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pgrig

"Geodetic Azimuth" and RMs (Again)

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I think I'm missing something.

 

A couple of weeks ago, I asked about the definition of "geodetic azimuth" as applied to a station's reference marks. I believe the consensus was that these were true (not magnetic) bearings from the station to the RM.

 

So the next couple of stations I found that actually had "box scores" and multiple RMs, I worked at finding the RMs (see MY4530 and MY4520). But my notes indicate that I measured these as magnetic bearings from the station to the marks. Both Descriptions are from 1934.

 

What's up?

 

-Paul

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pgrig -

 

Looking at the NGS datasheets for your two stations, the BOXSCORES list the "Geod. AZ." for the RMs. Geodetic azimuth is, to the best of my knowledge, belief and experience a true (not magnetic) direction from the station to the reference mark.

 

According to the NGS' website, the magnetic declination for the Boston, MA, area is - 15 degrees (the magnetic pole appears to be 15 degrees west of true north).

 

My question to you is this: you state that you found the RMs by using magnetic bearing (or, you measured the magnetic bearing of the RMs from the station). What do you mean by this? Do you mean that you took the value of the geodetic azimuth fopr RM1 of MY4530 (Geod. az. = 038-55-00 degrees) and determined that the RM is actually 039 degrees magnetic from the station?

 

What device did you use to measure the magnetic bearing? Handheld magentic compass or handheld GPS unit?

 

Will

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Hi Will--

 

You ask:

 

 

My question to you is this: you state that you found the RMs by using magnetic bearing (or, you measured the magnetic bearing of the RMs from the station). What do you mean by this? Do you mean that you took the value of the geodetic azimuth fopr RM1 of MY4530 (Geod. az. = 038-55-00 degrees) and determined that the RM is actually 039 degrees magnetic from the station?

 

Answer, "Yes."

 

For both RM1 at MY4520 and RM1 at MY4530, I took a bearing from the station to the RM, using a handheld Brunton pocket transit adjusted for 15 deg. W declination (so that North bears 345 deg.). In both cases, I believe the readings I obtained came very close (I didn't actually record these readings) to those listed on the datasheets in the box scores for the "Geod. Az" of each RM. I didn't record them precisely because I had already found both the station and the RM in each case. I just marked on each datasheet "frm stn to mark, magnetic." I remember being surprised at first that they checked as magnetic bearings, since I had been told previously to expect true bearings from the the box scores.

 

I don't think I simply overlooked a 15 deg. error in the measured bearing, but if you tell me yes it MUST be a true bearing, then that's the only possibility. It would then be time to go back and measure again. :laughing: But it wouldn't be the first time today I'd been told to go back and try again. I'm still learning...

 

-Paul

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<snip>

Brunton pocket transit adjusted for 15 deg. W declination (so that North bears 345 deg.)<snip>

 

Adjusting for 15º declination suggests your Magnetic instrument should now indicate True North.

 

Unless you adjust it the wrong way, in which case your readings would be off by 30º. :laughing:

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Hi Again, Will--

 

If the procedure I just used as a cross-check is correct, then I must have just been hasty when I visited these two sites, not really measuring my bearings, but just quickly checking the general direction of the RM's from the station/s, since I could SEE them and wanted to get moving... :laughing:

 

I went to my hard copy Google map for MY4530. I accepted the Google "map pin" as the station location (it checks fairly well with my recollection of the actual position). Assuming that the Google maps have their North orientation as True North, I marked off a bearing of N 39o E for the bearing of RM1 from the station, and this checked with what I recalled for the mark's actual position (it's right in the curb at the street end of the driveway) almost exactly. Adding 15o to this would put the RM way out of the way.

 

If "Google North" = True North, then I was just careless in assuming my RM bearings.

 

I went back over my 150 or so site visits to date, and found only about a half-dozen that were "Founds" and had sets of box score RMs that were "workable" (distances under 75' and not clearly destroyed over the years). So I guess I hadn't really needed to focus on this question of "Geodetic Az" bearings yet.

