Sun's True Bearing

[overshoot]

Anyone have a PDF version of TP 784E. This pub is only available in printed format and could take up to 4 weeks to get.

[200hr Wonder]

No but I do believe that it has been removed from the exams as of a few years ago.

[loopa]

No but I do believe that it has been removed from the exams as of a few years ago.

I had it on mine in 2008.

[ywgflyboy]

I had it on mine this summer!

[Airspeed-Alive]

If you're looking for the formula to figure it out send me a PM. For some reason I can't forget how to do it.

[loopa]

Why not share with the rest of us?

[Cat Driver]

I must be getting senile because I can't remember the formula, then again the last time I can remember using it was flying a Super Cub on Bradley big wheels on Banks Island in 1969.......it has to do with the time and your longitude and using the number 15 I think.

[ywgflyboy]

I was always taught to never look at the sun... So how can I use this formula?

[Cat Driver]

No need to worry about needing to know the formula in YWG because the magnetic compass works quite well there.

[Dagwood]

I don't have the Publication, but here is how to calculate the Sun's True Bearing:

You need the Zulu Time, your Longitude, and that handy little chart.

Take your Zulu time, and Subtract your Longitude west divided by 15, to find the hour, then take the remainder, and multiply by 4 for the minute. Easy!

Eg. Say you're 87`W at 1500Z

87/15 = 5 remainder 12.

so, you get 15Z - 5Hr = 10 Local minus 12*4 (48) minutes.

So, your actual local time is 9:12.

Plug that time into your chart, and viola, you get the Sun's true Bearing.

(Note that it is best to get the Zulu time from your GPS for accuracy, making this entire procedure a moot point.)

[Spandau]

A conversation at work the other day brought this topic up. There's actually an easier way to figure it out that was taught to me by the man that taught me to fly Twin Otter offstrip many years ago. He explained it like this:

The local hour angle (LHA) of the sun is the Greenwich hour angle (GHA) minus your west longitude or add you east longitude. I think the formula from "From the Ground Up" reads something like:

LHA = GHA -W/+E Longitude

But you don't need a table to figure it out, you can do it in your head. At noon on the Greenwich Meridian (0 degrees Long) the sun is at 180 degrees True. Everyday. It's altitude will change a little depending on your latitude and what day of the year it is but in the directional plane it will always be at 180 degrees True. Period. We also know that there's 360 degrees in a circle and 24 hours in a day, so relative to us and the Catholic Church the sun moves 15 degrees an hour (360/24 = 15), which it has to in order to be back in the same place this time tomorrow. Accepting this we can deduce a couple of things: if the sun is at 180 at noon, everyday, it must therefor be at 360 degrees True at midnight, every night. Expanding on that we can determine that at 0600 GMT the sun must then be at 090 degrees True. And if that is true then the sun must also lie at 270 degrees True at 1800Z. Starting from here we can make a pretty quick calculation as to what the sun's true bearing on the Prime Meridian is in our head. As I write this it's 1610Z. If the sun lies at 270 True at 1800Z and moves at 15 degrees an hour (which is 5 degrees every 20 minutes) the GHA of the sun right now would be 270 - 30 + 2.5 (call it 3) or 243 degrees True. My longitude according to my GPS at the moment is W113 42. Call it 114. 243-114 = 129. The LHA of the Sun, right now, for me, is 129 degrees True.

Not much magic in that, is there? And if because of the time of day and your Longitude you ever end up with a negative number as the sum of your calculation, just add 360 to it.

There's a slightly more refined version that escapes me, something like you take your calculated LHA and then multiply it by the cosine of you latitude or something, but it's not necessary. This calculation will give you something close enough to shoot an NDB approach with. I've done it many times.

[pelmet]

I must be getting senile because I can't remember the formula, then again the last time I can remember using it was flying a Super Cub on Bradley big wheels on Banks Island in 1969.......it has to do with the time and your longitude and using the number 15 I think.

GMT times 15 minus westerly longitude. Then set up the astrocompass....or an E6-B with a pen for a shadow.

https://www.google.ca/search?q=astro+co ... H4o3z1B06M:

But then again, how would you use the sun to get back to Ellesmere Island if you were at the north pole and your GPS failed seeing as every heading is south.

