About Amerisurv| Contact    
Magazine | Newsletter    
Flickr Photos | Advertise    
HomeNewsNewsletterAmerisurv DirectoryJobsStoreAuthorsHistoryArchivesBlogVideosEvents
 
advertisement


Subscriptions
Sponsored By

Software Reviews
Continuing Series
     RTN
An RTN expert provides everything you need to know about network-corrected real-time GNSS observations.
Click Here to begin the series,
or view the Article PDF's Here
76-PageFlip Compilation
of the entire series
Test Yourself

Got Answers?
Test your knowledge with NCEES-level questions.
  Start HERE
Meet the Authors
Check out our fine lineup of writers. Each an expert in his or her field.
Wow Factor
Sponsored By


Product Reviews
Partner Sites

machinecontrolonline 


lbszone.com

GISuser.com

GeoJobs.biz

GeoLearn

 

Spatial Media LLC properties

Associates

ASPRS

newsnow 

Home arrow Archives   The American Surveyor     

Footsteps: Best Practices for Very Large Boundary Surveys—Dealing With Distortions in Distance Print E-mail
Written by Landon Blake, PS   
Friday, 25 October 2013

A 585Kb PDF of this article as it appeared in the magazine—complete with images—is available by clicking HERE

When it comes to very large boundary surveys, distances can become distorted over large areas. Because effective boundary surveying requires accurate measurements, anyone doing very large boundary surveys should therefore consider using a bit of geodesy.

Let's say you've been tasked with a boundary survey for property in PLSS Sections 2, 3, and 4 along an area known as Three Meadows Creek. After completing your research and project set-up you perform a set of initial field surveys to search for evidence of PLSS monuments along the south line of the sections.

The south line in question runs parallel to Three Meadows Creek. The creek drains an east-west valley high in the mountains. Near the boundary common to Section 3 and 4 the valley makes a steep decline out of the mountains onto the flatlands. Figure 1 shows the results of your field survey. Regular flooding of Three Meadows Creek has destroyed all evidence of the original PLSS corners along most of the south line of Sections 2 and 3.

The topography of your survey area results in a major elevation change along your surveyed line. The segment between PC 106 and PC 110 is at approximately elevation 6,500.00. The segment between PC 110 and PC 112 is at approximately elevation 4,500.

After your field survey is complete, you decide to calculate the position of PC 110 based on proportioning. You want to determine how close the proportioned position is to an old fence corner found in your search area for PC 110.

If you performed a total station survey, can you just calculate your proportion using your measured ground distances? What if you used RTK GPS for your survey and you're already on the State Plane Coordinate System? Can you just use your grid distances to do the proportioning calculations?

You could, but you'll be introducing some error because of the significant surveyed elevation change on this project. How much error? Is this error significant?

A bit of simple math will help to answer those questions.

Down to the Ellipsoid
Because map projections will only complicate our calculations, we will instead reduce our distances to an (approximately) sea level ellipsoid. Now let's compare the right and wrong ways of going about it.

The Wrong Way Down
We can calculate a scale factor to convert our measured ground distances to distances on the sea level ellipsoid. For illustration purposes, we will use an approximation of the NAD83 ellipsoid and pretend the earth is a sphere and not an ellipse, only because it makes the math easier. (Before the geodesy purists cry foul, it should be noted that this simplification won't make a huge difference in our calculations.)

The scale factor we compute for the "wrong" way is shown in the first row of the scale factor table. This scale factor is 0.999784587. It is calculated using an elevation of 4,500 feet for the whole survey area. The table shows the result of using this scale factor to convert our distances to the ellipsoid surface. Our scale factor makes the ellipsoid distances slightly smaller than the measured ground distances. Hopefully when you look at Figure 2, which is a side view of the earth showing our survey area, you will understand why.

The Correct Way Down
Now take a look at the second row of the scale factor table. This time we've used the correct average elevation of 6,500 feet to scale our distance. The error when applying a single scale factor (using an elevation of 4,500 feet) to both distances is 1.01 feet.

For many purposes that isn't very big, and can be ignored, since it probably isn't going to change how we evaluate that fence corner. However, in other scenarios, with modern surveying equipment, an error like that is much bigger than the random error in our measurements; in many cases, several times bigger. It is important for boundary surveyors to understand such a source of error in measurements and calculations. Understanding the source and magnitude of an error and choosing to ignore it is not the same as ignoring an error because you're ignorant of its cause.

If you just turn on your GPS and start surveying, and then run your calculations with the default State Plane coordinates determined by your processing software, more than likely your software applied a single scale factor using one average elevation across the project site.

