This week we uploaded our updated Coastal Navigation course to Apple for publishing on iTunes as an interactive eLeanring App. We’re very excited about this update because of the HTML 5 animations we’ve used to explain some of the concepts. At the bottom of this post, we show you how to essentially get this App for free.
Specifically in regards to this post, no where on the web have we seen a decent explanation of how to do a very simple and elegant position fix using only one land position. The concept is called a running fix. In fact all we found was very poor, long, complicated and sometimes wrong explanations of how it works. Certainly we found no animated interactive explanations. So as usual, at NauticEd we have broken down the seemingly complicated to the very simple.
Play this animation below then read the explanation and solution below – then watch the animation again.
The Example Problem is:
You are sailing along on heading 57° psc (61° Mag) (47° T) your knot meter reads 5 knots. You are passing Horton Point Light to your starboard. At 1548, a hand held bearing shows that the bearing to Horton Point Light is 119°Mag (105°T). You decide to do a running fix. At 1615, the bearing to Horton Point Light is 160°M(146°T). Determine your running fix position.
The time elapsed is
1575 -1548 = 27 minutes (/60) = .45 hours
@ 5 knots you will travel 5 x 0.45 = 2.25 NM
You draw the true bearing line of 105° T to Horton Point Light. You then draw a vector 2.25 NM long in a direction of your heading 47° T starting anywhere on the 105° line. You then draw another line parallel to the first 105° T bearing that intersects the end point of the 2.25 NM vector. Finally, you draw in your second bearing line of 146° T. Where the 146° T line intersects the parallel 105° T line – you mark as your running fix position.
The theory behind this is simple but not usually explained. Initially you must lie on the 105 degree line somewhere but you don’t know where. You know that over the time elapsed you will travel the 2.25 NM from some where off the initial 105 deg line but you don’t know from where – yet. The parallel 105 deg line projected forward means that you will also lie somewhere on that projected line, again – somewhere. By doing the second bearing, off any object, the intersection of that bearing with the projected line means you must be at that point (given that your speed and heading were accurate).
LAT 41° 07.55’ N and LONG 72° 28.8’W
You can then draw your running vector from the fix position back to the original sighting line if you like to find your original position. This will also be your track.
Pretty slick ah? You’ll never be confused about a running fix again – and I bet you’re now wanting to get out on the water and practice next time out. Imagine trying to explain this using text and a paper book – yuk. Ahhhh no wonder people don’t like slogging through books anymore. In what?, less than a minute you grasped this concept fully.
eLearning is where it is all at.
Show off to your friends next time you’re out about your new found knowledge.
>>>> How to get this App for FREE <<<<
This above is the kind of stuff NauticEd is all about, but we not only break this stuff down to the simple using incredible multimedia eLearning techniques, but we back this up with an internationally recognized sailing certificate accepted by yacht charter companies world wide.
So here’s the deal that we will keep up for a few days in celebration of this App launch – invest the NauticEd Coastal Navigation online class using this promocode - 15degreeswest – and we’ll give you $15 off the regular online course price. This gives you access to the Online Coastal Navigation course and the associated test and certificate recognition.
If you have an iPad … When the App comes out in the next few days, the price of that is going to be $14.99. This means you’ll be getting the App essentially for free. The App does not include the test – it is solely the course content. As always with our iBooks or Book Apps – you need to invest in and pass the test to gain certificate recognition.
Scratching your head? What we mean is buy the online Coastal Navigation course now using the promocode and then apply the 15 bucks you save towards the App – we’ll let you know when that’s available. Then complete the test and – bang – it gets attached to your sailing certificate.
Or – if you’re really ready to get going properly why not invest in the BareboatCharter Master bundle of courses. The Coastal Navigation Course is included and you get a bonus of the Electronic Navigation course for free AND you save a ton of $ over the A La Carte Prices AND if you use this promocode – 15degreeswestbbcm – over the next few days you’ll still save the $15 above. That’s the best deal ever!!! (NOTE: this code will also work for the Captain’s Bundle of courses)
Posted by admin on February 27, 2012 under Coastal Navigation | Comments are off for this article
Currently we’re working on a cool project with SimRad to create a training simulator for a gps device. But to do that and to write the code and the statement of work for the programmer we had to be very clear about the math behind it all. At least to me, it’s all pretty interesting and so I thought I’d share it here. Kinda like “the making of…” in movie talk.
