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Hello:

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,

Bruce