Issue 50

A. Kakaliagos et alii, Frattura ed Integrità Strutturale, 50 (2019) 481-496; DOI: 10.3221/IGF-ESIS.50.40 492 over a short period of time, typically within a time window of certain fragments of milliseconds. The maximum developing temperature is related to the adiabatic gas temperature of the hot expanding gases produced during ignition and the gunpowder burning characteristics. In general, the associated temperature profile inside the gun is subjected to an exponential decay over time . The total event of temperature rise in the powder chamber, hence, from the abrupt temperature rise during powder ignition to the temperature drop close to ambient temperature is typically affected by gunpowder chamber volume, charge weight and propellant burning characteristics (Bannister et al [18]). Assuming that the adiabatic gas temperature is approximately at T m =2,000 K (1,728 o C) and using an ambient temperature T A =20 o C, the temperature rise T inside the bombard powder chamber over time t can be approximated with Eq.(18). This expression is used to simulate the situation with Orban’s gun and compare the resulting effects with corresponding historical reports. ൅ ஺ ൌ ௠ ቀ ௧ ೘ ௧ ቁ ሺఊିଵሻ ଶ⁄ ൏ ஻ ௠ ቀ ௧ ೘ ௧ ቁ ఊିଵ ஻ ൏ ൏ ௪ (18) where: ௪ ൌ ଵ ா , ஻ ൌ ா ଶ ⁄ , ௠ ൌ ா ଷ ⁄ , ൌ ቀ ௧ ೘ ௧ ಳ ቁ ି଴.ଵ଼ In the above equation t w is the time window, hence, the estimated total time required for the temperature inside the bombard powder chamber to drop at ambient temperature level. Additionally, t B is the estimated time at which the pro- pellant is all burned, t m is a scaled time, t E =44.8 msec is the time of cannonball exit from the bombard muzzle, A 1 , A 2 and A 3 are constants, whereby, γ =1.36 is the gas effective ratio of specific heats. Parameter A 1 was selected at 20,000 to set the time window t w at 15 minutes, large enough to monitor the temperature decay. It was considered that a relatively quick burning powder was present. Consequently, the time t B was estimated at 8.96 msec with A 2 =5, time which corresponds approximately to the cannonball travel at 0.5 m inside bore (Fig.8a). Considering the size of the powder chamber and the total weight of the propellant it was assumed that approximately around time t B the temperature in the powder chamber could be set close to the adiabatic gas temperature. This decision was supported by the method of powder preparation and compaction into the chamber as described in detail in historical reports. Herein, the bombard crew compacted extremely well the powder inside the chamber with a piece of wood and used that piece to seal the circular hole entrance to the chamber, using this piece apparently also as a stopper for the exact position of the cannonball inside the barrel (Critovoulos [3]). Consequently, parameter A 3 was set at 2,000 to yield a scaled time t m at 0.00240 msec. The model from Eq.(18) kept track of the developed temperature at time t x =2.5sec after ignition, time which corresponds to the time when the cannonball hits the Walls. This time marks the termination of the shot and is used as reference to check if the situation was safe for the crew to approach the bombard in order to cool the gun and launch preparations for the next shot. The developed temperature at time t B, when the propellant is all burned, was at 2,018 o C dropping significantly at 1,122 o C at time t E , when the cannonball exits the muzzle . It should be emphasized that from the time of ignition till time t E , at 44.8 msec, the resulting temperatures were substantially higher than the bronze melting temperature at approximately 900 o C. With continuous firing of the weapon this effect would certainly result in wear of the bombard. The resulting temperature at time t x was recorded at 248 o C. Correspondingly, the recorded temperature after 30 sec from ignition was at 90 o C, at 60 sec around 71 o C and at 5 minutes at ambient temperature (Fig.8b). It was realized that a variation of parameter A 3 from 2,000 up to 5,000 yields the same picture as presented previously, 1,708 o C temperature at time t B , 207 o C at 2.5 sec and at ambient temperature after 5 minutes. It was noted, that the developed temperature at the end of the shot, hence at time t x , was approximately around 200 o C, a reference value where bronze material properties are not affected by temperature. The picture emerging from the model supports a situation whereby the gun crew could approach the gun almost immediately after firing in order to cool the bombard. After each shot the bombard crew would soak the bombard in oil in an effort to cool the weapon. Although the model from Eq.(18), shows that the temperature inside the chamber had dropped at ambient temperature after 5 minutes, the amount of heat accumulated inside the powder chamber solid during the firing process would subsequently radiate and propagate towards the exterior chamber surface, hence, producing significant amount of heat. This is supported by the significant average chamber temperature at 389 0 C as expressed from the temperature impulse from time t B till t x divided by the time interval of approximately 2.5 sec. Considering the fact that at time t x the chamber temperature was approximately at 200 o C and the average chamber temperature at 389 0 C, as presented previously, it was decided that a temperature in the powder chamber at 200 o C could be addressed as reference temperature. It was considered that this temperature, when combined with powder chamber stresses due to internal pressure, could capture the associated effects of accumulated temperature and heat radiation