With traditional coastal navigation you are plotting positions on a chart then measuring the angles and distances. That’s all pretty easy and well described in the NauticEd Coastal navigation course. But once you start to do it electronically, you’ve got to have the mathematics of it all well understood in order to write the code. Turns out it’s again pretty easy but you’ve got to reach deep into some brain cells to drag out the trigonometry you’ve so desperately tried to forget from high school days and thought/hoped you’d never use again.
But this is a worthwhile read because you’ll exit out understanding the principles, which is really the point of the sailing blog entry.
So here’s one snippet of what we did:
We simulated a vessel moving at 20 knots that can be controlled using the autopilot. We input a static current to the east at 2 knots. For this scenario and for any direction the vessel is moving, we want to present the following variables in real time as they changed:
Bearing to Destination – BTD
Distance to Destination – DTD
Course to Steer to reach destination – CTS
Speed Over Ground – SOG
Time to Destination – TTD
Position of the vessel
The difficulty comes in with the current. You can’t just head towards your destination because the current will drag you off. So you’ve got to solve for a triangle where you have limited information and the triangle is not a right angle triangle.
We decided early on in the simulation to work in meters and meters per second because it makes the math a lot simpler. Also just by universal convenience meters per sec is ½ speed in knots. Thus 20 knots = 10m/s.
In a first example, the destination is at a point 500m to the north and 1000 m to the east of the vessel. Since we know the instantaneous position of the vessel and the position of the waypoint, we know the instantaneous distance to the waypoint. I say instantaneous because the vessel is moving.
Solving for Distance and Bearing to Destination
That’s a good start however the vessel is not moving at 20 knots towards the target. Due to the current the resultant vessel speed over ground is slightly different. To visualize what’s happening we drew this triangle. We added the current vector to the bearing vector to create a Course To Steer vector.
Vessel heading versus resultant track
There is a further complication however, since the whole process of getting to the destination doesn’t necessarily take 1 hour. We can’t say that the current vector is 2 nautical miles long. Thus in the distance triangle above we only know two variables, the angle (a) and the distance to destination – that’s not enough information. Instead we have to draw a velocity triangle whereby the current is 2 and the vessel speed is 20. Fortunately this triangle is exactly the same shape as the distance triangle. In that triangle we know three variables, vessel velocity, current velocity and the angle (a). Thus we can proceed to solve for the entire situation.
Solving for velocity triangles and distance triangles
Here’s the painful part from the ol days
A/sin(a) = B/sin(b) = C/sin(c) it’s called the sin rule.
The lower case letters are the angles and the upper case letters are the triangle side lengths opposite the same lower case letter. IE length A is opposite the angle a.
Just bare with us if that scares you. Actually it’s pretty simple from here you just have to plug and play. What it means is that if you know 3 pieces of information about any triangle you can find the others.
The first thing well solve for is the angle b. To do this, use the velocity triangle. The three pieces of information that we know are the current speed vector length, the vessel speed vector length and the angle to destination (a).
In this quadrant ie angle to destination is less than 90 deg, the Bearing to Destination is 90 minus the angle to the target ie BTD = 90-(a)
Solving the sin rule for angle (b) then
(b)= arcsin ( current x sin (a)/(vessel speed)) = arcsin (B x sin (a)/A)
= 2.6 deg
Since all angles in a triangle add to 180 the angle c must = 150.9 deg. This is the course that you would steer to arrive at the target due to the current.
The luck of it is that this is the same angle to plug back into the distance triangle
IE (c)= (c*).
Now we can return to the distance triangle because we know enough variables. If we plug the two known angles (a) and (c) in to distance triangle we can solve for the distance A*. We need to know A* because the vessel attempts to travel along this path at 10m/s but ends up at the destination. Solving for the time it would take the vessel to attempt A* is the same time it takes for the vessel to actually travel to the destination. IE the vessel is helped by the current.
From the sin rule:
A* = C* x sin(a)/sin(c) = 1027.2 meters
and at 10 m/s the time elapsed is 102.72 sec = ~ 103 seconds
The vessel actually travelled 1128 meters in 103 seconds thus the
SOG = 1128/103 = 10.9 m/s = 21.8 knots
The distance that the vessel was pushed to the east by the current = Set =B*
Set= current speed(drift) x time = 1 *103 = 103 meters.
