# NavList:

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

**Re: Measuring (and Calculating) Dip with Mirage**

**From:**Brad Morris

**Date:**2013 Mar 20, 23:33 -0400

Hi Bruce

This is a multi step experiment.

In the first step, we debate and resolve the equations. That's clearly still in play, as the basic dip equation(s) are for standard dip. What equations should I use when the conditions aren't standard?

In the next step, we need to confirm that our equipment is suitable and that we have the skills needed to measure dip. How will we know? Answer: When we can measure standard dip. For example, in Bill Morris' first round of data, we saw a strange problem. Turned out to be index error. In Bill's second round of sights, he was very nearly spot on to standard dip. In my opinion, that's harder than it sounds and Bill has demonstrated that he can use a theodolite for dip, without reference to two horizons. With the Prismatic Reflecting Circle (PCR) and the Soviet Dip Meter (SDM), Alex and I demonstrated similar performance, albeit not as strongly as Bill. We can get a good match to points on the standard dip model. But in my viewpoint, that's not the objective at all!

The standard dip model works well, and really doesn't need improvement. Heck, we used it to confirm our equipment. Its when the conditions are non-standard that the dip model requires refinement. In my view, the anomalous refraction conditions *are* the objective.

I'm not throwing a single data point out! My objective is to understand more about the anomalous dip. Here's a short list of things that can produce anomalous dip: abnormal air pressure, abnormal air temperature, abnormal air temperature gradients and air-water temperature differentials. I'm sure there are more. Some of these are understood and we have accepted equations for them. Others are not. We simply do not have a "unified dip model", that accounts for everything and has a strong correlation with real world conditions.

This topic has been in play since celestial navigation began. It has always been the view that if we could only get enough data points, we could analyze and resolve the "unified dip model". Nobody has done it yet.

Add in a bobbing vessel, with random and chaotic waves and you can see the result, or rather, the lack thereof! So naturally, I decided to eliminate some of this by putting the equipment on land. It eliminates all of the motion of the vessel. Frank, in conversation, pointed out that this adds in all of the effects of the heated land. hmmm.

Well Bruce, I seem to have rambled off course again. I wanted to give you a sense of scale of the issue. Its the biggest unknown in celestial. Maybe we can contribute a tiny bit of understanding to the community.

Maybe I'm just tilting at windmills ...

Regards

Brad

Hi Brad:This is a learning experience.Now we know mirages apparently cause invalid dip data high by 3 minutes or more, and the data should not be included along with other results which are deemed acceptable. Hopefully an optics/refraction expert can tell us why the results are high so it will all make sense. It is good the data were all high; you were consistent!It is difficult for someone who has taken a bunch of data, invested a lot of time , money and effort, to throw it out. It is quite painful to explain to a paying client. BUT it is even worse to include bogus data along with good results. I'm sure many Navlist members have been through this painful experience...... myself a number of times...ouch!

Bruce----- Original Message -----From:Brad MorrisSent:Wednesday, March 20, 2013 1:06 PMSubject:[NavList] Re: Measuring (and Calculating) Dip

