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

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Re: Measuring (and Calculating) Dip
Date: 2013 Mar 8, 21:08 -0500

Hi Bruce

You wrote:
sighting a horizon on a perfect day with no water waves.

That's a fairly unusual day.  There's always energy and waves.  Perfectly flat really doesn't exist, even on small lakes.  Maybe on a pond.  On the ocean?  Never.  A different approach is to understand the affect of the waves on your measurement.  The distance to the horizon is generally accepted to be 3860 meters * sqrt(Height of Eye, meters).  We can find the angle of a wave by the arc-tangent( wave / distance).  Just sight to the tops of the waves when you measure.

You wrote
With your 1 second Wild (a superb theodolite)....

You aren't the first one to be caught by this.  Bill Morris, in New Zealand, owns the theodolite.  Brad Morris, in USA, owns a reflecting circle.  We aren't brothers or related in any way that we know of.  We both correspond on NavList, this time directly on one topic.  It gets a pinch confusing.

About your accuracy and repeatability.  You need about 20 measurements.  10 from below, 10 from above.  That will be sufficient for the determination of accuracy and repeatability, both unidirectionally and bidirectionally.  In my view, 100's of measurements will be a test of your endurance, a different matter entirely!

And heck yes, get down to the beach, determine your height of eye, measure your dip and record your met data.  Please share!

Best Regards
The one in the USA  ;-)

On Mar 8, 2013 10:02 AM, "Bruce J. Pennino" <bpennino.ce@charter.net> wrote:

I herewith admit that my curiosity has been pique,  so I checked out the precision specs on my Topcon total station theodolite.  I'm trying to "wrap my brain" about my true precision and accuracy in making a dip measurement.

My 30 X theodolite has an optical scale where there are numerical values and "marks"  every six seconds of arc.  It is very easy to estimate or measure to 3 seconds, ie, midway between the two scaled marks.  I can also the guesstimate to 1/2 of  that value.  So my  maximum error in reading the scale is at most 1.5 seconds.  From the manufacturer's specs,  not very understandable, the total measurement error  of the device for vertical angles seems to be 3 seconds, which seems to make sense.

The next question is " What is my repeatability?" in measuring  a  small vertical angle .  When the snow melts( there is about 14 inches now and still falling), I'll go to a football field, set up my theodolite with a prism such that I'm reading a small negative  vertical angle below the horizontal.... less than 20-30 minutes.  Take 50 or 100 readings, find the mean and standard deviation.  I'm thinking I should repeat this measurement sighting a 1/4 " tape, because the horizon at best is a line. I would try to  sight the precise top edge of tape. Repeatability of this would be determined.  After all of this I'll consider taking the equipment to a beach to determine my repeatability when sighting a horizon on a perfect day with no water waves.  Opinions please.  Finding small errors becomes tricky.

With your 1 second Wild (a superb theodolite), how repeatable are your dip  measurements on a calm day with a good sharp horizon?   I should go back and look at your posted  data, but I recollect there was significant  scatter, but there were waves?

Bruce

----- Original Message -----
Sent: Thursday, March 07, 2013 11:39 PM
Subject: [NavList] Re: Measuring (and Calculating) Dip

Hi Marcel

I do understand your concerns.  I'm not looking for a silver bullet or some magical formula that will somehow improve, with only a few sample points, on the fundamental dip equation.

That said, I, like you and others, expect to learn from our efforts.  Part of that learning experience will be to hazard guesses and theories and test them against what data we have.

We have no idea what a single statistical deviation from the nominal will be, nor how Friesenleben's data actually looked with respect to the equations.  He mentions in one article a sample size of 179 Data points.  Considering the variability in weather conditions and height of eye, that doesn't seem terribly large.

Dr. Young indicated an equation which I accepted strictly based on his expertise.  That equation predicted an unrealistic tsub0, which Bill Morris seems to think may be related to his vertical.  He's checking that now.  We'll see.

Don't read too much into these early assessments.  We're just getting started!

