# NavList:

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

**Re: Longhand Sight Reduction**

**From:**UNK

**Date:**2014 Jun 12, 05:31 +0100

Hanno,

Re smaller Fullers. My current mini Fuller2 prototype is roughly same size as a Bygrave and folds up to about 13 inches long. Cant get it any smaller, already need magnifiers to clearly read condensed scales and smaller diameter tubes would lose accuracy due to reduced scale length.. However, because the design is Otis King style, it has 2 copies of main scale and a “handle” which extends the length accordingly. You could just build an exact copy of Fuller 2 at this diameter size, with only 1 main scale and the log(or maybe a cos scale instead?) and sine scale + the 2 brass cursers. This would be shorter, but have the disadvantage of the old Fuller re brass cursers on the high seas and anyway, see my previous reports on the moves. The Otis King style requires less moves with multiplication and division and you can do both direct from the sine scales easily. My next “improvement” will hopefully be a new sine scale with cosines in red going the other way. (If not too cluttered). At the moment, I have to convert all cos to sines first. Anyways, I may have a go at a “short mini Fuller 2” ie original design. That may be in a few months time.

I don’t know if you have read John Letcher’s book? He says he could do his lunar calc with a ordinary trig slide rule. Never tried it, but can anyone explain it if true? Hewitt Schlereth, in his book talks about using an 8 inch circular rule for his calcs.

Currently, the only slide rule that I know that fits your bill is my mini Fuller 2.

I shall watch this space with interest. I’m basically shore bound and beached this summer, so no sailing but therefore plenty of arm chair navigation!

Best wishes all

Francis

**From:** NavList@fer3.com [mailto:NavList@fer3.com] **On Behalf Of **Francis Upchurch**Sent:** 11 June 2014 20:16**To:** francisupchurch---.com**Subject:** [NavList] Re: Longhand Sight Reduction

Thanks Hanno.

Good challenge. Hospital next week. Out of action maybe 4 weeks, then ok for go. !

My slide rules cost about $5 a piece so far, but plenty of work!

Can be done.

Keep up the interesting work. My money is on Bygrave, but I’m biased!

Francis

**From:** NavList@fer3.com [mailto:NavList@fer3.com] **On Behalf Of **Hanno Ix**Sent:** 11 June 2014 17:01**To:** francisupchurch---.com**Subject:** [NavList] Re: Longhand Sight Reduction

Francis,

Given the choice *Danioli vs Bygrave*: What would Chichester have chosen?

Assuming, of course, he had access to and enough experience with both.

I celebrated Greg's RIC / Danioli yesterday by playing around with it.

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.

Now, there might be a challenge especially for you: a Fuller < = 10" that can

- do 4 digit multiplication, i.e. yields *vwxy = ABCD * abcd; v, w, x, y *being correct digits.

- can be built with standard and garage tools plus a PC and printer.

- in not more than, say, a week.

- for about $50 or less, $100 max.

It need not look like an exhibit in a museum, although it should be sturdy enough

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

Re: formulas. One example, with good or flawed results, is not really sufficient to

judge a formula or method. You need to show it yields accurate 4 digit results consistently

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

Any ideas out there?

I am studying the Bygrave in this respect right now. Stand by please.

Hanno

_____________________________________________________________________________________

For the record, Danioli claims*: *

**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);*

which is correct.

On Tue, Jun 10, 2014 at 11:11 PM, Francis Upchurch <NoReply_Upchurch@fer3.com> wrote:

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 the **Haversine** method? 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 method**

log 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°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!