So for this tiny moment point in time:
BTD= 63.4 degT
CTS=60.9 deg T
DTD = 1128 m
TTD = 103 sec
SOG = 10.9 m/s
In coding all this up and since the vessel is moving we have to solve all these at each instant in time using location information from the last moment in time. Again not too difficult it just takes a bit of thought in laying it all out.
If you know the velocity of the vessel over ground (solved from above) and the increment in time, you can calculate the change in position. This is done in Cartesian coordinates Ie x and y directions
Change in X = velocity in x direction times the time increment = Vx x dt
Change in Y= velocity in y direction times the time increment = Vy x dt
Where Vx and Vy are solved from the angles calculated from above and SOG
So the position at this instant is now the position at the last instant plus the distance travelled in the increment in time.
We have to solve all this for each instant in time because the vessel is also changing direction from input from the autopilot. In a real situation the position information is being gathered from the actual gps not the last instant. Altho some smarter systems will use this for predictive situations.
Another level of complexity is added in when you consider other quadrants. For example in the below drawing, the current works against the vessel. Note the SOG has slowed, the angle b reduces the CTS, and the triangle is quite different. Thus in the code we have to add a lot of if/then statements to determine what quadrant were working in to determine which formula to use.
Solving the velocity and distance triangles
OK ADMITTEDLY THAT MIGHT HAVE BEEN A BIT HEAVY GOING
Hopefully this gave you some insight into:
Some principles behind coastal navigation
Help in understanding electronic coastal navigation
Some insight into what we do at our sailing school to provide great sailing education
We can’t wait to deliver the SimRad Electronic Navigation simulator and training tool to you.
If you’re interested in properly understanding how to navigate a vessel using charts then take the NauticEd Coastal Navigation Course. Once we finish the electronic navigation simulator we’ll embed it into the Navigation sailing course.
The posting here is not a course in celestial navigation by any means. However it’s meant to simplify a few principles for you so that you’ll at least have some sort of celestial orientation. And… perhaps it’ll inspire you to learn the aging art.
This was written by Grant Headifen, Educational Director of NauticEd. NauticEd provides online sailing courses and Sailing Certifications accepted by charter companies worldwide.
Latitude: In the northern hemisphere, finding latitude is simple using one of the greatest gifts to human kind – The North Star. What ever angle the northern star is at from the horizon, that’s your latitude.
Imagine you’re an ant sitting on the top of an apple looking at a spot directly above you on the ceiling then the spot is 90 degrees from the surface you’re standing on. If you’re standing half way around the apple then you’d barely see the spot but it would be horizontal to the surface you’re standing on and so the spot would be at zero degrees. And if you were ¼ of the way down the apple then the spot would be at 45 degrees etc. ie the northern star is the spot on the ceiling to us.
You can also find latitude using other celestial sightings but they involve table lookups and are slightly more complicated. Not meant for this post and also note that there are a few more complicated variables not taken into account during this simplistic explanation like the height of your eyeballs above the earths surface etc etc. But at least you’ve now got the principle.
Longitude: Now this is a fun one and in an incredibly easy principle. But years ago (early 1700′s) while the principle was easy then the execution was difficult. Read on to see why.
The earth rotates through 360 degrees in 24 hours. That’s 15 degrees per hour. By convention, when the sun is at it’s highest point in Greenwich, it is noon in Greenwich. That means that at a place that is 15 degrees to the West of Greenwich the sun will be at it’s highest point one hour later. Six hours after Greenwich the sun will be at it’s highest point somewhere in over the USA and 12 hours later the sun will be at it’s highest point in New Zealand.
Animation of time zones
So if we know the time in Greenwich and sun just reached its highest point where we are then we can calculate our longitude.
Lets do a few examples. If it is 6 pm in Greenwich and the sun just peaked overhead here, then I am 6 x15 degrees to the west of Greenwich which is 90 degrees West which is right near St Louis Mo.
If the sun peaked overhead in Los Angeles what time would it be in London.?Well LA is 118.15 degrees West (from Google earth). Divide that by 15 degrees per hour and we get 7 hrs 53 minutes. Now since the times zones are created in bands this would round up to 8 hours. Thus it would be 8pm in London.
