AIS for collision avoidance - One for the maths gurus?

[T_C]

The debate on another thread about near misses with shipping refers a lot to the benefits of AIS in determining whether or not a risk of close encounter exists and in determining the CPA.

Now, I have the basic NASA "radar" (yes, I know it's not radar as we know it, Jim), which doesn't run to CPA etc. It does display the position, COG and SOG of a potential risk. Although I haven't yet used the set is real anger yet, my thinking is if a target appears to be a risk I can plot its position and course on the paper chart, plot my position and course, and then step the scenario forward by say 5 or 10 minutes to assess whether or not the relative bearing between the two of us has changed and hence whether or not there is a risk of getting up close with the big stuff.

Assuming we are both travelling in straight lines, I think that stacks up theoretically (no doubt someone will be along pretty sharpish to point out otherwise if not), but it is relatively slow and subject to inaccuracies in the plotting.
It must be possible to represent this mathematically, in which case my thinking is that, once modelled, it can be replicated in excel, and I can try to write a natty little spreadsheet that, by inputting the position, SOG and COG of the two vessels, will at least tell me if the risk of collision exists, or if one or other of us will pass ahead, and, with a little more modelling, tell me the CPA. I don't have a laptop or the likes on the boat and would intend to use the rather basic excel on the phone to interpret the results.

Any trig experts wish to comment or suggest how one might represent such a thing mathematically, or alternatively tell me it's a barking mad idea in which case I can stop puzzling over it?

Thanks

Tim

 

[johnchampion]

Ok, it's barking!

All that's needed is a bearing, if it changes you miss, if it doesn't you collide.

Why on earth do you want an excel spreadsheet to tell you?

 

[T_C]

because the NASA set doesn't tell you the bearing?
Agree if you can see it visullay, in which case there's no need for it?

 

[johnchampion]

OK, my point would be then that in restricted visibility there may be more pressing matters than playing around with a computer and spreadsheet.

Anyway if Mr Gates software decides to crash does that mean you do as well?

 

[awol]

Stick clingfilm or some'at over the display. Use magic marker to mark target, go worry about some'at else, come back and mark target again. If a line through the two target positions extends to the own boat position start worrying about that. Or get a hand bearing compass - there's probably an app for your phone that will do!

 

[T_C]

Thank you AWOL, I have three hand bearing compasses on board already! As I have already pointed out, if the vis is good there is no need for this.

I perhaps didn't explain very well, the display of the basic NASA unit displays a target with a line to depict it's relative bearing to you and the lenght of the line its speed, but I wouldn't say it's particular accurate when it comes down to close calls, hence the thought to predict relative bearings a little more accurately. I am familiar with the technique you describe when using radar proper, but that isn't an option in this case.

 

[johnchampion]

I've just had a quick look at the NASA manual on their site and it seems that the unit displays a relative track of the last 16 positions for targets with the time between inputs user selectable, so if it looks like the track is going through your position you have the answer already presented and it may be time to do something about it.

It's probably accurate enough and as accurate as you can get on a small boat without lots of extra effort which won't improve things a lot anyway.

 

[shmoo]

This link http://quanglewangle.com/optimumInterscept.pdf is a file containing the paper Optimal Intercept Course of Vessels to a Non-zero Range which, while not quite being a collision would be one if you modified the math for a zero range.

If is actually for (e.g.) patrol boats to catch (e.g.) pirates but if modified for zero range would be for any two boats colliding.

 

[AliM]

Yes, perfectly possible, but still far too slow and full of possibility of errors in entering data to be worth doing.

To get it working properly, assuming a perfect program (a good program is easy - a fool-proof one is not!), then you'd have to enter your position, SOG, COG and the ship's, with no errors, and make the unreliable assumption that neither will change. The paper chart is a better way to do this, because any errors in entering data are obvious, and it's probably not much slower, particularly since you'll be able to dismiss the ships going in the wrong direction immediately, without entering the rest of the data for them. Besides, you will be able to relate the blip/light on the horizon with the AIS target from the bearing quickly - that's really reassuring.

 

[Elemental]

I've not used it but someone has already done it for you. Excel spreadsheet to calculate CPA

 

[timbartlett]

Any trig experts wish to comment or suggest how one might represent such a thing mathematically, or alternatively tell me it's a barking mad idea in which case I can stop puzzling over it?

Not a trig expert, but I would stop puzzling over it.
The whole point of the Nasa "Radar" (and the reason for its contentious name!) is that it is like a radar display.
So if the blob is moving towards the centre, there is a risk that it is going to hit you.
If it's moving towards somewhere other than the centre, then you can estimate how far from the centre it will pass, and that is your CPA.
And if you "need" high precision, then your CPA is probably too small!

