Altitude correction, Sun, with reflecting artificial horizon

[stargazer]

The sun has a large apparent disc covering a big area. The lower limb has more atmospheric refractive bending than the upper limb. By the way, the bent light makes it look high, just like shooting at a fish with an arrow. With the lower limb appearing a bigger percentage higher than the upper limb, it makes the sun look flattened as it approaches the horizon.

So how have others been adjusting for the centerline of the apparent disc? Somewhere  between the upper limb and lower limb tabulated amounts, but not exactly half way which would not allow for the increased effect on the lower limb?

Heck, I'm not even sure how to figure the halfway point, which would at least be fairly close to correct. I added the two corrections, one is a negative number so I got a smaller negative number. Appears sensible but seems awfully easy, so I fear it may be wrong.

Anyone have any ideas or good/bad experiences?

Edit: I should have mentioned that I'm using a reflective artificial horizon.

[Fred_B]

The sun has a large apparent disc covering a big area. The lower limb has more atmospheric refractive bending than the upper limb. By the way, the bent light makes it look high, just like shooting at a fish with an arrow. With the lower limb appearing a bigger percentage higher than the upper limb, it makes the sun look flattened as it approaches the horizon.

So how have others been adjusting for the centerline of the apparent disc? Somewhere  between the upper limb and lower limb tabulated amounts, but not exactly half way which would not allow for the increased effect on the lower limb?

Heck, I'm not even sure how to figure the halfway point, which would at least be fairly close to correct. I added the two corrections, one is a negative number so I got a smaller negative number. Appears sensible but seems awfully easy, so I fear it may be wrong.

Anyone have any ideas or good/bad experiences?

The lowest I've shot the Sun in an AH is at about 5° off the horizon which would yield a 10° Hs.  That's very low and I had to lie on the ground far away from the AH.  People thought I was doing some weird prayer.

With an AH there are 3 different sights you can take of the Sun;

1- Upper Limb
2- Lower Limb
3- Center (superimposed)

From my experience here's what I've done in order or preference.

- Shoot the Lower Limb in the AH.

- Shoot the Upper Limb if clouds are in the way or something obscuring the
Lower Limb such as a tree branch.

- Shoot the sun superimposed in the AH.

I think what you're referring to as "half-way point" of the Sun is what is called the semi-diameter.  It's not the diameter- it's only part of the diameter.  Some genius, working on his doctoral thesis, probably came up with the term but it makes more sense than saying "radius".

If shooting the sun super-imposed in the AH no semi-diameter correction is necessary.  All I do is correct for refraction and maybe parallax.  Parallax at low altitudes is very small- about .14' from 0° to about 20° off the horizon.

Refraction is always subtracted and parallax is always added.

For refraction correction use TABLE 6.  Refraction which is found in HO-249 Vol 2. page 15.  Here- HO-249 Vol 2

(The same Table 6 is found in HO-249 Vol 3)

If you don't have Table 6 for refraction correction it can easily be calculated;

0.96 / Tan(Ha) 

Meaning- 0.96 divided by the Tangent of Ha

TheNauticalAlmanac.com has a lot of formulas here- Celestial Navigation Formulas

When using Table 6 base the altitude of your location at sea level.

The total corrections necessary to any sextant sight can be summarized by D.R.I.P.S.

Dip
Refraction
Index error
Parallax
Semi-diameter

When using the AH, since there is no Dip correction, Altitude Corrections Table for Sun, Star & Planets makes the determination of semi-diameter, parallax and refraction very easy (but only when shooting the Upper or Lower Limbs).

I hope that answers your question.

Fred
P.S. too cold here to make any sights- the water in the AH would freeze before I could lift my sextant.

[bletso]

Get a 1st surface mirror, no ripples, no freezing, (well except for you).  Remember to level it.  $20 for a 6 X 6 1/4 thick glass unit from www.firstsurfacemirror.com  It is more accurate to measure limb on limb.  Try UL in morning letting the sun rise up to the AH reflection and subtract semi-diameter.  In the PM LL let the sun fall into the AH reflection and add semi-diameter.

[LouisC]

Get a 1st surface mirror, no ripples, no freezing, (well except for you).  Remember to level it.  $20 for a 6 X 6 1/4 thick glass unit from www.firstsurfacemirror.com  It is more accurate to measure limb on limb.  Try UL in morning letting the sun rise up to the AH reflection and subtract semi-diameter.  In the PM LL let the sun fall into the AH reflection and add semi-diameter.

bletso, 

The problem is the cost of the levels.  They are expensive for precision ground vial levels (depending upon sensitivity).  I have no idea what sensitivity should be purchased.  Maybe 10 seconds?  Two would be needed for easier levelling.  I've seen a Plath AH.  

https://www.leveldevelopments.com/produc...und-vials/

Any ideas?

