Comparing the precision work of plane surveying and geodetic surveying

Question

In geodetic surveying, we consider the spherical geometry of the surface though the surface is not perfectly spherical.

In-plane surveying, we consider a small surface area which is considered as a plane or flat surface whose results upon surveying do not get affected. But can't totally neglect the curvature of the earth's surface so the assumption of flatness must affect results to some extent.

I know that geodetic surveying has great precision than plane surveying. However, both will be accurate though.

1. If both survey methods were performed for an area then what would be the "precision difference"(in terms of significant figures/numbers) between these two surveying methods for the same area?

   I am questioning about the "closeness of the results" of plane surveying to the actual/real parameters. So what is reality then? This is what we are trying to achieve with well equipped, periodically improved and advanced technology for great accuracy and precision that hadn't been achieved before. I want to compare their precision because I think results from geodetic surveying are very close to reality so "comparing these readings with plane surveying allows us to find out the extent to which the assumption of flatness affects results?"

2. And generally what is the precision (in numbers) for these(individual) methods when performed in their standard confined areas? I think this question can be answered with some experimental readings and experiences.

Answer 1

I'm not sure I totally understand your question. I believe you are saying in your third paragraph that "geodetic surveying has greater accuracy than plane surveying"? This is not really true. Every survey is as accurate as the methods employed to perform the survey irrespective of if the work is done in a geodetic coordinate system or a rectangular plane coordinate system. Your coordinate system is made up of several parts, an ellipsoid which approximates the shape of the earth, a datum which positions this ellipsoid relative to the earth, and for what you are calling "plane surveying", a map projection which "projects" a section of this ellipsoid onto a flat plane so we can use "grid" coordinates instead of "spherical" coordinates.

In your two questions it appears you are mixing the terms accuracy and precision. These are very different things. Accuracy is closeness to the "true" value and is never known. Precision is closeness between multiple measurements.

In designing a survey, we look at the precision of the instruments and procedures we will use to determine an expected precision for the observations. We then look at the observations we will make (including redundant observations) and from all of this we build a stochastic model which we can use to predict the precision of our end results. We adjust our observation model until we are achieving the precision we are seeking for the survey.

Until now we have not mentioned a geoid, which throws another whole level of complexity into the discussion. The "z" component above is based on ellipsoidal elevations. Typically we work in orthometric elevations (elevations relative to some form of mean sea level). The geoid model is the mathematical model which attempts to model this "mean sea level" surface, and allows use to convert our ellipsoidal elevations to orthometric elevations.

Maybe you can clarify what it is you are trying to ask so we can give a better answer.

Answer 2

While I do not discount your question's validity, I think it is quite hard, if not impossible for you to answer the first question as there are too many fine details that affect precision.

For example, even within plane surveying, the proximity of your survey points, how often you do look back checks, and all those can play a major role in how much error that your survey will have. Equipment can play a role, weather can play a role, and obviously, as you have already recognized, the size of the area surveyed can play a role as well.

Similarly, the number of satellites that you can "see", the number of epochs that you take for each determination of your actual coordinate results, atmospheric conditions, latency and other factors can affect the actual accuracy of your geodetic survey results.

So, what I am essentially pointing at here is that accuracy generally is less so affected by your method of data collection, but more so by the surrounding conditions of your data collection efforts. There are no necessarily any inherent errors within each method that will produce errors that will sufficiently invalidate the respective methodologies.

For question two, it depends on what you mean by "standard confined areas" mean. I recommend you reaching out to specific equipment manufacturers or survey equipment dealers for comparison of actual equipment that you may use.

Answer 3

There is no an absolute answer to your question... it always depends. When you are considering to use plane or geodetic surveying, is because you are expecting that you will get differences that will affect to your work.

Example 1: You are working on a Skyscraper (Burj Khalifa). Which grid will you setup? It is less than 1 km^2... so plane? geodetic? No. You need to go further... and you need to consider the geoid...Why? because your Nadir (plumb) on the base is not the same on the last levels.

Example 2: You are working in Center America... in 250 km2 you can cross some countries and then you have 2 different sea levels... How will you handle it? It can not be fixed neither with plane or geodetic survey, as they can not absorv the level gradient on this area...

So it always depends...

Simple question: On Guadarrama Tunnel, in order to create the geodetic grid on between both entries (29 km), how will you work???

For official grids (as they are usually very broad) geodetic surveying is used. When you need to increase the density in those networks, then plane geodesy. But those grids have an accuracy and precision that are ok for general mapping (just as reference), not for almost any work, just if you have a poor tolerance.