Reference frames and projections

Actually, the State Plane Zones have remained essentially the same (geometrically) since the 1930s (with a few exceptions like Montana). The UTM Zones were developed in the 1940s (or thereabouts).

The "100ppm" value is ONLY valid if you are working ON or very near the Ellipsoid ("sea levelish" for NAD27), and also varies somewhat by State & Zone. The effect of "elevation" has (and will remain) the Achilles's Heel of ALL "Large Scale" projections.
Dr. Burkholder's method would solve most (if not all) of these issues, but time will tell if there is any hope of moving away from the "classical" Lambert/Mercator systems.

I dunno the answer to your question, and in any case...it will VARY depending on where one is, what one is doing, and the [geodetic] sophistication of the parties involved.

Loyal

Thank you, Loyal. Good to hear from you again.

Loyal, post: 358262, member: 228 wrote: Actually, the State Plane Zones have remained essentially the same (geometrically) since the 1930s (with a few exceptions like Montana). The UTM Zones were developed in the 1940s (or thereabouts).

The "100ppm" value is ONLY valid if you are working ON or very near the Ellipsoid ("sea levelish" for NAD27), and also varies somewhat by State & Zone. The effect of "elevation" has (and will remain) the Achilles's Heel of ALL "Large Scale" projections.
Dr. Burkholder's method would solve most (if not all) of these issues, but time will tell if there is any hope of moving away from the "classical" Lambert/Mercator systems.

I dunno the answer to your question, and in any case...it will VARY depending on where one is, what one is doing, and the [geodetic] sophistication of the parties involved.

Loyal

Thanks Loyal. Always good to hear from you.

I am hoping more than one person can offer some insight on this.

I agree with Loyal regarding age of State Plane (30's and 40's for the most part). I also agree with 100ppm. There are two scalar (distance) distortions to contend with - Grid Factor and Elevation Factor. The 100ppm that was targeted in the design of SPC was only concerned with Grid Factor (which is determined by the "vertical" distance between the ellipsoid and the projection surface). As Loyal says, the Elevation Factor is not considered in the 100ppm design target. I am still short on answers on Dr. Burkholder's solution. What I've read (which is very little) gives some insight into what it will do but doesn't offer much in how it does it.

So long as the distortions are managed (convergence, elevation factor and scale factor) any of our State Plane, UTM or LDP conformal projections are suitable for surveying purposes.

Remember, too, that a reference frame/datum and a projection are not the same animal. A reference frame/datum is a combination of physical monuments and their relative positions. Sea Level has historically been a datum for elevations. It is a reproducible monument with an assigned coordinate of 0. A network of monuments have been developed from them (benchmarks). The reference frame is simply normal (perpendicular) to gravity. For 3D, the center of the Earth is the primary monument with an assigned ECEF coordinate of 0,0,0. The datum is established by the Earth rotation and an arbitrary definition of 0 Longitude. From this datum any point on Earth can be described with a unique location. Any point. Wow! But ECEF isn't terribly useful for contemporary surveying. So these coordinates are projected onto an ellipsoid. The ellipsoid is a mathematical figure, designed to be equal in volume to the geoid (sea level) for the entire planet, centered at 0,0,0 ECEF. This is a projection. Still Latitude, Longitude and Height aren't terribly useful for contemporary surveying. The mathematics of determining the vector between two points is daunting, but LLH has an advantage over ECEF in that at least LLH is now based on something resembling the surface of the Earth, where we live and work. State Plane is a projection of Geographic Latitude and Longitude coordinates to a grid surface. It really doesn't matter what the LLH is based on (NAD27 or NAD83) the math for a projection will still work. The numbers will change but that's because the reference frame/datum is different. The projection is simply a mathematical representation of perspective. It doesn't change the thing, it changes the way the thing looks. But the thing is still the thing. In this case, the thing is the ECEF coordinate. We can look at this ECEF coordinate as an ECEF, we can project it to the ellipsoid as a geographic coordinate (a change of perspective, but not position), and we can project the geographic coordinate to a conformal projection (again, a change of perspective, but not position).

Projection is all about Perspective. Perspectives have distortion, but in the case of conformal projections, we actually know very precisely what the distortions are. For our coordinates to be used to the fullest potential, these distortions must be carefully managed. No problem, we know what they are. The next step is building procedures that manage them. Some people use localizations to do this. Localizations provide a simple way to handle scale and rotation. The problem is that simple solutions are often relied upon as the manager instead of a tool for the manager. So you ask someone what their localization is doing and they have a blank look on their faces... The manager is being managed by the tool. Bassakwards.

I wish for 100ppm, just the scale factor can swamp that, let alone the elevation factor.

Still that's .5' per mile, not all that great even in the "old" days back in the 70's with a T-2 and a distance meter.

Doing control work then 1 part in 100,000 or better was not unusual, 10ppm with instruments available and in general use.

