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707 Captain >> 707 Captain >> TOD calculation
https://www.captainsim.org/forum/csf.pl?num=1335507282

Message started by Johan Nordqvist on Apr 27th, 2012 at 6:14am

Title: Re: TOD calculation
Post by windplayer on May 2nd, 2012 at 2:07pm
On the upper pic you arriving from the NWW. Say you flying magnetic HDG 110 on that pic. You know that at MISMA you gotta be at 5000, so you kno that TOD located 81 nm from MISMA. Thats correct for all directions from MISMA. From map you know position of MISMA. So you know 2 sides of triangle. Angle alfa is Your HDG - 35(radial of SVD VOR) = 75.

Then use cosine theorem X^2= 81^2 + 35.3^2 - 2*81*35.3 * cos(alfa)
Thats how you'll know distance to TOD from SVD VOR. Now you can find the angle between X, and 35.3 nm side using ptolemey's theorem, or using sin, or cosine theorem.

Thats links for required theorems in usable forms:

http://en.wikipedia.org/wiki/Law_of_cosines
http://www.cut-the-knot.org/proofs/sine_cosine.shtml

It is better to obtain not only TOD distance from SVD VOR, but radial, you have to cross at TOD distance. Upper trigonometric nuts can look overwhelming, but actually it is very simple, so you need calculator only (and you'll need it anyway for 707, 727 flying) ;)

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