 

If my assumption re Google is correct, then, as Emily Latella used to say, "Never mind" about my question...

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Your terminology and procedure is perhaps confusing.

 

If you have the proper magnetic declination set off on the compass then the bearings read from it will correspond to true bearings. The fact that you are using a compass to determine this does not mean that the bearings are magnetic. If you had set 0 degrees declination on your compass and read it correctly... THEN .. the bearings you obtained would be magnetic.

 

If your bearings obtained by the compass with the correct declination set off on it, correspond to the data sheet then all is as it should be. But you cannot say that they are magnetic bearings. You can say that they are bearings obtained by a compass with a declination of 15 d W set off. All you need to know and do is state that and you are fine. If it turned out that you had your compass set to 10 degrees west, that would be critical information for anyone trying to interpret your readings.

 

It is always important when using a compass to know the declination that the compass instrument has set off, and the approximate date that the reading was taken. This would allow anyone following your description to determine what you actually did, and compare it to what the proper settings might be and adjust accordingly.

 

Compass' can be very confusing in terms of whether the proper declination has been set off -and- whether it is set off in the right direction.

 

- jl wahl

 

 

Answer, "Yes."

 

For both RM1 at MY4520 and RM1 at MY4530, I took a bearing from the station to the RM, using a handheld Brunton pocket transit adjusted for 15 deg. W declination (so that North bears 345 deg.). In both cases, I believe the readings I obtained came very close (I didn't actually record these readings) to those listed on the datasheets in the box scores for the "Geod. Az" of each RM.

 

Edited by jwahl

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Thank you, jlw. I'll try to use better terminology in the future!

-Paul

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Paul -

 

I am convinced that the geodetic azimuths listed in the boxscores in NGS datasheets are relative to true north, not magnetic north.

 

The magnetic declination for the Washington, DC, area is - 12 degrees.

 

The gridlines on USGS topo maps are oriented true north-south.

 

The boxscore in the NGS datasheet for HV4442, (WASHINGTON MONUMENT) states that the geodetic azimuth from the Washington Monument to HV4165 (FINIAL ON THE DOME OF THE LIBRARY OF CONGRESS) is 91-52-43.2 degrees.

 

Using the NGS INVERSE calculator and the adjusted horizontal coordinates for the two above-named stations, the calculated forward azimuth from HV4442 to HV4165 is 91-52-43.2167 degrees.

 

So, for whatever it's worth, the boxscore for HV4442 and the NGS INVERSE calculator agree.

 

Now, if I plot a line between the Washington Monument and the Library of Congress on the Washington West USGS topo sheet (both stations are easily and reliably identifiable on the chart), extend the straight line to the west of the Monument so that it crosses several north-south gridlines (just to have more than two measurements upon which to base my conclusion), and measure the angular difference between the plotted line and the several gridlines, I get 092 degrees every time.

 

Conclusion: If the boxscore for the Washington Monument is representative of all NGS datasheets (that is, if "Geod. Az" means the same thing on every datasheet), then "Geod. Az" is an expression of an azimuth (or direction or bearing) relative to true north.

 

Will

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Don't know if this will help but

 

The astronomic azimuth is defined as the angle measured in the horizontal plane between the

astronomic meridian of P1 and the vertical plane spanned by the vertical at P1 and by point

P2. This value is physically measurable, and is what we measure when we observe the sun,

polaris, or other objects in space using an instrument which measures with respect to the

local plumb line (i.e. theodolite). The astronomic azimuth can also be determined by using a

gyro-theodolite, such as the Wild GAK-1.

 

The geodetic azimuth is defined as the angle measured in the horizontal plane between the

ellipsoidal meridian of P1 and the vertical plane spanned by the normal to P1 and by point P2.

This appears to be the same as the definition given above for astronomic azimuth. There are

two differences, namely the meridian (ellipsoidal versus astronomic) and the vertical

(affected by gravity) versus normal (normal to ellipsoid, mathematical quantity) reference.

The geodetic azimuth is what is determined using GPS, but is not directly measurable using

any other common survey equipment. However, if one were to sight another survey station,

and compute the geodetic inverse, then the resulting azimuth is a geodetic azimuth.

