Category: Exterior Ballistics

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Blog Entry (c) Thursday, November 21, 2024, by James Pate Williams, Jr. Comparison of Homegrown Fifth Order Runge-Kutta Method Versus a Limited Number of Predictor-Corrector Algorithm

The first table is based on Conte-de Boor Fourth Runge-Kutta formulas that I converted to Fifth Order Runge-Kutta. Initial values: V = 2600 feet per second angle of elevation 30 degrees diameter 16 inches coefficient of form 0.61 density ratio 1.00 are from LCDR Ernest Edward Herrmann’s Exterior ballistics, 1935 My results are given first then LCDR Herrmann’s results:

x deg min sec time v vx vy y
0 30 0 0 0.00 2600 2252 1300 0
563 29 50 45 0.25 2578 2236 1283 325
1122 29 41 24 0.50 2556 2221 1266 646
1677 29 31 57 0.75 2535 2206 1250 962
2229 29 22 25 1.00 2515 2191 1233 1275
2776 29 12 47 1.25 2494 2177 1217 1583
3321 29 3 4 1.50 2474 2163 1201 1887
3861 28 53 15 1.75 2455 2149 1186 2188
x deg min sec time v vx vy y
0 30 0 0 0.00 2600 2252 1300 0
561 29 50 7 0.25 2582 2259 1285 323
1120 29 41 4 0.50 2564 2227 1270 642
1675 29 32 2 0.75 2546 2216 1255 958
2228 29 22 5 1.00 2529 2204 1241 1270

It is amazing how accurate Herrmann’s results were based on only a couple iterations using the Mayevski seven zone velocity retardation formulas.

Blog Entry © Sunday, November 17, 2024, by James Pate Williams, Jr. Three Methods of Solving the Exterior Ballistics Problem for the Fast Battleship USS Iowa (BB-61) 16-Inch/50 Caliber Rifles

Blog Entry Sunday 11 17 2024Download

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

Estimated Babe Ruth 1921 Homerun Parameters by James Pate Williams, Jr.

“Babe Ruth is generally considered the owner of the record for the longest home run in MLB history with a 575-foot bomb launched at Navin Field in Detroit in 1921.” – https://www.msn.com/en-us/sports/mlb/what-is-the-longest-home-run-in-mlb-history/ar-AA1dGwlZ

As you can see, I estimated the pitch velocity at 90 miles per hour and Babe Ruth’s (Sultan of Swing) at 90 miles per hour also. My analytic calculations yield a range of the baseball’s trajectory as about 576 feet.