Category Archives: Navigation

Unfortunate Satellite Launch Problem Allows Test of Relativistic Time Dilation

In November 2015, the European Space Agency (ESA) had a launch problem with two of its Galileo navigational satellites that resulted in both satellites being placed into highly elliptical orbits. ESA can burn some of the satellites' station-keeping fuel to bring these orbits back to standard, but this will take some time. While the orbit adjustments are occurring, ESA will use the satellites to provide another test of Einstein's general theory of relativity. Specifically, they will test the prediction that clocks will run slower the closer they approach a massive object. Continue reading

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WW2 Submarine Endurance on Batteries

I have been reading the book The Bravest Man, a biography of the WW2 exploits of US Navy submarine commander Dick O'Kane. I have not formed an opinion on the book since I just started reading it, but the book does highlight the submerged maneuvering limitations imposed on a ww2 submarine because of its lead-acid battery-based power plant. The book's discussion made me curious about the operational characteristics of a Gato-class submarine when operating submerged on batteries. In this post, I will be examining the Gato-class submarine's run time versus speed plot (Figure 1). Continue reading

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The Bounty Mutiny and the Pitcairn Island Position Error

I liked reading the book Longitude by Dava Sobel and I also enjoyed the television movie version. I was recently doing some reading about the Bounty mutiny when I realized that the problem of measuring longitude played a role in that tale as well. The story of longitude is one of technology and obsession. While mariners had been able to measure their latitude accurately for centuries, measuring one's longitude required the development of accurate timepieces. Longitude is the story of the development of the marine chronometer. In essence, our modern GPS systems are extremely accurate clocks that provide the ultimate realization of the longitude goal. Continue reading

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Index/Instrument Error Correction in Sextant Measurements

Sextants make measurements that are subject to systematic errors – all instruments are subject to systematic errors. Alas, much of my career has been spent on calibrating out systematic instrument errors. Even with all my efforts, residual systematic errors remain. Continue reading

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Refraction Error Correction in Sextant Measurements

Refraction is probably the most difficult to understand of all the altitude observation corrections. It is also the most difficult to estimate accurately because it depends so strongly on atmospheric conditions, particularly the rate of temperature variation with altitude (see lapse rate). I will derive in this post a commonly used expression for the refraction correction required for a celestial object with an altitude greater than or equal to 15°. The accuracy of this expression degrades significantly for objects below 15°. Continue reading

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Correcting for Sextant Parallax Error

Navigators use the altitudes of solar system objects to assist them with determining their positions. The most commonly used solar system objects are the Sun, Moon, Venus, and Mars. There is a small error caused by the fact that navigators are making their sextant measurements from the surface of the ocean and not from the center of the Earth, which is the reference point used by nautical almanacs. Parallax has no practical significance when measuring the positions of stars because they are so far away relative to the radius of the Earth. Continue reading

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Correcting Sextant Measurements For Dip

I love to read stories of the sea and about the voyages made during the age of sail. I personally have never thought that I would have an opportunity for ocean sailing, but I recently began working with an engineer who is an avid sailor and teacher of sailing. He has sailed all over the world and recently trained another engineer in my group to sail. This newly trained sailor just returned from a trip to Bora Bora, which he found to be enjoyable and the sailing uneventful. Continue reading

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Compensating GPS Clocks for the Effects of Relativity

I occasionally read articles on Stumbleupon and I came across an interesting article called "8 shocking things we learned from Stephen Hawking's book" – the book they are referring to is called "The Grand Design". I personally would not call the statements in the article shocking, but that is just my opinion. Continue reading

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Computing a Ship's Course from Four Bearings

I have made no secret of my love for all things nautical – even my game playing has a nautical theme. When I have spare time, I like to play Silent Hunter 3 or 4. While these are older versions of the Silent Hunter franchise, I still enjoy playing them very much. What brings me back to Silent Hunter is how easily I can vary the level of realism to suite my gaming needs. Continue reading

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Ship's Course Correction for Cross-Current Rule of Thumb

I have lived most of my life in Minnesota, which is about as far away from the oceans as you can be in the United States. The idea of a planet mainly covered with water has always fascinated me. I will never forget the first time I saw an ocean (Pacific, Santa Monica, CA 1982). Fortunately, my work has provided me a bit of experience on ships and that experience was career changing − my early ocean experience involved laying fiber optic cable and that set the course of the rest of my career. Continue reading

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