# NavList:

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

**Meridional parts**

**From:**Pete Harmsworth

**Date:**1996 May 02, 12:18 -0600

I am attempting to set up an Excel spreadsheet in order to input Origin & Destination lat & long and output and output rhumb line course and distance. This involes calculating meridional parts. Page 552 of Bowditch (1995) gives the formula as M=7915.704468 log tan b (45+L/2)- 23.0133633 sinL-0.051353 sin^3L-0.000206 sin^5L... L is the latitude but I can find no mention of b in the text. Does anyone know if this is a typo (I wouldn't want to white it out in my book if it wasn't). Has anyone coded it into a spreadsheet. I left the b out but the result wasn't even close to the value in Table 6. Thanks for any input on this. Pete Harmsworth pharms{at}awinc.com ------------------------------------------------------------------------ This mail list is managed by the majordomo program. To unsubscribe from this list, send the following message to majordomo{at}ronin.com: unsubscribe navigation For help, send the following message to majordomo{at}ronin.com: help Do NOT send administrative requests to navigation{at}ronin.com. Thanks. -ben ------------------------------------------------------------------------ From mail Tue May 7 17:48 EDT 1996 Received: from dg-rtp by wellspring.us.dg.com (5.4R3.10/dg-gens08) id AA05975; Tue, 7 May 1996 17:48:26 -0400 Received: from gomoku.ronin.com by dg-rtp.dg.com (5.4R3.10/dg-rtp-v02) id AA18459; Tue, 7 May 1996 17:48:21 -0400 Received: (from majordom{at}localhost) by ronin.com (8.6.9/8.6.9) id RAA10004 for navigation-outgoing; Tue, 7 May 1996 17:29:51 -0400 Received: from mailout00.btx.dtag.de (mailout00.btx.dtag.de [194.25.2.148]) by ronin.com (8.6.9/8.6.9) with SMTP id RAA09990 for; Tue, 7 May 1996 17:29:23 -0400 Received: from mailto00.btx.dtag.de ([172.16.2.1]) by mailout00.btx.dtag.de with smtp (S3.1.29.1) id ; Tue, 7 May 96 22:32 MET DST Received: from funnel04.btx.dtag.de (0234263524-0001(btxid){at}[194.25.2.5]) by mailto00.btx.dtag.de with smtp (S3.1.29.1) id ; Tue, 7 May 96 22:32 MET DST To: navigation{at}ronin.com Subject: RE meridional parts formula Date: Tue, 07 May 1996 20:32:01 GMT Message-Id: <318fb337.7477050{at}mailto.btx.dtag.de> X-Mailer: Forte Agent .99d/16.182 X-Sender: 0234263524-0001{at}t-online.de (Hans Thomas Feuerhelm) From: HT.Feuerhelm{at}t-online.de (Hans Thomas Feuerhelm) Sender: owner-navigation{at}ronin.com Precedence: bulk Reply-To: HT.Feuerhelm{at}t-online.de (Hans Thomas Feuerhelm) Errors-To: owner-majordomo{at}ronin.com Content-Type: text Content-Length: 2089 Hi, Following the discussion about meridional parts, I have some remarks and questions : 1. The formula comes from integration of dS = (Earth radius) / cos(latitude) between the limits equator and current latitude. 2. After Integration, the formula is then S = R(Earth) * ln ( tan ( 45d + lat/2) ), assuming the Earth to be a SPHERE. 3. What Radius to use : We learned : make it 360d * 60' / (2 * pi) nautical miles, giving R(Earth) = 3437.74677.... 4. when using log instead of ln, one has to multiply with log (e), yielding the "magic number" 7915.71315.... When oher numbers do appear, I think the author uses some other definition of Earth radius... 5. Compensating for the ellispoidal form of the earth could be done in two ways (hi ho, guessing...) a) incorporate a latitude-dependant factor into the number for the earth radius or b) subtracting some latitude-dependant number, which will have to increase when going to the poles. This seems to be what the sine - power-series of subtractions is about. However, I do feel uncomfortable when having to apply corrections to formulae without knowing the assumptions behind. These corrections seem to have something to do with the different "Chart Datums", another big secret to all navigational textbooks i've seen so far. Does anyone have a hint, idea or link about how to find more about this ? Many Thanks in advance !! Until then, I will continue assuming the earth to be a sphere, use "ln" and 3437,74677 and forget about all these sinuses .. :-)) Best regards, and - Don't sink the ship... Tom ------------------------------------------------------------------------ This mail list is managed by the majordomo program. To unsubscribe from this list, send the following message to majordomo{at}ronin.com: unsubscribe navigation For help, send the following message to majordomo{at}ronin.com: help Do NOT send administrative requests to navigation{at}ronin.com. Thanks. -ben ------------------------------------------------------------------------ From mail Fri May 10 18:16 EDT 1996 Received: from dg-rtp by wellspring.us.dg.com (5.4R3.10/dg-gens08) id AA29827; Fri, 10 May 1996 18:16:42 -0400 Received: from gomoku.ronin.com by dg-rtp.dg.com (5.4R3.10/dg-rtp-v02) id AA11707; Fri, 10 May 1996 18:16:36 -0400 Received: (from majordom{at}localhost) by ronin.com (8.6.9/8.6.9) id SAA07316 for navigation-outgoing; Fri, 10 May 1996 18:03:45 -0400 Received: from mail.euronet.nl (mail.euronet.nl [194.134.0.67]) by ronin.com (8.6.9/8.6.9) with ESMTP id SAA07311 for ; Fri, 10 May 1996 18:03:41 -0400 Received: from p503.asd.euronet.nl (p503.asd.euronet.nl [194.134.1.164]) by mail.euronet.nl (8.7.5/8.7.3) with SMTP id AAA01042 for ; Sat, 11 May 1996 00:10:20 +0200 (MET DST) Date: Sat, 11 May 1996 00:10:20 +0200 (MET DST) Message-Id: <199605102210.AAA01042{at}mail.euronet.nl> X-Sender: puffelej{at}mail.euronet.nl X-Mailer: Windows Eudora Version 1.4.4 Mime-Version: 1.0 To: navigation{at}ronin.com From: puffelej{at}euronet.nl (Jan van Puffelen) Subject: Re: RE meridional parts formula Sender: owner-navigation{at}ronin.com Precedence: bulk Reply-To: puffelej{at}euronet.nl (Jan van Puffelen) Errors-To: owner-majordomo{at}ronin.com Content-Type: text/plain; charset="us-ascii" Content-Length: 1691 Status: RO Hans Thomas Feuerhelm wrote: >Hi, > >Following the discussion about meridional parts, I have some >remarks and questions : > >1. The formula comes from integration of dS = (Earth radius) > / cos(latitude) between the limits equator and current > latitude. > >2. After Integration, the formula is then > S = R(Earth) * ln ( tan ( 45d + lat/2) ), > assuming the Earth to be a SPHERE. > Rather than using the formula LN(TAN(45+lat/2)) the formula LN(TAN lat +1/COS lat) may be used as well. This saved a few memory positions in my CASIO FX 702P (BASIC) programmable calculator. I have never known that this method was called the Meridional Parts method. Can someone explain the origin of that name? It is called "Vergrotende Breedte" (lit. magnifying latitude) in Dutch while while the simple method is called Middenbreedte or Middel Breedte method (lit. mid or average latitude). There is a formula which compensates for the ellipsoidal form of the earth. It has a few more terms. I must have it somewhere (probably in the attic). I have tested that formula a long time ago and concluded that for all practical puposes the simpler formula for the perfect sphere is just as good. Regards, puffelej{at}euronet.nl (Jan van Puffelen) ------------------------------------------------------------------------ This mail list is managed by the majordomo program. To unsubscribe from this list, send the following message to majordomo{at}ronin.com: unsubscribe navigation For help, send the following message to majordomo{at}ronin.com: help Do NOT send administrative requests to navigation{at}ronin.com. Thanks. -ben ------------------------------------------------------------------------ From mail Sat May 11 11:50 EDT 1996 Received: from dg-rtp by wellspring.us.dg.com (5.4R3.10/dg-gens08) id AA26228; Sat, 11 May 1996 11:50:12 -0400 Received: from gomoku.ronin.com by dg-rtp.dg.com (5.4R3.10/dg-rtp-v02) id AA18401; Sat, 11 May 1996 11:50:07 -0400 Received: (from majordom{at}localhost) by ronin.com (8.6.9/8.6.9) id LAA26141 for navigation-outgoing; Sat, 11 May 1996 11:37:01 -0400 Received: from mailout01.btx.dtag.de (mailout01.btx.dtag.de [194.25.2.149]) by ronin.com (8.6.9/8.6.9) with SMTP id LAA26105 for ; Sat, 11 May 1996 11:34:51 -0400 Received: from mailto00.btx.dtag.de ([172.16.2.1]) by mailout01.btx.dtag.de with smtp (S3.1.29.1) id ; Sat, 11 May 96 17:37 MET DST Received: from funnel19.btx.dtag.de (0234263524-0001(btxid){at}[194.25.2.20]) by mailto00.btx.dtag.de with smtp (S3.1.29.1) id ; Sat, 11 May 96 17:36 MET DST To: navigation{at}ronin.com Subject: RE: meridional parts again + Datum