# 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:**Gary LaPook

**Date:**2009 Jun 16, 16:32 -0700

Very interesting. I have recently done a number of trial computations on my 10 inch rules using the Bygrave formulas instead of the sine-cosine formulas and it appears that I get better accuracy. Can you run a simulation similar to the one you did for Greg using the Bygrave method to confirm that this a preferable method if using a normal slide rule for celnav computations? Could you do the same with a Bygrave such as my flat implementation? On my flat Bygrave the Cosine scale from 0 to 89�16' covers 19 cycles each 126 mm long, a total length of 2.394 meters or about 94 inches and the cotan scale from 54' to 89�16' covers 37 cycles for a total length of 4.662 meters or about 183 inches. The original Bygrave is a bit larger but I am curious about the accuracy of the one I developed. I have found that the results fall within 2' and usually within 1' and often right on the money. gl On Jun 16, 3:35�pm, Paul Hirosewrote: > 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 -~----------~----~----~----~------~----~------~--~---