Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
Battle of Coronel
Introduction
In this notebook we calibrate the Heterogeneous Salvo Combat Model (HSCM), [MJ1, AAp1], to the First World War , [Wk1]. Our goal is to exemplify the usage of the functionalities of the paclet "SalvoCombatModeling", [AAp1]. We closely follow the Section B of Chapter III of [MJ1]. The calibration data used in [MJ1] is taken from [TB1].
Setup
Here we load the paclet:
In[7]:=
Needs["AntonAntonov`SalvoCombatModeling`"]
The battle
The Battle of Coronel was a First World War Imperial German Navy victory over the Royal Navy on 1 November 1914, off the coast of central Chile near the city of Coronel.
is a First World War naval engagement between three British ships {Good Hope, Monmouth, and Glasgow) and four German ships (Scharnhorst, Gneisenau, Leipzig, and Dresden). The battle happened on 1 November 1914, off the coast of central Chile near the city of Coronel.
The Scharnhorst and Gneisenau are the first ships to open fire at Good Hope and Monmouth; the three British ships soon afterwards return fire. Dresden and Leipzig open fire on Glasgow, driving her out of the engagement. At the end of the battle, both Good Hope and Monmouth are sunk, while Glasgow, Scharnhorst, and Gneisenau were damaged.
Out[218]=
| |||||||||||||||||
The following graph shows which ship shot at which ships and total fire duration (in minutes):
Out[232]=
Model
The British ships are in Good Hope, Monmouth, and Glasgow. They correspond to the indices 1, ,2, and 3 respectively.
In[213]:=
AssociationThread[Range[3],{"Good Hope","Monmouth","Glasgow"}]
Out[213]=
1Good Hope,2Monmouth,3Glasgow
The German ships are Scharnhorst, Gneisenau, Leipzig, and Dresden:
In[214]:=
AssociationThread[Range[4],{"Scharnhorst","Gneisenau","Leipzig","Dresden"}]
Out[214]=
1Scharnhorst,2Gneisenau,3Leipzig,4Dresden
Remark: The Battle of Coronel is modeled with a "typical" salvo model -- the ships use "continuous fire." Hence, there are no interceptors and or, in model terms, defense terms or matrices.
Here is the model (for 3 British ships and 4 German ships):
In[208]:=
m=
[{B,3},{G,4},"OffensiveEffectivenessTerms"True]
 | HeterogeneousSalvoModel |
Out[208]=
Remove the defense matrices:
In[211]:=
m=Cancelm//.
[___]0
 | γ |
Out[211]=
BUnits{B[1],B[2],B[3]},OffenseMatrix,,,,,,,,,,,,DefenseMatrix{{0,0,0},{0,0,0},{0,0,0}},GUnits{G[1],G[2],G[3],G[4]},OffenseMatrix,,,,,,,,,,,,DefenseMatrix{{0,0,0,0},{0,0,0,0},{0,0,0,0},{0,0,0,0}}
β[G,B,1,1]ε[G,B,1,1]Ψ[G,B,1,1]
ζ[B,1]
β[G,B,2,1]ε[G,B,2,1]Ψ[G,B,2,1]
ζ[B,1]
β[G,B,3,1]ε[G,B,3,1]Ψ[G,B,3,1]
ζ[B,1]
β[G,B,4,1]ε[G,B,4,1]Ψ[G,B,4,1]
ζ[B,1]
β[G,B,1,2]ε[G,B,1,2]Ψ[G,B,1,2]
ζ[B,2]
