The Ballistic Performance of the Bombard Mons Meg

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1bs_bs_query Q2 The ballistic performance of the bombard Mons Meg

2bs_bs_query Q1 3bs_bs_query Ian LEWTAS, Rachael MCALISTER *, Adam WALLIS, Clive WOODLEY, Ian CULLIS

4bs_bs_query QinetiQ, Fort Halstead, Sevenoaks, Kent T N14 7BP, UK

5bs_bs_query Received 28 September 2015; revised 30 November 2015; accepted 1 December 2015

6bs_bs_query Available online

7bs_bs_query

8bs_bs_query Abstract

9bs_bs_query The bombard Mons Meg, located in Edinburgh Castle, with a diameter of 19 inches (48 cm), was one of the largest calibre cannons ever built.

10bs_bs_query Constructed in 1449 and presented to King James II of Scotland in 1454, Mons Meg was used in both military and ceremonial roles in Scotland

11 bs_bs_query until its barrel burst in 1680. This paper examines the history, internal, external and terminal ballistics of the cannon and its shot. The likely muzzle

12bs_bs_query velocity was estimated by varying the propellant type and the cannon proﬁle was investigated to identify weak spots in the design that may have

13bs_bs_query led to its failure. Using the muzzle velocity calculated from the internal ballistics, simulations were performed with granite and sandstone shot for

14bs_bs_query varying launch angle and ground temperature. The likely trajectory and range of the cannonballs are described. The internal and external ballistics

15bs_bs_query informed the initial conditions of the terminal ballistic impact scenarios. The performance of the cannonball against both period and modern

16bs_bs_query targets, in the form of a pseudo-castle wall and a monolithic concrete target, respectively, were simulated and are presented and discussed.

18bs_bs_query Keywords: Analytical; Hydrocode; Muzzle velocity; Cannon barrel design; Trajectory; Castle brick target

19bs_bs_query

20bs_bs_query 1. Introduction that the ﬁrst cannonball ﬁred at the keep passed straight through 46bs_bs_query

the wall and severed the hand of Margaret Douglas as she was 47bs_bs_query

21bs_bs_query As one of the larger and well documented surviving medi- drinking inside. 48bs_bs_query

22bs_bs_query eval cannons, Mons Meg stands in pride of place at Edinburgh Once retired from active military service she found a new 49bs_bs_query

23bs_bs_query Castle and in its history (Fig. 1). Constructed around 1449 in role as a display piece at Edinburgh Castle. However, on 30 50bs_bs_query

24bs_bs_query Mons, part of what is now modern day Belgium, at the request October 1680, to celebrate the visit of James Duke of York and 51bs_bs_query

25bs_bs_query of Duke Philip the Good of Burgundy [2], the bombard was Albany to Edinburgh, the barrel burst, effectively ending her 52bs_bs_query

26bs_bs_query intended as a wedding present to King James II of Scotland, operational life. 53bs_bs_query

27bs_bs_query who, in 1457 married Duke Philips’ great niece, Mary of This paper investigates and discusses the internal, external 54bs_bs_query

28bs_bs_query Gueldres. and terminal ballistics of the cannon. The internal ballistics 55bs_bs_query

29bs_bs_query Customs records date Mons Meg’s ﬁrst arrival on Scottish

30bs_bs_query shores around 1457 [3], seemingly ﬁrst taking place in battle at

31bs_bs_query the siege of Roxburgh Castle in 1460, although this is not yet

32bs_bs_query backed up in any way other than stories from the time [3]. The

33bs_bs_query earliest written record of her active role in service is during the

34bs_bs_query 10 day bombardment of Norham Castle in 1513 [3] during

35bs_bs_query which she is reported to have destroyed both the castle’s inner

bs_bs_query 36 and outer wall. Her last use as a defensive weapon was during 56bs_bs_query

37bs_bs_query the Lang Siege 1571–73, after which she was only used for

38bs_bs_query ceremonial duties.

