Navigating our way through the world of slide rule history these past few months has brought us from Mercator maps to evaluating hyperbolic functions and back.
Mike, very much enjoyed this article. I am sure there is more math to be mined from other map projections than just Mercator.
For example the projections used to map the celestial sphere include the one dating back to antiquity that was used in the astrolabe and the famous Prague city square clock dating back to the Middle Ages.
Basically the complexity here is integrating calculations based on the sphere with the Mercator projection.
Current practices for long distance flights before computers would use a different map that was available in the flight planning room and transfer the coordinates. I will search for this projection. Great circle routes are essential for over the pole routes but are not used in the over water tracks in the Atlantic.
Hi George. Thanks for your interesting insights, and glad you enjoyed the article! Yes, I was very intrigued by the fact that the Great Circle path on a Mercator map can be described by a hyperbolic trig function proportional to a standard trig function -- and the fact that the Hemmi 153 slide rule had just the right function built in! But I also felt that going through this helped (at least me) to see how much harder it would have been to try to follow a Great Circle at sea in the 1600s than to simply maintain a bearing, for not all that much gain in most instances. I've enjoyed learning more about general navigational practices. I believe I may have seen mentioned this other projection in my investigations, but look forward to any references you recommend. Thanks!
I really enjoyed this one.
Mike, very much enjoyed this article. I am sure there is more math to be mined from other map projections than just Mercator.
For example the projections used to map the celestial sphere include the one dating back to antiquity that was used in the astrolabe and the famous Prague city square clock dating back to the Middle Ages.
Basically the complexity here is integrating calculations based on the sphere with the Mercator projection.
Current practices for long distance flights before computers would use a different map that was available in the flight planning room and transfer the coordinates. I will search for this projection. Great circle routes are essential for over the pole routes but are not used in the over water tracks in the Atlantic.
Hi George. Thanks for your interesting insights, and glad you enjoyed the article! Yes, I was very intrigued by the fact that the Great Circle path on a Mercator map can be described by a hyperbolic trig function proportional to a standard trig function -- and the fact that the Hemmi 153 slide rule had just the right function built in! But I also felt that going through this helped (at least me) to see how much harder it would have been to try to follow a Great Circle at sea in the 1600s than to simply maintain a bearing, for not all that much gain in most instances. I've enjoyed learning more about general navigational practices. I believe I may have seen mentioned this other projection in my investigations, but look forward to any references you recommend. Thanks!