That looks eerily familiar from somewhere
RADAR, post: 357358, member: 413 wrote:
Approximating curved lines with straight lines is always an interesting topic. Archimedes used polygons to approximate circles in order to find upper and lower limits for pi. Later, Newton used a similar approach to verify his inverse square law for gravity, inventing the calculus as he went.
State Plane Coordinate Systems extend the concept to approximate the surface of an ellipsoid with a plane. Just as Archimedes had to use a large number of shorter sides in his polygons to get close to pi, and Newton had to use a short distance of the moon's path around the earth, so we have to limit the extent of a State Plane in order to get good approximations.
A "good approximation" was defined to be 1 in 10,000 accuracy achieved in measurements on the plane compared to measurements on the ellipsoid. Note that the ellipsoid is not the earth's surface.
The maximum breadth of a State Plane that guarantees 1 in 10,000 accuracy is 158 miles. That's north-to-south for Lambert planes and east-to-west for Mercator planes. In State Plane terms, it implies that the minimum scale factor will be 0.9999 and the maximum scale factor will be 1.0001. One reference to the 158 miles figure is on page 4 here:
http://www.iowadot.gov/rtn/pdfs/IaRCS_Handbook.pdf
This diagram shows how that number (158 miles) is determined. For simplicity, I used a sphere with radius 3959 miles instead of an ellipsoid; the difference is insignificant to the nearest mile and the math is so much easier. It all boils down to an application of the Pythagorean Theorem.
This is how a surveyor sees the earth. Many flat sides. Those are the planes, of a given SPC. however, they are irregular shaped (Unlike the above). The scale factors, are how we correct from the plane, to the surface. And, that, is an approximation. The illustration above, of taking a total station, and shooting a long distance, from a mountain top, to a valley, yields a longer horizontal distance, than a distance, corrected to horizontal, from the valley, back to the mountain top. I have pondered, will we someday use pure lat lon and distance, to describe a given point on the earth?
I don't know.
Nate
Goldarn it, guys. Next, someone is going to announce that all lines are curves and that the Earth is not flat. Heresy, I say, heresy.
The lawyers are heading for a field day if too much of this gets out.
Neighbour 1 claims a dispute over Neighbour 2 who can't settle whether their 2.5 chain common boundary is ground, grid, spheroidal, slope, horizontal distance.
Let battle commence.
Someone should make an app, a game or similar.
Oh. Forgot to mention gravity. With proof such exists as seen in Einstein's gravity waves that'll probably add another dimension.
This is one topic that many of our clients have a hard time wrapping their heads around. We do a lot of DOT work throughout the state and we often have the design engineer ask us to move the coordinates to "The surface". There is no one surface that SP grid coordinates can be moved to, so we have to explain that we are moving to "A surface". It all depends on what part of the zone or state you are in. TxDOT has published county wide SAFs to use but these don't necessarily work the best for every part of that specific county.
What makes things even more difficult is when we are asked to place a NE on the POB of a boundary, or even on all monuments called for. This works well for clients that are building or maintaining a GIS database of parcels. As long as you note the project datum this is not too bad. It gets dangerous when people don't understand that coordinate systems are forever evolving and when they don't understand dignity of calls. We've had people stake out points and tell us that our boundary is incorrect because their GPS told them it was.
This is where continuing education and keeping up with technology comes into play. This is also why we have so many problems with people getting lazy just using data collectors and not understanding fundamentals of what they are measuring. The technology itself is a great thing and makes our lives easier, but younger people or people coming into the industry don't know any better and are not being educated. As surveyors we tend to focus a lot on boundary education (and rightfully so), but we often let the other parts of the industry slide as far as education goes.
We are fortunate here in Tasmania.
There's only one grid datum and zone.
The general public whilst ignorant really don't need an appreciation of this.
And whilst engineers etc can get a handle on this, the real problem exists of data being transferred without any reference to its nature or origins.
I put note on all my electronic cad, GIS etc stating it's datum for horizontal and vertical.
Together with its datum origins and grid or ground. If ground the origin of the scaled point. In both cases the combined scale factor.
Stripping that information as it's past on for others is a real concern.
Not sure how you overcome that, but education is as stated vital as we become more spatially aware and oriented.
Actually here, it's so easy to work grid, everything then fits together.
I can imagine real headaches when interplay with different coordinate datums.
Explaining grid to ground as some of you describe above is like trying to tell someone who knows nothing of the subject the difference between NGVD and NAVD.
Actually it gets worse as the years wear on and we drift about.
It's something the experts are aware of but don't know or haven't yet worked out a response.
Continental drift won't depart us so times ahead will be interesting as they look back to where we once were. And make appropriate adjustments and start another round of data transformation some which will be well documented, other not so.
I'm referring to our databases today that may or not contain sufficient detail in regards of coordinates and their origins, nature etc.
It's a coordinate system, not a religion.
All you have to do is get close enough for practical purposes.
Dave Karoly, post: 357580, member: 94 wrote: It's a coordinate system, not a religion.
All you have to do is get close enough for practical purposes.
A surveyor needs to know enough to know if he's "close enough" with his coordinate system.