39bs_bs_query One of the most famous stories about the bombard was the

40bs_bs_query two month siege of Threave Castle by James II. The story goes

41bs_bs_query

42bs_bs_query

43bs_bs_query Peer review under responsibility of China Ordnance Society. + 44bs_bs_query * Corresponding author. Tel.: 44 1959514029. Fig. 1. Mons Meg at Edinburgh Castle. Licensed under creative commons 57bs_bs_query

45bs_bs_query E-mail address: [email protected] (R. McAlister). attribution-share alike 2.0 generic license [1]. 58bs_bs_query

Please cite this article in press as: Ian Lewtas, Rachael McAlister, Adam Wallis, Clive Woodley, Ian Cullis, The ballistic performance of the bombard Mons Meg, Defence Technology (2015), doi: 10.1016/j.dt.2015.12.001 ARTICLE IN PRESS

2 I. Lewtas et al./Defence Technology ■■ (2015) ■■–■■

Table 1 bs_bs_query 59bs_bs_query calculates the likely muzzle velocity of the cannon and 100

Pressured produced by period black powder compositions [7]. 101bs_bs_query 60bs_bs_query analyses the possible reasons for the barrel bursting. The exter-

Period Composition name Range of Average muzzle 102bs_bs_query 61bs_bs_query nal ballistics uses the results from the internal ballistics to −1 pressure/ velocity/(m·s ) 103bs_bs_query 62bs_bs_query analyse and predict the cannonball trajectory and likely ﬁnal

MPa 104bs_bs_query

63bs_bs_query velocity and impact angles. This is used to investigate its ter-

14th century John Arderne Feuerwerkbuch 44–51 328.6 105bs_bs_query 64bs_bs_query minal performance against modern targets and period, castle-

16th century Whitehorne 22–25 231.1 106bs_bs_query

65bs_bs_query type targets. 16th century Bruxelles 66–76 385.4 107bs_bs_query

66bs_bs_query 17th century British government Formula 92–105 425.3 108bs_bs_query

67bs_bs_query 2. The cannon

109bs_bs_query

68bs_bs_query Mons Meg is constructed of wrought iron, sometimes called

3. Internal ballistics 110 bs_bs_query 69bs_bs_query charcoal iron, a highly variable iron, both in chemical compo-

70bs_bs_query sition and slag content. However it is a very ductile metal and 3.1. Muzzle velocity 111 bs_bs_query

71bs_bs_query the levels of slag have made the iron extremely resistant to

To calculate the muzzle velocity of Mons Meg, the analytical 112 bs_bs_query 72bs_bs_query corrosion [4]. It measures over 4 m in length, with a bore of

code Proteus was used. Proteus is a 1 dimensional, lumped 113 bs_bs_query 73bs_bs_query 50 cm and weighing over 6000 kg [5], easily making it one of

parameter code used to solve for combustion of gases and 114 bs_bs_query 74bs_bs_query the largest (by calibre) stone ﬁring cannons in history.

internal pressures; it is similar to IBHVG2 [8], and internal 115 bs_bs_query 75bs_bs_query It is divided into 2 distinct parts, the powder chamber, and

studies have shown the predictions of both codes to be 116 bs_bs_query 76bs_bs_query the barrel. The powder chamber measures 1.16 m in length, and

comparable. 117 bs_bs_query 77bs_bs_query varies from 0.59 to 0.53 m in diameter (Fig. 2). It is likely that

There were three likely black powder compositions in use 118 bs_bs_query 78bs_bs_query the powder chamber is constructed from one billet of iron

during Mons Meg’s operation lifetime and one from when the 119 bs_bs_query 79bs_bs_query which has been hammer-beaten on a mandrel to achieve the

barrel burst, each with a different range of pressure produced. 120bs_bs_query 80bs_bs_query correct inner dimensions. The barrel measures 2.88 m in length

Proteus matched these shot pressures to calculate the muzzle 121bs_bs_query 81bs_bs_query externally, and varies from 0.63–0.75 m in diameter. It is con-

velocities. The results shown in Table 1 average the propellant 122bs_bs_query 82bs_bs_query structed from 25 staves running the length of the barrel which

mass and pressure range, whilst assuming a 160 kg granite 123bs_bs_query 83bs_bs_query are covered and held in place by 33 hoops. These would have

cannon ball, to produce a single muzzle velocity for each 124bs_bs_query 84bs_bs_query been heated in a furnace and placed over the staves, as these

composition. 125bs_bs_query 85bs_bs_query cooled they would tighten to hold the barrel together and fasten

