NavList:

Antoine is right in saying: “Only the presence of higher order terms (in t**4 and maybe t**6) prevented Andres to do the perfect pick of the exact Culmination time.”

I have simulated two theoretical cases with very high speed, and the curve obtained for the altitude near meridian transit is like this:

R=180º

V=3000 kt

R=135º

V=3000 kt

In this case the least squares fit gives for Hmax:

yLS = a0+a1*x+a2*x2+a3*x3+...+anxn

a0 = -51168.479530

a1 = 4885.116188

a2 = 118.025783

a3 = -20.281600

a4 = 0.107351

a5 = 0.025145

a6 = -0.000455

And the solution is:

Andrés Ruiz

Navigational Algorithms

http://sites.google.com/site/navigationalalgorithms/

Asunto: [NavList 10061] Re: Time of meridian passage accuracy

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I am quite surprised by these results because for culminations close to zenit (say above 85d) the effect of a high N/S speed component and/or change in declination significantly skews the heights vs times curve. Given the almost perfect symmetry of this Altitude curve, the algorithm used by Andres - apparently a second degree best fit as seems to be indicated on his site - was very powerful to pick up almost the exact the Culmination time. Only the presence of higher order terms (in t**4 and maybe t**6) prevented Andres to do the perfect pick of the exact Culmination time.

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Antoine M. "Kermit" Couette