Calculation of Sunrise and Sunset Inflight
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FLEXPWR,
You seem to be only taking into account the actual "horizon distance" for a given FL at a given position, which already makes a significant 20 minutes or so difference.
But.... if you're doing about 600 mph TAS westwards, by the time you've reached the "sunset position" you calculated for your earlier position, the earth will have rotated also, and the sun won't have set there yet...
See my earlier post about Concorde.
While written "tongue in cheek", the scenario is perfectly real.
Even at the equator the rotation of the Earth is "only" about 1000 mph.
So at 45° N or S, it's "only" about 700 mph. So if you're flying westwards at 600 mph TAS, sunset will come at a considerably later time.
And, as said, in a Concorde at 1350 mph... it won't come at all until you land at JFK.
CJ
You seem to be only taking into account the actual "horizon distance" for a given FL at a given position, which already makes a significant 20 minutes or so difference.
But.... if you're doing about 600 mph TAS westwards, by the time you've reached the "sunset position" you calculated for your earlier position, the earth will have rotated also, and the sun won't have set there yet...
See my earlier post about Concorde.
While written "tongue in cheek", the scenario is perfectly real.
Even at the equator the rotation of the Earth is "only" about 1000 mph.
So at 45° N or S, it's "only" about 700 mph. So if you're flying westwards at 600 mph TAS, sunset will come at a considerably later time.
And, as said, in a Concorde at 1350 mph... it won't come at all until you land at JFK.
CJ
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Hi ChristiaanJ,
You are absolutely correct, that's the reason why I stated no correction for longitude when flying northbound or southbound.
Made my life easy...
You can also view it as follows, but the calculation is more approximate than plotting a position with GPS: As you mentioned, we'll take the speed of earth rotation over the equator as an example, since we all know how to calculate the difference for other latitudes. Take 1000 MPH, that's about 14.5 NM per minute. Then take your own speed and do the same, eg. 0.8M is roughly 8 NM per minute( let's keep it real, 0.1M difference gives us something like 10seconds difference over a mile) remember, this is only if you fly due east/west, otherwise you have to correct by the cosine of the angle as well to get you speed in relation to a meridian (eg. fly Hdg 150 is 60 degrees off the 090, then it's 8(NM/min)xcos60=4). Pick a point far enough so you know the sun at that point has not risen yet and find the rising time from the almanach, then plot what was you position at the same time. Add up or subtract (depending if you fly east or west) the calculated speed in NM/min (like a collision course or take over from 2 airplanes, for example flying due east will give us 14.5+8=22.5NM/min. You can deduct at what time you will reach the horizon together, we will have to apply the previous method to correct for altitude.
This becomes waaayyy too inaccurate in the end and waaaayy too little time to work out if you realised you wanted to know the time only a few minutes before the sun rises. But I guess on long haul, with a nice big calculator and a lot of willpower...
In the end, you divide the inaccurate by the square root of roughly, and we should get there in no time...
Any other ideas, maybe more practical?
Cheers,
Flex
You are absolutely correct, that's the reason why I stated no correction for longitude when flying northbound or southbound.
Made my life easy...You can also view it as follows, but the calculation is more approximate than plotting a position with GPS: As you mentioned, we'll take the speed of earth rotation over the equator as an example, since we all know how to calculate the difference for other latitudes. Take 1000 MPH, that's about 14.5 NM per minute. Then take your own speed and do the same, eg. 0.8M is roughly 8 NM per minute( let's keep it real, 0.1M difference gives us something like 10seconds difference over a mile) remember, this is only if you fly due east/west, otherwise you have to correct by the cosine of the angle as well to get you speed in relation to a meridian (eg. fly Hdg 150 is 60 degrees off the 090, then it's 8(NM/min)xcos60=4). Pick a point far enough so you know the sun at that point has not risen yet and find the rising time from the almanach, then plot what was you position at the same time. Add up or subtract (depending if you fly east or west) the calculated speed in NM/min (like a collision course or take over from 2 airplanes, for example flying due east will give us 14.5+8=22.5NM/min. You can deduct at what time you will reach the horizon together, we will have to apply the previous method to correct for altitude.
This becomes waaayyy too inaccurate in the end and waaaayy too little time to work out if you realised you wanted to know the time only a few minutes before the sun rises. But I guess on long haul, with a nice big calculator and a lot of willpower...
In the end, you divide the inaccurate by the square root of roughly, and we should get there in no time...
Any other ideas, maybe more practical?
Cheers,
Flex
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In the end, you divide the inaccurate by the square root of roughly, and we should get there in no time...
Did you patent that ? .. or can anyone use it ?
Love it.
Did you patent that ? .. or can anyone use it ?
Love it.
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can't find my air almanac
Going back to the idea of "Rule of Thumb" I think it is more difficult than you might think.
I could not find a copy of the Air Almanac and also looked in vain for a small booklet by Peter Duffett-Smith called "Practical Astronomy with Your calculator". That had useful equations and a piece about the equation of time. This latter equation is a sort post hoc stab at the way the earth is orbiting with an estimate for the next year and was pretty vital in the days before atomic clocks.
