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Hi Bruce

I compared your results to a nominal 0.971sqrt(h,feet).

Location HoE dipMeasured dipCalculated error

AP
5A 13.5 4.42  3.57  +1.15
5B 13.1 2.99  3.51  -0.52
5C 22.5 4.41  4.61  -0.20
BH
4B 627.0 23.10  24.31  -1.21
4C 676.5 24.50  25.25  -0.75

These aren't bad at all, in fact.

You can see that 5A and 5B are within inches of the same height yet the resultant measurements differ by 1.43 minutes.  This could be from
1) index or vertical error in setup
2) HoE error
3) measurement error
4) change in environment conditions

Are you measuring as Bill did?  That is front facing for point 1 then rotate in azimuth 180 degrees and flip elevation for point 2.  This eliminates and index or vertical error.

Its my view that getting HoE accurately measured is having an impact on all of our results (mine included).   I'm trying to use a GPS, but even with long term averaging I'm not 100% sure.   Bill managed to measure it directly.  I take it you measured 5A and 5B?  How?

You asked: " it would be nice to see dip equation with the geometric component standing alone and a separate "corrective" component. "

Geometric dip is just as Marcel shows;  DIPgeom = acos(6400000/(6400000+HoE,meters))

To find the refraction portion, again its as Marcel shows.  Assume k=.164 for nominal conditions.  Then calculate a new effective radius of the earth R=6400000/(1-k)=7655502meters.  Then calculate DIPrefr=acos(7655502/(7655502+HoE,meters))
Then finally the refraction portion only refrOnly = DIPgeom-DIPrefr

So DIP = DIPgeom - refrOnly.
(I'm pretty sure I've got the signs right, but as usual ...)

Marcel and I are attempting to correlate the corrections found in the Nautical Almanac for non-standard conditions, with our equations. We seem to be having some difficulty (or maybe its just me having difficulties!) So I will stop here. 

Regards
Brad

On Apr 6, 2013 10:28 PM, "Bruce J. Pennino" <bpennino.ce---net> wrote:

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Hello Frank, Brad,Bill, Marcel , Other folks with favorite dip equation, and All:

After looking at the recent posts today regarding the prediction of dip, I want to know if anyone has compared my measured dip to predicted dip? When I was at Blue Hill Observatory tower, my theodolite was within 10 ft of the weather data sensors!I sighted toward Boston Logan Airport where there is a weather recording station.

I've collected some met. data, but please get the data you need for your equations. How good or bad (compared to equations) were my measurements from BHO and Avery Point?

Here is the BHO data for April 1, 2013 at about 11:00 Eastern daylight time
Data Set 4A HoE 676.5 feet, measured dip 24.5 minutes. At BHO atmos. pressure 29.6" temp about 50 F

At Logan: atmospheric pressure 29.56", at 2:00 PM temp about 60 F

Data Set 4B on April 1, 2013 at 1 PM. HoE 627.0 ft, dip 23.1 minutes

Please look at the Avery Point data because I discovered there is a meteorological station at New London and at Ledge, Ct in Long Island Sound.
Precise location 41* 18' 18N, 72* 04 36 W. Ideal for taking data at Avery Point. On April 4, 2013, from 12 noon to 1 PM, air temp about 34 F (should be confirmed by you), atmos. press 1026.5 mb ; at 6 PM, temp 42 F about,
p=1023.8 mb.

Avery Point Data Set
5A HoE 13.5 ft measured dip = 4.42 minutes , at 12:30 or so
5B HoE 13.1 ft measured dip = 2.99 minutes , at 5 PM or so to 5:30

In an earlier email I had some typos.....sorry.

On a related point, it would be nice to see dip equation with the geometric component standing alone and a separate "corrective" component. One of my surveying books mentioned that the "corrective" component, mostly refraction I recollect, was roughly equal to 10-15 % of total measured dip. This was mentioned earlier.

Lastly, next weekend I'll be on Cape Cod where there are two beaches that will allow dip measurement. First Encounter Beach faces an often still Cape Cod Bay.
On another beach I might be able to measure dip up to 35 or 40 ft. I'll establish permanent vertical datums for easy set up at a later time. There is a weather recording station in nearby Provincetown.

Bruce
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