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

Sponsored By

Software Reviews
Continuing Series
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







Spatial Media LLC properties




Home arrow Archives   The American Surveyor     

The HP 35s Calculator: Elgin 911-Reverse Curve Problem Print E-mail
Written by Jason E. Foose, PS   
Saturday, 28 November 2015

A 471Kb PDF of this article as it appeared in the magazine—complete with images—is available by clicking HERE

Dr. Elgin, The American Surveyor Staff, and I collectively strive to educate our peers and readers of this publication. I have continually enjoyed Dr. Elgin's effort to advance knowledge through problem solving. The HP 35s is a true problem solver and I find great honor in demonstrating how to solve one of Elgin's enigmas with this tool. The goal is for everyone to appreciate the mechanics of problem solving and instill the necessary logic to tackle larger problems. There is no digital witchcraft or ghost in the machine here, nope. Just logic, brain cells, and two CR2032 batteries. You may find several approaches to solving any given problem. The more the merrier, I say! Let's refer to TAS October 2015 issue. Dr. E's ultimate request is to "Compute the radii of the replacement curves" so that a 100.00 foot tangent separates them. This problem is all about the tangents. First, let's organize our given information.


There is something we need to understand along with this simple curve data. With reverse curves the tangent direction out of C1 is the same as the tangent direction into C2, or a "straight line" to us hill folk. Consequently the distance between P.I.'s in a reverse curve is simply the sum of their tangent distances. That's very convenient because we can solve both tangent values by simply multiplying the TAN of one-half delta by the radius.


So the distance between the P.I.'s on a straight line could be expressed verbally as "the tangent of half of one-hundred and twenty degrees fifty-seven minutes times three-hundred plus the tangent of half of one-hundred and four degrees thirty-seven minutes times one-hundred and sixty."



In our case the solution equals 736.79 feet between points. Dr. E. wants 100.00 feet of tangent to separate P.T. #1 and P.C. #2 and we shall deliver. "Seven-hundred thirty six point seventy-nine feet minus one-hundred point oh-oh feet equals six-hundred thirtysix point seventy-nine feet". Done!


We have 636.79 feet of tangent to distribute among each side of the 100.00 tangent. Keep in mind that after the dust settles our final tangent values should equal this number. The challenge of this whole problem lies in writing an equation that will express our given 's, equal radii, and maintain 100.00 feet of tangential separation. Hmmmmmm...

Let's start by recognizing the facts. Our 's are fixed and our unknown radii values are constrained by the condition of being equal. That leaves us with elastic tangent values, right? So another table:


Ultimately we are solving for "R" which according to Dr. E must be the same value in both curves. So, if we can form a statement from C1 that equals "R" and the same statement applied to C2 also equals "R" then doesn't it stand to reason that both statements are equal? Yes, it's true and we can form a larger statement by substituting smaller statements into singular variables. That's handy because the HP 35s EQN Library and solver also will do just that. Let's jot down equations that express some common elements between each curve:

We've already figured out distance between P.I.'s minus Dr. E's requested hundred feet.

Jason Foose is the County Surveyor of Mohave County Arizona. He originally hails from The Connecticut Western Reserve Township 3, Range XIV West of Ellicott's Line Surveyed in 1785 but now resides in Township 21 North, Range 17 West of the Gila & Salt River Base Line and Meridian.

Equations & Solver

The HP SOLVER and EQN Library are very powerful tools. Simply queue up any equation and BRS EQN initiates the SOLVER. You will be prompted to select a variable to solve for and input the remaining variables. You can solve for any variable residing within the equation regardless of its location. Variables are stored so you may resolve a series of progressive equations and carry variable solutions, or better yet write the equation itself incorporating the sub-equations for the variables. For example Y=mX+b represents how many "Y's" are equal to a certain number of "X's" where X progresses from a known point (b) at a certain rate (m). "m" (slope) is equal to (the differences in your sample points). So instead of hand computing "m" by itself, why not just substitute "m's" equation in place of the "m" variable? Get it?

A 471Kb PDF of this article as it appeared in the magazine—complete with images—is available by clicking HERE

< Prev   Next >

 American Surveyor Recent Articles
Marc Cheves, PS 
Editorial: A Great Year to be a Surveyor
Some magazines have what are called "theme" issues. That is, most of the content is focused on one particular subject. In my 22+ years of survey magazine publishing, my philosophy has always been to have a little bit of everything in each issue, thereby eliminating the possibility that ....
Read the Article
Jason E. Foose, PS 
Decided Guidance: Case Examinations: Halverson v. Deerwood Village
Whew! We really beat the snot out of Bryant v. Blevins and practical locations. Well this month we're back on new case that hit the Minnesota Supreme Court's docket in 1982. We've got the familiar gymnastics of jurisprudence featuring an extraordinary array of flying rope stretchers ...
Read the Article
Michel Philips 
Extreme Environment Surveying
A Franco-Chilean team of cave divers used the Nautiz X8 rugged handheld for marine cave surveying, gathering data to classify the inaccessible northern half of Madre de Dios for UNESCO World Heritage. The team of cave divers used the Nautiz X8 ....
Read the Article
Erik Dahlberg 
The Original Green Engineers
Sometimes, it's best just to leave things as you found them. That's the lesson shared by Dr. Richard Miksad and his students at the University of Virginia. As a result of studies covering nearly a decade, Miksad's teams have developed detailed ....
Read the Article
Dave Lindell, PS 
Test Yourself 49: No Dimensions
In square A-C-D-B with side S, C-E is tangent to the semicircle Q1 with diameter B-D. Q2 is the inscribed circle of A-C-E. The tangent to Q1 and Q2 meets the sides of the square at F and H and intersects C-E at t G. Q3 is the inscribed circle of C-G-H. What is the ratio of the radii of circles ....
Read the Article
Jerry Penry, PS 
Discovery on Grizzly Peak
When First Lieutenant Montgomery M. Macomb arrived in Carson City, Nevada, from Washington D.C., on July 28, 1878, his assigned survey crew from the 4th Artillery was waiting and ready for the new field season. At age 25, Macomb was the leader ....
Read the Article
Wendy Lathrop, PS, CFM 
Vantage Point: Fighting City Hall Over Land
Once upon a time (1989 to be exact) in a place not so far away from where I live, a man (Francis Galdo) bought a home across the street from a vacant parcel owned by the City of Philadelphia. That parcel, along with others, had been acquired by condemnation back in 1974 subsequent to a 1956 ....
Read the Article
Patrick C. Garner, PS 
Book Review: Boundary Retracement: Processes and Procedures
When I was in my mid-twenties and learning the honorable profession of land surveying, I was lucky to be guided by a mentor who would grab a book off his office shelf and say, "Every surveyor should have a copy of this!" The first example he waved at me was Davis, Foote and Kelly's Surveying ....
Read the Article


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


Sokkia Intros
T-18 Controller

press [at] amerisurv.com
Online Internet Content


News Feeds

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

Need Help? See this RSS Tutorial

Historic Maps

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 



The American Surveyor © All rights reserved / Privacy Statement
Spatial Media LLC
7820B Wormans Mill Road, #236
Frederick MD 21701
301-695-1538 - fax