There certainly used to be in the Air Almanac data for the extension of daylight according to latitude and height amsl. The following link NOAA Improved Sunrise/Sunset Calculation is handy, particularly with regard to refraction in air but takes no account of height. I have an old wartime copy of AP1234 which shows this seasonal variation Jan-Dec for Latitude 50 deg and its big... 22mins either way and that surely swamps refraction. But not dip, the angle of depression of the sun below true horizon. Using a maritime sextant reliant on shooting the horizon there is a dip correction for refraction which must be subtracted. Back in WW2 and immediately post-war when bubble sextants were used in aircraft there is no dip horizon correction for refraction but there is one to be subtracted for the altitude of the sun just as for a maritime sextant. Except that this refractive correction varies strongly with height.
But going back to the rule of thumb, no, can't think of one principally because the extension of daylight with latitude is a "sinusoidal" seasonal variation complicated by dip with actual height and prevailing refraction.
Stephen Michael Schimpf makes or made available a handy bit of software called Cybersky which should be good for sunrise sunset prediction and if the Air Almanac still has tables of daylight extension for height and latitude that is probably the best that can be done. Hardly a rule of thumb. Though a wild-assed guess might be on a "typical" commercial flight you can expect sunrise to be 10-20 minutes earlier than sea level almanac figures and similarly for sunset 10-20 minutes later.
I wish I could have found something simple and easy but it has been fun trying.
I could not find a copy of the Air Almanac and also looked in vain for a small booklet by Peter Duffett-Smith called "Practical Astronomy with Your calculator". That had useful equations and a piece about the equation of time. This latter equation is a sort post hoc stab at the way the earth is orbiting with an estimate for the next year and was pretty vital in the days before atomic clocks.
There certainly used to be in the Air Almanac data for the extension of daylight according to latitude and height amsl. The following link NOAA Improved Sunrise/Sunset Calculation is handy, particularly with regard to refraction in air but takes no account of height. I have an old wartime copy of AP1234 which shows this seasonal variation Jan-Dec for Latitude 50 deg and its big... 22mins either way and that surely swamps refraction. But not dip, the angle of depression of the sun below true horizon. Using a maritime sextant reliant on shooting the horizon there is a dip correction for refraction which must be subtracted. Back in WW2 and immediately post-war when bubble sextants were used in aircraft there is no dip horizon correction for refraction but there is one to be subtracted for the altitude of the sun just as for a maritime sextant. Except that this refractive correction varies strongly with height.
But going back to the rule of thumb, no, can't think of one principally because the extension of daylight with latitude is a "sinusoidal" seasonal variation complicated by dip with actual height and prevailing refraction.
Stephen Michael Schimpf makes or made available a handy bit of software called Cybersky which should be good for sunrise sunset prediction and if the Air Almanac still has tables of daylight extension for height and latitude that is probably the best that can be done. Hardly a rule of thumb. Though a wild-assed guess might be on a "typical" commercial flight you can expect sunrise to be 10-20 minutes earlier than sea level almanac figures and similarly for sunset 10-20 minutes later.
I wish I could have found something simple and easy but it has been fun trying.
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can't find my air almanac
.. is not PPRuNe a literal wealth of esoteric information ? I never cease to be amazed at the corpus of knowledge amongst the folk here ...
.. is not PPRuNe a literal wealth of esoteric information ? I never cease to be amazed at the corpus of knowledge amongst the folk here ...
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Hi all,
Thanks for all the interesting and informative inputs. By the way, is there any links to take a look at the Air Almanac online? Apart from the sunrise and sunset table, what other informaton can I get from it?
Thanks
lion-g
Thanks for all the interesting and informative inputs. By the way, is there any links to take a look at the Air Almanac online? Apart from the sunrise and sunset table, what other informaton can I get from it?
Thanks
lion-g
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Hi
Out of interest, how do the long haul pilots log their hours in terms of day and night columns in the log book?
Do they print something out from the FMC at the end of the flight that breaks it up and enter into the day and night columns for that one sector?
I am assuming if you fly Seattle > Heathrow in June you dont have much darkness and your not really going to look out the window every flight and note the time against GMT ....
Out of interest, how do the long haul pilots log their hours in terms of day and night columns in the log book?
Do they print something out from the FMC at the end of the flight that breaks it up and enter into the day and night columns for that one sector?
I am assuming if you fly Seattle > Heathrow in June you dont have much darkness and your not really going to look out the window every flight and note the time against GMT ....
"your not really going to look out the window every flight and note the time against GMT ...."
That's pretty much what I do...our FMC/ACARS certainly doesn't do day/night splits - does anybody's???
That's pretty much what I do...our FMC/ACARS certainly doesn't do day/night splits - does anybody's???
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When I was a C130 Captain, I would often have a bet with the navigator as to who could make sunrise/sunset prediction most accurately.
