# NavList:

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

**Re: Longhand Sight Reduction**

**From:**Hanno Ix

**Date:**2014 Jun 11, 08:52 -0700

Given the choice

*Danioli vs Bygrave*: What would Chichester have chosen?

It indeed works and is fast. Comparison with the standard formula is attached below.

Greg seems to think one can do that single multiplication with a 10" slide rule.

I am skeptic. In praxis, ten inchers do not yield correct 4 digits consistently,

and that's what I need for accuracy over the useful ranges of L,D,t.

*vwxy = ABCD * abcd;*

*v, w, x, y*being correct digits.

to survive a 1-week sailing trip in the Virgin Islands. ( Where and when can I sign up? )

for the full useful ranges of L,D,t. I am unsure, though, what "useful" means for our CelNav friends.

_____________________________________________________________________________________

*:*

**sin(h) = n - ( n + m ) * a ;***n: cos(L-D); m: cos(L+D); a: [1 - cos(t) ] / 2 or hav(t);*

Let's see. By inserting:

* sin(h) = cos(L-D) - [ cos(L-D) + cos(L+D) ] * [ 1 - cos(t) ] / 2;*

which is in more detail:

* sin(h)*

*=**cos(L-D) - cos(L-D) * [ 1 - cos(t) ] / 2 - cos(L+D) * [1 - cos(t) ] / 2;*and more detail yet:

* ** sin(h)*

*= cos(L-D) - cos(L-D) / 2 + cos(L-D)*cos(t) / 2 - cos(L+D) / 2 + cos(L+D)*cos(t) / 2;*Collecting:*
*

* ** sin(h) = cos(L-D)/2 - cos(L+D) / 2 + [ cos(L-D) / 2 + cos(L+D) / 2 ] * cos(t);*

** = sin(L) * sin(D) + cos(L) * cos(D) * cos(t);**

Oh dear. Is it time to put my beloved Bygrave away? Cant wait to here more details of the Bygrave maths.Chichester said he preferred the Bygrave when flying single handed, because he made mistakes with log tables. (Perhaps he did not have Haversines?) But, could someone explain the main difference/advantages/disadvantages of the

versine method(Vers ZD=Vers LHAxCos Latx Cos Dec+Vers(Lat+/-Dec) and theHaversinemethod? My versine method (Reeds Astro Nav Tables) uses tables of natural and log versines and log cos (total 11 pages).Does not need sines.

Versine methodlog vers LHA 9.9019

log cos Lat 9.9177

log cos Dec 9.9642

add 29.7838

Nat Vers of 9.7838= 0.6081

Lat-Dec=11°13' Nat vers=0.0191. Add= 0.6272=68°6'. =ZD. 90°-68°6'= 21°54'

Not a lot in it I would say? quicker for me than reduction tables and I understand what we are doing.

Please correct me and explain the advantages of the Haversine over the versine. (I do not have haversines but do have versines! Where do I get haversines?)

Bygrave. H=360°-LHA=78°21', co-lat=55°50', y(w)=64°31', X=colat+y(w)=120°21', Y=180°-X=59°39', >Az =76°24'>Hc 21^{0}54'No contest! Took a fraction of the time and no mistakes from looking up 4 figure logs etc.

And I've got Az(OK done hundreds of Bygrave LOPs and only a couple of Versines!)I'll stick to my Bygrave!