Calculation of Sunrise and Sunset Inflight
Seeing the Sun rising in the “wrong” place is not exclusive to Concorde, as is shown by compressor stall’s nice picture. I enjoyed it a number of times way back when flying from Europe to Alaska. You can also see it on some other routes in a subsonic aircraft, provided you fly at high enough latitude.
With the good old B707, we used to take off around 10 am and, in February or November sunset occurred behind us as we passed in the area of Jan Mayen Island. Since we arrived at ANC a little before noon, local time, there was a sunrise to the south sometime later over the Beaufort Sea.
We were INS equipped already but still had the HO-249 tables and the periscopic sextant on board. We could use them to check the grid heading of the excellent “Polar Path” gyroscopic compass should our INS system become unreliable.
Not necessary for navigation but more as a challenging diversion, we used to predict sunset and sunrise times by drawing what we called “the absolute trajectory of the airplane” on the polar stereographic chart. The trick was first to draw a line representing separation between day and night at a time when the position was known. The tables gave the GHA and declination of the Sun and the necessary corrections. The line was a quasi-straight line on this type of projection. Then, you had to rotate counterclockwise each downstream waypoint around the North Pole by an angle depending on the time difference between its ETO and the time over the starting waypoint using a rate of 15 deg per hour. Joining these new points gave a nice curve, the “absolute trajectory”, and its intersections with the day/night separation line corresponded to sunset and sunrise.
DJ.
With the good old B707, we used to take off around 10 am and, in February or November sunset occurred behind us as we passed in the area of Jan Mayen Island. Since we arrived at ANC a little before noon, local time, there was a sunrise to the south sometime later over the Beaufort Sea.
We were INS equipped already but still had the HO-249 tables and the periscopic sextant on board. We could use them to check the grid heading of the excellent “Polar Path” gyroscopic compass should our INS system become unreliable.
Not necessary for navigation but more as a challenging diversion, we used to predict sunset and sunrise times by drawing what we called “the absolute trajectory of the airplane” on the polar stereographic chart. The trick was first to draw a line representing separation between day and night at a time when the position was known. The tables gave the GHA and declination of the Sun and the necessary corrections. The line was a quasi-straight line on this type of projection. Then, you had to rotate counterclockwise each downstream waypoint around the North Pole by an angle depending on the time difference between its ETO and the time over the starting waypoint using a rate of 15 deg per hour. Joining these new points gave a nice curve, the “absolute trajectory”, and its intersections with the day/night separation line corresponded to sunset and sunrise.
DJ.
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Yes!
Looking at the GridHDG and the True HDG diplayed, they either just overflew the Northpole, heading south or they are flying towards the Southpole. They must be close to 180 E/W, telling form the difference of grid and true.
Looking at those waypoints (from: HM65S, to: HM70S) it looks like they are approaching the Southpole (actually passing "left" of it, I am not sure if "east" doesn't stop to make sense so close to the pole).
As I have never even heard of these waypoints, I beleive those guys must be flying as far away from Europe as possible; they must be Aussies or Kiwis going to Capetown, maybe. My guess is 3-4 hours into the flight.
And the sun in the south? It must be right over the pole, or close. So I'd give it a dec/jan estimate.
So who flys an A340 down there?
Nic
Looking at the GridHDG and the True HDG diplayed, they either just overflew the Northpole, heading south or they are flying towards the Southpole. They must be close to 180 E/W, telling form the difference of grid and true.
Looking at those waypoints (from: HM65S, to: HM70S) it looks like they are approaching the Southpole (actually passing "left" of it, I am not sure if "east" doesn't stop to make sense so close to the pole).
As I have never even heard of these waypoints, I beleive those guys must be flying as far away from Europe as possible; they must be Aussies or Kiwis going to Capetown, maybe. My guess is 3-4 hours into the flight.
And the sun in the south? It must be right over the pole, or close. So I'd give it a dec/jan estimate.
So who flys an A340 down there?
Nic
Top of the class ATCast. Hobart (YMHB) to McMurdo, Antarctica(NZPG) in an Aussie A319. And, correct, we're not heading to Cape Town - we're going the wrong way for that!
As for the wide body assumption - wrong, but not a bad guess as there aren't too many narrow body Airbii around with the Polar Nav mod.
