A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Bruce J. Pennino
Date: 2016 Oct 1, 08:20 -0700
A friend recently gave me Dutton's, 13 edition. As I was flipping through the pages I noticed the section on great circle courses, calculating waypoints etc. I've done some surveying and staked out many circular curves/courses using a theodolite. So the math was interesting. Surveyors basically use deflection angles from a back tangent and chord distances to locate points (waypoints) along the arc. A surveyor moves up on the curve(course) and then can layout points ahead using subdeflection angles. Of course there is no concern with curvature and non-parallel meridians.
Anyway using HO 208 for initial course and distance, and using Dutton's mid latitude calculation methods with a hand calculator, I tried to do a great circle course from Charleston, SC to the Lizard Point, UK. With only 4 intervals (5 waypoints), my results did not agree very well with an online calculator. With 6 waypoints, results were somewhat better. But the course was too far north. The rhumb line distance and course is only 3-4 % longer more than great circle. My first question: What is the best method/equations for locating waypoints when the initial course and great circle distance is known? I assume latitude change = distance * cosinecourse, but longitude change?
Second question: How many waypoints would I practically need to establish a proposed course from Charleston, SC to Lizard Point? Based on the online calculators, 6 or 7 waypoints are sufficient? I would update my course with actual CN positioning and using HO 208 . I assume no onboard computer, GPS, etc. I imagine back in the sailing and steamship days navigators using previous courses and just repeated their previous successful crossings. Interesting.
Thanks and best regards,