Showing posts with label Surveying. Show all posts
Showing posts with label Surveying. Show all posts

Thursday, March 14, 2024

The Physical Relationship of Pi to the Area of a Circle


Today is Pi Day. I know I've posted this before, but as a former Navigator and Full Charge Estimator of Earthworks and Utilities, I am proud of this piece of work. I did this many years ago and framed it. I simply wanted to understand why Pi is Pi. And no one could tell me. So, I drew it out to understand it.

I also wanted an easier way to compute the area of circles. To this day I simply use the factor of .785 to arrive at the total area of any circle. I divided the area into 100 squares and counted the squares inside of the circle, using a 6" round piece of pipe for an example. Then I counted the squares outside of the circle.

I then used .5 ft. X .5 ft. (to represent the 6" pipe) X .785 (the total of squares inside the circle). Not a great discovery, but it satisfied my curiosity and sped up my calculations. Having failed Math all through High School, I have always been amazed at having taught myself Trigonometry and Advanced Algebra. At sea,  using a Sextant, I needed those skills. The same applied to Surveying and Estimating.

But nothing has ever given me the satisfaction of this piece of paper, which is framed and hangs on my wall, next to my Third Mates License and the Engineering Certifications in two different states, with no college degree. You see, it wasn't that I couldn't learn math. It was that the people attempting to teach me simply didn't know how to reach me. And that, as Paul Harvey used to say, is the Rest of the Story.....

Happy Pi Day to all. 🙂

P.S. Last night I made a startling discovery. My diagram, hand drawn just as it appears here, is on a web site showing the various "official" visual explanations of Pi. All advanced and carefully laid out. 

The difference between mine and the others is astonishing. While all the others require some advanced knowledge of mathematics, mine is the only one which can be understood by a 6th grader. 

That it is included with the others, is like an honor for me. That is exactly what I was trying to create. You can view the whole layout, with all the other diagrams, by using the following link. Just look for the yellow handrawn one. 

https://www.google.com/search?sca_esv=483c85010fc377d1&sxsrf=ACQVn08yn_NpVuWevqVdtLXi6CuBIwJ4Lw:1710468678145&q=images+of+the+physical+relationship+of+pi+to+the+area+of+a+circle&tbm=isch&source=lnms&prmd=ihvsnbmtz&sa=X&ved=2ahUKEwi49davmPWEAxWxKFkFHSTbDMQQ0pQJegQICxAB&biw=1600&bih=699&dpr=1.2

Thursday, May 15, 2014

Geodetic Survey Markers

Most people; myself included; get these markers confused with being the responsibility of the United States Coast Guard; and there is good reason for that. The initials USCGS, which stands for U.S. Coast and Geodetic Survey, are awfully similar to USCG, which stands for the United States Coast Guard. They are probably plagued by calls about these survey markers.

The USCGS became the National Geodetic Survey (NGS), and in 1970 was transferred to the control of NOAA, which stands for the National Oceanic and Atmospheric Administration. I guess that now would be a good time to tell you who they are and what they do. And also; why it’s important.

NGS; I’m going to stick with that acronym; is the agency that creates and then maintains the records for the grid system upon which all surveying in the United States is based. They have, since the 1800’s, provided a series of “bench marks”, or known coordinates, along with the height above sea level, upon which all other surveys; public and private, are based. That’s quite a challenge, and an even greater responsibility.

One of the nearest markers which I know of is about 15 minutes from my house. It sits in the brick wall of the old Davis Forge Company Building store off of Route 115 in Huntersville. The building has been there for many years. It’s kind of a local landmark which people come to look at. The marker is located on the wall on the right side of the front of the building, about waist high.

The system of coordinates which NOAA; formerly the NCGS; maintains is described as "a consistent coordinate system that defines latitude, longitude, height, scale, gravity, and orientation throughout the United States." Not only do private developers use these coordinates to build things, but the resultant Emergency response imagery rapidly provides aerial imagery for emergency relief in times of flood and other natural disasters.

The original USCG was established in 1807 by Congress during President Jefferson’s time in office. Under the original accomplishments of the agency was to map and chart our coast in the interest of expanding international trade. It was 4 more years before the agencies first representative, F.R. Hassler, even set sail for Europe in order to obtain all of the instruments necessary for that endeavor. And once there, he was stuck for the entire duration of the War of 1812. So, effectively, the work didn't begin until 1815.It would be another 20 years before that first undertaking was satisfactorily completed.

Hassler planned to use simple triangulation in order to accomplish his task. He began in New York, with his first baseline verified in 1817. In 1818 Congress placed the Navy and the Army in charge of Hassler’s work. This virtually stopped the program dead in its tracks until 1832. The reason was simple enough; there was no longer anybody clearly in charge of the work.

In 1832 Hassler was reappointed as head of the project and work began to move forward once again. The work was resumed in 1833. Although the Navy was officially in charge of the project, this time Hassler was able to turn things around slightly and had the Navy assisting him. The project was then turned over to the Treasury Department in 1836.

Ocean soundings were a part of this program as well as land surveys. Ocean soundings had long been measured by hand held “lead lines’ which were knotted at intervals in much the manner of the “sea log”, which was used to gauge the speed of a ship at sea. It wasn't until the invention of Sigsbee Sounding Machine in the latter half of the 19th Century that things really took off.

Lieutenant Commander Charles Dwight Sigsbee, USN, served as an Assistant in the Coast Survey. He developed his sounding machine and commanded the ship Blake during the first “sound” surveys in the Gulf of Mexico. The ships were commanded by the Navy but manned with civilians and even one of the most famous scientists of the time, Alexander Agassiz, for assistance. NGS would not get their own ships; which were the precursors to today’s NOAA weather ships; until 1900.

The history behind these markers is long and sometimes complicated, as agencies and budgets changed over the years. By 1965 the agency was part of the Environmental Science Services Administration, but that only lasted for 5 years until NGS was transferred once again, this time to NOAA, where it remains today.

You may not have ever heard of these little markers, but the part they play in your daily lives cannot be disputed. For that reason these markers are federally protected, and require great effort to be removed, if they are allowed to be removed at all.

In the second picture I am taking a picture of a woman who came to visit the “old store.” Sue took the photo of me taking the photo of her. You can be sure that she didn't get her camera back until after I had told her about the Geodetic Survey.