Best Practices
1. Understand how significant changes of elevation over a survey area may distort distances.
2. Evaluate the distortion and determine if it is significant for your purposes. If necessary, run some calculations to determine at what magnitude of elevation change the error is small enough to be ignored.
3. If the distortion to distances caused by significant changes of elevation is important in your survey, break your project into zones based on average elevation and use unique scale factors for each zone.
4. If you are working on a very large boundary survey, consider the best way to reduce your distances to a common working surface (like a sea level ellipsoid surface).

Come Back Up
Depending on the final results of your survey, you may need to lay out points in the field (for example, to set property corner monuments at calculated positions). If you are going to do this, don't forget to scale your sea-level ellipsoid distances back up to ground before the layout is performed.

Spreadsheets to assist with these types of calculations are available for download at the Footsteps Boundary Surveying Blog, where you'll also find a more detailed explanation on the calculation of scale factors.

Landon Blake is currently project manager and project surveyor for a small civil engineering and land surveying company in California's Central Valley. Licensed in California and Nevada, his many activities include speaking and teaching at group conferences around the state.

A 585Kb PDF of this article as it appeared in the magazine—complete with images—is available by clicking HERE

 
< Prev   Next >

 American Surveyor Recent Articles
Editorial 
Thought Leader: Land is Too Important to Be Left to Land Specialists
A while back I was searching the Internet for an old treatise on land titles. A Google query yielded a book published in 1914. The author was Charles Claudius Kagey and the book was titled "Land Survey and Land Titles, a book for boys and girls, a reference volume for property owners, a text ....
Read the Article
Jason E. Foose, PS 
Decided Guidance: Wacker vs. Price - Irony in Sevenfold
This month's case takes us to Phoenix, Arizona in 1950. The Arizona Supreme Court went all guns-a-blazin' in Wacker vs. Price (216 P.2d 707 (Ariz. 1950)). Maybe it's just me, but I'm sensing plenty of irony and have taken license to point it out along the way. I like what the Court did with this case ....
Read the Article
Allen E. Cheves 
Around the Bend - A Visit to Carlson Software
The Ohio River is one of America's greatest, running near 1,000 miles between Pittsburgh and the Mighty Mississippi. Much of the coal and other products that fueled our nation's industrial expansion flowed between the shores of this maritime ....
Read the Article
Lee Lovell, PS 
Surveying & Mapping Economics Part 3 - Customers & Services
This article continues an inquiry into the economic conditions of the Surveying and Mapping industry (NAICS 541370) using data from the U.S. Census Bureau. This time we will look at customers and services. The data comes from the Economic Census conducted every 5 years on American ....
Read the Article
Jerry Penry, PS 
True Elevation: Black Elk Peak
Black Elk Peak, located in the Black Hills region of South Dakota, is the state's highest natural point. It is frequently referred to as the highest summit in the United States east of the Rocky Mountains. Two other peaks, Guadalupe Peak in Texas and ....
Read the Article
Larry Trojak 
Bringing The Goods - Mobile Scanning an Integral Component
When Jim Smith, Jerrad Burns and Charlie Patton left the Memphis division of a major construction company in 2015, they took with them the knowledge of how to get even the most complex jobs done and what equipment could best serve them in making that happen. So when they joined West ....
Read the Article
 
Lee Lovell, PS 
Test Yourself 41: Integers, Integers, and Integers
ABF is a 5:12:13 triangle, ACF is a 48:55:73 triangle, ADF is a 3:4:5 triangle, and AEF is a 7:24:25 triangle, all with integer sides and inscribed in a semi-circle. What are the lengths of BC, CD, and DE? ....
Read the Article
Wendy Lathrop, PS, CFM 
Vantage Point: Sunset or Sunrise?
While we often think of legislated government programs as static, they do change over time. Such evolution and opportunity for transformation are part of the dialogue in reauthorizing these programs. Every so many years there is a sunset on each government program, and this September is the ....
Read the Article
 

deliciousrssnewsletterlinkedinfacebooktwitter

Amerisurv Exclusive Online-only Article ticker
Featured Amerisurv Events
List Your Event Here
please
contact Amerisurv


Google
 
AMERISURV TOP NEWS

JAVAD Intros
Spoofer Buster

GOT NEWS? Send To
press [at] amerisurv.com
Online Internet Content

Sponsor


News Feeds

 
Subscribe to Amerisurv news & updates via RSS or get our Feedburn
xml feed

Need Help? See this RSS Tutorial

Historic Maps
Careers

post a job
Reach our audience of Professional land surveyors and Geo-Technology professionals with your GeoJobs career ad. Feel free to contact us if you need additional information.

 

Social Bookmarks

Amerisurv on Facebook 

Amerisurv LinkedIn Group 

Amerisurv Flickr Photos 

Amerisurv videos on YouTube 

twitter

 




The American Surveyor © All rights reserved / Privacy Statement
Spatial Media LLC
905 W 7th St #331
Frederick MD 21701
301-620-0784
301-695-1538 - fax