Departed Hobart shortly after local midnight. Not an everyday occurrence seeing the sun rise like that. It took a lot of mucking around with the exposure to get the right pic, but was worth it in the end.
Pic taken at the dot on this route map.
As for the wide body assumption - wrong, but not a bad guess as there aren't too many narrow body Airbii around with the Polar Nav mod.
Departed Hobart shortly after local midnight. Not an everyday occurrence seeing the sun rise like that. It took a lot of mucking around with the exposure to get the right pic, but was worth it in the end.
Pic taken at the dot on this route map.
Last edited by compressor stall; 9th Aug 2011 at 07:15.
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Enroute sunrise or moonrise predictions
You know the distance between departure and destination.
Calculate sunrise time for the departure and destination, using the cruise altitude. [To compensate for altitude: if using the sine formula you solve instead for hour angle, using a sun height which is the combination of -16' (semidiameter of disk), -34' (astronomical refraction), and the arcdistance to the horizon of about [-1.15'√(elevation in feet above the horizon)]. Combine that hour angle with airport longitude, then look in the almanac for when exactly the Sun had that GHA.]
The course distance divided by the time interval (between the sunrise times) is the groundspeed of the sunrise line along your direct course line.
Add your average groundspeed to that and you have the (combined) closing speed.
At the takeoff time, where was the sunrise line? You can find out because you know when it is predicted over your destination, and already found out how fast it is moving.
So you know how far away the sunrise line is at takeoff time, and about how fast you and it are converging. So you can predict how long it will take (after takeoff) for you and it to coincide. (Distance/closing speed) = time interval.
To refine the prediction, you note the time passing some known distance from the destination. That way the uncertainties of climb speed and departure routing don't influence the prediction.
Calculate sunrise time for the departure and destination, using the cruise altitude. [To compensate for altitude: if using the sine formula you solve instead for hour angle, using a sun height which is the combination of -16' (semidiameter of disk), -34' (astronomical refraction), and the arcdistance to the horizon of about [-1.15'√(elevation in feet above the horizon)]. Combine that hour angle with airport longitude, then look in the almanac for when exactly the Sun had that GHA.]
The course distance divided by the time interval (between the sunrise times) is the groundspeed of the sunrise line along your direct course line.
Add your average groundspeed to that and you have the (combined) closing speed.
At the takeoff time, where was the sunrise line? You can find out because you know when it is predicted over your destination, and already found out how fast it is moving.
So you know how far away the sunrise line is at takeoff time, and about how fast you and it are converging. So you can predict how long it will take (after takeoff) for you and it to coincide. (Distance/closing speed) = time interval.
To refine the prediction, you note the time passing some known distance from the destination. That way the uncertainties of climb speed and departure routing don't influence the prediction.
Last edited by bethpage89; 10th Sep 2012 at 02:13. Reason: Symbol and diction
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Hi,
Doing sundials, I am used to compute sunset and sunrise at specified true altitude, UTC time (for time equation), Latitude and Longitude (ask your GPS or satnav). I use a very ordinary programmable pocket calculator CASIO graph 25+. The program i wrote gives me crepuscule times (sun at height of -6°, -12°, -18°) and time where the sun appears and disappears on the top of the mountains. As you know you may use center of the sun, or the edge of the sun. You also have to do correction for refraction.
Formulaes founded in a good cosmology book.
Easy !
Doing sundials, I am used to compute sunset and sunrise at specified true altitude, UTC time (for time equation), Latitude and Longitude (ask your GPS or satnav). I use a very ordinary programmable pocket calculator CASIO graph 25+. The program i wrote gives me crepuscule times (sun at height of -6°, -12°, -18°) and time where the sun appears and disappears on the top of the mountains. As you know you may use center of the sun, or the edge of the sun. You also have to do correction for refraction.
Formulaes founded in a good cosmology book.
Easy !
Last edited by roulishollandais; 18th May 2012 at 18:58.
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My rule of thumb, sunrise/sunset time at present position based on Almanac, plus 25 sec/1000 ft of your altitude if heading west, minus 25 sec/1000 ft if heading east..... not accurate but almost spot on ......... 
VR
VR
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Lookup present (local) sunrise sunset in the EFB allow 1 minute per 5000 (actually 4921 ft) feet, of course this is going North or South, going East or West add or subtract a bit, sometimes a bit more than a bit. I stand to be corrected.