As there is no deﬁnite source for which type of powder was 126bs_bs_query 86bs_bs_query the staves to the powder chamber.

used in Mons Meg, an average of the 14th and 16th century 127bs_bs_query 87bs_bs_query Mons Meg ﬁred cannonballs roughly 490 mm in diameter.

powders (its operational timespan) was used as the expected 128bs_bs_query 88bs_bs_query During Mons Meg’s operation lifetime in the 15th and 16th

muzzle velocity of the cannon, 315.0 m/s. This value was taken 129bs_bs_query 89bs_bs_query centuries, iron shot was not available and the cannonballs were

forward to be used in the external ballistics section. 130bs_bs_query 90bs_bs_query made from local stone. There are records [7] which indicate

The above value of 315.0 m/s was reached after several 131bs_bs_query 91bs_bs_query both sandstone and granite shot was used to give mass ranges

reﬁnements to the model. An initial value of 319.1 m/s was 132bs_bs_query 92bs_bs_query of 130–140 kg and 160–170 kg for the different stone,

previously calculated and used in both the external and terminal 133bs_bs_query 93bs_bs_query respectively.

ballistics work as the research was running in close to parallel 134bs_bs_query 94bs_bs_query Black powder was used as the propellant charge for the

due to time and resource limits. 135bs_bs_query 95bs_bs_query bombard but there is no speciﬁc data about the amount used for

136bs_bs_query 96bs_bs_query Mons Meg. A minimum and maximum likely propellant mass

3.2. Internal pressure and the bursting of the barrel 137bs_bs_query 97bs_bs_query [7] of 29.5 kg and 34 kg, respectively, was assumed.

As mentioned above in 1680, the barrel of Mons Meg burst 138bs_bs_query

during ceremonial duties. This section investigates whether the 139bs_bs_query

amount or type of powder could explain the manner and loca- 140bs_bs_query

tion of failure. 141bs_bs_query

Following research from various sources, agreed values for 142bs_bs_query

the key dimensions of the cannon were used in the QinetiQ 143bs_bs_query

Barrel Design Software (QQ-BDAS). Although the method of 144bs_bs_query

manufacture of Mons Meg is different from that assumed in 145bs_bs_query

98bs_bs_query

QQ-BDAS, it was decided that this software would give sufﬁ- 146bs_bs_query

ciently representative pressure limits. 147bs_bs_query

QQ-BDAS is a QinetiQ proprietary code and thus has not 148bs_bs_query

been referenced in open literature, although it was developed 149bs_bs_query

using the gun design calculation methods outlined in “Text- 150bs_bs_query

book of Ordnance and Gunnery” [9] authored by William H 151bs_bs_query

Tschappat, and “Vickers and Sons Maximum Ltd – Their works 152bs_bs_query

and manufacturers” [10] by Alex Richardson. 153bs_bs_query

99bs_bs_query Fig. 2. External and cross-sectional view of Mons Meg [6]. The cannon proﬁle input in QQ-BDAS is show in Fig. 3. 154bs_bs_query

I. Lewtas et al./Defence Technology ■■ (2015) ■■–■■ 3

155bs_bs_query Fig. 3. External and internal proﬁles of Mons Meg used in QQ-BDAS.

bs_bs_query 156 Fig. 5. A comparison of black powder energetic potential [7]. 179bs_bs_query

157bs_bs_query An output from QQ-BDAS is a graph showing pressures 180bs_bs_query

158bs_bs_query along the barrel; this is shown in Fig. 4. In this case the key

extends roughly between hoops 3 and 7 from the breech end. 181bs_bs_query 159bs_bs_query information is the Safe Maximum Pressure which is shown in

This drop in factor of safety is caused by the internal diameter 182bs_bs_query 160bs_bs_query red, and the Margin of Safety shown in black.

of the cannon increasing dramatically where the powder 183bs_bs_query 161bs_bs_query QQ-BDAS does not use the internal pressure calculated in

chamber opens out to accommodate the cannon ball. 184bs_bs_query 162bs_bs_query Proteus but uses the propellant impetus. This was set as a

The Margin of Safety Minimum Requirement is only rel- 185bs_bs_query 163bs_bs_query standard value for all the black powder compositions so they

evant in modern weapons during strength of design investiga- 186bs_bs_query 164bs_bs_query could not be individually compared. This does however show

tions, but it gives a good reference point to show how safe Mons 187bs_bs_query 165bs_bs_query any “weak” points in the weapon using a black powder

Meg was likely to have been to ﬁre. 188bs_bs_query 166bs_bs_query propellant.

