NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: Logarithms by Hand
From: Hanno Ix
Date: 2014 Jun 4, 12:08 -0700
Actually, CORDIAC is not a bad bet.
You might do something like this - written in an impromptu version of Pseudo Basic:
x=0;
y=1;
The error is less than 10^-4 which is sufficiently small for
CelNav sight reduction using trig functions - not log-trig functions.
From: Hanno Ix
Date: 2014 Jun 4, 12:08 -0700
Hello,
Peter and Noell
Re: calculating sin() and cos() from scratch.Peter and Noell
y=1;
L=157; * equal to approximately pi/4*100
for i = 1 to L
dx = 0.01*y; * no calculation - just shift y two digits to the right ...
x = x - dx; * and subtract from x
x = x - dx; * and subtract from x
X(i) = x;
dy = 0.01*x; * analogous to above
y = y + dy;
Y(i) = Y;
end
In "only" 157 steps you get sin() in -Y and cos() in X with the period 100*pi.
That means the angles 0:90 deg are mapped into 0:25*pi.
That means the angles 0:90 deg are mapped into 0:25*pi.
The error is less than 10^-4 which is sufficiently small for
CelNav sight reduction using trig functions - not log-trig functions.
Of course, you have also to transform the range 0:25 *pi of the angles
into 0:90 deg or the other way around to match the sextant scale.
This complexity is the prize for simplifying division by shifting.
A subtle issue: the angles for sin() are located between the angles of cos().
A subtle issue: the angles for sin() are located between the angles of cos().
The process is actually very simple and easy to commit to memory.
In particular, you don't have to memorize any constants or parameters.
It would be certainly a laborious but not a hopeless task.
In particular, you don't have to memorize any constants or parameters.
It would be certainly a laborious but not a hopeless task.
I attach two graphs done in MATLAB. They are self - explanatory I think.
H
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PS:
Noell, I thought you did a very nice job in describing how to
Noell, I thought you did a very nice job in describing how to
establish a log() table.
You realize the sight reduction by hand I recently described aims at
NOT using log(), though.
On Wed, Jun 4, 2014 at 5:56 AM, Noell Wilson <NoReply_Wilson@fer3.com> wrote:
Hi Peter,
No tables of any kind?! Wow! That would probably eliminate some of the index card cheat sheets also.If possible, I'd invoke the strict reading of "no tables" and pull out my trusty slide rule.
If that's not legal, I'd probably run down a latitude line and approach the shore carefully.
I'd probably make land before I could derive the formulas.
Regards, Noell
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