Similarly, this is the type of azimuth required in the “direct” geodetic problem, where it is

desired to compute the coordinates of P2, given the coordinates of P1, the geodetic azimuth,

and the ellipsoidal distance between the two. Although the difference between the

astronomic and geodetic azimuths is usually small, it is important to understand the

difference, and know how to transform one to the other when needed.

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Don't know if this will help but

 

WHAT IS AN AZIMUTH?

An azimuth is defined as a horizontal angle reckoned clockwise from the meridian. There are

several types of "north". Astronomic north is with respect to the astronomic meridian, which

varies from point to point in an irregular manner under the influence of gravity. Geodetic

north is with respect to the ellipsoidal meridian, which differs from the astronomic meridian

by a varying amount. Grid north is with respect to a central meridian of a mapping

projection. Finally, magnetic north is the direction of the magnetic field of the earth. This

also varies from point to point (and over time) in an irregular manner. The astronomic north

is often used (incorrectly) in geodetic computations, although the geodetic north is what is

required. The difference between the two (Laplace correction) is due to the deflection of the

vertical in the prime vertical, caused by variations in gravity. Actually, the Laplace

correction is a function of the east-west slope of the geoid. Astronomic north does have some

uses, for example, to align inertial navigation systems. The magnetic declination at a point

can be interpolated using a model from the USGS. However, the accuracy of determining

geodetic north using a compass is about 1°, at best, and will not be addressed further. This

paper will deal with the first three types of north mentioned, namely astronomic, geodetic,

and grid, and the relationships between the three. For explanation purposes, P1 is the

standpoint (i.e. occupied by the theodolite) and P2 is the forepoint (i.e. occupied by a target).

 

The astronomic azimuth is defined as the angle measured in the horizontal plane between the

astronomic meridian of P1 and the vertical plane spanned by the vertical at P1 and by point

P2. This value is physically measurable, and is what we measure when we observe the sun,

polaris, or other objects in space using an instrument which measures with respect to the

local plumb line (i.e. theodolite). The astronomic azimuth can also be determined by using a

gyro-theodolite, such as the Wild GAK-1.

 

The geodetic azimuth is defined as the angle measured in the horizontal plane between the

ellipsoidal meridian of P1 and the vertical plane spanned by the normal to P1 and by point P2.

This appears to be the same as the definition given above for astronomic azimuth. There are

two differences, namely the meridian (ellipsoidal versus astronomic) and the vertical

(affected by gravity) versus normal (normal to ellipsoid, mathematical quantity) reference.

The geodetic azimuth is what is determined using GPS, but is not directly measurable using

any other common survey equipment. However, if one were to sight another survey station,

and compute the geodetic inverse, then the resulting azimuth is a geodetic azimuth.

Similarly, this is the type of azimuth required in the “direct” geodetic problem, where it is

desired to compute the coordinates of P2, given the coordinates of P1, the geodetic azimuth,

and the ellipsoidal distance between the two. Although the difference between the

astronomic and geodetic azimuths is usually small, it is important to understand the

difference, and know how to transform one to the other when needed.

 

reference: http://www.terrasurv.com/azimuths.pdf

Edited by Z15

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...

The gridlines on USGS topo maps are oriented true north-south.

...

Terminology clarification:

 

To be precise, the gridlines on topo maps are the lines that indicate the UTM (or whatever projection was used for the sheet) easting and northing in meters, and are not exactly north and south, but are slightly tilted with respect to true north, although they are aligned to the boundary lines (the neat line) of the map. The graticule, if present, is the lines that indicate the latititude and longitude. They will normally be slightly tilted with respect to the grid and neat line, but they will indicate true north.

 

On the printed topo maps, there is usually a north arrow that shows the difference between true north, grid north, and magnetic north.

 

edit: correction -- on the USGS topo quads, the boundary neat line is not aligned to the grid, but rather to the bounding parallels and meridians for the sheet. If you look closely, however, you can see that the boundary is not exactly parallel to the edges of the sheet or the projection grid.

