Category Archives: Naval History

Index/Instrument Error Correction in Sextant Measurements

Posted on 31-October-2015 by mathscinotes

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 →

Posted in Naval History, Navigation | 2 Comments

Refraction Error Correction in Sextant Measurements

Posted on 27-October-2015 by mathscinotes

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 →

Posted in Astronomy, Naval History, Navigation | 3 Comments

Correcting for Sextant Parallax Error

Posted on 24-October-2015 by mathscinotes

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 →

Posted in Astronomy, Naval History, Navigation | 1 Comment

Correcting Sextant Measurements For Dip

Posted on 21-October-2015 by mathscinotes

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 →

Posted in Naval History, Navigation | 8 Comments

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

Posted on 22-January-2015 by mathscinotes

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 →

Posted in Naval History, Navigation | Comments Off on Ship's Course Correction for Cross-Current Rule of Thumb

Sub Missile Launch Physical Model

Posted on 5-December-2014 by mathscinotes

I like it when instructors use physical models to illustrate how things work. I was watching this video on submarine design when I saw a physical model used to illustrate how a submarine launches a missile. The demonstration is excellent. … Continue reading →

Posted in Naval History | Comments Off on Sub Missile Launch Physical Model

Submarine Fuel Math

Posted on 26-November-2014 by mathscinotes

Introduction I just read an interesting article about an arctic environmental problem being presented by a Soviet-era nuclear submarine that had been scuttled back in 1982 (Figure 1). Apparently, scientists are now concerned that the submarine's reactor could leak dangerous … Continue reading →

Posted in General Science, Military History, Naval History | 3 Comments

World War 2 Submarine Hull Thickness Math

Posted on 12-December-2013 by mathscinotes

Quote of the Day How are the children? — Masai warrior greeting, intended to ensure that the warriors always keep their number one priority in mind. I was reading a blog post on Gizmodo that did a bit of math … Continue reading →

Posted in Military History, Naval History | 2 Comments

A Problem Solved in Excel and Mathcad

Posted on 30-November-2013 by mathscinotes

I use both Excel and Mathcad in my daily work. Most people would consider me very proficient in both. I frequently get asked, "Which tool is better?" Like all other interesting questions in Engineering, the answer is "it depends".

As an example, I decided to work a simple problem in both Excel and Mathcad. A number of the advantages and disadvantages of both tools can be seen in this example. The key problem with Excel is its cell-oriented approach. While the cell-oriented approach works for small problems, it has major issue with large problem Continue reading →

Posted in Ballistics, History of Science and Technology, Military History, Naval History | 2 Comments

Image of a Submarine At Periscope Depth

Posted on 28-September-2013 by mathscinotes

If you have ever wondered what a submarine looks like at periscope depth, here is a photo of the USS Key West (SSN-722). Source is the Wikipedia.

Posted in Naval History, Personal | Comments Off on Image of a Submarine At Periscope Depth