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Here or my some of my prior posts on the Bygrave.

gl

http://www.fer3.com/arc/m2.aspx?i=108423&y=200905

http://www.fer3.com/arc/m2.aspx?i=108411&y=200905


http://www.fer3.com/arc/m2.aspx?i=108490&y=200906

http://www.fer3.com/arc/m2.aspx?i=108424&y=200905




glapook@pacbell.net wrote:
> Very interesting.
>
> I have recently done a number of trial computations on my 10 inch
> rules using the Bygrave formulas instead of the sine-cosine formulas
> and it appears that I get better accuracy. Can you run a simulation
> similar to the one you did for Greg using the Bygrave method to
> confirm that this a preferable method if using a normal slide rule for
> celnav computations?
>
> Could you do the same with a Bygrave such as my flat implementation?
> On my flat Bygrave the Cosine scale from 0 to 89�16' covers 19 cycles
> each 126 mm long, a total length of 2.394 meters or about 94 inches
> and the cotan scale from 54' to 89�16' covers 37 cycles for a total
> length of 4.662 meters or about 183 inches. The original Bygrave is a
> bit larger but I am curious about the accuracy of the one I developed.
> I have found that the results fall within 2' and usually within 1' and
> often right on the money.
>
> gl
>
> On Jun 16, 3:35 pm, Paul Hirose  wrote:
>   
>> Greg Rudzinski wrote:
>>     
>>> Would it be possible to simulate for both 10" and 20" slide rules
>>> using the altitude sight reduction formula
>>>       
>>> ALT = Inverse SIN ( COS meridian angle x COS declination x COS
>>> latitude
>>>                     +/- SIN declination x SIN latitude)
>>>       
>> That's about the easiest problem you could have given. In a slide rule
>> simulation there's no need to simulate table lookup. And, since the
>> sight is worked from the DR position, I don't have to simulate plotting
>> a LOP from an assumed position. So I was able to knock this out in one
>> sitting.
>>
>> I consider the basic slide rule operation to be two settings followed by
>> one reading. These are assumed to be without error. However, right
>> before the reading is taken, I simulate giving the cursor or slide (as
>> the case may be) a tiny random nudge equivalent to .1% root mean square
>> error in multiplication.
>>
>> The magnitude of the nudge may be modified to suit the actual formula.
>> For instance, the triple cosine product requires three settings and one
>> reading. That's four operations vs. the nominal three. Error will
>> increase with the square root of the number of operations, so the nudge
>> is multiplied by the square root of 4/3.
>>
>> I assumed a 20 inch slide rule is equivalent to a 10 inch with the nudge
>> cut in half.
>>
>> Addition is assumed to occur without error.
>>
>> For each test run I used 500,000 randomly generated targets. Observer
>> latitude was in the range 0 - 70 degrees. Here are the root mean square
>> and worst case errors:
>>
>>             10 inch        20 inch
>>    alt     RMS  worst     RMS  worst
>>   0 - 30   1.9'  14'      1.0'   7'
>> 30 - 45   3.6'  20'      1.8'  10'
>> 45 - 75   8.1'  64'      4.0'  34'
>>
>>   0 - 75   4.7'  63'      2.4'  29'
>>
>> In all test runs, practically 95% of the solutions were accurate within
>> twice the RMS figure. The worst case results always occurred near the
>> upper altitude limit.
>>
>> --
>> 
>>     
> >
>
>   


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