Edited by holograph

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WIKI:

True north is compared to magnetic north (the direction of the magnetic north pole) and grid north (the direction northwards along the grid lines of a map projection).

 

The direction of true north is marked in the skies by the north celestial pole. For most practical purposes, this is the position of Polaris. However, due to the precession of the Earth's axis, true north rotates in an arc that takes approximately 25,000 years to complete. In 2002, Polaris was at its closest approach to the celestial north pole. 2,000 years ago, the closest star to the celestial north pole was Thuban.

 

On maps issued by the United States Geological Survey, and the U.S. military, true north is marked with a line terminating in a five-pointed star. Maps issued by the Ordnance Survey contain a diagram showing the difference between true north, grid north and magnetic north at a point on the sheet.

 

Now with the Westward progression of the Stars or Annual Westward slippage.(The North Star Polaris) was not the original Pole Star.

It has moved farther west.

As has the magnetic declination.

 

Now we would have to go back and back calculate to find out what REAL True North is (was) for a specific time frame.

From the observance on the USGS maps that were done around the 1960s and field checked in the 70s the difference on the 5th Principal Meridian is approximately 1.5 degrees.

 

If you use an Astrolabe and pre date it farther back you see this cumulative effect of this annual Westward Movement.

 

But maybe OH well just another theory......................

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It's true that the 5th Principal Meridian does not run due exactly North-South (astronomic, geodetic, true, whatever). Based on what I've observed from USGS 7.5 minute topo maps, the section of the 5th Principal Meridian that runs from the mouth of the Arkansas River to the Initial Point (established by Prospect Robbins and Joseph Brown in 1815) has an azimuth of about 1 degree (1 degree East of "True" North.) However, I don't think this divergence has anything to do with the precession of the Earth. It's my understanding that surveyors in the early 1800's were well aware that polaris appears to rotate around celestial North. That's why they would normally make their star observations at Eastern or Western elongation, when Polaris' East-West motion was minimal and when the azimuth of Polaris could be accurately determined. So in theory, finding "true" North (actually determining magnetic declination) wasn't a problem. I think the problem was in accurately placing the line on the ground using the tools of the day (compass and chain) through heavily forested low-land hardwood swamps.

Edited by tosborn

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The original GLO surveyors operated under instructions from a particular Surveyor General. In that era the instrument used was the well known survey compass which had a vernier for setting off the declination. Many early instructions provided relatively easy ways to obtain true north at any place from polaris at upper or lower culmination by means of 'pointer stars' in adjacent constellations.

 

However one theory is that in regards to the 5th PM, it may be that the surveyors set their instruments based on an established meridian or true north line at the surveyor general's office in St. Louis and then proceded down the river and commenced their surveys. The fact that the magnetic declination varies with time and place was known in that time frame, but perhaps not known to everyone.

 

In any case there is a difference between the proper declination at St. Louis and down in SE Arkansas that one theory has it, they did not correct for and this accounts for what we refer to as the "Arkansas Windage". Apparently other subsequent deputy surveyors used existing lines to set their compasses and perpetuated the basis of bearing which was off.

 

There is no where else in the PLSS, (except all the oddities in Ohio), where this occurred and most of the PLSS is on the average at least fairly well oriented to true north.

 

- jlw

 

 

It's true that the 5th Principal Meridian does not run due exactly North-South (astronomic, geodetic, true, whatever). Based on what I've observed from USGS 7.5 minute topo maps, the section of the 5th Principal Meridian that runs from the mouth of the Arkansas River to the Initial Point (established by Prospect Robbins and Joseph Brown in 1815) has an azimuth of about 1 degree (1 degree East of "True" North.) However, I don't think this divergence has anything to do with the precession of the Earth. It's my understanding that surveyors in the early 1800's were well aware that polaris appears to rotate around celestial North. That's why they would normally make their star observations at Eastern or Western elongation, when Polaris' East-West motion was minimal and when the azimuth of Polaris could be accurately determined. So in theory, finding "true" North (actually determining magnetic declination) wasn't a problem. I think the problem was in accurately placing the line on the ground using the tools of the day (compass and chain) through heavily forested low-land hardwood swamps.

