Write Up 12: The Battle of Trafalgar


The Battle of Trafalgar was a naval battle which took place in 1805. One side of the battle was a combined Spanish-French force assembled and led by Napoleon whereas the other side was the British fleet force led by Lord Nelson. Napoleon's fleet consisted of 33 ships while the British fleet consisted of 27 fleets.

Assumptions and Conditions:

Suppose during each stage of an encounter, each side suffers a loss equal to 5% of the numbers of ships of the opposing force.

Assume fractional values are meaningful- indicate that a ship (or ships) are damaged and cannot perform at full capacity

Hypothesized Battle with Assumptions and Conditions:

If each side suffers a damage loss equal to 5% of the numbers of ships of the opposing force, then we can see that the Spanish-French Force would win the naval battle by an extremely large margin. In this hypothesized battle, Napoleon would not only win the battle, but go back home with 18 undamaged ships while the British force would have lost all 27 ships in the battle.

What Actually Happened:

Napoleon's Fleet Alignment:


1) You can engage the forces one at a time, in pairs, or all at once

2) You can split your fleet into forces, but if you use over 4/5 of your entire fleet to attack a force, Napoleons's entire fleet will attack yours.


The British Victory Strategy:

1) The British attacked Napoleon's Force A with 20 ships which is under the 4/5 mark of the 27 ship fleet. Hence Napoleon's fleet will not attack. Let's observe the spreadsheet in this first battle against Force A.

After the first British attack on Napoleon's Force A, the British fleet only loses 1 ship while the entire Force A of Napoleon is wiped out.

2) The British attacked Napoleon Force B with 20 of their 26 ships available since the British Fleet only lost 1 ship in the first battle. Again, the 20 ships will be under the 4/5 mark and therefore Napoleon's fleet will not attack.

After the second battle, the British fleet of 20 ships defeats Napoleon's Force B and leaves the battle with 10 ships left over. This means that the British fleet now have a total of 16 ships left while Napoleon's fleets only has 13.

3) In the final battle, the British will send the remainder of their fleet since the 4/5 fleet rule is not in effect since this is the last battle. The British will send 16 ships against Napoleon's remaining fleet of 13 ships.

After the Battle against Force C, the British come out victorious will a remainder of 9 ships, while the entire Napoleon Fleet is wiped out. Therefore the British has won the Battle of Trafalgar and goes back home with 9 undamaged ships remaining.

In Conclusion:

The British won the Battle of Trafalgar with a great strategy against a weak fleet alignment by Napoleon In the end, the British went home with 9 undamaged ship and Napoleon lost an entire fleet of 33 ships.