Issue 50

A. Kakaliagos et alii, Frattura ed Integrità Strutturale, 50 (2019) 481-496; DOI: 10.3221/IGF-ESIS.50.40 484 L G (mm) L (mm) c (mm) B (g) p (g) d (mm) D (mm) D 1 (mm) D 2 (mm) t (mm) t 1 (mm) k (mm) 300 270 65 184 50 31 36 65 110 22 37 30 Table 2 : Schematic representation of Loshult Gun and geometrical parameters. Powder Type Year Saltpetre KNO 3 (%) Sulphur S (%) Charcoal C (%) computed R (---) Rouen 1338 50 25 25 127 Lille 1340 55.6 22.2 22.2 167 Marcus Graecus 1350 66.7 11.1 22.2 186 Rothenburg 1380 75 12.5 12.5 212 Table 3 : Values of R for different types of 14 th century gunpowder mix proportions. Aiming to get an estimate for R corresponding to a powder recipe closer to the date of the siege at 1453 it was decided to simulate numerically available information from a 16 th Century full-scale gun fire test. This would yield chamber pressures corresponding to an improved powder recipe when compared to the recipes originating from the 14 th Century (Table 3). In September 1544, a full-scale gun fire test with a Venetian Navy Cannon was executed in Venice close to the Church of San Niccolò di Lido. The bronze gun used in the test was a colubrina bastarda - legittima da 50 of caliber 32, firing a 16.4 kg iron cannonball with 13.12 kg gunpowder at 7.5 degrees gun elevation. The gunpowder recipe was according to the Venetian recipe 5-asso-asso, corresponding to 71.4% saltpetre, 14.3% sulphur and 14.3% charcoal. Finally, engaging the geometrical properties of the cannon together with an R value at 1,550 and Eq.(1), the muzzle velocity at 685 m/sec was confirmed (Santarini [17]). In general, it was considered that there was a rapid increase of gunpowder quality and associated methods of gunpowder production and handling, as well as a drastic improvement in the procedures for servicing a gun from the 13 th Century (R=212, Table 3) till the 16 th Century (R=1,550, Venice Test). On the average it was concluded that the corresponding R value for Orban’s gun could be set close to the mean value between 212 and 1,550. Consequently, the R value for Orban’s gun was estimated approximately at 1,000, realizing that the improvement of gunpowder production and handling was not a linear process over time. The use of R at 1,000, could reflect approximately a saltpeter portion in the gunpowder mix between 66.7 and 75%, together with certain impurities, typically present for the 15 th Century gunpowder. In the ensuing sections of present paper R was set at 1,000 and the bombarding effect on Constantinople Wall was evaluated. In general, evaluated bombard ballistics and associated computed effects on target when compared to information from eyewitness historical reports confirmed the use of R at a value of 1,000. Orban’s gun external ballistics – Cannonball aerodynamics The cannonball trajectory after leaving the barrel can be expressed by Newton's equations of motion. Herein, an additional drag force F p is acting on the cannon ball as a result of the air resistance to the projectile forward motion. Considering the air density ρ Α =1.225 kg/m 3 , the instantaneous projectile velocity v, the cannonball diameter d and the aerodynamic drag C A (M), the drag force F p can be computed using Eq.(2) as function of the corresponding Mach number M. The aero- dynamic drag for spherical projectile C A (M) was modelled with Eq.(3), valid up to Mach 1.5. Given the muzzle velocity, the initial position of the gun and the elevation of the barrel, the trajectory of the cannonball is evaluated using a linear step by step numerical procedure with a time integration step of 0.001 sec. This provision was necessary in order to provide a numerically stable trajectory path. Muzzle velocity at 216 m/sec was used to evaluate the corresponding cannonball trajectory and resulting cannon range. Herein, the average firing position of the gun was set at