Stochastic Lanchester Square-Law Simulation for 40 vs. 46

This stochastic Lanchester square-law simulation represents Lord Nelson's original plan of attack for Trafalgar. Lord Nelson assumed that the Spanish and French would have 46 ships and that the British would have 40 ships. The parameter than varies in this simulation is time ... where the time to the next casualty is exponentially distributed.

This simulation is a consolidation of 100,000 runs. Time t is located in the upper-left corner. The x-axis (lower-right) represents the number of British ships [0,40], the y-axis (lower-left) represents the number of Spanish and French ships [0,46], and the z-axis represent the probability of any given (x,y) combination at the displayed time t. The z-axis only runs from 0 to 0.06 (instead of 0 to 1) to highlight the probability wave. The blue line represents the point of highest probability for every point in time t.

This only represents Lord Nelson's plan, not the actual battle. In the actual battle of Trafalgar, both sides had less ships than Lord Nelson's plan assumed.

Statistics:

X Survivors:
Mean = 1.76979
Standard Deviation = 5.07266
Max = 35
Min = 0
Number of Observations = 100000

Y Survivors:
Mean = 20.4206
Standard Deviation = 10.7024
Max = 44
Min = 0
Number of Observations = 100000

X Survivors | X Wins:
Mean = 13.5016
Standard Deviation = 6.15705
Number of Observations = 13108

Y Survivors | Y Wins:
Mean = 23.5012
Standard Deviation = 7.7086
Number of Observations = 86892

Battle Length:
Mean = 142.915
Standard Deviation = 52.3397
Max = 647.359
Min = 46.9161
Number of Observations = 100000

Note: The simulation was programmed in Mathematica for Students 6.02.

Category:

Science & Technology

Tags:

• simulation
• Lanchester
• Square
• Law
• Trafalgar
• Lord
• Nelson
• Mathematica