# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

**Re: Magnetic Variation (Declination) Calculator**

**From:**Lu Abel

**Date:**2009 Aug 04, 15:33 -0700

Greg, thanks for the comment. I was going to point out to Brad that
there are two commonplace problems experienced with formulas, at least
one of which probably lies at the heart of the problem with the
declination web site:

1. Some fairly common formulas, especially trigonometric ones, often have "singularity points" where the answer blows up or becomes undefined. I suspect this is the case with the declination web site; the calculations have likely been programmed to return "undefined" as an answer for latitudes sufficiently close to 90 degrees which is then displayed as zero.

As another example, try calculating the initial course for a great circle between two antipodal points (ones opposite each other on the globe) -- any course is a great circle!

2. Even when the mathematical formula doesn't blow up, they always are for calculations of infinite precision. Computers and calculators don't have an infinite number of digits and strange things can happen as a result. For example, the most common formula for great-circle distance requires the subtraction of two numbers. These numbers become nearly equal as the two points approach each other. Most calculators and computers produce gibberish answers when asked, for example, for the great circle distance between two points 100 feet apart. That's why all GPS units use an alternate formula involving haversines to compute great circle distance; the numbers stay tractable down to zero distance.

Lu Abel

Greg Rudzinski wrote:

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1. Some fairly common formulas, especially trigonometric ones, often have "singularity points" where the answer blows up or becomes undefined. I suspect this is the case with the declination web site; the calculations have likely been programmed to return "undefined" as an answer for latitudes sufficiently close to 90 degrees which is then displayed as zero.

As another example, try calculating the initial course for a great circle between two antipodal points (ones opposite each other on the globe) -- any course is a great circle!

2. Even when the mathematical formula doesn't blow up, they always are for calculations of infinite precision. Computers and calculators don't have an infinite number of digits and strange things can happen as a result. For example, the most common formula for great-circle distance requires the subtraction of two numbers. These numbers become nearly equal as the two points approach each other. Most calculators and computers produce gibberish answers when asked, for example, for the great circle distance between two points 100 feet apart. That's why all GPS units use an alternate formula involving haversines to compute great circle distance; the numbers stay tractable down to zero distance.

Lu Abel

Greg Rudzinski wrote:

Brad, Manoj C. Nair of NOAA University of Colorado responded to my email reguarding the zero result for 90° of latitude and said that the current program recognizes latitudes above 89.999 as undefined. The zero result must be a default number. I noticed another program glitch where 13° West declination was displayed as 167° East. Greg On Aug 4, 10:20 am, Brad Morris <bmor...{at}tactronics.com> wrote:Hi Greg I just entered the pole for a gee-wiz kind of exercise. To my surprise, it returned zero, so I tried a location close to the pole. That returned non-zero, indicating that the software has some sort of bug. Since I have no way to verify any other result it may present to me, I will distrust the data. How many other lat long locations give 'bad' data? How would I know? Should NOAA fix this? Certainly. How silly of them to permit an entry which provides erroneous results. Do navigators depend exclusively on a compass within 366 feet of the north pole? I sure hope not... Best Regards Brad -----Original Message----- From: NavList@fer3.com [mailto:NavList@fer3.com] On Behalf Of Greg Rudzinski Sent: Tuesday, August 04, 2009 1:03 PM To: NavList Subject: [NavList 9329] Re: Magnetic Variation (Declination) Calculator Brad, It looks like values above 89.998996° of latitude are all zero instead of 14° 24'W. Does NOAA need to correct this since it is only 366 ft from the pole? Greg "Confidentiality and Privilege Notice The information transmitted by this electronic mail (and any attachments) is being sent by or on behalf of Tactronics; it is intended for the exclusive use of the addressee named above and may constitute information that is privileged or confidential or otherwise legally exempt from disclosure. If you are not the addressee or an employee or agent responsible for delivering this message to same, you are not authorized to retain, read, copy or disseminate this electronic mail (or any attachments) or any part thereof. If you have received this electronic mail (and any attachments) in error, please call us immediately and send written confirmation that same has been deleted from your system. Thank you."

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