Hi Bruce We did three measurements on the ferry, all were high by more than 2'20". The average error was + 3'10". That's a lot to explain by measurement scatter, since all were on one side. Consider, the expected dip for standard conditions is 5'50". Our error term is very large. All of these measurements were taken when we could SEE mirages, like islands floating above the water. Alex and I agree that we measured anomalous dip. It persisted for more than 1 hour. We saw high readings with both instruments at Orient Point and on the ferry from Orient Point to New London. I think this lucky. Imagine the boredom should we always measure standard dip. :-( Brad On Wed, Mar 20, 2013 at 9:34 AM, Bruce J. Penninowrote: > ________________________________ > > Hi Brad: > > Everything you wrote makes sense , but I would say the the "six minutes of > error" is not error. I can already hear the mathematicians /statisticians > pouncing on me. It is scatter in your measurements due to "real world" > fluctuations in conditions. If you made 10 measurements and averaged them, > would the "six minutes" mostly "go away". The smaller the vessel, the > bigger the scatter. That is why I want to try to measure the vertical angle > to the horizon wave over the passsage of time and not use data from some > other location, no matter how close. All data comes after some sort of > filters are applied. It is very difficult to get clean data. I'm hoping I > can 'average out " the swells and short period waves, and obtain an average > horizon, which is what a viewer sees when looking through a relatively low > powered scope. > > I was quite surprised at my own scatter with a total station focusing on a > horizontal strap on a water tank at 2.5 miles. Greater scatter occurred > when I focused on a rounded mountain top at 12 .5 miles. However, my > average of the vertical angles seems to make sense. > > I'll try to make some beach measurements in a couple of weeks. > > Bruce > > > > > > > > > > > > > > > > > ----- Original Message ----- > From: Brad Morris > To: bpennino.ce---net > Sent: Wednesday, March 20, 2013 12:47 AM > Subject: [NavList] Re: Measuring (and Calculating) Dip > > ________________________________ > > Hi Bruce > > Glad to see you playing with the numbers for dip. That will come in handy. > > Its the refraction portion thats the tricky bit. Its affected by air > temperature gradient, air turbulence, water temperature, air pressure & etc. > Its been a basic problem for a long time. There is no obvious answer to the > calculation. > > The first and most obvious point is that instead of trying to calculate the > dip, you should just measure it. Then simply deduct the measured value > from the observed altitude (Ho). The SDM (Soviet Dip Meter) was designed > for exactly that purpose. It seems obvious and practical, yet did not > catch on. Perhaps the incremental increase in accuracy just wasn't worth > the labor & expense. > > As to the wave height correction, its clear that it can have an obvious > impact. Yet the advice to navigators is the overly broad "take your > altitude at the top of the waves". Without accelerometers and a reasonable > inertial integrator, I don't see how you would *know* that your vessel is > responding with the same amplitude of the predominant waves. That becomes > even trickier when the swell is coming from one direction and the wind waves > another, creating a "peaky" wave pattern (constructive/destructive > interference). > > Throw in turbulence of the air, odd air temperature gradients or non > standard pressure and its clear that the "standard dip" calculation will > yield incorrect results. Consider what Alex & I saw on the ferry up to > Connecticut. Our measurements showed up to *SIX* minutes of error. Wow! > Its not like we sucked at measuring, we could repeat our measurement (well, > nominally). We had some non standard condition that just didn't agree with > the standard calculation. > > Brad > > On Mar 19, 2013 10:35 PM, "Bruce J. Pennino"wrote: >> >> ________________________________ >> Hi Brad: >> >> Good. Glad to learn that your results makes sense and compare to dip table >> , more or less. >> >> Considering roundings, radius of earth,etc and exact trig formulas used >> dip (degrees) = .0298sqrt h meters is