 

[st599]

I've not used it but someone has already done it for you. Excel spreadsheet to calculate CPA

That requires values for variables he says the Nasa doesn't provide. And it seems to assume a flat Earth.

 

[fireball]

And it seems to assume a flat Earth.

If the thing is ~15Nm away then curvature of the Earth is insignificant!!

 

[IanR]

I have such a spreadsheet

I created such a sheet for the very reasons you describe
It was a bit of fun after a radar course it was an interesting project and helped me with my EBL and VRMs for my non stabilised Radar.

I have used it in anger and it seems to work OK

Please feel free to have a go. If it is not obvious I can write some instructions
Basically enter the time your own course and speed and then the target EBL and VRM and the time. Put a couple of targets in and you get a CPA

Don't sue me see usual disclaimers about navigation, skippers own responsibility etc......

 

[AliM]

I think those are different questions.

The Nasa, the OP says, displays position SOG and COG. The excel spreadsheet wants distance and bearing. Its pretty easy to caluslate those from your and the ship's position (and to answer Fireball, that is where the curvature of the earth is significant).

Like I said, it's possible, and the maths isn't difficult, but it's not a useful tool for navigation because of the unreliability of the data entry and the need for a completely idiot-proof program.

 

[idpnd]

Get yourself a netbook or laptop, use opencpn for free and get all your TCPAs and CPAs calculated for you?

The NASA should have some collision warning built in though?

 

[ferrymaniom]

Rather than do it in a spread sheet I would suggest using a plotting sheet. Easy to do and it makes it easy for you to visualise the situation around you.

 

[fireball]

(and to answer Fireball, that is where the curvature of the earth is significant)

One quick bit of research later ...

from: http://www.movable-type.co.uk/scripts/gis-faq-5.1.html

" (This answer was prepared by Robert G. Chamberlain of Caltech (JPL): rgc@solstice.jpl.nasa.gov and reviewed on the comp.infosystems.gis newsgroup in Oct 1996.)
If the distance is less than about 20 km (12 mi) and the locations of the two points in Cartesian coordinates are X1,Y1 and X2,Y2 then the

Pythagorean Theorem

d = sqrt((X2 - X1)^2 + (Y2 - Y1)^2)

will result in an error of
less than 30 meters (100 ft) for latitudes less than 70 degrees
less than 20 meters ( 66 ft) for latitudes less than 50 degrees
less than 9 meters ( 30 ft) for latitudes less than 30 degrees
(These error statements reflect both the convergence of the meridians and the curvature of the parallels.)

The flat-Earth distance d will be expressed in the same units as the coordinates.

If the locations are not already in Cartesian coordinates, the computational cost of converting from spherical coordinates and then using the flat-Earth model may exceed that of using the more accurate spherical model.

Otherwise, presuming a spherical Earth with radius R (see below), and the locations of the two points in spherical coordinates (longitude and latitude) are lon1,lat1 and lon2,lat2 then the

Haversine Formula (from R.W. Sinnott, "Virtues of the Haversine", Sky and Telescope, vol. 68, no. 2, 1984, p. 159):

dlon = lon2 - lon1
dlat = lat2 - lat1
a = sin^2(dlat/2) + cos(lat1) * cos(lat2) * sin^2(dlon/2)
c = 2 * arcsin(min(1,sqrt(a)))
d = R * c
"

So - around the UK we can expect errors of between 9 and 20meters ... go south quite a bit and we're talking a massive 30 meters ...

Hmm ... now ... if you're bothered about a 30 METER difference in CPA ...

Me - I'll stick to Flat Earth theory

 

[timbartlett]

I created such a sheet for the very reasons you describe
It was a bit of fun after a radar course it was an interesting project and helped me with my EBL and VRMs for my non stabilised Radar.

I have used it in anger and it seems to work OK

Please feel free to have a go. If it is not obvious I can write some instructions
Basically enter the time your own course and speed and then the target EBL and VRM and the time. Put a couple of targets in and you get a CPA

Don't sue me see usual disclaimers about navigation, skippers own responsibility etc......

I'm probably being dense, but I still don't see how all this business of entering things into spreadsheets is any quicker, easier (or more accurate) than looking at the movement of the blob to see whether it's heading for the centre of the screen.

On the assumption that "If you can keep your head when all about you are losing theirs, then you probably haven't grasped the seriousness of the situation, my son" I'm guessing that I have missed something. Can anyone tell me what, please?

 

[fireball]

I must admit - nor can I ... but an excel worksheet makes an interesting interlude ... even if just for the theory ..