PPRuNe Forums - View Single Post - Converting 2 angular measurements to distance on the earth.
Old 20th April 2020 | 14:53
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oggers
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From: Zulu Time Zone
Originally Posted by buzzc152
If 2 aircraft at roughly the same latitude measure the sun in the sky at 2 different angle, how can you use that to estimate distance between the 2 aircraft ?
To my puny brain I can just take the number of arc minutes difference and call that nautical miles between them. Does that work ?
It is not enough information to make an estimate.

eg, Aircraft A measures the sun to be 10º above the horizon and aircraft B measures it as 5º. So, 5º difference between them equals 5ºx60" = 300nm separating the two. If so, why does that work ?
The two aircraft could theoretically be anywhere from 300 to 9900nm apart based on the angles in your example. It would be the same if the two aircraft reported DME from a VOR. You could not estimate the distance between them with that information alone - not even if you knew they were on the same latitude. You need azimuth as well. Then, the vertical angle will give you a range from the reference point (ie the point on Earth where the Sun is directly overhead at that moment), and given azimuth for each sighting you could solve the problem using the sine rule or plotting but I can't think of a clever way to do it in your head. For a rough approximation it could be visualised on an HSI in a similar manner to this IF trick - although I would be very happy to see if anyone can come up with something more useful.
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