[Spandau]

You have to pick the line of Longitude that you want to travel south on.

[photofly]

But you don't need a table to figure it out, you can do it in your head. At noon on the Greenwich Meridian (0 degrees Long) the sun is at 180 degrees True. Everyday. It's altitude will change a little depending on your latitude and what day of the year it is but in the directional plane it will always be at 180 degrees True. Period.

Not true.

The sun transits the Greenwich meridian ahead of noon GMT by up to 16 minutes and behind by up to 14 minutes depending on the time of year. The discrepancy between mean solar time and apparent (observed) solar time is called the Equation of Time:
https://en.wikipedia.org/wiki/Equation_of_time
It even changes year-to-year.

It is not easy to calculate, and you cannot do it "in your head". That's why tables are published.

The position of the sun at the same time (say noon) every day of the year traces a curve called the analemma:
https://en.wikipedia.org/wiki/Analemma

In fact the sun is overhead Greenwich at noon precisely on only four days per year:

Analemma plotted as seen at noon GMT from the Royal Observatory, Greenwich (latitude 51.48° north, longitude 0.0015° west).
https://upload.wikimedia.org/wikipedia/ ... _Earth.png

if the sun is at 180 at noon, everyday, it must therefor be at 360 degrees True at midnight, every night. Expanding on that ...

It isn't, and you can't.

[Spandau]

Well sir, it works empirically. 14 or 16 minutes one way or the other is only on the order of three or four degrees anyway - well within an acceptably workable margin. This isn't rocket science, it's flying an airplane.

[pelmet]

You have to pick the line of Longitude that you want to travel south on.

Hmmm....sounds like a plan but how exactly are you going to do that? You don't want to end up in Russia you know.

[Spandau]

Approach the problem like this; you're at the North Pole, so everywhere on earth is south. But "which south" do you want to go? You know the GHA from either the Almanac or the "quick and dirty" way, and you know which line of longitude you want to go home on.

I have been to "the Pole" (very overrated experience) and have never been to Russia - not even accidentally.

[pelmet]

Approach the problem like this; you're at the North Pole, so everywhere on earth is south. But "which south" do you want to go? You know the GHA from either the Almanac or the "quick and dirty" way, and you know which line of longitude you want to go home on.

OK, so you have decided that you want to go to Alert and it is 1200Z. How do you ensure that you are flying southbound on the proper line of longitude? Your partner Twin Otter is broken but once fixed, can takeoff at 16Z. What will he do?

[Spandau]

You're right, in that kind of scenario up at the pole you can't really do it "from the hip". Let me blow some dust off the books when I go back to work next week, dig out an astro compass and I'll try and explain the math. I haven't thought about this in quite awhile. Even when I was doing it often we just GPS'd it to our best guess as to where the fuel cache should be (it moves) and then headed for Eureka.

[pelmet]

You're right, in that kind of scenario up at the pole you can't really do it "from the hip". Let me blow some dust off the books when I go back to work next week, dig out an astro compass and I'll try and explain the math. I haven't thought about this in quite awhile. Even when I was doing it often we just GPS'd it to our best guess as to where the fuel cache should be (it moves) and then headed for Eureka.

Actually, just use the position of the sun to figure out what track to fly. At 12Z, it is over 0 degrees longitude(or very close to it) which is 60 degrees to your left as you fly toward Alert(it is actually at 65 degrees W but you should pick up the NDB as you get closer). Four hours later, the sun will have moved 60 degrees(15 per hour) so adjust it to be 15 degrees further to the right per hour as you head toward Alert. The guy starting at 16Z can head toward the sun initially. Maybe make a mark on the window every half hour and keep a shadow in place for that time period to prevent wandering. The resultant leg will be a series of straight lines with a heading change every 30 minutes that generally heads toward your destination. Hopefully you had enough fuel for Eureka anyways with....shhhhhhh....in-flight refueling and the false logbook entry that you stopped somewhere enroute and refueled for a "max gross weight" takeoff. Well, I heard that used to happen on occasion.