My first day ever in surveying I was told "the measure of a good surveyor is knowing how accurate he needs to be".
First ignorance, then education, now apathy? Well at least I'm learning things here. Thanks guys, that's why i like this forum so much.
Just do engineering plans & CL's in SPC.
Having SPC ground Control every 1000' or so (BC, EC, POL)
Use ground distance of you want for layout. It never amounts to anything actually significant.
Anything in construction closer than 0.1' horizontal? Ever?
Besides, it's a relative distance, say two ends of a bridge will be right on.
BobKrohn, post: 357586, member: 6827 wrote: Just do engineering plans & CL's in SPC.
Having SPC ground Control every 1000' or so (BC, EC, POL)
Use ground distance of you want for layout. It never amounts to anything actually significant.
Anything in construction closer than 0.1' horizontal? Ever?
Besides, it's a relative distance, say two ends of a bridge will be right on.
Not so. It can be up in the .5 ft in a thousand. This is a component where assuming will cook your goose. Around here, in sw ar where I am, the smallest difference I have seen, is around 20 ppm. That's 0.02 per thousand. Or just over a tenth in a mile, and, as you go west, you can have 150 ppm. Or 0.15 per thousand. That's 0.80 per mile. None of the above numbers are a problem. If you know where the scale base is, and you know what all that means. If your scale base is many miles away, and somebody assumes... Well, that's why it matters. Another issue is international survey feet, vs the USA survey foot. They are close nuff to the same, aren't they?
In a few miles, there is not much diff. Right? Where is your scale base? Of its an hundred miles away, it shifts your coord values by several feet.
Shawn, is an excellent thread.
Thanks for starting it.
N
I agree absolutely with DK and WGD above. Why do you want SPCs? For a lot of use, it's so your plans can be in a GIS in the correct general location. A geodesist might want something much more accurate.
Also, speaking of accuracies, there are a couple of different accuracies we should consider: that being the gobal accuracy and the other being the local accuracy. If you are staking a house on a lot, you want the measurements between building corners to be as tight as you can get them (local accuracy), but the lat. and long of the house you want to be within a few feet if you need it @ all.
A similar philosophy can be portrayed for boundary surveying. It ain't so much where it sits on the planet as it is where it sits in relation to the point of beginning and the local senior lines, and in relation to the other corners. I think that is some of the struggle we all have about this GPS business.
Tom Adams, post: 357610, member: 7285 wrote: A similar philosophy can be portrayed for boundary surveying. It ain't so much where it sits on the planet as it is where it sits in relation to the point of beginning and the local senior lines, and in relation to the other corners. I think that is some of the struggle we all have about this GPS business.
That's an excellent point. I would say that if you nail down the global accuracy, the local accuracy will follow in suit. But I would prefer to have my rural boundaries nailed to the tenth even if the global accuracy may be two or three times that. Heck with proper metadata, I wouldn't even be opposed to a submeter (or even a couple of meters) at the POB. But with DPOS, OPUS, NRCAN PPP, AUSPOS, etc., combined with the availability of high quality, inexpensive dual frequency receivers, submeter positioning for such a purpose seems like trading down. Sorry. I went on a tangent there.
SPC distortions really depend on your location.
I work with distance distortions between .2' and .7' per 1000' or 200ppm to 700ppm, clearly more distortion than good chaining practice.
Then there is the angular rotations from "true" which are between 0 and 4 degrees.
I tend to want an LDP more to simulate "true" bearings than getting on a "surface" distance, the distance correction is easy to do with state plane anyway.
But no matter what you design, you still have an error imbedded in your projection, if you can reduce it to 1 or 2ppm that's about as good as it gets, and that's just for flat "small" areas.
MightyMoe, post: 357619, member: 700 wrote: But no matter what you design, you still have an error imbedded in your projection, if you can reduce it to 1 or 2ppm that's about as good as it gets, and that's just for flat "small" areas.
Glad to see this subject getting the opening it needs.
N
So, this is a bit of a side-track, but someone mentioned gravity above, so I think it is appropriate.
The whole concept of the various grid systems and state plane coordinate systems and so on was very interesting to me when I was in college. And I understand it well enough to know my own limits. And I work to understand more all the time.
One of the things I find interesting is that many of the agencies with which we work for various plan sets and exhibits and so on have very little (if any) understanding of these concepts. I can't count how often one of the engineers in my office will ask, "Is this in SPC? The city says that it has to be in SPC." I'll ask them, "Why does it have to be in SPC?" and the response is typically, "I don't know, it is in the standards."
Anyway, my side-track got side-tracked. I recently have been watching a video series online called PBS Space Time. It is a really well made series on some pretty intense physics topics (one of my interests). A recent episode I watched worked through the explanation of curved space-time. They were talking about geodesics and how on small scales in a local system, the observation of a geodesic appears to be straight. I was watching the video on my tablet and when I say that I said (out loud) "Yes! Exactly!" and my gal looked at me and asked, "Interesting video I take it?"
Needless to say, my understanding of "flat" surveying on a curved surface was a helpful thing when watching this video and trying to understand WTF Einstein was talking about!