You’re sailing in the Greek islands in the Mediterranean and a little bird just told you your latitude is 34 deg 54 minutes north but failed to tell you the longitude. Fortunately you have your handy sextant and just as you take a shot, the sun just reached its apex overhead. You look at your watch and the local time is 12:10:48 pm. Where are you?
Since you’re in time zone B you are 2 hours ahead of Greenwich. Thus the time in Greenwich is 10:10:48 am. And since the sun peaked just now (=noon) then you are 12:00:00 minus 10:10:48 = 1 hour 49 minutes and 12 seconds from Greenwich. Putting this into decimal time this is 1.82 hours. Multiply this by 15 degrees per hour and we have 27.3 degrees East or 27 degrees, 18 minutes East.
You’re in the harbor north of the town of Kos on the Island of Kos.
That was incredibly easy, so why all the hoopla back in the 1700′s? The King of England even offered up a ₤10,000 reward to anyone who could solve the issue of Longitude. The above math was well known but the issue was telling the time. No one could accurately keep time at sea. After 27 years of work on the project, John Harrison, finally invented the Chronometer more commonly known as the watch. The watch was not susceptible to the sudden crashes of waves at sea and thus kept proper time.
James Cook on his second trip around the world in 1772 sailing on Rendezvous, took Harrison’s watch with initially much skepticism. Stating that he’d give it a try. After six months at sea, Cook stated that the Chronometer would almost certainly become the way of the future for Navigators. Cook then went on to reposition many of the Islands in the Pacific including Tahiti, his favorite island. His map of New Zealand astounds people even today with its accuracy.
Again there were a few simplistic assumptions taken in that explanation. But now, at least you understand the principle of longitude determination from a noon shot of the sun. You can also determine your latitude from a noon shot of the sun as well using tables and a bit of math. Again beyond this posting.
If you’d like to delve deeper into these topics, NauticEd provides online sailing lessons and an Introductory Celestial Navigation Sailing Course, or maybe you’re just happy with your handy boring ol GPS.
We had a blast putting this Ocean Navigation Discussion video together.
The big time fun part was coming up with the dialog. By the constraints of the program to create it we had to use an astronaut and Napolean. Take a view of the video and let us know if it was at least mildly funny.
We’re going to embed it into the start of the NauticEd Coastal Navigation Sailing Course to get the student in the right mood for learning the basics of ocean navigation. Our thoughts are if some one is in a good mood they can absorb more info. So you’ll find that, through out all NauticEd courses, we try to inject a little humor. It’s something that I think can be done more effectively in online learning as opposed to a paper book.
We used Google Earth to find the distance from the Taj Mahal to Auckland New Zealand. The line it drew was accurately a “great circle” which on a sphere is the shortest distance between two points.
Great Circle Distance from Taj Mahal to Auckland New Zealand
Please enjoy the video but also the NauticEd Coastal Navigation Course.
They say that there are two types of sailors – those that have hit the bottom and liars. Well, with this blog, I can firmly place myself in type I.
I believe the reason “they” (I never really know who “they” are) make this statement is to promote caution, that you’re never too immune from the bottom of the ocean no matter how much experience you have.
Certainly – I’m one of those who demonstrated to myself that the bottom is to be kept at a distance. Here’s a story that happened to me that will hopefully stick with you and help reduce (probably not eliminate) the number of times you’ll be introduced intimately to the bottom of the ocean.
The setting is the beautiful Bay of Islands, New Zealand. We were motoring amongst the picturesque islands photo documenting the anchorages for a website that we were building for Sailing New Zealand (http://www.sailingnewzealand.co.nz).
When rocks like these are present it's a good sign others are lurking under the water
In one particular instance, there were two ways to get around to the next bay. Cut through a 30 meter wide channel between a set of rocks and the island or around the outside of the rocks. We consulted the GPS map and the paper map, both indicated deep water between the rocks and the island. And on top of that, it was high tide (2.5 meters above datum). Clear Right?
BONK! Said the rock and the boat simultaneously.
So what happened? Was I off on my positioning? Nope – I infinity checked that after we’d given the keel the headache of it’s life.