the same equation as dip (minutes) = >> 0.971 sqrt h ft . The latter is easier to remember, especially if you just >> remember square root of h ft. >> >> I did the basic trig/geometry formulation for dip from the viewpoint of a >> surveyor doing a circular curve layout as offsets from a tangent to a >> circle, with varying h. My results were the same as the nautical almanac, >> which closely agrees with a table in the front cover of Mixter, Primer of >> Navigation. >> >> Here are some results for Dip angle Minutes showing results from three >> sources: >> >> height of eye (ft) Distance to horizon NM Dip angle minutes >> Mixter Table Tangent Offset >> NA, .971 >> sqrt h Method >> >> 25 5.8 3.1 >> 3.1 3.1 >> 100 11.7 9.7 >> 9.8 9.8 >> 250 18.5 15.4 >> 15.5 15.5 >> 500 26.1 21.7 >> 21.9 22.0 >> >> etc up to height of eye = 4,000 ft. NOTE: Distance to horizon is >> approximate. >> >> Bruce >> >> >> >> >> >> >> >> >> >> >> >> >> >> >> >> >> ----- Original Message ----- >> From: Brad Morris >> To: bpennino.ce---net >> Sent: Tuesday, March 19, 2013 9:23 PM >> Subject: [NavList] Re: Measuring (and Calculating) Dip >> >> ________________________________ >> >> Hi Bruce >> >> The Nautical Almanac has a table giving dip. Its so commonly used its on >> the inside of the cover. >> >> Someone on the list, I forget who now (Paul H?), modeled that and >> determined that the table really is >> dip = 0.02977 * sqrt(h) >> Where dip is in degrees and h is the height of eye in meters. >> >> So instead of using the table and interpolation, I used that equation for >> 'standard dip'. >> >> Next I used my equation for wave height correction, which Mr. Reed >> pronounced as "bullshit". ;-) >> >> I then corrected the calculated dip by the waveheight. >> >> I then compared this value to the reading of either the SDM and or the >> PCR, ignoring the sign of the comparison. >> >> In cases where there was anomalous refraction (non-standard dip), the >> agreement was poor. This occurred at Orient Point and on the ferry to New >> London. We expected this because of the readily apparent mirages (islands >> floating ABOVE the water). >> >> In other cases, we had very close agreement. One observation was about 2 >> seconds from the calculated dip, probably due more to luck than skill at >> this point. I could not see apparent mirages, and so I expected standard >> dip to apply. We saw close agreement at Montauk Point and on the return >> ferry ride. >> >> I tried to get Mr. Reed to comment on the non-standard dip equation, where >> temperature and pressure are inputs, but his focus was ... elsewhere ;-) >> >> +++++ >> >> I'm not afraid to publish my equations. If they are wrong, the list will >> pounce and correct them for me! This means that as we get serious, the >> methodology will be properly vetted and we only need concern ourselves with >> the input data. >> >> I'm not afraid to publish my measured data. I need the practice with the >> instruments and not many people on list have access to this type of >> equipment. I do hope that theodolite data (yours!) can add to the mix. >> >> I will state that the SDM is a breeze to use, while the PCR can be a real >> pain. It took me ~ 3 hours to figure out my body movements to be even able >> to take the measurement with the PCR, while the SDM was intuitive and rapid. >> >> I hope that answered your questions. Feel free to jump in for >> clarifications. I don't mind being the strawman. >> >> Regards >> Brad >> >> >> On Mar 19, 2013 8:41 PM, "Bruce J. Pennino"wrote: >>> >>> ________________________________ >>> Sorry to say, but I don't follow all of the data you measured with the >>> SDM and PCR. >>> >>> Do the final values of dip as measured (and corrected by error term?) >>> from either or both instruments agree with the standard equation dip =0.971 >>> sqrt h, h in ft, dip in minutes of arc? If I subtract the error term from >>> the measured values, I calculate the dip as stated in the standard table?? >>> >>> Bruce >>> >>> >>> >>> >>> >>> >>> >>> >>> >>> >>> >>> >>> >>> >>> >>> >>> ----- Original Message ----- >>> From: Brad Morris >>> To: bpennino.ce---net >>> Sent: Tuesday, March 19, 2013 2:37 PM >>> Subject: [NavList] Re: Measuring (and Calculating) Dip >>> >>> ________________________________ >>> >>> To: All