By comparison between the graph and the location of failure 189bs_bs_query 167bs_bs_query The Safe Maximum Pressure is the theoretical maximum

along the cannon, shown in Fig. 4, the damaged portion of 190bs_bs_query 168bs_bs_query pressure that the cannon can contain, without sustaining

Mons Meg, from the 1680 ﬁring lines up very closely to the 191bs_bs_query 169bs_bs_query damage, predicted by QQ-BDAS. The Maximum Internal Pres-

predicted drop in safe pressure from QQ-BDAS. This shows 192bs_bs_query 170bs_bs_query sure Weald Hills (W/H) shows the theoretical propagation of

that the modern model of the cannon is a valid representation of 193bs_bs_query 171bs_bs_query gas pressure along the proﬁle. The Margin of Safety is calcu-

the actual item and correctly predicts the area of failure. 194bs_bs_query 172bs_bs_query lated as the ratio between the Safe Maximum Pressure and

Calculations from the Journal of the Ordnance Society [7] 195bs_bs_query 173bs_bs_query Maximum Internal Weald Hills Pressure. It is evaluated at every

suggest that based on the mode of construction and the quality 196bs_bs_query 174bs_bs_query point along the cannon and varies from 1.3 to 9.6. A safety

of iron used, the maximum permissible pressure within Mons 197bs_bs_query 175bs_bs_query factor of 1.3 does not allow much room for error; this drop in

Meg before damage starts to occur is 87 MPa. The same article 198bs_bs_query 176bs_bs_query safety occurs between 1.36 m and 1.74 m along Mons Meg, and

states that a pressure of 110 MPa and over would be enough to 199bs_bs_query

destroy the barrel. 200bs_bs_query

The pressure ranges of the black power compositions (as 201bs_bs_query

well as an earlier, weaker powder and a composition created 202bs_bs_query

after the bursting) compared to the two pressure limits above is 203bs_bs_query

show in Fig. 5. This indicates the use of a more powerful 204bs_bs_query

powder, unavailable during Mons Meg’s operational lifetime, 205bs_bs_query

as the possible cause of the cannon’s failure in 1680. It cannot 206bs_bs_query

be ruled out that other factors may have assisted in the failure of 207bs_bs_query

the barrel; an inferior quality powder could have been used, 208bs_bs_query

bs_bs_query 177bs_bs_query which may have led to unstable deﬂagration, causing pressure 209

waves to propagate along the barrel and in its worst form this 210bs_bs_query

could lead to a minor detonation. Although it cannot be stated, 211bs_bs_query

with certainty, to be the cause of the barrel burst, we can show 212bs_bs_query

that the damage occurred at a weak point in the barrel’s 213bs_bs_query

construction. 214bs_bs_query

215bs_bs_query

4. External ballistics 216bs_bs_query

4.1. Drag and pressure 217bs_bs_query

The most important factor to consider when determining the 218bs_bs_query

178bs_bs_query Fig. 4. QQ-BDAS output compared Mons Meg failure location. trajectory of a fast moving projectile is drag. Drag refers to 219bs_bs_query

4 I. Lewtas et al./Defence Technology ■■ (2015) ■■–■■

220bs_bs_query forces acting opposite to the relative motion of any object

221bs_bs_query moving with respect to a surrounding ﬂuid and it is therefore

222bs_bs_query used to calculate the deceleration of an object. Below is the drag

223bs_bs_query equation

224bs_bs_query

225bs_bs_query 1 2 FuCADD= ρ (1)

226bs_bs_query 2 = ρ = 227bs_bs_query where FD drag force; mass density of the fluid (air in the = 228bs_bs_query case of Mons Meg); u flow velocity relative to the object; = = 229bs_bs_query CD drag coefficient; A reference area.

