calculated elevation, should be very small, in any event, less than 30
miles or 30 minutes of arc. You will notice that when doing sightings and lines of
position with data different than that used in this tutorial, you may find much larger
differences. The reason is that I’m not 100% sure of all the parameters of VS’ “celestial
mechanics” and there might be slight differences that I may have not taken into
account.
However, this is not really important; what’s important is that one learns how to
position itself with a sextant; I will endeavour to fix very soon my excel spreadsheet.
In the meantime play around with the GHA angle at 00:00. The reason is that in the
actual world the earth doesn’t rotate exactly by 360 degrees in 24 hours. In order to
correct this, what I do is to vary that angle. It seems that for morning sightings, that
angle is somewhere between 170 and 180 and in the afternoon between 180 and 190.
Try to find the GHA at 00:00 which will give you the smallest intercept, but only go by
0.5 degree increments. The target function in excel would allow to find the exact
difference but if you do that, you are just making the whole exercise pointless: mind as
well use the GPS !!! Keep a reasonable difference, roughly 10 nauticals, and then
practice doing your line of position.
This is not a very orthodox way to proceed, I entirely agree, but this will allow you
training using the sextant until i sort this out once and for all (I hope !!!). I thought
however that it would be just fair to mention it.
3.6
Drawing the line of position
Now that we have the ASE - Assumed Elevation - and Az – the azimuth of the sun – we can
draw our line of position as follows:
3.6.1 Step 1 – Determine the Intercept. Compare the value of ACE (Actual Elevation) and ASE
(Assumed Elevation). In our case, ACE is greater than ASE. This difference is called the
intercept. In some cases, ASE is greater than ACE.
Calculate that difference by doing ACE minus ASE = 31.13 – 31.08 = 0.05 degrees or 2.75
minutes of arc or 2.75 nautical miles approximately (the “Intercept”) (please see decimals for
rounding).
IMPORTANT POINT TO KEEP IN MIND WHEN DRAWING YOUR LINE OF POSITION: if
ACE > ASE (or if the intercept is positive) that means you are “closer to the sun than
you though; otherwise you are “further away” from the sun.
3.6.2 Step 2 – Draw a line that starts from your assumed position AP orientated towards the azimuth
of the sun and in the direction of the sun: . Take the value of the Intercept: it is equal to
approximately 2.75 nautical miles. Go back to paragraph 3.3.2 and use the scale you
determined there: 1 nautical mile on your chart is 1.4 cm. Measure a distance of 2.75 x 1.4 =
3.85 cm from your Assumed Position goint towards the sun i.e. in its direction - see below:
3.6.3 Step 3 – draw a double line perpendicular to the Intercept, about one nautical miles on each
side => this line is your line of position and your are somewhere on that line. – You can check
this by opening the GPS window in VS: the GPS coordinates should (ideally) be somewhere
on that line, but in practice it is always NEAR that line.
4.
Conclusion
So what happens next ? Well, you were able to check your line of position was (more or less)
correct BECAUSE you were able to use your GPS. This is what I would do in real life. But
whether or not you can check with a GPS, ALWAYS BEAR THIS IN MIND:
•
Your line of position will only make sense if the 3 following conditions are met: (i) latitude
is less than 60 degrees (so near the poles, things are different); (ii) elevation is less than
80 degrees (for sighting near the equator or in the tropical zone, we use another
technique – we’ll talk about this in future tutorials); and (iii) the Intercept you find is less
than 30 miles (if it exceeds that value, start over your calculation but use as your
assumed position, the point where the intersection of the Line of Position and the line
going towards the sun);
•
You “keep” your first line of position, because in the next tutorial, we’ll learn how to
determine precisly our position by using the Line of Position we just made with the one
we’ll determine during the next leg of the trip. We will make these 2 lines cross each
other: their intersection is our position.
Frank Sarfati aka Frankie the Funky Sailor – London 7th October 2006.