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» Online Classroom   » Celestial Navigation   » Public Discussion of Cel Nav   » HBS Problem 27: Calculating Great Circle by hand

Author Topic: HBS Problem 27: Calculating Great Circle by hand

 - posted December 19, 2020 12:29 AM      Profile for Jon           Edit/Delete Post 
(I'm showing my work in the interest of a) seeing if anyone else attempted this and b) whether I have made any logic errors.)

One of HBS' final problems is to calculate the Great Circle distance from Cape Flattery. As I have NGA Chart 56 (GC Chart of North Pacific), I decided to try it by hand. Per the chart's instructions, I calculated a bearing of 235 and a distance (from Cape Flattery to Pailolo Channel) of 2190 nm. This compares to this site's GC shareware of 234.4 and 2237, respectively.

Within NGA 56's instructions on how to calculate your course, there is a description of moving your longitude by 20 deg from your DR-Lon then using the chart's "Great Circle Course Diagram" (and some parallel rulers) to determine your subsequent course heading. Starting with 125 West, I did this for every 5 degrees--from 125 W to 155 W (about 270 nm due north of the Big Island). My course headings were as follows:

Cape Flattery to 130 West: 235T
130W to 135W: 231T
135W to 140W: 227T
140W to 145W: 224T
145W to 150W: 221T
150W to 155W: 218T
155W to Pailolo Channel: 216T

Well, I ended up approx. 51 nm due west of Pailolo Channel in Kaiwi Channel (between Molokai and Oahu). I realize my mechanical approach is unrealistic as to real navigation, especially as you incorporate your celestial fixes, your destination nears, etc., but I'm more interested in whether the general logic I applied is reasonable.

From: Parallel 47

 - posted December 19, 2020 12:46 AM      Profile for Jon           Edit/Delete Post 
Addendum: Using my arbitrary "change course every 5 deg of longitude" approach, my overall GC distance estimate of 2190 nm expanded to approx. 2335 nm.
From: Parallel 47
David Burch

 - posted December 19, 2020 10:48 AM      Profile for David Burch           Edit/Delete Post 
Very nice work! It is good practice to solve these things by hand.

Here is the 5º Lon step solution from our StarPilot program that you can use for comparison, starting at 48º 23'N, 124º 45' W to the destination indicated.

Dist(nm)/Course(T)/Len(nm)/Next Lat/Lon
2238.36 234.4° 12.31 048°15.8'/-125°00.0'
2226.08 234.2° 259.12 045°37.8'/-130°00.0'
1967.51 230.5° 287.11 042°29.0'/-135°00.0'
1681.01 227.1° 320.33 038°44.5'/-140°00.0'
1361.36 223.8° 358.83 034°19.6'/-145°00.0'
1003.27 220.8° 401.91 029°09.9'/-150°00.0'
602.18 218.2° 447.46 023°13.4'/-155°00.0'
155.63 216.0° 155.94 021°07.0'/-156°38.0'

We do also have calculators online at www.starpath.com/calc and I think you have found them but we also have hi-res great circle charts online at https://www.starpath.com/downloads/downloads_title.htm

From: Starpath, Seattle, WA

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