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    Re: Azimith forumula for Great Circle sailings- having problems
    From: Gary LaPook
    Date: 2014 Dec 24, 00:51 -0800
    I was trying to make the point that you can't just take numbers down from a GPS without thinking about what they represent. GPS's like to give you readouts with many digits to impress the buyer but the GPS is not that accurate so the additional digits are meaningless. You computation of Hc, distance, course or ZN cannot be more accurate than the least accurate data that went into the computation. You gave the present latitude only to a precision of one minute, one nautical mile, about 6,000 feet. This means that the latitude is somewhere between 39° 57.5' and 39° 58.5', a band one nautical mile wide. So it is meaningless to give the other latitude to a precision of 0.1 seconds. 1/600 NM, just 10 feet. There is no way that you could know the destination latitude to an accuracy of ten feet. Even using your method of just copying down what is displayed on your GPS it can't give you a latitude for the destination since you are not there so can't read out what the GPS will say when you do get there.
    No matter how many decimal places you have in your answer it cannot be more accurate than one nautical mile since the original latitude had that much uncertainty. Any more precise result is meaningless. 

    Looking at the LHA. In order to have and LHA accurate to 0.1 second you would have to know your longitude to 0.05 seconds (1/2 of 1/10th of a second) and you would also have to know the longitudes of the destination to the same level of accuracy because you have to combine these two numbers and that causes the combined precision to 0.1 seconds, 0.05 for the longitude at the start plus the 0.05 from the longitude of the destination equals 0.10 seconds. Your GPS can't give you that level of accuracy, just 5 feet. But even more obvious, if doing celnav, you can't get the GHA to a precision better that 6 whole seconds (0.1 minutes) which is 120 times more uncertain than the value you were using. 

    So let me suggest that you round off the seconds in your GPS display to the nearest 6 seconds which is the same as 0.1 minute which is the level of precision available for celestial coordinates in the Nautical Almanac if you are using your GPS position for celestial navigation. If you are doing great circle computations then round off your GPS coordinates to the level of the accuracy of the destination. If you only know the destination to whole minutes of latitude and longitude then round off your starting GPS readout to whole minutes. If you know the destination to 0.1 minutes then round off your starting coordinates to 0.1 minutes, 6 seconds.

    Using your numbers the distance is 105.7837724 NM according to my calculator. The seven decimal place answer means the distance is expressed to to 1/10,000,000, one ten millionth of a NM or 7/1,000 of an inch. Just because the readout shows all those decimal places it is ridiculous to pay any attention to them. Since the least accurate latitude is only good to one nautical mile it would be appropriate to round this to a whole number of nautical miles, 106 NM. If you had rounded off the values to one minute accuracy before you started you would have computed 106.2694834 which also rounds to 106 NM. Also, the course of azimuth is - 3.917400689 or 356.0825993 degrees. Do you think you could hold a heading or draw a line on a chart accurate to 1/10,000,000 of a degree or even 1/10 of a degree?
    LHA= 0d 9m 40.9sec
    Present Latitude- N 39d 58m
    Destination Latitude= N 41d 43m 31.8sec


    From: Samuel L <NoReply_SamuelL@fer3.com>
    To: garylapook---.net
    Sent: Tuesday, December 23, 2014 11:11 PM
    Subject: [NavList] Re: Azimith forumula for Great Circle sailings- having problems

    Do you have a solution to my question?
    Now to get those super-accurate figures here's how I do it;
    Get into my car.
    Turn the GPS on ('have to wait for it to "acquire satellites")
    Press the "location" button.
    Write down the coordinates it provides.
    That's it!
    Amazing isn't it?!

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