Calculation of Sunrise and Sunset Inflight

[lion-g]

Hi all,

Out of curiousity, any of you guys have a rule of thumb regarding calculation of sunrise or sunset timing inflight ?

The usual way of us doing it is by trial and error, based on the LAT and LONG along our flight path and cross reference to the sunrise and sunset tables provided.

Another way which works along the equator is to plot 2 straight lines, 1 line being the takeoff time and landing time and the other being the sunrise/sunset time at departure airport and destination airport, both on the same graph. The point where the 2 lines intercept is where the sun will rise/set.

From my understanding, as we travels up north or down south, the relationship ceases to be linear anymore. Do correct me if I am wrong.

Any better ways of doing the calculation?

Thanks for sharing,

Cheers,
lion-g

[pilotdude]

try:
Compute Sunrise, Sunset & Twilight For Cities & Airports Worldwide With Local TZ (http://www.mindspring.com/~cavu/sunset.html)

For USA:
Complete Sun and Moon Data for One Day (http://aa.usno.navy.mil/data/docs/RS_OneDay.php)

[Alpine Flyer]

Sorry I can't explain the formulae, but there is a free Palm OS program called SunFly (http://www.aviationreviews.com/sunfly.html) that does the calculations.

[Intruder]

I look outside and estimate when the big, bright ball disappears/re-appears from view at the horizon...

[Checkboard]

Ask one of the FAs to bring up a paper once a passenger is finished with it, and read it there. :ok:

[captjns]

Ask one of the FAs to bring up a paper once a passenger is finished with it, and read it there. http://images.ibsrv.net/ibsrv/res/src:www.pprune.org/get/images/smilies/thumbs.gif

But what happens if it was yesterday's paper?:E

[tocamak]

The usual way of us doing it is by trial and error, based on the LAT and LONG along our flight path and cross reference to the sunrise and sunset tables provided

This sounds familiar although an iterative process sounds better whereby you estimate the position at sunrise/set and then calculate the predicted time before then refinining your postion according to the time so found (i.e trial and error!). My own experience was a bit easier as the moving platform was doing maximum 15kts but basically we used Nautical Almanac figures in the above process so as to be ready for star sights. Correction for altitude was not a factor.

[munster]

i was working as a flying spanner last year in the middle east. during ramadan it was hilarious to see the passengers suffer waiting for sunset as we departed flying west, prolonging their agony...

[lion-g]

Thanks for all the interesting comments :}

Well, I would like to estimate the sunrise time in flight, say I departed out of middlle east midnight and arriving South east asia in noon. Those poor FA will need the guessimated time to serve those who are going to fast. Just in case they miss the dinner, otherwise they got to wait till sunset before they can eat. :)

Any more pointers?

Cheers

[Pugilistic Animus]

There's also the Air Almanac

I like Old Smokey's method:ok:

[lion-g]

Old smokey method?

Care to elaborate ?

Thanks:)

[JAR]

Sunrise/sunset tables for major cities in the en-route supplement carried on flight deck?

[ChristiaanJ]

Now THAT must have been "fun" on Concorde flying West from LHR or CDG on the evening take-offs.

Take-off just after sunset.
All the sheiks on board heave a sigh of relief.
But, no... the sun comes up again in the West.
Cries of dismay.
"Purser, purser !"
"Yes, Sir ?"
"How long will this last ?"
"Until we're in New York, Sir..."

[sycamore]

I would have most company Ops/Planning people ought to be able to tell you for your flight plan.Most GPSs will also tell you for a selected `position ` en-route(ie user w/pt). The `Air Almanac `will also give you corrections for height.....good little task for co-pilots who are bored on long trips... anothe is `how far has a fan blade tip travelled on this leg ?`

[Pugilistic Animus]

Night = Dark
Day = Light

the OS method

[FLEXPWR]

Lion-g,

Do you mean calculating the actual time the sun rises/sets at your flight level, or the sunrise/sunset time on the ground you fly over at this point in time?

Flex

[lion-g]

The more accurate answer would be the sunrise time at our Flight Level along our flight path. But of course, if I am able to get the time on the ground for sunrise, we can deduce a pretty accurate guessimate.

The reason being some of our pax are fasting and they need to know the time so that they can either start or end their fast.

Cheers

[Intruder]

I would not attempt to provide an allegedly "correct" time for religious purposes. I have no idea what their definition of "sunset" might be! I might:

Tell them the published time of sunset at the takeoff point.
Tell them the published time of sunset at the landing point.
Tell them "It appears the sun has set" when/if that happens airborne.

[FLEXPWR]

Well, it's been a few years since I worked that one out, I'll try to remember...

We'll have to make a few assumptions in regards to where the sun stands at the time you see it rising or setting: using the formula for line-of-sight range (eg. range of a VOR, VHF...) and making the correction from a known sunrise/sunset table.

