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    Re: Sight reduction formulae
    From: Gary LaPook
    Date: 2011 Dec 1, 15:34 -0800
    If you want to give the Bygrave method a try here is a step by step description of the calculator keys to press. I am also attaching the form to use with the formulas. To read more about this method go here:
    https://sites.google.com/site/fredienoonan/other-flight-navigation-information/modern-bygrave-slide-rule

    ---------------------------------------------------

    CHECKING YOUR COMPUTATIONS

    An easy way to check the computation on a Bygrave is to do the same computation on a calculator since this allows you to check the intermediate steps.

    Just use the standard Bygrave formulas in the three step process following along on the form I have posted.

    First calculate co-latitude and save it in a memory in the calculator. If you are using a value for hour angle that is not a whole number of degrees you might want to make the conversion to decimal degrees and save it in a memory since it will we used twice. If you are using whole degrees then this step is not necessary.

    Then you calculate "W" using the formula:

    tan W = tan D / cos H

    and sum it to the memory where you have saved co-latitude which is then X and then make any adjustment necessary to convert X to Y. (If you are just making trials you can avoid this step by your choice of the trial values.) There is no reason to store W itself since it is not used again. You can then convert W to degree and minute format to compare with the Bygrave derived value.


    Then you compute azimuth angle using the formula:

    tan Az = (cos W / cos Y ) x tan H.

    If you want you can also convert Az to degree and minute format to compare with the Bygrave.

    The last step is to calculate altitude with the formula:

    tan Hc = cos Az x tan Y.

    Then convert to degree and minute format to compare with the Bygrave result.



    (When entering values in the format of degrees minutes seconds, change decimal minutes to seconds, 6 seconds per tenth of a minute, in your head  before punching in the assumed latitude, declination  and hour angle if necessary.)

    Using whole degrees for declination, assumed latitude and hour angle, using a TI-30 with only 3 memory locations the key strokes are:

    ---------------------------------------------------------------------

                 (co-latitude = 90 - Assimed latitude)

    90
    -
    Assumed Lat
    =
    STO 1  (co-latitude stored in memory 1)

    ---------------------------------------
                   
                  
    (tan W = tan D / cos H)


    Declination  

    tan
    /
    H
    cos
    =   
    inv
    tan    (computed W)
    SUM 1  (X now stored in memory 1)(change X to Y if necessary)

    --------------------------------------


          
    (tan Az = (cos W / cos Y ) x tan H)

    cos    (of W from prior step)  

    /
    RCL 1  (recalls Y from memory 1)
    cos
    x
    H
    tan
    =
    inv
    tan (computed Azimuth angle)



    ------------------------------------

          
    (tan Hc = cos Az x tan Y)


    cos    (of Az from prior step)  

    x
    RCL 1  (recalls Y from memory 1)
    tan
    =
    inv
    tan  (computed altitude, Hc)


    2nd
    D.D - DMS (changes Hc in decimal degrees to degrees, minutes and seconds)



    DONE

    gl



    ----------------------------------------------------------------------

    --- On Thu, 12/1/11, Alan <alan202@verizon.net> wrote:

    From: Alan <alan202@verizon.net>
    Subject: [NavList] Re: Sight reduction formulae
    To: NavList@fer3.com
    Date: Thursday, December 1, 2011, 2:01 PM

    Randy:

    One more point:

    Dec comes from the Nautial Almanac, which spedcifies Dec as being either North or South. With Lat being North, is Dec is "same name" go straight ahead. If Lat is North and Dec is South, you need to use the change sign button on your calculator, however it is described. On my old HP 11C, the appropriate button is identified as CHS.

    Good luck.

    Alan
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