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.