A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Frank Reed
Date: 2020 Sep 28, 22:55 -0700
Yes, I agree with everything you wrote with only minor differences in detail. By the way, sometimes some NavList members assume that I have already worked these things out, and I am just setting you all up by posting them as puzzles. Occasionally I put in a little thought before I post one of these nautical astronomy-connected photos as an interesting puzzle, but this is a case where I had absolutely no idea how it would turn out. I saw an intriguing photo Saturday evening and posted it as a puzzle. That we have reached nearly identical conclusions says that these analysis methods really work!
Don, you wrote:
"I was hoping that some of the aviators on this forum would weigh in on commercial aircraft climb rates and traffic patterns around JFK. "
Yeah, me, too, but I guess they're busy with the "boo rah!" over furlongs and quarts. :/
"I watched some take offs on runway 22R using JFK radar view, and it seemed that it was at least 4 NM, out over Long Island Sound, before aircraft reached an altitude of 4000’ that was consistent with the moon being 3 deg above the horizon. But then the azimuth would have been off."
Yes, I think it all makes reasonable sense now. Nothing definitively proved that I would try to defend in court, :), but "reasonable sense". The plane took off on 22R, maybe left the ground halfway down that long runway, a little earlier than a fully-loaded 767-300ER, and it was just above the extreme southwest end of the runway, where the pavement ends on "Jo Co Marsh", the easternmost of the marshy islands in Jamaica Bay, when the photo was taken. Its angular altitude seen in the photo, which I estimate to be just about 100 minutes of arc in true altitude (above true level), at that range would correspond to an altitude of nearly 2500 feet. That still seems a little high, but it's well within the range of possible. There's a lot of room to get in the air on 22R, and by the very end of the runway climbing out at angle of perhaps 22°, it could have been 2500 feet high. And that does appear consistent with the angular orientation of the airplane in the photo. It all fits.
So here's a little navigation-related puzzle we haven't addressed, not in this discussion or in any others recently that I can recall. If I see some very distant object in the sky at a certain measured angular altitude above true level, how high is it above the ground out there? For example, suppose I spot a zeppelin off in the distance through my binoculars. From its apparent size, I calculate its distance to be 60 nautical miles. I also measure its angular altitude above true level to be 20'. How high is it off the ground? You can't use the angular altitude alone. You have to add in the angular drop-off of the surface of the globe. In all cases, from a few miles... out to all the way around the globe, this is equal to the angular distance (distance in nautical miles) divided by two. So if the distance is 60 n.m., the drop-off from the curvature of the earth is 30'. That means that if we had "x-ray vision" and could see through the earth, we would see the zeppelin 20'+30' above the exact spot on the ground beneath it "out there". So its angular altitude above the ground is really 50' at a range of 60 n.m. And in this case, that implies, by the usual relationship for small angles, (50'/3438) = ht/60n.m. or ht=3000/3438 n.m. or about 5300 feet altitude. Notice that if you ignored the "drop-off" from the curvature of the Earth, you would instead estimate a height of about 2100 feet ...way off.
Speaking of JFK runways...
As I end the night, I'm just now indulging in one of my 2020 rituals. Since May, I have been watching every few days an episode of the series "Mayday" about plane crashes and investigations. Seems appropriate to watch plane crashes in slow motion since that's a good metaphor for the year. For tonight's episode I picked "Queens Catastrophe". This discussion of runways at JFK and climb-out angles reminded me of the horrific and insane coincidence of the crash of American Airlines Flight 587 just two months after the terrorist attacks of September 11, 2001. That plane broke up, completely unrelated to terrorism, at a location and altitude quite close to the position of the airplane in this Moon photo... So that's what I'm watching for "light tv" viewing to close out the night tonight.