Numerical Analysis – Page 24 – Numerical Explorations

Power Series – MacLaurin Series by James Pate Williams, Jr., BA, BS, MSwE, PhD

Baseball Ballistics by James Pate Williams, Jr., BS, BS, MSwE, PhD

There are analytic equations that are applicable to the trajectory of a batted or thrown baseball:

Click to access 04-LAJPE-782_Chudinov.pdf

I created a C# application to test the preceding equations against numerical methods of calculating the trajectory of a baseball. The baseball has an initial velocity of 90 miles per hour and an angle of inclination of 20 degrees. The classical model certainly overestimates the trajectory.

System of Ordinary Differential Equations Model of the United States COVID-19 Pandemic by James Pate Williams, Jr., BA, BS, MSWE, PHD

Siacci’s Method by James Pate Williams, Jr. BA, BS, MSwE, PhD

Siacci’s Method Chapter 5 and Appendix A of “Exterior Ballistics, 1935” by Lieutenant Commander Ernest Edward Herrmann of the United States Naval Academy. This is an approximate technique for solving exterior ballistics trajectories with between 12 to 15 degrees of elevation. The artillery is the 16 inch / 50 caliber rifled guns of the Iowa class of fast battleships (BB-61 USS Iowa, BB-62 USS New Jersey, BB-63 USS Missouri, and BB-64 USS Wisconsin).

Range Table 0 Range Table 2 Range Table 1 ExteriorBallisticsRK5 Main Form

From “Exterior Ballistics, 1935” by Lieutenant Commander Ernest Edward Herrmann by James Pate Williams, Jr., BA, BS, MSwE, PhD

Exercises Page 9

My Near-Term Agenda by James Pate Williams, Jr. BA, BS, MSwE, PhD

Merry Christmas to all you devout Christians. I am not one of you. I am about to embark on a mission to carefully annotate with open source C# computer code my copy of “Exterior Ballistics, 1935” by Professor Ernest Edward Herrmann of then the United States Naval Academy at Annapolis, Maryland. This book set the standard for naval gunnery in World War II. Of course, our navy and especially our battle-wagons had the largest rifled artillery of any United States service. The 105 mm = 105 mm / 25.4 mm / inch = 4.13 inches, 120 mm / 25.4 mm / inch = 4.72 inches, and 155 mm / 25.4 mm / inch = 6.10 inch of our excellent United States Army and United States Marine Corps (semper fidelis) are puny in comparison to the mighty 8, 10, 12, 14, and finally 16 inch mostly rifled artillery of our incredible navy’s cruisers, dreadnoughts, and battleships of the World War I and World War II era ships. Even a destroyer of the USN Fletcher class had 5-inch (127 mm) / 38 caliber rifled artillery which had a 5 inch * 38 = 190-inch barrel length. Our mightiest naval artillery was, of course, my favorite the mighty 16 inch (406.4 mm) / 50 caliber rifles that had a barrel length of 16 * 50 inches = 800 inches = 66.6 feet!

Thanks,

James Pate Williams, Jr.

Bachelor of Arts Chemistry LaGrange College 1979

Bachelor of Science Computer Science LaGrange College 1994

Master of Software Engineering Auburn University 2000

Doctor of Philosophy Computer Science Auburn University 2005

Gratis Open Source Computer Software Developer Since Summer 1978

1980 – 1983 Graduate Work in Chemistry and Mathematics at Georgia Tech

A Current Website I developed for my friends Wesley “Wes” and Missy Cochran:

http://thecochrancollection.com/Home

Powers of Two – Excel by James Pate Williams, Jr. BA, BS, MSwE, PhD

First Function in Excel (Assumes that You Have Access to an Office 365 Subscription)

Please attempt the following procedure:

Type Excel in the Windows 10 Search Box
Select the Excel App
Select Blank workbook
Maximize the Excel Window
Type x in Cell A1
Tab to Cell B1
Type y in Cell B1
Type 0 in Cell A2
Type 1 in Cell B2
Type 1 in Cell A3
Type 2 in Cell B3
Type 2 in Cell A4
Type 4 in Cell B4
Type 3 in Cell A5
Type 8 in Cell B5
Type 4 in Cell A6
Type 16 in Cell B6
Type 5 in Cell A7
Type 32 in Cell A8
Highlight Cells A1 and B1
From the Toolbar Select Alignment and Right Alignment
Select File Save As
Select “Documents” and “Powers of Two” as the filename
Highlight Cells A1 to B7
Select Insert from Toolbar
Select Charts Scatter
Select the Chart
Select the Big + Sign on the Right
Label the y-axis “y = 2 ^ n”
Label the x-axis “n”
Relabel the Title of the Chart as “Powers of Two”

Note that x is in the finite set { 0, 1, 2, 3, 4, 5 }

Note that y is the function y = 2 ^ x where ^ is the exponentiation operator

Powers of Two Table Powers of Two Chart

Global Primary Greenhouse Gas Concentrations by James Pate Williams Jr BA, BS, MSwE, PhD

I designed and implemented a C# computer language application to model the global greenhouse gas concentrations data found on the NOAA website:

https://www.esrl.noaa.gov/gmd/aggi/aggi.html

I used the latest recommended data for time period 1979 to 2017. The concentrations of three greenhouse gases were modeled: carbon dioxide (CO2), methane (CH4), and nitrous oxide (N2O).

The empirical modeling paradigm I used was simple linear regression. My model goes out to the year 2300. The key formulas used by the model are:

See the website:

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

Some plots of the concentrations in parts per million (PPM) and parts per billion (PPB) are given below.

**Carbon Dioxide Concentration in Parts Per Million**

**Methane Concentration in Parts Per Billio**n

**Nitrous Oxide Concentration in Parts Per Billion**

NOAA Contiguous United States of America Precipitation by James Pate Williams Jr BA, BS, MSwE, PhD

I designed and implemented a C# computer language application to model the precipitation data found on the NOAA website:

https://www.ncdc.noaa.gov

I used the latest recommended data for time period 1895 to 2017. The empirical modeling paradigm I used was simple linear regression. My model goes out to the year 2300. The key formulas used by the model are: