Issue 50

A. Kakaliagos et alii, Frattura ed Integrità Strutturale, 50 (2019) 481-496; DOI: 10.3221/IGF-ESIS.50.40 483 Orban’s gun interior ballistics The force of the expanding gunpowder gas during ignition of the charge creates a force which in turn accelerates the cannonball inside the barrel towards the muzzle. Integrating the work produced by the cannon ball running across the barrel and setting this work equal to the projectile kinetic energy, the muzzle velocity is calculated (in m/sec) with Eq.(1). Herein, R is a factor accounting for the effect of hot gunpowder expanding gases after ignition inside the gunpowder chamber (Robins [8], Collins [9]). This factor captures the initial ratio of gunpowder chamber hot gas pressure to atmospheric pressure, with the atmospheric pressure set at 101,325 Pa. In addition, factor R reflects the quality of the gunpowder, the gunpowder charge compaction and the skill of the gun crew. The dimensionless factor ψ equals 6.13 for granite cannon balls capturing projectile density ρ at 2,700 kg/m 3 . 1 2 2 676 1 α ψ λ v R lnα β          where: L c   , d D   , L d   (gun caliber) and ൌ 0.00227 (1) In the above expression an effective projectile weight was employed, typically corresponding to the original projectile weight increased by one third of the gunpowder weight, with gunpowder density at approximately 881 kg/m 3 . (Taylor [16]). This effective cannonball weight increase models the energy consumption which is required to accelerate the burning powder and hot gas along the barrel as well as the cannonball. The phenomenon was also monitored for the 17th and 18th century smooth bore cannons, with cannon bore and cannonball manufactured with cast iron (Collins [9]). It was considered that Orban’s gun was manufactured in bronze with granite cannonball ammunition (Critovoulos [3]). Admittedly, both materials employed differ from cast iron. However, effects such as pronounced gun thermal effects and projectile surface imperfections present in Orban’s gun, ultimately decelerated projectile’s forward accelerated motion inside the barrel after ignition. These factors ultimately counterbalanced the associated effects as introduced by cast iron material. It is considered, that under repeated gun firing, residual thermal stresses and corresponding dilatations and/or micro- distortions of the cannon bore, may have resulted ultimately in imperfections of the original cannon bore geometry. Those factors lead to pronounced contact friction of granite cannonball to internal bore surface. According to historical reports, the gun produced a pronounced increase in temperature along the barrel, effect which in turn, may have resulted in an early explosion of the gun (Chalkokondyles [2], Phrantzes [6]). It was considered that Orban’s gun cannonballs were manufactured by stone masons. This procedure may not necessarily have resulted in an absolutely perfect smooth cannonball surface when compared to cast iron cannonball projectiles. As a result of this, an increased friction would be present at granite cannonball contact to bore internal surface. The deployment of an effective cannonball weight was deemed necessary in order to realistically model gun firing capability. Using data from Table 1 together with R=1,000, the cannonball muzzle velocity results 216 m/sec with the cor- responding time for cannonball exit from bombard bore at 44.8 msec. Pressure inside the gunpowder chamber In order to estimate the pressure inside the gunpowder chamber, hence, the factor R from Eq.(1), information from full scale gun testing of a Medieval cannon was used. The tested gun was a replica of the Medieval Loshult Gun (Ho Group [12], McLachlan [11]). The Loshult Gun originating from Sweden, was known and apparently used in France with the name “ pot de fer ” and in Italy with the name “ vasi ”. The Gun was tested using early gunpowder recipes from the 14 th Century with different proportions of saltpeter, firing a 184 g lead ball with 50 g of gunpowder (Table 3). Using the geometrical properties of the gun the input parameters for Eq.(1) were evaluated (Table 2). They were used together with the experimentally recorded muzzle velocity to solve Eq.(1) for the corresponding R value (Table 3). It must be emphasized that the Loshult test results were furnished with a total of 19 shots and they should be treated with caution. However, an overall trend is identified where R is increasing when the corresponding saltpetre portion in the gun- powder mix is increased (Table 3). Considering the fact that the results from Table 2 demonstrate the average effectiveness of the 14 th Century gunpowder recipes, it can be expected that the corresponding R value for Orban’s gun could be marginally higher as gunpowder production techniques were further developed in the 15 th Century. Admittedly, powder chamber internal pressure as result of gunpowder ignition is also function of powder chamber volume and propellant characteristics (Culver [10]). It was recognized, that for the early 18 th Century U.K smooth bore guns, muzzle velocities could be evaluated with an R value at approximately 1,500, whereby, for the early 19 th Century guns, an R value of 1,600 would be appropriate (Collins [9]).