Of course one might say...but what about on a cloudy day or at night but who goes to the north pole at night and who goes on a cloudy day when you don't have proper lighting to analyze the icepack for landing.

All subject to confirmation by others....otherwise, I might be the one to end up in Russia.

[photofly]

Worth remembering that at the north pole, civil polar night lasts for weeks!

[photofly]

Spandau’s method is based on assuming the sun’s azimuth angle varies linearly with time of day, at 15 degrees per hour.

Some though will convince you that’s not true anywhere except at two spots, one in the polar region of each hemisphere, on any day. It may be “good enough” at high latitudes but it’s not even slightly true at the equator: if you’re on the equator (at one of the equinox days, to make things easy) the sun rises in the east, and stays in the east, switching instantly to west as it passes overhead at noon. It’s never anything other than directly east, overhead, or west.

So while the sun sweeps out 15 degrees of longitude per hour at the pole as it trundles around the horizon (again, let’s assume on one of the equinoxes) this is less and less true when you move away from the pole.

In general the sun’s azimuth angle changes fastest at culmination, when it’s highest in the sky. At the equator the azimuth rate is zero the whole day except for the instant when the sun is exactly overhead when it sweeps infinitely fast, 180 degrees from east to west in no time at all.

There’s an equation for the azimuth angle on wikipedia: it’s not something you can do in your head:
https://en.m.wikipedia.org/wiki/Solar_azimuth_angle

More generally this is the difficulty in converting from azimuth/altitude coordinates (easy to measure by observation) to hour-angle/declination coordinates (easy to coordinate to solar time).

[Spandau]

While that may be true, one generally does not operate in True in the vicinity of the equator, it's more of a fairly northern (or southern) latitude thing. But for the sake of argument, you are correct.

[Spandau]

You're right, in that kind of scenario up at the pole you can't really do it "from the hip". Let me blow some dust off the books when I go back to work next week, dig out an astro compass and I'll try and explain the math. I haven't thought about this in quite awhile. Even when I was doing it often we just GPS'd it to our best guess as to where the fuel cache should be (it moves) and then headed for Eureka.

Actually, just use the position of the sun to figure out what track to fly. At 12Z, it is over 0 degrees longitude(or very close to it) which is 60 degrees to your left as you fly toward Alert(it is actually at 65 degrees W but you should pick up the NDB as you get closer). Four hours later, the sun will have moved 60 degrees(15 per hour) so adjust it to be 15 degrees further to the right per hour as you head toward Alert. The guy starting at 16Z can head toward the sun initially. Maybe make a mark on the window every half hour and keep a shadow in place for that time period to prevent wandering. The resultant leg will be a series of straight lines with a heading change every 30 minutes that generally heads toward your destination. Hopefully you had enough fuel for Eureka anyways with....shhhhhhh....in-flight refueling and the false logbook entry that you stopped somewhere enroute and refueled for a "max gross weight" takeoff. Well, I heard that used to happen on occasion.

Of course one might say...but what about on a cloudy day or at night but who goes to the north pole at night and who goes on a cloudy day when you don't have proper lighting to analyze the icepack for landing.

All subject to confirmation by others....otherwise, I might be the one to end up in Russia.

That would work, I suppose - I see where you're going with it.

We did generally have a fuel cache around 88 north, but it was usually continuously making about two or three knots. During the last few seasons there was often a (brave) guy staying there and relaying his position back to Resolute every few hours so we'd usually have a position update via HF. I think he'd get moved back "upstream" with every new cache. The homer in the Twin Otter would only pick up the beeper at the cache from about twenty miles or so (when it worked) as I recall. I think the tourist trips to the pole have basically stopped now as there's just no way to even remotely make it look legal. On wheel-skis with bellies and tips we were probably fifteen and change if we were an ounce.

You can't go to the pole when the light is flat, it is strictly a VERY vfr operation. The pressure ridges there are monstrous in places. It really makes you appreciate pavement.

[North Shore]

So why is this even a thing?
It seems to be a dusty, little used corner of aviation knowledge with a very specific target audience. And, if you do need it, it's more than likely that you'll be taught it as OJT by an experienced vet.