Concerned >>> >>> This past weekend, Alex Eremenko and I got together to measure some dip. >>> Alex is in possession of a Soviet Dip Meter ( >>> http://sextantbook.com/?s=Russian+dip+meter ). I am in possession of a >>> Prismatic Circle of Reflection ( >>> www.fer3.com/arc/imgx/Prismatic-Circle-of-Reflecti.ppt ). Both of these >>> instruments are capable of measuring the angle between two horizons. Yet the >>> optical principle in each is remarkably different. >>> >>> The Soviet Dip Meter (SDM) provides a direct reading of the average dip >>> between Dip A and Dip B. >>> >>> The Prismatic Circle of Reflection (PCR)requires mathematical >>> manipulation to provide the dip result. >>> >>> The calculation of dip is by the best fit to the Nautical Almanac or >>> dip=0.02977*sqrt(h), where h is the height of eye, in meters. The result is >>> in degrees >>> >>> The wave height correction is by atan((wvht/2)/(3860*sqrt(h))), where h >>> is the height of eye, meters, and wvht is the peak to trough predominant >>> wave height from the corresponding buoy. >>> >>> On 14 March 2013, Alex and I journeyed to Montauk Point. The height of >>> eye was estimated to be 13 feet and the waves were reported at 5.9 feet. >>> Thus, the calculated dip-wave height correction = 3' 8.95" (3minutes 8.95 >>> seconds). >>> PCR Measured 3' 22.5" >>> Error Term 0' 13.55" >>> >>> SDM Measured 5' 09.00" >>> Error Term 2' 00.05" >>> >>> SDM Measured 4' 39.00" >>> Error Term 1' 30.05" >>> >>> SDM Measured 5' 00.00" >>> Error Term 1' 51.05" >>> >>> On 16 March 2013, Alex and I journeyed to Orient Point. The height of eye >>> was estimated at 13 feet and the wave height was 1 foot. The calculated >>> nominal dip should have been 3' 28.97" Distinctly visible were mirages and >>> as a result we expected anomalous refraction and dip. >>> PCR Measured 10'05.50" >>> Error Term 6' 36.03" >>> >>> We then hopped on the Orient Point -> New London Ferry to see Frank Reed. >>> Height of eye was estimated to be 36 feet and the wave height continues at 1 >>> foot. Since the ferry is quite large and long, the wave height correction >>> continues as before. Calculated Dip is 5' 52.09". Mirages continued to be >>> visible. >>> >>> PCR Measured 8' 12.50" >>> Error Term 2' 20.41" >>> >>> PCR Measured 9' 17.50" >>> Error Term 3' 25.41" >>> >>> PCR Measured 9' 40.00" >>> Error Term 3' 47.91" >>> >>> SDM Measured 7' 12.00" >>> Error Term 1' 19.91" >>> >>> After a wonderful visit with Frank, we returned on the New London -> >>> Orient Point ferry. The same height of eye and wave conditions yields the >>> same calculated dip 5' 52.91". No apparent mirages were visible >>> >>> PCR measured 5' 50.00" >>> Error Term 0' 02.91" >>> >>> PCR Measured 6' 30.00" >>> Error Term 0' 37.91" >>> >>> +++++++++++ >>> >>> Frank - in >>> http://fer3.com/arc/m2.aspx/Biruni-radius-Earth-dip-FrankReed-jan-2011-g15188 >>> You wrote: >>> >>> beta = alpha0*Q*Re/s >>> and the equivalent "refracted radius" for the Earth is >>> R = Re/(1-beta) >>> where alpha0 is the the index of refraction of air minus one equal to >>> 0.000281, Q is just the usual temperature/pressure factor >>> (=(P/1010mb)/(T/283K)), Re is the true radius of the Earth, and s is the >>> scale height of the atmosphere. >>> >>> I believe this to fit into an equation of dip >>> dip = arcos((R/(1-beta))/(h+(r/(1-beta))) >>> where we have non-standard pressure and temperature. >>> >>> I would like to be sure that s is supposed to be 9000 meters. >>> >>> ++++++++ >>> >>> Alex has graciously permitted me to retain the Soviet Dip Meter for a >>> period of time, such that comparative measurements can be evaluated. Thank >>> you Alex. >>> >>> Best Regards >>> Brad >>> >>> >>> ---------------------------------------------------------------- >>> NavList message boards and member settings: www.fer3.com/NavList >>> Members may optionally receive posts by email. >>> To cancel email delivery, send a message to NoMail[at]fer3.com >>> ---------------------------------------------------------------- >>> >>> : http://fer3.com/arc/m2.aspx?i=122957 >>> >>> : http://fer3.com/arc/m2.aspx?i=122985 >> >> : http://fer3.com/arc/m2.aspx?i=122986 >> >> : http://fer3.com/arc/m2.aspx?i=122989 > > : http://fer3.com/arc/m2.aspx?i=122990 > > : http://fer3.com/arc/m2.aspx?i=122995