Horizontal flat projection distance vs true slope distance

Slope versus horizontal is one thing.?ÿ Horizontal ground versus grid is another.

When you project the round earth on a flat plane (like SPC or UTM) there is a scale factor for the projection, and then an elevation factor because you usually are not standing on the projection plane but somewhere above or below it.

Posted by: @timd1971

Is that what Grid to Ground is?

I.e. using a horizontal grid projection coordinate system.?ÿ Design and stake out points for a terrain from top down.?ÿ What if the terrain has very steep hills or lots of hilly surfaces??ÿ How are those steep slopes accounted for in order to design correctly along those curved elevations??ÿ Seems a hilly terrain would be treated totally different than a flat piece of land?

On a relatively small survey all distances are reduced to horizontal for mapping purposes. The spheroidal shape of Earth is ignored.

Over larger areas points on the spheroid are projected onto a flat plane (often near sea level). This simplifies coordinate calculations but there is a cost to paid in distance and direction distortion. Most of the time true distances over the ground are longer than distances over the projection plane (called the grid). At higher elevations grounds distances become increasingly longer than grid distances.

Since the grid is rectangular but meridians converge at the North Pole the direction of grid north varies from the direction of geodetic north except at the central meridian of the projection.

In the simplest of cases, it's a right triangle. As Dave Karoly said, if dealing with true state plane grid to ground, it's a bit more complicated, but the right triangle is still an integral part when broken down.

"Grids" were created because before easily accessible computing power was available the calculations required to work on the curved surface of the earth were cost (time) prohibitive, the calculations required to reduce slope distances to horizontal distances are relatively simple, so only some of the very oldest land descriptions in North America report slope distances.?ÿ

Most documents created by land surveyors in the 20'th and 21'st centuries report horizontal distances.

A continuing frustration for me is land surveors?ÿ instantace that we continue working on flat approximations of the earth's surface. We go on and on about low distortion projections without realizing that we have the technology at our fingertips to effortlessly recognize the earth is not flat and to remove the idea of a grid projection, a constant source of error, and confusion, once and for all.?ÿ

It appears that you are trying to learn & understand the art of surveying. If you are trying to understand the basics, you might want to visit NCEES.org and purchase the Land Survey Review Manual.?ÿ This manual will explain the basics and get you up to speed.?ÿ That said, I DO NOT want to appear that I am discouraging you from asking questions on this forum.?ÿ I encourage the expansion of knowledge into surveying.?ÿ Most of us here have been surveying for decades and are still learning something different each day. Good luck in your search for knowledge & wisdom.?ÿ

Posted by: @aliquot

A continuing frustration for me is land surveors?ÿ instantace that we continue working on flat approximations of the earth's surface. We go on and on about low distortion projections without realizing that we have the technology at our fingertips to effortlessly recognize the earth is not flat and to remove the idea of a grid projection, a constant source of error, and confusion, once and for all.

I'm curious what you would suggest as an alternative to projections, low distortion or otherwise. The ellipsoids and reference frames from which geodetic LLh / ECEF are measured are still best-fit approximations of the earth.

I don't think the A&E sector is going to be on board with using geodetic values for design, especially considering the inherent problems with ellipsoid heights for such purposes.

Posted by: @kevin-hines

If you are trying to understand the basics

Buy a copy of Wolf & Ghilani's Elementary Surveying.?ÿ An edition one or two back is still good and much cheaper than the latest.

@aliquot?ÿ

Agree.

Why use a flat map when you can use Google Earth.

@kevin-hines thanks!!

@bill93?ÿ

THANKS!

Posted by: @aliquot

A continuing frustration for me is land surveors?ÿ instantace that we continue working on flat approximations of the earth's surface. We go on and on about low distortion projections without realizing that we have the technology at our fingertips to effortlessly recognize the earth is not flat and to remove the idea of a grid projection, a constant source of error, and confusion, once and for all.?ÿ

I don't find this to be the case at all.?ÿ Every surveyor I know DOES realize that we have the technology at our fingertips to "effortlessly recognize the earth is not flat and to remove the idea of a grid projection".?ÿ Just because we can do it doesn't mean it's a good idea.?ÿ There are massive computational and practical advantages in continuing to work with map projections.?ÿ It's not because every surveyor except you is a dumb-dumb.

Posted by: @timd1971

Is that what Grid to Ground is?

I.e. using a horizontal grid projection coordinate system.?ÿ Design and stake out points for a terrain from top down.?ÿ What if the terrain has very steep hills or lots of hilly surfaces??ÿ How are those steep slopes accounted for in order to design correctly along those curved elevations??ÿ Seems a hilly terrain would be treated totally different than a flat piece of land?

@bill93 noted slope vs. horizontal distances, which may be what you're asking about.?ÿ

However, it is also the case that over large distances with large terrain variations, concessions must be made in representing horizontal distances effectively on a map.?ÿ One solution to this is to report all distances at datum elevation "0" (sometimes referred to as "sea level").?ÿ This is the solution used in the modern era by BLM Alaska with their Township plats, and was also used in the right of way mapping for the Trans Alaska Pipeline corridor.

Posted by: @aliquot

"Grids" were created because before easily accessible computing power was available the calculations required to work on the curved surface of the earth were cost (time) prohibitive, the calculations required to reduce slope distances to horizontal distances are relatively simple, so only some of the very oldest land descriptions in North America report slope distances.?ÿ

Most documents created by land surveyors in the 20'th and 21'st centuries report horizontal distances.

A continuing frustration for me is land surveors?ÿ instantace that we continue working on flat approximations of the earth's surface. We go on and on about low distortion projections without realizing that we have the technology at our fingertips to effortlessly recognize the earth is not flat and to remove the idea of a grid projection, a constant source of error, and confusion, once and for all.?ÿ

In other words, go to a geodetic system? Every bearing reported forward, back and mean? Perhaps on a township scale survey, but for most practical every day applications? Just seems a little extreme. I mean, we already do that whether we realize it or not with ever application of GPS technology, but as far as the practical applications of using cartesian coordinates to simplify every day applications, I just don't see the justification for what you are proposing. Enlighten me.

What about the 3D spatial model?

As for the reduction of distances to various surfaces, see the NOAA NGS TM 10 on the Use of Calibration Baselines on NGS site. Images below were taken from the TM.

See: https://geodesy.noaa.gov/library/pdfs/NOAA_TM_NOS_NGS_0010.pdf

@timd1971?ÿ

Uh, Google Earth is a flat map. Scroll down to Formulas here before you read the rest.

https://en.wikipedia.org/wiki/Web_Mercator_projection

?ÿ

@mathteacher?ÿ

For sure. Not only are the vast majority of online maps projected, that Web Mercator projection uses spherical calculations rather than ellipsoidal.

It's convenient, but?ÿso far off real-world that the federal government had to issue an advisory to geospatial contractors warning about it.

Another way of looking at the issue:

An introductory article on grid to ground by Mr. Ghilani:

https://www.xyht.com/professional-surveyor-archives/3088/

@rover83 I am suggesting we work geodeticaly. Grid projections take your location data and "project" them in a distorted way onto a flat a surface. You are right that the location data is imperfect to begin with, but I don't see that as a justification to further distort your work and add another opportunity for error.?ÿ

I don't have any problems with the way we report elevations.

I don't see how this would be a problem for the A&E sector. What am I missing. The only effect I can see on them is that it would eliminate the mistake of designing on the grid.?ÿ