The word **artillery **is a collective name given in the beginning to every gitto machine and every war device used before the invention of gunpowder. The launch machines were widely used in the East, from where they also arrived to us, around the sec. XV and XVI. The ancient or mechanical artillery and guns used during the war were in particular cannons, colubrine, mortars, bombards, falcons, falconets, pushers …

Cannon means a fire mouth that fires at direct range (in the first arc of the dish), so it must have a relatively high velocity at the mouth. The gun remained stationary in the horizontal direction, against the effects of the shot, from a robust structure to the back of the cradle. The carriage had low and full wheels, and leaned on the ground with a tail similar to that of modern artillery.

The bombers were machines of artillery, parabolic, gigantic, able to frighten with the mere thunder. They fired large stone balls up to two thousand paces away, although the shot was rather inaccurate, as the short mouth did not allow to exploit all the thrust capacity that could provide the charge used.

Colubrina, also called a hand gun, was a widely used weapon since 1447. Its barrel was wedged onto a lath and it was used as a crossbow to throw balls of stone the size of a walnut.

The mortar is a piece of curved artillery, which normally fires only in the second arc (the angle of the barrel is always greater than 45,- 2), used to support indirect fire by throwing low-speed bombs and to beat targets that cannot be hit by shooting directly-fired artillery pieces, as they are placed behind vertical obstacles. It is a fairly simple weapon, consisting essentially of a barrel and a support plate.

The falconet is a small-caliber gun, transportable by hand, which fired full balls, weighing between one and three pounds, and machine guns, that is, ammunition consisting of metal armor filled with lead balls.

Another example of artillery is the pusher, a war machine in the shape of a large crossbow, used to throw large stones or crystals. The larger ones were fixed on trestles and held with wooden stumps; the smaller ones became real small arms.

All the artillery analyzed so far, in the past was used to throw projectiles or bombs (they are called “projectiles” the ammunition of the guns, which, once launched, rotate on themselves; while they are called “bombs” those mortar, that do not rotate). In physics, the** bullet** is an object thrown and left free to follow a trajectory determined only by the force of gravity. This trajectory corresponds to a parabola, for this reason the motion of the projectile can be defined a **parabolic motion**, a type of two-dimensional motion expressed through the combination of two parallel and independent straight motions: the straight uniform motion (**MRU**) and evenly accelerated straight motion (**MRUA **a = g).

In the **motion of the projectile **the following simplifications are used:

- the
**whole body mass**is concentrated at a single point; - the
**acceleration**of the motion is only vertical and its modulus is equal to the acceleration of gravity on the Earth’s crust (g = 9.81 m/s2), so the body is in a uniform and time-independent gravity field; **The velocity**of the projectile can be decomposed along the two x and y components of the Cartesian axis reference system and its intensity gradually decreases until it cancels when the projectile reaches the highest point of the trajectory; then the vertical component of the velocity is inverted and its intensity is increasing more and more rapidly.

In the artillery range the parabolas described by the projectiles are distinguished in **first and second arches.** The first arc starts from the theoretical straight line that would be obtained for the shooting to raise (that is angle of shot regarding the ground) zero, up to the parabola that allows the bullet to reach the greater distance (range), ideally 45 years, actually a little less because of the air resistance. The second arch, on the other hand, is obtained by higher elevations, which shorten the range, but allow to overcome higher obstacles. The second arc shot is usually less accurate than the first arc shot.

The **bullet path **equation is: **y = y _{0} + (v_{y}/v_{x}) x – (g/2v_{x}^{2}) x^{2}**

#### THE EXTERNAL BALLISTIC

External ballistics is the science that studies the motion of a projectile from the moment it finishes its acceleration phase until it hits the target. Ballistics as a science was born with Galileo Galilei and the publication in 1632 of his studies shows that the trajectory of a projectile in a vacuum is a parabola.

**BALLISTICS IN THE VACUUM**

In ballistics in a vacuum the projectile proceeds in a vacuum and is subject only to the force of gravity, applied to the center of gravity and constantly vertical. In this case the motion is evenly decelerated and the trajectory is a parabola that intersects the plane of fire in the two points constituted by the position of the mouth of fire and the point of impact of the bullet.

The main variables of motion are:

**g**: the force of gravity, approximated to 9.81 m/s2 at the Earth’s surface;**θ**: the angle of elevation (or elevation) formed by the axis of the cannon in the horizontal plane;**v**: the muzzle velocity of the gun;**y0**: the initial share of the projectile;**d**: the horizontal range, that is the total distance travelled by the projectile.

**The range**

The range is the total horizontal distance the projectile traveled before landing. It is derived from the equation of the parabola, from which, after a series of passages and simplifications, it is obtained: **d = v _{x}/g * [v_{y} + √(v_{y}^{2} + 2gy_{0})] **The maximum value of the range is obtained with angles equal to 45º degrees

**: d = v**.

^{2}/g**The flight time**

The duration of the journey, or flight time (t), is the time taken by the projectile to complete the tunnel. It is derived from the following equation:** t = d/vx**

**The maximum height**

Since the parabolic motion is symmetrical with respect to the axis passing through the vertex and parallel to the y axis, the abscissa of the landing point is twice the abscissa of the vertex of the parabola, which is twice the abscissa of the point of maximum height. This abscissa corresponds to:**x _{v} = d/2 = (v_{x}v_{y})/g.**Replacing then the abscissa of the point of maximum height in the equation of the parabola has:

**y**

_{v }= v_{y}^{2}/2g**The angle of elevation**

The angle of elevation is the angle that must form the shooting axis of the projectile with the horizontal in order to reach the distance d, at the initial speed v. Starting from the formula of distance and calculating the inverse formula we can, therefore, derive the angle:** θ = 1/2 sin ^{-1}(gd/v^{2})**

**THE BALLISTICS OF AIR**

So far, we’ve assumed that air has no effect on the motion of the bullet, which is reasonable at low speeds. For **high speeds**, however, air resistance may become relevant. So the science that studies the motion of the bullet in this case is ballistics of air.

In it the air resistance is directly proportional to the velocity of the projectile up to high velocities (subsonic). This occurs between 240 m/s and 340 m/s. The effects on the trajectory compared to that in the vacuum are:

- a significantly decreased range;
- the highest point of the trajectory is no longer in the middle of the route, but is reached earlier;
- the terminal velocity on the target is lower than the initial one.

**Sithography**

http://zweilawyer.com/2016/09/28/artiglieria-medievale-xv-secolo/

https://www.treccani.it/enciclopedia/artiglieria_%28Enciclopedia-Italiana%29/

https://it.wikipedia.org/wiki/Balistica_esterna#Gittata_orizzontale

https://it.wikipedia.org/wiki/Balistica_esterna#Balistica_nell’aria

https://it.wikipedia.org/wiki/Falconetto

https://it.wikipedia.org/wiki/Moto_parabolico