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Jerry:

 

Thanks for that.

 

I've heard you speak about the "Arkansas Windage" before, but I don't think I heard a possible explanation for why it may have occurred. It's interesting that this phenomenon is unique to this part of PLSSia.

 

I've read through the 1815 field notes of Prospect Robbins and Joseph Brown and I don't find any mention of how they set the "variation of the needle" nor do they even mention periodically checking the length of their chains. Some 15 years later in 1830, Deputy Surveyor Nicholas Rightor who did a lot of work in Arkansas establishing townships and sections does mention such things. Apparently in retracing portions of the 5th P.M. he determines that his compass must be set to a variation of 8 degrees to 8 degrees 10 minutes East to coincide with the 5th P.M., and as you say, he perpetuates that direction. One thing that I am unsure of it why doesn't the Arkansas Windage eventually get filtered-out at some Guide Meridian East or West of the 5th P.M.?

 

In checking historic declinations from the National Geophysical Data Center website, it indicates that the declination at the 5th P.M. initial point was 8d 22' E in 1815 and 8d 36' E in 1830. In St. Louis, the NGDC indicates the declination was 8d 10' in 1820 and 8d 14' in 1830. Based on that it doesn't appear that the declination difference between St. Louis and SE Arkansas would account for the "Arkansas Windage." Of course, the NGDC declination numbers are modeled and are apparently only accurate to about 30 arc minutes.

 

Do you know of any other information that would give a clue as to what Robbins and Brown actually did other than their terse field notes? Are there other theories that would account for the Arkansas Windage?

 

Tim Osborn

Edited by tosborn

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I have to admit that I have never verified whether that theory worked out or not. It was just a theory that I have heard to try to explain a 'why'. If the St. Louis difference does not work then perhaps someone decided to use a specific declination from some prior surveys.

 

I will do more investigation and see if I come up with anything. If the standards and guide meridians all used the same incorrect declination or assumptions then it would never be corrected. It seems like once they got up to southern Missouri someone decided to straighten it out.

 

- jerry

 

Jerry:

 

Thanks for that.

 

I've heard you speak about the "Arkansas Windage" before, but I don't think I heard a possible explanation for why it may have occurred. It's interesting that this phenomenon is unique to this part of PLSSia.

 

I've read through the 1815 field notes of Prospect Robbins and Joseph Brown and I don't find any mention of how they set the "variation of the needle" nor do they even mention periodically checking the length of their chains. Some 15 years later in 1830, Deputy Surveyor Nicholas Rightor who did a lot of work in Arkansas establishing townships and sections does mention such things. Apparently in retracing portions of the 5th P.M. he determines that his compass must be set to a variation of 8 degrees to 8 degrees 10 minutes East to coincide with the 5th P.M., and as you say, he perpetuates that direction. One thing that I am unsure of it why doesn't the Arkansas Windage eventually get filtered-out at some Guide Meridian East or West of the 5th P.M.?

 

In checking historic declinations from the National Geophysical Data Center website, it indicates that the declination at the 5th P.M. initial point was 8d 22' E in 1815 and 8d 36' E in 1830. In St. Louis, the NGDC indicates the declination was 8d 10' in 1820 and 8d 14' in 1830. Based on that it doesn't appear that the declination difference between St. Louis and SE Arkansas would account for the "Arkansas Windage." Of course, the NGDC declination numbers are modeled and are apparently only accurate to about 30 arc minutes.

 

Do you know of any other information that would give a clue as to what Robbins and Brown actually did other than their terse field notes? Are there other theories that would account for the Arkansas Windage?

 

Tim Osborn

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The NGS has lots of survey stations where it gives the lat-lon for the station itself and also for one or more of the reference marks-- e.g. LY2606 and LY2605. They give the "Geod. Az" from each to the other, and you can use the NGS calculator with the lat-lons (for the station and RM) to confirm that "Geod. Az." is the geodetic azimuth and not the magnetic. If you want details, speak up.

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