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## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

**Re: Refraction near the Horizon ? Observation vs. Calculation**

**From:**Brad Morris

**Date:**2013 Apr 8, 19:23 -0400

Hi Marcel

Now that I too have found the relevant section, I can see that the refraction correction is indeed as you thought, astronomic. The 'H' in R0=0.0167/tan(H+7.32/(H+4.32)) is the altitude of the body after dip is taken out.

This nominal refraction R0 is then adjusted for non-standard T & P by

f=0.28*P/(T+273)

where P is in millibars

and T is degrees C

The refraction for conditions is then R=R0*f

'f' therefore is perfectly synonymous with 'Q' in the adjustment of the refraction portion. We would adjust the refraction portion of our Dip by f or Q.

++++++

I solved for f under the 4 extrema of 880mb, 1082mb, Death Valley 57.7C and Antarctica -89.2C

f=0.28*880/283 = 0.870671

f=0.28*1082/283=1.071519

f=0.28*1010/(56.7+273)=0.857749

f=0.28*1010/(-89.2+273)=1.538628

I then resolved for Q1=(P/1010)/(283.15/T)

Q1=(880/1010)/1= 0.871287

Q1=(1082/1010)/1=1.072277

Q1=1/(283.15/(56.7+273))=1.164400

Q1=1/(283.15/(-89.2+273))=0.649125

I then tried Q2=(P/1010)/(T/283.15)

Q2=(880/1010)/1=0.871287

Q2=(1082/1010)/1=1.072277

Q2=1/(56.7+273)/283.15)=0.858811

Q2=1/(-89.2+273)/283.15)=1.540533

I think it clear that both Q1 and Q2 agree with f for pressure. From a practical standpoint, the first two digits after the decimal point are sufficient. It is also clear that only Q2 agrees with f for temperature. Q1 does not, Q1=1/f for temperature.

I'll leave it at this point for you to draw your conclusions. I've drawn mine

Brad

Thanks to all of you for the information regarding the N.A. The idea is to start by comparing my observations with results corresponding to the N.A. and then show whether better agreeing results can be found or not. Marcel On Mon, Apr 8, 2013 at 11:10 PM, Paul Hirosewrote: > ________________________________ > > Marcel Tschudin wrote: >> The refraction formula is indeed the one from Bennett in a form which >> provides the resutls in degrees. Bennett provided also a second >> formula for further improving the result of this first formula. Does >> your N.A. 1998 edition makes reference to it? > > There's no reference to a more accurate formula. > > The formula (including the corrections for pressure and temperature) > duplicates the almanac's high and low altitude refraction > tables within 0.1′ for the values I tried, assuming 10 C and 1010 mb. I > didn't test the almanac table A4 corrections for nonstandard conditions. > >> Just in case these finding should one day be documented in a paper: >> How is the correct reference to this N.A. edition? > > 1998 Nautical Almanac Commercial Edition, published jointly by Paradise > Cay Publication and Celestaire Inc., "Sight Reduction Procedures" > chapter, p. 280. > > Does anyone have a newer almanac? Are the refraction and dip formulae > still included? > > -- > > > : http://fer3.com/arc/m2.aspx?i=123455