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.
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
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
We use an evolutionary hill-climber and the solution of the quadratic equation to solve the easy problem below:
Solution of f(a,x)=sin(sqrt(ax-x^2))=0
Subject to the constraint x+y=100
Where x and y are the two roots of
g(a,x)=ax-x^2-n*n*pi*pi=0
and n=15
a = 100.347888933988
x = 32.947113268776
y = 67.400775665213
g = 0.000000000000
s = 100.347888933988
runtime in seconds = 43.730000
Numerical Explorations 