What happened was pure thoughtlessness. What was I thinking? I had put pure trust into data. Assuming that each and every rock in the entire world has been accurately positioned and that data exists on all electronic and paper maps.
Very simply, that is just not the case and I should have known better. Would Captain Cook made such a rudimentary mistake as he performed his amazing exploration of the unchartered world? I doubt it! In those days they constantly lead lined off the bow and sent dinghies in to doubtful waters. Lives were at stake.
While I do believe that it’s pretty safe now-a-days to assume that in deep waters almost every rock has been marked – at least in the first world countries, the mistake I had made was in shallow water close to an island.
Fortunately the story ends ok with out any injuries except to my wallet and to my two year old who bonked her head in the berth below decks while sleeping. That’s a really sucky way to wake up by the way. We reported the issue to the charter company. They hauled the boat and we paid for the damages. Even though we were going slow, the abrupt stop caused a separation gap between the keel and the hull introducing a leak.
Moral of the story. The ocean’s beauty allures us to it but it can be treacherous. Keep your head screwed on and play it safe – every time. Your experience does not give you a get out of jail free card. In fact your experience can lead you into a false sense of security. Time for me to push the reset button on what I think I know and go back to the basics. Lesson well learned. I hope this story helps you “go around the outside”.
To learn more about coastal navigation, take the NauticEd Coastal Navigation Sailing Course.
One final note – it’s really important to report incidences like this to the yacht charter company. First – it’s a matter of integrity and secondly it is a safety concern for the next charterer. There are a lot of awful what if scenarios you could probably think of and for the price of the insurance deductible the peace of mind is worth it. And after it was all said and done and amortizing it out over my sailing career the cost was about 50 cents per sail. No big deal but the re-learned knowledge is worth so much more.
Recently on our NauticEd flotilla with the Moorings to the Kingdom of Tonga we wanted to pass through the Fanua Tapu Pass which is a gap in the reef to get to the eastern islands of the Vava’u archipelago. Normally the gap is marked by a series of buoys, however the latest storm ate them.
The pass is well documented by two waypoints. Traversing using a GPS map, however, was out of the question because Tonga is one of the last places on earth to be accurately placed on the world coordinates. Yes you’re reading that right – the islands are not actually where the maps say they are and especially reefs and rocks are not where they are positioned on the maps. That’s pretty absurd for this day and age but it’s true. Call the Moorings base in Tonga for your self.
Navigation is performed using good old eyesight (some of our eyesights are older than others) coupled with map reading skills, a depth sounder and a keen watch out on the foredeck.
So anyway we had to get the first waypoint dead on to pass through the reef. The first waypoint was 18 deg 43.914 min South and 173 deg 59.12 min West. Our position was 18 deg 44.902 South and 173 deg 62.014 West.
So it’s a bit funny trying to hit a point like this because you’ve got to be able to work with a few obvious things but understanding the principles makes it much easier. First you’ve got to know which directions you need to be heading based on the hemispheres you’re in.
In the northern hemisphere to increase the latitude you’ve got to head north but in the southern hemisphere to increase latitude you’ve got to head south.
Similarly, in the eastern hemisphere to increase longitude you’ve got to head east where as in the western hemisphere to increase longitude you’ve got to head west.
OMG how do you remember that? Especially in the heat of the moment with waves and rocks all around you and your life depending on it.
I’m sure there is a memonic for it but it’s best to understand the principle first and below is the way where I can best understand it. For me, I find that principles are better than memonics.
Imagine you’re standing on the intersection of the prime meridian (below grenwich) and the equator. You’re at 0 deg Latitude and 0 deg Longitude. Move in any distance to the North and the latitude increases North. Move any distance to the South and the Latitude increases South. Now place yourself at about 17 degrees south latitude. Move North and you’re moving towards the equator and towards 0 deg Latitude.
So in principle then, if you understand this; move towards the equator you’re decreasing the Latitude no mater which north or south hemisphere you’re in. So in our example above our latitude was greater than the waypoint so we needed to head towards the equator. We were in the southern hemisphere so we needed to head north.
IE when dealing with latitude – just figure out if you need to head towards the equator or not. That should take care of that from an understanding principles point of view.
