Blog Entry (c) Monday, June 2, 2025, Exercises from “Exterior ballistics, 1935” by James Pate Williams, Jr.

Below are some Exercises from the textbook Exterior ballistics, 1935 by former Lieutenant Commander Ernest Edward Herrman of the United States Navy Naval Academy in Annapolis, Maryland, see Chapter Four:

Density         Published Density

1.183473        1.183472
1.306584        1.306582
1.202410        1.202408
0.694163        0.694162

Exercises from Exterior ballistics, 1935
By Lieutenant Commander Ernest Edward Herrmann
Exercise 1 Page 41

Book            Mine

0.157100        0.157563
0.492680        0.492810
0.517340        0.517829
0.675240        0.675580
0.844370        0.844597
1.018110        1.018197
1.014010        1.014027
1.094820        1.094910

Percentage Differences Exercise 1 Page 41

Percentage Difference [1] = 0.294283%
Percentage Difference [2] = 0.026383%
Percentage Difference [3] = 0.094477%
Percentage Difference [4] = 0.050340%
Percentage Difference [5] = 0.026880%
Percentage Difference [6] = 0.008545%
Percentage Difference [7] = 0.001676%
Percentage Difference [8] = 0.008220%

Three Altitude Related Density Calculations
Rho1 is from Exterior ballistics, 1935
Rho2 is from NASA
Rho3 is from Wikipedia

h ft    Rho1 SI         Rho2 SI         Rho3

0       1.000000        1.226614        1.208993
1000    0.968902        1.215727        1.174010
2000    0.938772        1.204914        1.139806
3000    0.909578        1.194175        1.106369
4000    0.881292        1.183510        1.073689
5000    0.853886        1.172917        1.041752
6000    0.827332        1.162397        1.010547
7000    0.801604        1.151949        0.980062
8000    0.776676        1.141574        0.950286

Three Altitude Related Ballistic Density Calculations
Rho1 is from Exterior ballistics, 1935
Rho2 is from NASA
Rho3 is from Wikipedia
STP = Temperature = 59 F Pressure = 29.53 Humidity = 78%

Temp    Press   h ft    Rho1 SI         Rho2 SI         Rho3

65      29.60   1000    0.968902        1.203134        1.161848
85      29.75   18000   0.566291        0.992154        0.656245
57      30.25   8000    0.776676        1.174418        0.977626
69      29.80   13000   0.663193        1.077573        0.801819
32      30.15   15000   0.622587        1.157366        0.822138

Exercise 3 Problems 1 - 4 m below means mine
Ra Ram are the Mayevski Retardations
Rf Rfm are the forces of Air Resistence
V Vm are the Applicable Velocities

Ra      Ram     Rf      Rfm     V       Vm

567.20  567.22   229.28  229.19 2626    2626
323.85  323.86   503.50  503.29 3114    3114
 91.58   91.58  2477.50 2476.50 2862    2862
 62.02   62.02  4049.40 4047.83 2584    2584

Exercise 4 - Problems 1 to 5
Ra      Ram     BC              Density

293.82  306.84   3.110358       0.989712
160.92  185.47   4.737834       1.009200
119.06  123.90   6.991926       0.952504
 73.58   84.81  10.328256       0.987977
 60.52   69.59  12.442559       1.080786

Exercise 5 - Problems 1 to 4
Ra      Gv      i-book          i-mine

511.76   803.10 1.001500        0.959553
334.04  1071.14 0.602720        0.578983
 90.62   922.06 0.601870        0.577421
 57.30   799.71 0.616870        0.593688

Test Case from Exterior ballistics, 1935
Temperature 84 F        Pressure 29.90 In Hg
Density SI = 0.959428   Book Density = 0.960
Altitude 18,000 Feet
Density SI = 0.999439   Book Density = 0.991

The differences above are probably due to the fact that Lieutenant Commander Herrmann used logarithms and logarithm tables and perhaps a slide-rule. I use double precision C/C++ real numbers.

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Author: jamespatewilliamsjr

My whole legal name is James Pate Williams, Jr. I was born in LaGrange, Georgia approximately 70 years ago. I barely graduated from LaGrange High School with low marks in June 1971. Later in June 1979, I graduated from LaGrange College with a Bachelor of Arts in Chemistry with a little over a 3 out 4 Grade Point Average (GPA). In the Spring Quarter of 1978, I taught myself how to program a Texas Instruments desktop programmable calculator and in the Summer Quarter of 1978 I taught myself Dayton BASIC (Beginner's All-purpose Symbolic Instruction Code) on LaGrange College's Data General Eclipse minicomputer. I took courses in BASIC in the Fall Quarter of 1978 and FORTRAN IV (Formula Translator IV) in the Winter Quarter of 1979. Professor Kenneth Cooper, a genius poly-scientist taught me a course in the Intel 8085 microprocessor architecture and assembly and machine language. We would hand assemble our programs and insert the resulting machine code into our crude wooden box computer which was designed and built by Professor Cooper. From 1990 to 1994 I earned a Bachelor of Science in Computer Science from LaGrange College. I had a 4 out of 4 GPA in the period 1990 to 1994. I took courses in C, COBOL, and Pascal during my BS work. After graduating from LaGrange College a second time in May 1994, I taught myself C++. In December 1995, I started using the Internet and taught myself client-server programming. I created a website in 1997 which had C and C# implementations of algorithms from the "Handbook of Applied Cryptography" by Alfred J. Menezes, et. al., and some other cryptography and number theory textbooks and treatises.

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