Shawn Billings, post: 358452, member: 6521 wrote: I agree with Loyal regarding age of State Plane (30's and 40's for the most part). I also agree with 100ppm. There are two scalar (distance) distortions to contend with - Grid Factor and Elevation Factor. The 100ppm that was targeted in the design of SPC was only concerned with Grid Factor (which is determined by the "vertical" distance between the ellipsoid and the projection surface). As Loyal says, the Elevation Factor is not considered in the 100ppm design target. I am still short on answers on Dr. Burkholder's solution. What I've read (which is very little) gives some insight into what it will do but doesn't offer much in how it does it.

So long as the distortions are managed (convergence, elevation factor and scale factor) any of our State Plane, UTM or LDP conformal projections are suitable for surveying purposes.

Remember, too, that a reference frame/datum and a projection are not the same animal. A reference frame/datum is a combination of physical monuments and their relative positions. Sea Level has historically been a datum for elevations. It is a reproducible monument with an assigned coordinate of 0. A network of monuments have been developed from them (benchmarks). The reference frame is simply normal (perpendicular) to gravity. For 3D, the center of the Earth is the primary monument with an assigned ECEF coordinate of 0,0,0. The datum is established by the Earth rotation and an arbitrary definition of 0 Longitude. From this datum any point on Earth can be described with a unique location. Any point. Wow! But ECEF isn't terribly useful for contemporary surveying. So these coordinates are projected onto an ellipsoid. The ellipsoid is a mathematical figure, designed to be equal in volume to the geoid (sea level) for the entire planet, centered at 0,0,0 ECEF. This is a projection. Still Latitude, Longitude and Height aren't terribly useful for contemporary surveying. The mathematics of determining the vector between two points is daunting, but LLH has an advantage over ECEF in that at least LLH is now based on something resembling the surface of the Earth, where we live and work. State Plane is a projection of Geographic Latitude and Longitude coordinates to a grid surface. It really doesn't matter what the LLH is based on (NAD27 or NAD83) the math for a projection will still work. The numbers will change but that's because the reference frame/datum is different. The projection is simply a mathematical representation of perspective. It doesn't change the thing, it changes the way the thing looks. But the thing is still the thing. In this case, the thing is the ECEF coordinate. We can look at this ECEF coordinate as an ECEF, we can project it to the ellipsoid as a geographic coordinate (a change of perspective, but not position), and we can project the geographic coordinate to a conformal projection (again, a change of perspective, but not position).

Projection is all about Perspective. Perspectives have distortion, but in the case of conformal projections, we actually know very precisely what the distortions are. For our coordinates to be used to the fullest potential, these distortions must be carefully managed. No problem, we know what they are. The next step is building procedures that manage them. Some people use localizations to do this. Localizations provide a simple way to handle scale and rotation. The problem is that simple solutions are often relied upon as the manager instead of a tool for the manager. So you ask someone what their localization is doing and they have a blank look on their faces... The manager is being managed by the tool. Bassakwards.

This is a great explanation! I like how you've given the explanation about how a projection is simply a perspective, or "way of looking at a thing". I don't think I could have described it so succinctly myself. I might paraphrase this to share with my field crews so I can explain to them more about what their localization (or calibration as they call it) is really doing.

It's time for LDP. The reference frames are not the issue.
We will never look back
LDP

Moe messaged me directly asking what I thought about LDPs. Here's what I wrote:

I'm all for LDP as long as the ellipsoid / datum are left alone.

The Minnesota county systems and the older Wisconsin ones apply corrections to the ellipsoid and it causes havoc in a lot of GIS software packages. If the ellipsoid is adjusted, it generally means that a custom ellipsoid, datum, and geographic coordinate reference system (GeoCRS) have to be defined.

Then you have to decide what to do for a datum transformation--you don't really want to use the custom GeoCRS because once the points are in lat-lon, they're on the regular GeoCRS, not the custom one.

There are ways around that, like a "null" transformation from the custom GeoCRS to NAD83, but having to define one for each custom GeoCRS is messy.

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There was a similar problem with the "web Mercator" CRS used by most web services. It's based on WGS84, but the spherical Mercator equations have to be used with a radius = 6378137 m (a major auxiliary sphere). GIS software has an ellipsoid-based Mercator implementation by default, so the way to force the spherical equations was to use a modified WGS84 definition that contained a "sphere." That caused issues with non-WGS84 data as you had to use a datum transformation to get to WGS84, then a 'null' transformation to get the sphere-based WGS84 thing, then finally project the data. Nowadays the "web Mercator" definition uses the standard WGS84 with a spherical Mercator implementation.

mkennedy, post: 358548, member: 7183 wrote: I'm all for LDP as long as the ellipsoid / datum are left alone.

The Minnesota county systems and the older Wisconsin ones apply corrections to the ellipsoid and it causes havoc in a lot of GIS software packages. If the ellipsoid is adjusted, it generally means that a custom ellipsoid, datum, and geographic coordinate reference system (GeoCRS) have to be defined.

AGREED! I have just a tiny amount of experience with the Minnesota system. The custom ellipsoid added a lot of grief trying to implement. With LDP, it's needless complication changing the ellipsoid.

I've had experience using Oregon LDPs and I can't think of a reason to not use them. The current zones each span a number of counties, and I don't see why there couldn't be a zone for every county. That would make for more zones but even smaller distortions.