Category: Numerical Analysis

Blog Entry (c) Wednesday, October 2, 2024, by James Pate Williams, Jr. First Order Coupled Ordinary Differential Equations

First Order Coupled ODEDownload

Blog Entry (c) Saturday, September 28, 2024, by James Pate Williams, Jr. New Iowa Ballistics Table

I created the following fast battleship Iowa class ballistics table using a single coefficient of form with the value 0.531. The ballistic coefficient is 19.86229.

For comparison use the actual October 1941 Iowa class ballistics tables:

https://eugeneleeslover.com/USN-GUNS-AND-RANGE-TABLES/OP-770-1.html

Click to access op-770-range-tables-for-16inch-50-caliber-gun-1.pdf

Iowa Range Table 531Download

Blog Entry © Thursday September 26, 2024, by James Pate Williams, Jr. Atmospheric Air Density Two Models

I wrote a C# program to graph NASA’s Earth Atmospheric Model’s variation of air density with height in Imperial Units and the United States Navy’s air density altitude equation.

Earth Atmosphere Model – Imperial Units (nasa.gov)

The USN’s formula for density – altitude is found in “Exterior ballistics, 1935” by Lieutenant Commander Ernest Edward Herrmann who was an instructor at the United States Naval Academy.

Blog Entry (c) Thursday September 19, 2024, by James Pate Williams, Jr. Ship to Ship Ballistics

The following graphs and data are for a hypothetical engagement between the Battleship Iowa (BB-61) and an unlucky enemy warship. My numbers are very close to those found in Ordnance Pamphlet 770 at the following website:

https://eugeneleeslover.com/USN-GUNS-AND-RANGE-TABLES/OP-770-1.html

Ship to Ship BallisticsDownload

Blog Entry (c) Monday September 16, 2024, by James Pate Williams, Jr. Variation of the Gravitational Acceleration on Earth with Height

Variation of the Gravitational Acceleration with HeightDownload

Blog Entry (c) Saturday August 31, 2024, by James Pate Williams, Jr. An Elementary School Problem Found Online

Solve for a real root of the equation
f(x)=log6l(5+x)+log6l(x)=0
First we test our log6l(x) function
log6l(12) = 1.386853
log6l(36) = 2.000000
x = 0.1925824036
f = 0.0000000000
Online Logarithm Problem C Source CodeDownload