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    Re: Closest point of approach.
    From: Gary LaPook
    Date: 2012 Jan 2, 17:03 -0800
    This is not a problem that comes up since most planes have no way to determine the instantaneous altitude of the other aircraft and that information is needed for a solution to this problem. Airplanes are separated by 1,000 feet of altitude which provides enough safety margin because planes rarely change altitude at a high rate. Airliners are required to have onboard collision avoidance equipment (TCAS) that works in cooperation with the similar equipment on the other airliner to exchange altitude data and this equipment uses some algorithm to predict the future position of the other aircraft in three dimensions and provide warnings and collision avoidance commands to the pilot. These commands override any prior commands given by flight controllers on the ground and the pilot is required to follow them. This is important because the TCAS equipment is giving the other pliot commands predicated on you following the commands being given by your equipment, the two TCAS units agreed on the avoidance maneuvers. A midair a few years ago in which a plane load of kids on a Russian plane were killed when the pilot did not follow the commands of his TCAS and climbed instead of descending as commanded. The TCAS on the other plan had commanded its pilot to climb predicated on the Russian pilot following the agreed upon solution of descending. So both plane climbed and bumped into each other. The crew on the other plane was also killed, fortunately   in was hauling only cargo. So if you have a couple of hundred thousand dollars you don't need, then just go out and buy a TCAS.


    --- On Mon, 1/2/12, P H <pmh099@yahoo.com> wrote:

    From: P H <pmh099@yahoo.com>
    Subject: [NavList] Re: Closest point of approach.
    To: "NavList@fer3.com" <NavList@fer3.com>
    Date: Monday, January 2, 2012, 4:44 PM

    Hello Amrin,

    Following up on the response from Andres Ruiz, please see the attached PDF file.  Individual "action steps" are highlighted with bullets.  This is the algorithm encoded into the cpa.xls spreadsheet that I posted earlier for the 2-D case, but it works just as well in 3-D.  I left the specification of angles deliberately vague, since I actually don't know how pilots define those relative to their own aircraft.  It's a bit of a chore to carry out this procedure explicitly, but if it is encoded into a programmable electronic device, the results come out instantaneously.

    The elegant solution using planar trigonometry posted a few days by Gary LaPook for 2-D would in fact work in 3-D as well, since a point (your aircraft) and a straight line (the other aircraft) on which the point does not lie (hopefully!!) define a plane  (see the attached cartoon).  You'd just have to take extra care with those angles.

    Peter Hakel

    From: Amrin Shahziya <ammushaz@gmail.com>
    To: NavList@fer3.com
    Sent: Monday, January 2, 2012 1:04 AM
    Subject: [NavList] Re: Closest point of approach.

    please explain this in 3d space
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