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    Re: The Great Circle Challenge
    From: David Pike
    Date: 2014 Dec 26, 17:39 -0800

     

    Well, if this was a navigation course, the leader would say “What have you learned today”.  I’ve learned a lot.  I’ve seen some interesting methods, and some I’d like to try out.  I also learned a couple of other things.  Firstly, don’t let your enthusiasm trick you into calculating spherical geometry when you’re tired.  I started after a day out driving the family around and walking in the cold, and my first attempt was a disaster with the distance coming out as 6573nm.  A quick Google of “Distance New Zealand to Hawaii” showed I’d screwed up big-time.  This led to another discovery.  I read that the cosine rule isn’t suitable for big triangles, so at first I thought that was the problem and that I’d have to get into haversines for the first time in 40 years.  However, after a little nap, I decided to have one last try with the cosine rule, this time using a triangle based on the South instead of the North Pole. While doing this I realised that in my haste, first time I’d used the lat and not the co-lat of the destination.  My second attempt: distance = 4069nm Initial bearing = 025.88degrees agrees with most others.  The time taken for the second attempt was 39minutes, but working longhand I have to check all the written figures at least three times.  My working is shown in the snaps below.

     

     By way of redemption, let’s try the B52’s great circle route in Stanley Kubricks “Dr Strangeglove” from Burpleson Air Force Base 61d 15’N 149d 48’ W to the Doomsday Device 58d 45’N 030d12’E.  Dave

     



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