A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: Measuring (and Calculating) Dip
From: Bruce J. Pennino
Date: 2013 Mar 9, 17:24 -0500
From: Bruce J. Pennino
Date: 2013 Mar 9, 17:24 -0500
Hi Paul and All:
Thanks for comments on instrument error. I just drove around looking for objects at long range I can sight . I want to get some sense of my repeatability with my Topcon theodolite/EDM. We just got 24" of heavy wet snow,so these measurements must wait for it to melt. I found a spot where I can sight the top of a rounded water tank, distance a mile or so. I can see the same water tank from 5 or 8 miles away when I'm standing on the top of a dam. I've also found two spots where I can see Mt Wachusett (local ski hill) from a few miles and maybe 7 miles or so. I'll scale the distances from a map.
My logic is I can bring the horizontal crosshair from top down and from bottom up to these rounded surfaces and estimate the top elevation. The mountain has an irregular top so I'll have to "balance" the horizontal hairline to get an average top reading. The tank has a regular shape , so I would expect the vertical angles to show less scatter. When I'm on the dam I can sight the opposite waterline a 1 or 2 miles away.
Brad, you reminded me to calculate the random error that can result if one sights a water wave and tries to set the horizontal crosshair on the average top or average water level, whichever you intend to sight. If height of eye (Topcon or T2 horizontal crosshair) is 3 meters above water (10 ft), the horizon is about 4.1 miles away (6,686 m). Then a 1 FOOT error ( mismeasurement ) of the water line (horizon) introduces a 9.5 seconds arc error in measuring dip. Hopefully if you take ten or twenty readings this error cancels. But there is always bias of some sort. This is a tolerable error because my instrument precision (not accuracy) is probably only about +/- 3-5 seconds. An ordinary metal sextant only reads to 6 seconds, and the index error/correction is probably precise/accurate to +/- 6 or 12 seconds. I'm sure someone on the LIST knows far more than I do about the precision of index error.
So, big irregular waves could be a problem in measuring dip with a theodolite, but an error band on the data could be estimated.
I'll take the mountain top and water tank sightings in a week or two , then I'm going to find a quiet ocean cove, inlet or harbor.
----- Original Message -----From: Paul HiroseSent: Saturday, March 09, 2013 4:16 PMSubject: [NavList] Re: Measuring (and Calculating) Dip
Bill Morris wrote: > When I checked it, the theodolite turned out to have a substantial index error, quite enough to account for most of the differences between the dip from the NA and the dip I measured. > > I have negotiated another visit to the beach with the staff (wo)man and have removed nearly all the index error, a none-too-easy task with a bubble that has a sensitivity of 15 seconds per 2.5 mm movement. I will take readings off each face (not strictly necessary with the T2) if my assistant's patience will allow it. Bill, a mean of the readings on both faces is always good technique. It simultaneously reveals and eliminates index error. The T2 manual discourages single face vertical angle readings, except when one minute of error is acceptable and the theodolite is known to be in good adjustment (index error not more than 30 seconds). That is from the Wild manual for the late type T2 with automatic compensator. I understand yours has the manually centered vertical index bubble. However, I believe the recommendation above is still applicable, since the compensator only removes the effect of minor dislevelment, not index error. Even for their first order theodolite, the T3, Wild says the horizontal collimation and vertical index errors should be left alone unless they exceed 15 or 30 seconds, respectively. I have been able to adjust to that modest accuracy indoors by sighting through a window - far more comfortable than fiddling with the instrument outdoors. For your dip measurements, perhaps a reasonable compromise would be to do half on one face, half on the other. Or, begin by taking the vertical angle on both faces to some suitable target (not necessarily the horizon). Then do all dip measurements on one face. Finally, take another pair of vertical angles on both faces. The final target need not be the same as the first. In fact, a different target would be better - you would be unlikely to make the same reading blunder in the microscope. Before leaving the site, calculate and compare the initial and final index errors. I agree with your remark that the scale reading microscope "has its limits and variations." The U.S. Coast & Geodetic Survey first order triangulation manual says two successive readings on a Wild T3 should rarely differ by .3", and usually agree to .1". I'm not that good - "usually within .3, rarely within .1" is closer to my standard! -- I filter out messages with attachments or HTML.
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