NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: Hav-Doniol
From: Hanno Ix
Date: 2015 Jun 14, 11:11 -0700
First, I do indeed prefer the standard algebraic sign rules.
I can give you a string of arguments why those rules are de rigeur
when you do algebraic work frequently. One of them is the unambiguous
From: Hanno Ix
Date: 2015 Jun 14, 11:11 -0700
Hi,
Re: using the hav - Doniol in CelNav
First, I do indeed prefer the standard algebraic sign rules.
communication of formulas throughout and their implementation on computers.
For people who do not frequently do any algebra, e.g. hobby sailors,
For people who do not frequently do any algebra, e.g. hobby sailors,
the, let me say, Gary-rules are easier to comprehend and to use. This, however,
may lead to misunderstandings / errors when sin, cos, tan etc appear in a formula
which can be positive or negative, and one does not recall their sign rules as a matter of course.
Also, I think, there is no standard calculator that uses any but.
And this is one GREAT advantage of the haversine(x) and the hav - Doniol:
haversine(x) is always a positive number, no matter the sign, the size, or the
range ( -180...+180 vs. 0...360) of the angle x.
haversine(x) is always a positive number, no matter the sign, the size, or the
range ( -180...+180 vs. 0...360) of the angle x.
So, A - haversine(x) will always call for a numerical subtraction like A - 5.
However A - sin(x), A - cos(x), A - tan(x) may end numerically up as a subtraction
or an addition! You can see how the haversine avoids possible confusion for both, the hobby number
cruncher and the strict mathematician.
or an addition! You can see how the haversine avoids possible confusion for both, the hobby number
cruncher and the strict mathematician.
Secondly, throw in any logarithms, and the sign rules will become a real challenge.
As I noted before, famous classical books about CelNav have plenty of such errors which
were, astonishingly, repeated throughout several editions!
Logarithms are the classical way to execute multi - digit multiplications. I think we
agree now that 4 - digit numerical operations are sufficiently accurate for standard CelNav.
In contrast, I never saw such agreement or a similar one in the old Navy books. 4 - digit
multiplication, particularly when only the leading 4 digits of the product are needed, are
quite manageable without logarithms, their tables, rules and errors. This is probably so
even for the casual reckoner.
And the hav - Doniol requires just a single one!
So, please enjoy it.
H
On Sat, Jun 13, 2015 at 5:56 AM, Stan K <NoReply_StanK@fer3.com> wrote:
Last night I sent a message to Greg Rudzinski describing a really silly, even obvious, mistake I was making in using the Greg/Hanno hav-Doniol sight reduction method. This got me thinking (something I apparently should do more often), so I went through the fer3 archive looking at all the posts regarding longhand sight reduction. This is what came out of it:
Greg presents two sets of formulas:n = hv(L - d) m = hv(L + d) same namen = hv(L + d) m = hv(L - d) contrary namewhere L (latitude) and d (declination) are unsigned (absolute) values, i.e. 40ºN and 40ºS would both be represented as 40º.
Hanno appears to prefer a single set of formula, equivalent to the "same name" formulas above (though he uses one different letter), where L and d are signed, i.e. 40ºS would be represented as -40º.
These are different approaches but are functionally equivalent. What I would like to know is if anyone has a strong feeling as to whether either of these approaches would be better than the other one in a classroom environment, that is, whether students would have an easier time understanding, and instructors would have an easier time teaching, one compared to the other.
Stan