1- If you fly at, let's say FL300, that would be 1.23x(sqrt of 30000)= 213 NM. This means the sun would rise about 213NM away from your present position.

2- The earth day being 24 hours, we have 360/24=15. So 15 degrees an hour is our rotation speed, so 1 degree equals 4 minutes.

3- Next, you correct your line-of-sight distance for latitude, to obtain degrees/minutes of longitude, so if you fly along the 45N parallel for example, you apply 213NM / (cos 45)=213/0.707= 301. Attention, the 301 value is no more a distance, but is the number of minutes of angle at your present latitude (since 1 NM equals 1 minute of angle of a great circle, corrected by the cosine of latitude).

4- You then convert the result in degrees, then in minutes of time: 301 minutes of angle equals 301/60= 5 degrees. Since there is 4 minutes of time for every degree, you get 5x4=20.

The end result is 20 minutes. So the sun will rise 20 minutes earlier and set 20 minutes later at you position than what it's showing on the almanach (Jeppesen for example). Any latitude less than 30 north or south, you can disregard the Cosine correction, as the numbers change very little (cosine 30 is roughly 91%).

I have tried this method a number of times years ago when flying cargo for DHL, it works quite ok, max error I ever got was about one minute. Of course it is easier if you fly a northbound or southbound track, because you don't have to calculate the estimated position of the aircraft in regards to longitude, but with GPS nowadays, you can easily estimate any position you choose along your route.

I hope this is what you were looking for, anyhow, comments and corrections are welcome.

Flex

[Pugilistic Animus]

FLEXPWR you sound like you've had some navigator training!

[FLEXPWR]

Haha! No, just some night hours getting bored and trying to stay awake! But is there is any other way, I'm willing to learn. :)

[ChristiaanJ]

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

[Deano777]

Before I got an electronic log book that does it for me I used to use this program

SunTimes (http://www.snapfiles.com/get/suntimes.html)

I found it to be very good.

Hope it helps

D777

[FLEXPWR]

Hi ChristiaanJ,

You are absolutely correct, that's the reason why I stated no correction for longitude when flying northbound or southbound. :E 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...:}:ok:

Any other ideas, maybe more practical?

Cheers,

Flex

[john_tullamarine]

In the end, you divide the inaccurate by the square root of roughly, and we should get there in no time...http://images.ibsrv.net/ibsrv/res/src:www.pprune.org/get/images/smilies/badteeth.gifhttp://images.ibsrv.net/ibsrv/res/src:www.pprune.org/get/images/smilies/thumbs.gif

Did you patent that ? .. or can anyone use it ?

Love it.

[FLEXPWR]

John, I just made that up...but you're granted with full copyrights! :} Let me know how many you'll convince with it...

Flex

[mathy]

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 (http://www.srrb.noaa.gov/highlights/sunrise/sunrise.html) 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.

[john_tullamarine]

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 ...

[lion-g]

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

[turbine100]

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 ....

[wiggy]

"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???

[jackharr]

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 (http://en.wikipedia.org/wiki/Green_flash)

Jack

[Low Flier]

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 (http://phys.ubbcluj.ro/~zneda/suncalc/spc/spc.zip) 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.

[lion-g]

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

[jackharr]

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

[MD83FO]

any new developments "tools" or applications to calculate sunset/rise? at altitude?

[gearpins]

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

[EYZ]

Just get the sunflight app on your iPhone, it does everything you need. Fill in the blanks, press the button and make the P.A!!
It's very easy, made by a pilot for pilots!

[compressor stall]

OK EYZ,

How would it work here?

http://i663.photobucket.com/albums/uu353/stallie001/aviation/ScreenShot2011-08-03at165630.png

:hmm:

[MD83FO]

Excellent app thanks a lot!

[DJ77]

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.

[MD83FO]

Southbound with the sun in front?

[Admiral346]

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

[ssflying]

flex that was brilliant

[ATCast]

Admiral346:
So who flys an A340 down there?

Why an A340?
My guess: it's an A319 (http://www.antarctica.gov.au/living-and-working/travel-and-logistics/aviation/intercontinental-operations/a319-background-information/a319-photo-album), and it isn't going all the way to Cape town :}

[compressor stall]

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. :cool:

Pic taken at the dot on this route map (http://www.gcmap.com/mapui?P=ymhb-nzpg%0D%0As66E153.5%0D%0A&MS=bm&MP=o&MC=66S153.5E&PC=magenta&DU=nm).

[bethpage89]

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.

[MD83FO]

Does anyone know an IOS application better than SUNFLIGHT to calculate sunset sunrise at altitude?

[roulishollandais]

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 !:)

[Virtual Reality]

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 ......... :ok:


VR :cool:

[de facto]

You bunch of sad ...:E

[Enecosse]

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.