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Author Topic: Excessive altitude intercept
 Gary Rose posted March 04, 2005 05:33 PM                   At what point does the altitude intercept, "a-value," become excessive?
 David Burch posted March 04, 2005 06:15 PM                   The overall method of computing intercept and azimuth from an assumed position and then plotting straight-line LOPs for an intersection is an approximation to the exact solution. The LOPs are actually circles of position that have a radius equal to the zenith distance. As this radius becomes small (ie Ho above some 80° or so, yielding zenith distances below 10° (600 nmi) then the overall method begins to break down, because the Lines of Position are no longer good approximations to the Circles of Position.Therefore, when dealing with very high sights, we must take this into account with an all new ploting procedure.... but this is not the actual topic at hand.The question at hand, excessive intercepts, is, however, a related question. The azimuth line is a segment of a great circle, and the intercept is a distance along that line. That then intersects at right angles with the LOP which, as mentioned, is a segment of a circle of position.Thus, for any altitude of sight, if the DR is rather off the actual fix, the a values can end up being long lines, 60 or 100 miles or more. When this happens, the resulting graphic plot (all in straight lines) can be in error from the intended plot, and the resulting intersection leads to errors in the final fix.There is no hard and fast way to set limits on this, but simple guidelines will always work. Use this rule:If the final fix ends up being more than 60 nmi from the DR you used to choose the assumed position, then call the fix your new DR and redo the sight reduction from that position.Or if any of the a-values end up being 60 miles or so long, then i would do the same thing. Go ahead and plot them, then find the fix, then call this the DR, choose a new AP based on that, and plot again.=========a fun exercise along these lines is to use New York City for your DR (for any set of sights you might have) and then keep iterating as above to see how long it takes you to find your true postion. From: Starpath, Seattle, WA
 David Burch posted February 23, 2019 09:33 AM                   We now have a more specific answer to this question.See https://davidburchnavigation.blogspot.com/2019/02/check-assumed-positions-after-plotting.html From: Starpath, Seattle, WA

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