Louis

[bletso]

   

I bought two 80 mm - 20' / 2mm levels for $11 ea.  That is about 0.4 degrees.  Amazon  I also resurrected an old telescope mount for easy of levelling

[LouisC]

That's a solid looking arrangement of your AH.

Can you give us a link to the levels?


Lou

[bletso]

These are what I bought; http://www.amazon.com/Accuracy-Engineers...ge_o02_s00  If my math is correct they work out to 0.04 degrees  2mm deflection in 6M.

[LouisC]

These are what I bought; http://www.amazon.com/Accuracy-Engineers...ge_o02_s00  If my math is correct they work out to 0.04 degrees  2mm deflection in 6M.

Just ordered two of those levels.  Hopefully, the price isn't equal to the precision.

What have been your results with them?

Lou

[LouisC]

The levels arrived earlier this week. They were placed flat 90° apart on a first surface mirror (1/8") thick. The fs mirror was placed on a 1/2" thick piece or Corian. My AH has 3 screws for adjustment to level.

The results star sight LOPs were typically 10 to 15 to 20 nm from my actual position. I then removed the vials from their aluminum holders and placed them directly on the mirror. Same results.

But- for an unknown reason when a sun sight was taken, the 4 LOPs were perfect. They were right on top of each other and passed directly through my position.

The levels probably need some work or calibration to figure out where "level" is on them because certainly the bubble in the middle of the vial does not indicate level.

Lou

[Douglas Denny]

The sun has a large apparent disc covering a big area. The lower limb has more atmospheric refractive bending than the upper limb. By the way, the bent light makes it look high, just like shooting at a fish with an arrow. With the lower limb appearing a bigger percentage higher than the upper limb, it makes the sun look flattened as it approaches the horizon.

So how have others been adjusting for the centerline of the apparent disc? Somewhere  between the upper limb and lower limb tabulated amounts, but not exactly half way which would not allow for the increased effect on the lower limb?

Heck, I'm not even sure how to figure the halfway point, which would at least be fairly close to correct. I added the two corrections, one is a negative number so I got a smaller negative number. Appears sensible but seems awfully easy, so I fear it may be wrong.

Anyone have any ideas or good/bad experiences?

Edit: I should have mentioned that I'm using a reflective artificial horizon.

The diameter of the Sun is approx half a degree (angular subtense at the eye).

Theoretically there is a difference in atmospheric refraction  between the upper and lower limb due to the difference in altitude measured,  but this is completely negligible in practical celestial navigation.

If you look at Table A2 in the Nautical Almanac:  Altitude Corrections Tables 10 -   90, 
you can see the effect is not significant and does not become highly significant even when altitudes are becoming much less than 10 degrees . . .even when one is measuring altitudes down to around only one or two degrees altitude.

It is not recommended sights should be taken below 10 degrees in general if best accuracy is wanted,  because the absolute value of the refractive correction becomes uncertain due to local atmospheric conditions which can be very variable.

If lower than 10 degrees altitude sights are to be used,  then additional corrections are obtained with Table A4  Altitude Correction Tables - Additional Corrections.  I will be seen from this table that even at Apparent altitudes of only one degree to two degrees,  the difference in correction is only 0.9'  - where it follows for the Suns diameter of half a degree the difference between upper and lower limbs will be 0.45' . . . still only half a minute or error between upper and lower limb.

In Table A2 (used for most cases of sight correction for altitudes above 10 degrees),  you will see as an example the difference in correction for refraction between  altitude 9deg33'  and 10deg33' (a whole degree),  is only 0.4' (minute of arc).

It follows for the Sun's diameter of half a degree, the difference in refraction between upper and lower limb at altitude 10 degrees is therefore half of this   i.e.  0.2 moa.

For greater altitudes measured the difference will be even less.

At 50deg43' to 54deg46' for example,   the difference in correction is only 0.1 moa for an altitude difference of 4 degrees. 
It follows the difference in upper and lower corrections at altitude 50 degrees for the Sun 's diameter of half a degree is one eighth of 0.1 moa  i.e. 0.0125 moa  (which is equal to 0.75 seconds of arc).

This kind of refractive problem and corrections are only a difficulty with scientific precision astronomy.

Douglas Denny.  Bosham.  England.