Date: Sat, 11 May 1996 15:37:10 GMT Message-Id: <3194b420.62945203{at}mailto.btx.dtag.de> X-Mailer: Forte Agent .99d/16.182 X-Sender: 0234263524-0001{at}t-online.de (Hans Thomas Feuerhelm) From: HT.Feuerhelm{at}t-online.de (Hans Thomas Feuerhelm) Sender: owner-navigation{at}ronin.com Precedence: bulk Reply-To: HT.Feuerhelm{at}t-online.de (Hans Thomas Feuerhelm) Errors-To: owner-majordomo{at}ronin.com Content-Type: text Content-Length: 3888 Status: RO Hi Crew, Meridional parts (MP) are still bothering us over here... This is what I've collected so far : 1) Here in Old Germany, all the books say that MP's are ok for practical navigation assumming the Earth being a sphere (e.g. M?ller Krauss, the "bible" for merchant navy education, and also Fulst, Nautical Tables). M?ller Krauss mentions that correcting for the ellipsoid is done in chart making, but doesnt bother to tell the dumb guys how this is done... So, to stay friends with my european sailing buddies, I'd have to stick to the following : - Earth is a shpere -1 nm = 1852,000. m, - the equator has 360 * 60 = 21600 nm - Earth radius from this is 21600 / (2pi) = 3437,74677078 nm giving the equivalent formulae : (USING NATURAL LOGARITHMS) MP(LAT) = 3437,74677 * ln ( tan ( 45 + LAT/2) ) or, many thanks to Jan van Puffelen (!!): MP(LAT) = 3437,74677 * ln ( tan (LAT) -1/cos(LAT) ) ( USING LOG to Base 10 ) MP(LAT) = 7915,70447 * LOG ( tan ( 45 + LAT/2) ) MP(LAT) = 7915,70447 * LOG ( tan(LAT) - 1/cos(LAT) ) I checked Jan's Formula (using the cos..) and it gave exactly the same results, except for LATs above 85d, but who'd want to go there, anyway. It looks like tan (45 + x/2) is the same as tan(x) -1/cos(x). Seems worthwhile to refresh all that trig stuff from high school.... 2.) Assuming Earth an ellispoid, as many Silicon sea navigators do (and honestly, nothing wrong with that!!) gives need for correction with the sine power series from the postings. Checking this, it looks sufficient to me to just use the first term, as DAN already said. Redoing the last DR from Silicon Sea leg 12, I have : 111,3 d / 1167,8 nm ( MP "elliptical") 111,4 d / 1164,5 nm ( MP "sphere" ) 111,4 d / 1163,3 nm ("mid Latitude") At first sight, MP "sphere" is closer to "mid Latitude", which until now, I've always used as a parallel check. Second thought : "mid-Latitude" also assumes a sphere and not an ellipsoid (sigh !) This is a hard life for beginning navigators !!! So what do I do, stick with my old german buddies, ignore the ellipoid and make a bad impression on the "elliptical" people, or become "ellipsoidal", resulting to fail german exams on navigation ? BTW : the "sphere" .model is 3,3 nm "faster", an equivalent of 25 minutes at 7,8 knots, but what's 25 minutes on a leg of 6,5 days with all possible surprises to come..... 3. Referencing the ellipsoid Reading about the different ellipsoids (there's 20 I've collected so far), the books say that apart from using the equator and polar radius, one has to define a well established reference ("DATUM"), so that the ellipsoidal grid of LATs + LONs is adjusted to a certain wellknown point. The ones I've found : Potsdamer Datum : uses Bessel ellipsoid and references to "Helmert Turm" 52d 22'' 53,954'' N, 013d 04' 01,153'' E European Datum : uses "international Hayford" and references to "Helmert Turm" 52d 22' 51,45'' N, 013d 03' 58,74'' E (now used for German Maps of Europe) What "Datums" are used in the US ? This would mean, that you'd have different LATs and LONs even when reading exactly the same object from different chart designs. Well, I do hate to think about these consequences. What about all these waypoint tabulations ? GPS ? (ha,ha), the integrated navigation programs ? Almost being as lost as Odysseus, I'll go for some sherry.. bye for now, TOM ------------------------------------------------------------------------ This mail list is managed by the majordomo program. To unsubscribe from this list, send the following message to majordomo{at}ronin.com: unsubscribe navigation For help, send the following message to majordomo{at}ronin.com: help Do NOT send administrative requests to navigation{at}ronin.com. Thanks. -ben ------------------------------------------------------------------------