# NavList:

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

**Re: slide rule sight reduction accuracy**

**From:**Paul Hirose

**Date:**2009 Jun 16, 15:35 -0700

Greg Rudzinski wrote: > Would it be possible to simulate for both 10" and 20" slide rules > using the altitude sight reduction formula > > ALT = Inverse SIN ( COS meridian angle x COS declination x COS > latitude > +/- SIN declination x SIN latitude) That's about the easiest problem you could have given. In a slide rule simulation there's no need to simulate table lookup. And, since the sight is worked from the DR position, I don't have to simulate plotting a LOP from an assumed position. So I was able to knock this out in one sitting. I consider the basic slide rule operation to be two settings followed by one reading. These are assumed to be without error. However, right before the reading is taken, I simulate giving the cursor or slide (as the case may be) a tiny random nudge equivalent to .1% root mean square error in multiplication. The magnitude of the nudge may be modified to suit the actual formula. For instance, the triple cosine product requires three settings and one reading. That's four operations vs. the nominal three. Error will increase with the square root of the number of operations, so the nudge is multiplied by the square root of 4/3. I assumed a 20 inch slide rule is equivalent to a 10 inch with the nudge cut in half. Addition is assumed to occur without error. For each test run I used 500,000 randomly generated targets. Observer latitude was in the range 0 - 70 degrees. Here are the root mean square and worst case errors: 10 inch 20 inch alt RMS worst RMS worst 0 - 30 1.9' 14' 1.0' 7' 30 - 45 3.6' 20' 1.8' 10' 45 - 75 8.1' 64' 4.0' 34' 0 - 75 4.7' 63' 2.4' 29' In all test runs, practically 95% of the solutions were accurate within twice the RMS figure. The worst case results always occurred near the upper altitude limit. -- I filter out messages with attachments or HTML. --~--~---------~--~----~------------~-------~--~----~ Navigation List archive: www.fer3.com/arc To post, email NavList@fer3.com To unsubscribe, email NavList-unsubscribe@fer3.com -~----------~----~----~----~------~----~------~--~---