Great Circle routes..

Next question: When a course spirals into the pole - where does it go afterwards?

Mathematically, there is no course when, at the pole, all meridians intersect so does it cease, shoot off at random or just keep going in a straight line?
 
Got it in one.

Next question - every 15° you travel East you advance 1 hour in time. If you go to one of the poles and walk round it in small circles, do you travel through time?
 
" Next question - every 15° you travel East you advance 1 hour in time. If you go to one of the poles and walk round it in small circles, do you travel through time? "

Well done ... I asked this same question of my Geography teacher when I was 12 or so.

The answer ? " Don't be so stupid, boy..."

It's puzzled me ever since ... !!!
 
What am I going to do with this white bear? It's dripping blood all over the shop /forums/images/graemlins/smile.gif
 
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I teach this stuff professionally - so if I can help any further - please PM me.

Hope this helps.

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Whilst you may teach it professionally, prior to GPS the only logical way to perform a GC passage would be to draw the start and finish on the gnomic chart take off the latitudes at every 5 or 10 degrees of longitude these positions are then transferred to the mercator chart for the composite GC using Rhumb lines. The alternative is also to do the calculations using the Cosine rule and calculate the course and distance between the positions.

This was the professional application of the theory when navigating the bigger ships. And Yes, it was in the tickets from Second Mates through to Extras in the MN and FNO's with the RN.
 
And the answer is - if you start for the sake of argument at 179°W and travel east, you advance 1 hour for every 15 degrees you cross until you arrive at 179° east when you will have picked up almost 24 hours. Then you go a little further across the date line and lose it all back again in one go.

But of course you knew that, didn't you?
 
Thanks everyone for those geat replys!

The conclusion I have come to is this.. either I have had too much, or not enough rum.. haha!

No, like your man said, if you stretch a piece of string across a globe, you can see it cuts each meridian at differant angles.
I needed to see it for it to make sense.

Thank you one and all!
 
Yes - but thanks for that - did I see your cat just off Millbrook ? mate has a boat or two near yours - I think...

Thanks for your very lucid ( and obvious) explanation.
 
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Next question: When a course spirals into the pole - where does it go afterwards?

Mathematically, there is no course when, at the pole, all meridians intersect so does it cease, shoot off at random or just keep going in a straight line?

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It would never reach the pole. If you sailed on a rhumb line at a constant bearing, you would never reach the pole. You would get infinitesimally close to it, and you would end up sailing up your own pushpit, but you'd never get there.

The Mercator projection, the only projection on which rhumb lines are straight lines, illustrates this nicely - the poles cannot be represented as the mathematics work out that on the map they would be an infinite distance from the equator!
 
Of course you could always use the Transverse Mercator Projection but that's just getting silly /forums/images/graemlins/smile.gif
 
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If you sailed on a rhumb line at a constant bearing, you would never reach the pole. You would get infinitesimally close to it, and you would end up sailing up your own pushpit, but you'd never get there.

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I think that's a variation of the "Hercules and the tortoise" fallacy. (This discussion also came up a few years ago.)

Let's say your forward speed is V knots and, to keep the maths simple, that you maintain a course of 60 deg T. The northward component of your speed is therefore V cos 60 or V/2. If you started X nm from the pole then you would reach the pole in exactly 2X / V hours. I agree that your rate of turn would be infinite at the point of reaching the pole, but that is not, of itself, a reason why you couldn't get there.
 
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