Cannons and Shot: Conservation Laws
HMS Victory Gun Deck
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The primary armament used by ships during the Battle of Trafalgar were smooth bore cannons loaded with a variety of ammunition. This ammunition could be grapeshot for anti-personnel use, chain shot for destroying enemy rigging, or general purpose round shot. Each type of ammunition possessed a different mass when compared to another, and often the mass of the round shot was used to define the strength of a cannon. For example, a 15-pounder (firing 15 pound round shot) was significantly less powerful than a short barreled carronade which fired a 30 pound round shot. When firing the a cannon, potential energy (chemical) is transformed into kinetic energy through the process of detonating a gunpowder charge. Using the Conservation of energy this may be modeled by the equation:

P1 + K1 = P2 + K1

In order to simplify the calculations we may assume that the shot began at rest, and possesses no potential energy in its final position. As such

P1 = K2    =>   P1 = (1/2)m(v)^2

For example: If a 13.6 kg (approximately 30lb) shot travels at 250 m/s (820 ft/s) as it leaves the barrel we may determine the chemical potential energy required from the gunpowder charge.

P1 = (1/2) (13.6 kg) (250 m/s)^2 = 425 kJ

Using conservation of momentum we may calculate the velocity that the cannon recoils after being fired. As both objects start at rest the interaction may be classified as an explosion. Assuming the initial net momentum is zero:

0 = m1v1 + m2v2   =>   m1v1 = -m1v2

Using the values from above and assuming the cannon itself has a mass of 1000 kg:

(13.6 kg) (250 m/s) = - (1000 kg) v2   =>   v2 = -3.4 m/s    Where the negative sign indicates direction.

So the cannon recoils at 3.4 m/s.




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