Best Regards

On Mar 7, 2013 9:49 AM, "Marcel Tschudin" <marcel.e.tschudin---com> wrote:

These dip equations may have given you the impression that they would allow you to calculate the dip "exactly" by considering some additional parameters than the height of eye only. However, the large uncertainties in the measurement of such additional parameters like e.g. the large relative errors of small temperature differences and the differences in atmospheric properties between assumed model and real condition, suggest, that the calculated values will scatter with considerable spread around the real ones. It could therefore well be that the NA did not consider such additional parameters because the error from their measurement (or their estimation) did not really lead to an improved accuracy of the calculated dip. Or, in other words, in the presence of the existing noise the signals of the additional parameters were too weak to be of real use. It is only by comparing with measurements that one can recognise how accurate a certain estimation procedure is. The publications from Freiesleben and Hasse do unfortunately not show how the proposed dip formulae compare with the measurements which they used for deriving them; i.e. they did not show by how much the calculated values scatter around the measured ones. May be you understand now  why I suggested to produce a systematically collected data set of measured Dips. Such a data set could serve as a reference for comparing the accuracy of different formulae.

Bill,
Thank you for your measurements which is a valuable drop in the bucket. The differences to calculated values may possibly only belong to the "natural" scatter. May I ask you the date, approx. time and approx. location of these observations? I ask you this just in case your measurements should become one day part of a substantial data set.

Marcel

On Wed, Mar 6, 2013 at 2:25 AM, Brad Morris wrote:

I have been having an off line conversation with Dr. Andrew Young at SDSU about calculating dip. As you may recall, Dr. Young's website at SDSU has a wealth of information about calculating dip and also about the green flash at sunset.

Andy, as he prefers to be called, has pointed out that I should be using Friesenleben's paper from 1954. This article appears in the Institute of Navigation release of 2007. I have attached it herein. (linked? a fine test of the new system!)

Andy was careful to point out that there was a typographical error in the paper, but then wanted me to find it. Sneaky way to see if I'm comprehending the paper or just mindlessly copying an equation. So after I found the typo, I confirmed it with Andy. He indicated that indeed the correct typo had been located. The equation in question should say
Dip=5.04*sqrt(.1123*h+tsub0-tsubh)
The typo is the last operator, correct is a minus sign, incorrect as published is the plus sign.

Why so much fuss? Because Dr. Young has stated that this is the best dip equation to use, assuming you don't fall into the typo trap! Andy specifically indicated that I should not be using Friesenleben's earlier (1948&1951) linearized equations (which I was, to wit Dip=1.74sqrt(h)-tsubh+tsub0 ) The delta temperature belongs in the square root.

+++++
Next, Andy was quite emphatic that I not use the water temp for tsub0. Tsub0 is the temperature (degrees C) layer of air right next to the water, not the water itself. Tsubh is the temperature of the air at eye level, degrees C.

When I asked him about how to calculate tsub0 as a function of the air temp, wind velocity and water temp temp; he responded as follows:

QUOTE
This has been very extensively studied by the boundary-layer meteorologists. I user the "Dyer-Businger" formulation of Monin-Obukhov similarity theory to calculate the temperature profile under unstable (i.e., inferior-mirage) conditions. The main problem is knowing what value to assign to the aerodynamic roughness length, as well as the Obukhov length itself (for which I rather arbitrarily adopted a value of -10 meters, as I don't usually have wind speeds or heating rates to do a proper calculation). R.B.Stull's "An Introduction to Boundary Layer Meteorology" (Kluwer, Dordrecht, 1988) is a very readable introduction to the subject; but you will need to consult journal articles to get into the necessary details.

Here's a quickie shortcut for you:

http://www.shodor.org/os411/courses/_master/tools/calculators/oninobukhov/index.html

END QUOTE

I just wanted to set the record straight on the calculation of dip. The more I understand, the less I understand.

One thing is becoming crystal clear to me. The dip corr'n, as provided by NA Table, contains major uncertainty. The effect of waves on the horizon, un-accounted for. The bob (heave) of the ship on the surface, un-accounted for. Any anomally in refraction, as it would affect dip, un-accounted for.

Kind Regards

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