β[G,B,2,2]ε[G,B,2,2]Ψ[G,B,2,2]
ζ[B,2]
β[G,B,3,2]ε[G,B,3,2]Ψ[G,B,3,2]
ζ[B,2]
β[G,B,4,2]ε[G,B,4,2]Ψ[G,B,4,2]
ζ[B,2]
β[G,B,1,3]ε[G,B,1,3]Ψ[G,B,1,3]
ζ[B,3]
β[G,B,2,3]ε[G,B,2,3]Ψ[G,B,2,3]
ζ[B,3]
β[G,B,3,3]ε[G,B,3,3]Ψ[G,B,3,3]
ζ[B,3]
β[G,B,4,3]ε[G,B,4,3]Ψ[G,B,4,3]
ζ[B,3]
β[B,G,1,1]ε[B,G,1,1]Ψ[B,G,1,1]
ζ[G,1]
β[B,G,2,1]ε[B,G,2,1]Ψ[B,G,2,1]
ζ[G,1]
β[B,G,3,1]ε[B,G,3,1]Ψ[B,G,3,1]
ζ[G,1]
β[B,G,1,2]ε[B,G,1,2]Ψ[B,G,1,2]
ζ[G,2]
β[B,G,2,2]ε[B,G,2,2]Ψ[B,G,2,2]
ζ[G,2]
β[B,G,3,2]ε[B,G,3,2]Ψ[B,G,3,2]
ζ[G,2]
β[B,G,1,3]ε[B,G,1,3]Ψ[B,G,1,3]
ζ[G,3]
β[B,G,2,3]ε[B,G,2,3]Ψ[B,G,2,3]
ζ[G,3]
β[B,G,3,3]ε[B,G,3,3]Ψ[B,G,3,3]
ζ[G,3]
β[B,G,1,4]ε[B,G,1,4]Ψ[B,G,1,4]
ζ[G,4]
β[B,G,2,4]ε[B,G,2,4]Ψ[B,G,2,4]
ζ[G,4]
β[B,G,3,4]ε[B,G,3,4]Ψ[B,G,3,4]
ζ[G,4]
Put tooltip interpretations of the terms:
In[212]:=
Blockvrules=Map#1Tooltip#1,#2,
&,
[{B,3},{G,4}],ReplaceAll[m,vrules]
 | SalvoVariableRules |
Out[212]=
BUnits{B[1],B[2],B[3]},OffenseMatrix,,,,,,,,,,,,DefenseMatrix{{0,0,0},{0,0,0},{0,0,0}},GUnits{G[1],G[2],G[3],G[4]},OffenseMatrix,,,,,,,,,,,,DefenseMatrix{{0,0,0,0},{0,0,0,0},{0,0,0,0},{0,0,0,0}}
β[G,B,1,1]
ε[G,B,1,1]
Ψ[G,B,1,1]
ζ[B,1]
β[G,B,2,1]
ε[G,B,2,1]
Ψ[G,B,2,1]
ζ[B,1]
β[G,B,3,1]
ε[G,B,3,1]
Ψ[G,B,3,1]
ζ[B,1]
β[G,B,4,1]
ε[G,B,4,1]
Ψ[G,B,4,1]
ζ[B,1]
β[G,B,1,2]
ε[G,B,1,2]
Ψ[G,B,1,2]
ζ[B,2]
β[G,B,2,2]
ε[G,B,2,2]
Ψ[G,B,2,2]
ζ[B,2]
β[G,B,3,2]
ε[G,B,3,2]
Ψ[G,B,3,2]
ζ[B,2]
β[G,B,4,2]
ε[G,B,4,2]
Ψ[G,B,4,2]
ζ[B,2]
β[G,B,1,3]
ε[G,B,1,3]
Ψ[G,B,1,3]
ζ[B,3]
β[G,B,2,3]
ε[G,B,2,3]
Ψ[G,B,2,3]
ζ[B,3]
β[G,B,3,3]
ε[G,B,3,3]
Ψ[G,B,3,3]
ζ[B,3]
β[G,B,4,3]
ε[G,B,4,3]
Ψ[G,B,4,3]
ζ[B,3]
β[B,G,1,1]
ε[B,G,1,1]
Ψ[B,G,1,1]
ζ[G,1]
β[B,G,2,1]
ε[B,G,2,1]
Ψ[B,G,2,1]
ζ[G,1]
β[B,G,3,1]
ε[B,G,3,1]
Ψ[B,G,3,1]
ζ[G,1]
β[B,G,1,2]
ε[B,G,1,2]
Ψ[B,G,1,2]
ζ[G,2]
β[B,G,2,2]
ε[B,G,2,2]
Ψ[B,G,2,2]
ζ[G,2]
β[B,G,3,2]
ε[B,G,3,2]
Ψ[B,G,3,2]
ζ[G,2]
β[B,G,1,3]
ε[B,G,1,3]
Ψ[B,G,1,3]
ζ[G,3]
β[B,G,2,3]
ε[B,G,2,3]
Ψ[B,G,2,3]
ζ[G,3]
β[B,G,3,3]
ε[B,G,3,3]
Ψ[B,G,3,3]
ζ[G,3]
β[B,G,1,4]
ε[B,G,1,4]
Ψ[B,G,1,4]
ζ[G,4]
β[B,G,2,4]
ε[B,G,2,4]
Ψ[B,G,2,4]
ζ[G,4]
β[B,G,3,4]
ε[B,G,3,4]
Ψ[B,G,3,4]
ζ[G,4]
Concrete parameter values
Concrete parameter values
Setting the parameter values as in [MJ1]:
In[206]:=
ClearAll
,
,
,
| β |
| ζ |
| ε |
| Ψ |
In[112]:=
 | β |
| β |
 | β |
| β |
| β |
| β |
| β |
| β |
| β |
| β |
| β |
| β |
Damage calculations
Damage calculations
How many salvos to achieve total damage of Good Hope and Monmouth:
That is close to the 28 min of fire by Scharnhorst and Gneisenau at Good Hope and Monmouth.
Total damage of on Glasgow -- Leipzig and Dresden fire for 2 min at Glasgow:
References
Articles, theses
Articles, theses
Paclets
Paclets
[AAp1] Anton Antonov, "SalvoCombatModeling", (2024), Wolfram Language Paclet Repository.