230bs_bs_query As can be seen from Eq. (1), the drag force will increase as Fig. 6. Relative change in drag coefﬁcient with respect to Reynolds number 274bs_bs_query

bs_bs_query 231 the velocity increases. The drag coefﬁcient is a function of the [10]. 275bs_bs_query

232bs_bs_query Reynolds number and is therefore not constant meaning it will

276bs_bs_query

233bs_bs_query change for different velocities. There is no set formula to cal-

bs_bs_query 234bs_bs_query culate it as it can only be approximated using experimental data for the Mons Meg cannon ball. This velocity would be a lot 277

bs_bs_query 235bs_bs_query and changes with numerous variables. The Reynolds number, higher if the projectile were smaller. The effect of Reynolds 278

bs_bs_query 236bs_bs_query Re , is a dimensionless quantity which is used to help predict number on the drag coefﬁcient is shown in Fig. 6. 279

280bs_bs_query 237bs_bs_query similar flow patterns in different fluid flow situations and incor-

4.2. Trajectory programme 281bs_bs_query 238bs_bs_query porates several of these variables.

To calculate the trajectory of the cannonball, an analytical 282bs_bs_query 239bs_bs_query ρ ==inertial forces uL R (2) computer programme was written in MATLAB. The pro- 283bs_bs_query e μ 240bs_bs_query viscous forces gramme requires the user to deﬁne ground temperature, muzzle 284bs_bs_query

= velocity, angle of the cannon with respect to the horizon and the 285bs_bs_query 241bs_bs_query where L characteristic linear dimension (the diameter of the

μ = mass of the projectile. The programme calculates an initial air 286bs_bs_query 242bs_bs_query cannonball in this case); dynamic viscosity of the ﬂuid.

viscosity and density and resolves the velocity into x and y 287bs_bs_query 243bs_bs_query Eq. (2) indicates that Re increases with velocity. Air density

components. 288bs_bs_query 244bs_bs_query and viscosity also affect the Reynolds number and how this is

The Mons Meg trajectory model calculates new air densities 289bs_bs_query 245bs_bs_query calculated will be discussed later. All ranges of Reynolds

and viscosities as it steps through time. This is calculated from 290bs_bs_query 246bs_bs_query number have been included in the calculation of the drag coef- = an initial ground temperature (i.e. when y 0). At the beginning 291bs_bs_query 247bs_bs_query ﬁcient but in reality only high velocity ranges will be needed as

time step, a new temperature is calculated using the lapse rate, 292bs_bs_query 248bs_bs_query the projectile will still be travelling at over 100 m/s when it

the rate at which the temperature decreases with increasing 293bs_bs_query 249bs_bs_query reaches its trajectory end point.

altitude and is equal to 6.4 °C/km under normal atmospheric 294bs_bs_query 250bs_bs_query The Reynolds number relating to the drag on a sphere can be

conditions [11]. Using this temperature the air density and 295bs_bs_query 251bs_bs_query separated into ﬁve separate categories [9]: ρ() viscosity can be calculated with the functions T and η()T . 296bs_bs_query

252bs_bs_query 1) Ideal or attached flow: Re <1, These functions are polynomial interpolations of tables con- 297bs_bs_query << 253bs_bs_query 2) Separated flow: 110Re , taining air density and viscosity as a function of temperatures 298bs_bs_query 5 254bs_bs_query 3) Unsteady oscillating flow: 10<10 . arrays every 0.01 seconds, taking into account both drag and 301bs_bs_query

gravity. A time step of 0.01 seconds was used as a smaller time 302bs_bs_query 257bs_bs_query The most important stages when considering the Mons Megs

step does not affect the trajectory but does signiﬁcantly increase 303bs_bs_query 258bs_bs_query cannonball trajectory are the fourth and ﬁfth stages as the

the computation time of the programme. This runs until the 304bs_bs_query 259bs_bs_query projectile would remain within these ﬂow stages for the dura- = trajectory reaches ground level (y 0). 305bs_bs_query 260bs_bs_query tion of its ﬂight due to the high velocity at which it would be

The drag model used in the programme is taken from [13] Q3 306bs_bs_query 261bs_bs_query travelling.

and the trajectory model has been validated with data from [14]. 307bs_bs_query 262bs_bs_query In the fourth case, a laminar boundary layer with a wide

