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Author
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Topic: AM To PM Running Fix
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rafonga
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posted January 11, 2023 02:03 PM
In relation to:
Book: Celestial Navigation, 2nd Edition
11.15 AM To PM Running Fix
Exercise (2) page 155
Can you please explain how you got the answer ~67 degrees.
A linear interpolation gives me 62.4. I know that the response is some kind of interpolation between 51 and 70, but I'm not sure how to get to it using this table. My Ho is 78 degrees.
Can you also please clarify the result of (4) and (5) of the same exercise? thanks
From: Christchurch
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David Burch
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posted January 11, 2023 03:23 PM
I will take a look at these. Your interpolation seems right to me. Let me check this more and get back to you.
From: Starpath, Seattle, WA
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David Burch
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posted January 11, 2023 04:07 PM
As for no (4), the Ho max is 57º.
At Ho = 50º, a 30º cut angle occurs at 42 mim.
For Ho = 60º, the 30º cut occurs at 31 min, so at 57 I get 42 - 0.7x11 = 34.3, not "~42"; so it looks like that one is wrong as well in the book.
Let me compute the exact values to check these. I would hope that I checked this 19th century table when we published it. Most likely just solution errors that have not been caught till now, some 30 years later!
Back soon.
From: Starpath, Seattle, WA
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David Burch
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posted January 14, 2023 08:32 AM
Very sorry for the delay in finishing this up. I have numerically confirmed that this old table is correct, and am now looking for a convenient free interpolation app that can do the double interpolations needed for the last two. I think I have an iOS version, and am checking it now.
Also as a curiosity, I checked and see that this table was in our original 1977 set of cel nav materials so it seems these exercises have not been checked for 46 years. I am also still pondering the significance of that fact.
From: Starpath, Seattle, WA
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David Burch
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posted January 14, 2023 03:16 PM
Actually only one was a double interpolation, so here are the correct answers and their solutions as I see it. Please let us know if any are not clear or seem wrong.
I will add this to the book errata. After working with this table, It is not as helpful for practical decisions as it could be so I will redesign that table and report back when done.
It seems to me now that has been there all these years in large part because it has not been questioned till now, so I thank you again for bringing this us.
At the time (1977) I must have been so happy to see that in the Golden Age of Sail they were also thinking about optimizing rfix spanning LAN, which is what we were teaching, that this table got all that prominence and longevity.
The ideas are all still good, but we can make a better table to judge this from.
From: Starpath, Seattle, WA
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rafonga
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posted January 15, 2023 12:34 AM
a
From: Christchurch
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rafonga
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posted January 15, 2023 12:49 AM
Hi David,
Thanks for your time looking into this.
I got different responses for (4) and (5). I couldn't attached my calculations here, so I have sent them via email.
For (4), I calculated the angles for Ho = 57 interpolating between 50 and 60, and time values of 28-32-36. The values obtained were 24.9, 28.6 and 32.6. At the right side, I then used the last two values to find what exact time will give me 30 degrees. My final response is 33.4min.
For (5), it's a simple interpolation, so I think ours should match.
I'm satisfied with your response, and I think this is just an interpolation divergence now.
Anyway, I wanted to say that I love the didactic style of this book. The content is dense for a new reader but it's fairly easy to read and follow. I haven't finished this one yet, but have 3x others Starpath books underway.
Thanks for your help.
From: Christchurch
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rafonga
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posted January 15, 2023 12:51 AM
Forgot to say my final response for (5) is 8.6min.
From: Christchurch
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David Burch
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posted January 15, 2023 11:51 AM
I agree. in (5) I took 41-28 and got 29! 8.6 is correct for (5).
Can you please tell me what you see wrong with the computation in the picture above for (4).
I will then update the image and errata.
From: Starpath, Seattle, WA
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rafonga
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posted January 19, 2023 11:51 AM
Hi David,
Sorry for the delay - I'm away until early next week. I will have a look at this when I'm back.
From: Christchurch
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