It is easy enough (Air Almanac or whatever it’s called) to calculate the time over a fixed point at a particular altitude. But you never know exactly where you will be at the moment of sunrise/sunset. So I would plot a simple linear graph of aircraft position against time and another using same scale of sunrise (set) for particular localities along track. The intersection of the lines would be the point of sunrise (set). The intersection of the two lines on the graph can alternatively be determined by the solving simultaneous equations but I found the graphical method much simpler.
I only made the challenge when the sun could be seen from the flight deck, ie sunrise when heading (vaguely) eastwards or sunset when westwards. Far greater accuracy can be achieved with the sunrise than with sunset due to a steeper angle of intersection in the sunrise case. I would invariably achieve +/-2 minutes for sunrise but the error with sunset could be well over 5 minutes. Of course, when flying at very high latitudes, sunset might in practice be virtually unpredictable if the aircraft’s groundspeed approximates to the rate of the earth’s rotation.
An interesting phenomenon most easily visible from the air (far less often from the ground) is the Green Flash. Wiki explains here: Green flash - Wikipedia, the free encyclopedia
Jack
It is easy enough (Air Almanac or whatever it’s called) to calculate the time over a fixed point at a particular altitude. But you never know exactly where you will be at the moment of sunrise/sunset. So I would plot a simple linear graph of aircraft position against time and another using same scale of sunrise (set) for particular localities along track. The intersection of the lines would be the point of sunrise (set). The intersection of the two lines on the graph can alternatively be determined by the solving simultaneous equations but I found the graphical method much simpler.
I only made the challenge when the sun could be seen from the flight deck, ie sunrise when heading (vaguely) eastwards or sunset when westwards. Far greater accuracy can be achieved with the sunrise than with sunset due to a steeper angle of intersection in the sunrise case. I would invariably achieve +/-2 minutes for sunrise but the error with sunset could be well over 5 minutes. Of course, when flying at very high latitudes, sunset might in practice be virtually unpredictable if the aircraft’s groundspeed approximates to the rate of the earth’s rotation.
An interesting phenomenon most easily visible from the air (far less often from the ground) is the Green Flash. Wiki explains here: Green flash - Wikipedia, the free encyclopedia
Jack
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I know that Ramadan is well and truly over for another year, but I'd like to bring a useful solution to the forum.
Sun Position Calculator is a rigorous calculation of sunset/sunrise times, including the difference between lower and upper limb of the sun and also including a correction for refraction and aircraft altitude.
Note that the QNH or QFE needs to be in kPa form, ie a tenth of QNH (or QFE) in milliBars.
Of course you'll have to iterate to converge of the solution for where the aircraft will be at local sunset, but that's simply a matter of making a wild-arsed guess and then retrying with the position that your FMS shows for that time; rinse and repeat.
Remember that for your Islamic customers the relevant time is the local time that the sun's upper limb appears or disappears at the local horizon from their viewpoint.
Sun Position Calculator is a rigorous calculation of sunset/sunrise times, including the difference between lower and upper limb of the sun and also including a correction for refraction and aircraft altitude.
Note that the QNH or QFE needs to be in kPa form, ie a tenth of QNH (or QFE) in milliBars.
Of course you'll have to iterate to converge of the solution for where the aircraft will be at local sunset, but that's simply a matter of making a wild-arsed guess and then retrying with the position that your FMS shows for that time; rinse and repeat.
Remember that for your Islamic customers the relevant time is the local time that the sun's upper limb appears or disappears at the local horizon from their viewpoint.
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HI Jack,
Thanks for your inputs. In my opinion, sunrise and sunset are not linear when there is a great change in Latitudes. Does your plotting work accurately for flights up north or down south? From my experience, it works for flights with destination in the same latitudes but not flights up north or down south.
Any comments ?
lion-g
Thanks for your inputs. In my opinion, sunrise and sunset are not linear when there is a great change in Latitudes. Does your plotting work accurately for flights up north or down south? From my experience, it works for flights with destination in the same latitudes but not flights up north or down south.
Any comments ?
lion-g
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lion-g said: From my experience, it works for flights with destination in the same latitudes but not flights up north or down south.
You are dead right of course and I hadn’t really thought of that. I usually had my little contest over the Mediterranean when roughly 090 degs on the way to Cyprus.
Jack
You are dead right of course and I hadn’t really thought of that. I usually had my little contest over the Mediterranean when roughly 090 degs on the way to Cyprus.
Jack
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rough guide
lets take the example of sunrise.
1.we know sunrise time at place of departure.
2.we know airborne time
3.sun travels 15 dg of lat / hour (as mentioned in previous post 5 deg in 20 min)
4.provided you are not at lattidudes too far north or too far south where there may not be a sunrise or sunset.(depending on the time of the year)
one can estimate time of crossing lattitude and thus local sunrise time based on weather you are flying east or west.
cheers
1.we know sunrise time at place of departure.
2.we know airborne time
3.sun travels 15 dg of lat / hour (as mentioned in previous post 5 deg in 20 min)
4.provided you are not at lattidudes too far north or too far south where there may not be a sunrise or sunset.(depending on the time of the year)
one can estimate time of crossing lattitude and thus local sunrise time based on weather you are flying east or west.
cheers
