An alternative to the percussion cap is the friction tube. This is described in detail in EB11/Ammunition; essentially this is a T-shaped device, the vertical branch communicates with the vent hole, and the horizontal branch contains a copper friction bar surrounded by a "friction composition." The lanyard causes the friction bar to be pulled out, igniting the composition which ignites the powder in the vertical tube.
The great advantage of electric ignition was that it reduced the firing interval. However, the reliability of the power source is the sticking point. While it would be possible to have the ship carry a generator and run lines from it to all the guns, that would mean that a shot that took out the generator rendered them useless. Hence, each gun must have its own battery. And developing a working battery itself took some time. An 1894 article (Morgan) noted that while electrical ignition had until then been in limited use, the Bureau of Ordnance had recently adopted a zinc-carbon dry battery as well as a new electric primer design. By WW I, electric ignition was the norm, with percussion systems as backup.
Internal Ballistics
The term "ballistics" was coined by Marin Mersenne in 1644. Ballistics may be divided into three broad categories: interior (internal) ballistics, explaining what happens inside the gun barrel; exterior ballistics, describing the flight of the projectile through the air; and terminal ballistics, dealing with its penetration of the target.
Gun designers manipulate the internal ballistics of a gun so that it projects the desired projectile at the desired muzzle speed without bursting the gun.
A good propellant is one whose ingredients react very quickly ("deflagrate") to form a gas. At normal temperature and pressure, this gas would occupy a much greater volume than the original ingredients; but initially the volume of the gas is limited by that of the propellant (powder) chamber, and so there is instead an increase in pressure. The deflagration reaction also generates heat, which further increases pressure.
As the reaction continues, the pressure reaches the point that it's sufficient to overcome the friction holding the projectile in place ("shot-start force"), and it starts traveling down-bore.
The propulsive force on the projectile is the pressure times the area of the projectile base; the acceleration it feels is the force divided by the mass of the projectile. For spherical shot, the base area is proportional to the square of the diameter, and the mass to the cube, so acceleration is inversely proportional to the diameter.
You can cheat to some degree by using a sabot as a gas check. The sabot ensures that the pressure is exerted on the largest possible area, but the projectile may be subcaliber (narrower than the bore) and therefore less massive.
For a given caliber and shape, stone projectiles have a lower sectional density (mass/frontal area) than lead or iron and that means that for a given barrel length, they require less force to accelerate them to a given muzzle velocity. Less force means less pressure which means a smaller charge. Stone projectiles can therefore be fired from lighter cannon than metal ones of the same weight. As of the early-seventeenth century, stone throwers (pedreros) were being phased out in Europe, but they remained popular in the Ottoman Empire.
As the projectile moves, the volume available to the gas increases, which tends to reduce the pressure. On the other hand, if the deflagration reaction is still going on, the newly-produced gas and heat will tend to increase the pressure. One can thus draw a pressure-time or pressure-travel curve, and the location of its peak will depend on the specific characteristics of the powder. Likewise one can draw velocity-time or velocity-travel curves for the projectile. Sample curves appear in EB11/Ballistics.
Once the powder is completely consumed, the propulsive force on the projectile can only decrease as it moves down-bore, and once that propulsive force is less than the resisting forces, any further travel will reduce the projectile's speed.
After the projectile exits the muzzle, the pressure on it drops precipitously, although it may experience a brief period of additional acceleration from the escaping gases.
Internal Ballistics: Barrel Stress
A gun barrel, in essence, is a pressure vessel, containing the gases generated by the rapid combustion of the powder. We want to design the barrel so the gun is safe to fire, without inordinately increasing its weight and cost.
One way to do this was to put the metal where it was needed, i.e., where the pressure was greatest. It was certainly known to the down-timers that the thickness had to be greater at the breech than at the muzzle-they figured twice as much (see Manucy 37 for the detailed thickness variation)-but they had no quantitative knowledge of the pressure variation. That was revealed by nineteenth-century experimentation, as discussed below.
It is also important not to impair the barrel's function. Until the mid-nineteenth century, it was customary to bedeck cast cannon with a variety of ornamentation. However, these protuberances acted as "stress raisers," weakening the gun. (Hazlett 147-8, 221).
For a thin-walled (thickness not more than one-tenth diameter) cylindrical pressure vessel, the hoop stress is pressure * radius / thickness, in which case thickness should be proportional to bore diameter if pressure held constant. However, a cannon can't be considered thin-walled; the cannon of the Santissimo Sacramento (sunk 1668) had a maximum barrel thickness about equal to the bore diameter. (Guilmartin).
The thick-walled tube hoop stress formula, if external pressure is ignored, is
(Ri2*p/(Ro2-Ri2)) * (1+ Ro2/r2)
with
Ri inner radius
Ro outer radius
p internal pressure
r radius at which stress is calculated. (Labossier; McEvily 53).
So, at r=Ri, stress is
p*(Ro2+Ri2)/(Ro2-Ri2)
and at r=Ro, it is
2*p*Ri2/(Ro2-Ri2)
It's immediately evident that the stress is greater at the inside radius (Ri) than at the outside radius (Ro); the gun will crack first on the inside and the crack will grow each time the gun is fired.
Wall thickness of course is Ro-Ri and bore diameter is 2*Ri. When increasing the barrel thickness, each additional layer decreases the stress inflicted by a given internal pressure, but with diminishing returns (Table 2–1):
If we express Ro as k*Ri, so thickness is (k-1)*Ri, then the inside stress is proportional to
(k2+ 1)
– -
(k2- 1).
The even more complex "Gunmaker's formula," for built-up guns (see part 1), appears in EB11/Ordinance.
I mentioned pre-stressing in connection with cannon manufacture; this is to "make the outer layers of metal in the barrel bear a greater proportion of the bursting load." (Payne 264).
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With real guns, the pressure varies according to the position of the projectile. In 1861, the distance-pressure curve for a 42-pounder with the powder of that time might feature a maximum pressure of 45,000 psi, dropping to one-tenth that by the time the shot exited the muzzle. (Bruce 138). Hence thickness (and thus weight) can be reduced if you know how pressure varies.
It is possible to control the curve to some degree by powder design. A progressive powder (burn rate increases with time) reduces the peak pressure, and thus the required barrel strength. This also reduces barrel wear, which tends to be more dependent on peak pressure than average pressure (Rinker 43). And it's likely to provide the highest exit velocity. On the other hand, if you have a short barrel, then use a degressive propellant, so you develop high projectile velocity quickly. (ES310).