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Re: Sight reduction formulae
From: Gary LaPook
Date: 2011 Dec 1, 15:34 -0800
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:
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