Longitude. Back to our Prime Meridian/Equator intersection. Looking towards the North pole, everything towards your left is West Longitude right? And everything towards the right is East Longitude. So anything from England, past the Americas and all the way around to Hawaii is West longitude. Any everything from England, past Asia and all the way to Australia and New Zealand is East Longitude. This is why the USA is known as western society and Asia is known as eastern society.
So now you just got to know where you are East or West. In Tonga we were on West Longitudes. So anything back towards the Americas or England from that point was decreasing the Longitude numbers towards the zero prime meridian in Grenwich. Which meant to get to our waypoint we had to head East to the America’s.
So overall we needed to head to the North and to the East. Next we looked at what was the relative differences between desired and present positions for latitude and longitude. The longitude difference was about 3 times that of the latitude difference. This means we needed to head more east than north.
In the old days (I mean the old old days) before longitude could accurately be determined, traders would head north from Africa and purposefully miss England far far to the west of England. Then once on the latitude (easily discovered by the angle the north star makes with the horizon) they would then travel East. This ensured they would miss all the potential dangers. Hundreds of ships were being lost due to the difficulty in accurately determining the longitude. In early 1700’s the King of England offered a 10,000 pound reward to figure out how to accurately determine Longitude. For those of you interested, watch the history channel show on this or read the book “Longitude”. Both are excellent!
So lets go back to the principle. Where ever you are you should establish this before any issues come up. IE if you’re on a bareboat charter – answer these questions before you leave the base.
Am I in the southern or northern hemishere? Then based on that, embed into your head which way do you go to increase/decrease latitudes. Should you head towards the equator or away.
Am I in Eastern Longitudes or Western Longtiudes? Then decide which continent you should head to decrease or increase longitudes.
Here’s a little test then. You’re in the Aegean Sea at:
36 deg 56 min North Latitude, 27 deg 19 min East Longitude
you want to get to:
36 deg 57.897 min North Latitude, 27 deg 17.295 Min East Longitude.
Which way should you be heading?
Simple enough – we’re in the North Eastern hemisphere. We want to increase the latitude so we need to move away from the equator and thus head north. We also want to decrease the longitude and head towards Grenwich England which means head west.
Both are almost 2 minutes in difference and so the VERY APPROXIMATE direction should be North East. We say VERY APPROXIMATE because the latitude lines and longitude lines are not the same distance apart and vary according to latitude. The closer to the poles the closer are the longitude lines. Therefore the heading would be more north of northeast.
In this blog we’re placing quite an importance on this concept. The reason being is a funny (potentially not so funny) story attached. On the Tonga trip one of the crew was an ex Airforce Navigator. He got turned around for a second in the reef because we were heading east to reach the waypoint but his brain was telling him to head west. The reason is that he was used to Navigating around New Zealand which is in the Eastern Longitudes. Tonga is just on the otherside of the 180th Meridian in the Western Longitudes. Whoops being turned around in the middle of reefs is NOT good. There were rocks all around us and correct decisions had to be made fast.
OK and here’s a real scenario to scare you into taking this blog and the NauticEd sailing simulator serious. A family member falls overboard at night and you hit the MOB button on your hand held GPS. You’ve got the lat and long where they went over. By the time you get turned around and the sails down with all the confusion – all you’ve got is their lat and long and yours and a compass. How do you save your family member’s life?
MOB is at 16 deg 33.250 min N and 62 deg 11.501 W
You are at 16 deg 33.200 min N and 62 deg 11.595 W
Which way do you head? Quickly now the current is drifting them away from that position.
Yesterday we launched our most requested clinic. Coastal Navigation! We’re very excited to have this course completed and up. It was written by our resident faculty member Captain Ed Mapes with Offshore Voyages. Ed has taught navigation courses with thousands of students on board his ocean learning passages.
The Coastal Sailing Navigation course incorporates most all the elements required by the United States Coast Guard Captain’s License Navigation section. Some of the topics covered are Coastal Sailing Navigation tricks and techniques using lines of position, gps, running fix, bearing fixes, true versus magnetic bearings, using navigation tools, calculate set and drift from tides and current, determine your heading with a known set and drift etc. In addition there is a review of the ATONs (aids to navigation) during the day and at night which was presented in the NauticEd skipper course.
The course is presented with lots of graphics and video’s explaining the navigation techniques from very basic terms to ensure everyone grasps the navigational concepts.