308bs_bs_query 263bs_bs_query turbulent wake, the boundary layer on the windward side of the 4.3. Results 309bs_bs_query

264bs_bs_query sphere is laminar and orderly and the chaotic wake is initiated

265bs_bs_query as the ﬂow turns onto the leeward side of the sphere [9]. Initially the Mons Meg trajectory model was used to inves- 310bs_bs_query

266bs_bs_query The ﬁfth case is a turbulent boundary layer with a narrow tigate the effect of changing the air temperature, initial angle 311bs_bs_query

267bs_bs_query turbulent wake. The boundary layer transitions to chaotic tur- and muzzle velocity has on the range of the bombard. Unless it 312bs_bs_query

268bs_bs_query bulent ﬂow with vortices of many different scales being shed in is the variable being varied, the initial conditions of the program 313bs_bs_query

269bs_bs_query a turbulent wake from the body. The separation point is initially were a muzzle velocity of 300 m/s, initial angle of 15°, ground 314bs_bs_query

270bs_bs_query slightly downstream from the laminar separation point, so the temperature of 15 °C and a projectile mass of 149 kg. This 315bs_bs_query

271bs_bs_query wake is initially slightly smaller and the drag is less than the refers to a cannonball made from sandstone. 316bs_bs_query

272bs_bs_query corresponding laminar drag (stage 4) [9]. In normal atmo- Table 2 shows that increasing the temperature from 0 °C to 317bs_bs_query

273bs_bs_query spheric conditions this equates to a velocity of around 250 m/s 30 °C increases the range of the cannon but only by 2.77%. This 318bs_bs_query

I. Lewtas et al./Defence Technology ■■ (2015) ■■–■■ 5

319bs_bs_query Table 2

320bs_bs_query Table showing how range varies with ground temperature including percentage increase from 0 °C result.

321bs_bs_query Temperature/°C 0 5 10 15 20 25 30

322bs_bs_query Range/m 2863.1 2872.3 2880.7 2888.5 2904.2 2921.5 2942.6

323bs_bs_query Increase N/A 0.3% 0.6% 0.9% 1.4% 2.0% 2.8%

324bs_bs_query

325bs_bs_query Table 3

326bs_bs_query Table showing how range varies with initial cannon angle including percentage increase from 10° result.

327bs_bs_query Angle/(°) 10 15 20 25 30 35 40 45

328bs_bs_query Range/m 2207.2 2888.5 3412.0 3811.9 4106.8 4305.4 4413.3 4432.1

329bs_bs_query Increase N/A 31% 55% 73% 86% 95% 100% 101%

330bs_bs_query

331bs_bs_query Table 4

332bs_bs_query Table showing how range varies with muzzle velocity including percentage increase from 210.8 m/s result.

−1 333bs_bs_query Muzzle velocity/(m·s ) 210.8 255.1 299.4 343.7 388.0 432.3

334bs_bs_query Range/m 1750.1 2317.0 2880.3 3491.8 4082.0 4647.8

335bs_bs_query Increase N/A 32% 65% 100% 133% 166%

336bs_bs_query

337bs_bs_query relationship is the lower air densities at higher temperatures Simulations have also been run using alternative methods, for 373bs_bs_query

338bs_bs_query which, when substituted into Eq. (1), will produce a slightly example, using different atmosphere models and different drag 374bs_bs_query

339bs_bs_query lower drag forces. Table 3 shows how range varies with initial models. However, the results showed that there were little differ- 375bs_bs_query

340bs_bs_query cannon angle including percentage increase from 10° result. ences in the predicted ﬁnal velocities and ranges, and the numbers 376bs_bs_query

341bs_bs_query Again, intuitively the range will increase as the initial angle stated in the paper represent typical values from the study. 377bs_bs_query

bs_bs_query 342bs_bs_query is raised to 45°; however, this relationship is not linear. This is 378

bs_bs_query 343bs_bs_query because the ranges are converging to a maximum which occurs 5. Terminal ballistics 379

344bs_bs_query at 45°. This was to be expected as can be seen in the experi- 5.1. Background 380bs_bs_query

345bs_bs_query mental results found in [13]. A 45° initial inclination would

346bs_bs_query mean the muzzle of the cannon would be 2.86 m off the ground One of the most famous stories about the bombard was the 381bs_bs_query

347bs_bs_query which is infeasible considering the mass of the cannon. It was two month siege of Threave Castle (Fig. 7) by James II in 1455. 382bs_bs_query

348bs_bs_query agreed that a 15° inclination would be used for future trajectory

349bs_bs_query calculations.

350bs_bs_query It is interesting to note that between 10° and 30° the terminal

351bs_bs_query velocity decreases. This is because the projectile is spending

352bs_bs_query longer in ﬂight and is therefore affected by more drag. However,

353bs_bs_query between 30° and 45° the terminal velocity increases again. This

354bs_bs_query is because the projectile is reaching a higher altitude so the

355bs_bs_query Q4 acceleration due to gravity is having a greater effect. Table 4

356bs_bs_query shows how range varies with muzzle velocity including per-

357bs_bs_query centage increase from 210.8 m/s result.

358bs_bs_query As to be expected, the higher muzzle velocities produced a

359bs_bs_query signiﬁcantly greater range. The muzzle velocity range tested 383bs_bs_query

360bs_bs_query was suggested by the internal ballistics.

361bs_bs_query Two speciﬁc muzzle velocities were also tested, 319.1 m/s

362bs_bs_query and 315.0 m/s. These are the pre and post reﬁnement predic-

363bs_bs_query tions for the expected muzzle velocity of Mons Meg using

364bs_bs_query period black powder. Table 5 shows the Mons Meg trajectory

365bs_bs_query model results for the two calculated muzzle velocities.

366bs_bs_query

367bs_bs_query Table 5

368bs_bs_query Table showing the Mons Meg trajectory model results for the two calculated

369bs_bs_query muzzle velocities.

−1 −1 370bs_bs_query Muzzle velocity/(m·s ) Final velocity/(m·s ) Final angle/(°) Range/m

371bs_bs_query 315.0 208.0 22.12 3170.6 Fig. 7. Modern day Threave Castle. Licensed under creative commons 384bs_bs_query

372bs_bs_query 319.1 209.2 21.33 3229.8 attribution-share alike 2.0 generic license [15]. 385bs_bs_query

6 I. Lewtas et al./Defence Technology ■■ (2015) ■■–■■

386bs_bs_query The story goes that the ﬁrst cannonball ﬁred at the keep passed However, the large calibre of the projectile, 0.24 m for the 439bs_bs_query

387bs_bs_query straight through the wall and severed the hand of Margaret cannonball, pushed the equations into non-realistic regimes 440bs_bs_query

388bs_bs_query Douglas as she was drinking inside. Although historians have with V1 becoming imaginary. This is obviously unusable and 441bs_bs_query

389bs_bs_query discredited this account, this work investigated whether this was therefore an earlier form of the spherical cavity expansion 442bs_bs_query

390bs_bs_query possible. model was used [13]. These equations were non-ideal and 443bs_bs_query

391bs_bs_query This section also looks at the terminal ballistics of the closed-form as several of the constants in the equations were 444bs_bs_query

392bs_bs_query cannon against modern targets, speciﬁcally a reinforced, mono- derived from speciﬁc target sets. Forrestal et. al. looked at the 445bs_bs_query

393bs_bs_query lithic concrete target. The impact conditions have come from sensitivity to certain constants and found the difference to be 446bs_bs_query

394bs_bs_query the internal and external ballistics simulations discussed earlier. negligible. However, the analytical equations for this study are 447bs_bs_query

395bs_bs_query Both analytical equations and hydrocode modelling were mainly to provide added conﬁdence to the hydrocode simula- 448bs_bs_query

396bs_bs_query used to assess the capability of Mons Meg against period and tions and do not need to be precise. It was therefore decided that 449bs_bs_query

397bs_bs_query modern targets. The cannonball was modelled as a 160 kg, these equations would be sufﬁcient to guide the hydrocode 450bs_bs_query

398bs_bs_query 490 mm diameter granite sphere and the target designs are modelling and assumed that they hold valid for these scales of 451bs_bs_query

399bs_bs_query described later. Several assumptions were made in this work, problem. 452bs_bs_query

400bs_bs_query importantly the cannonball ball was assumed to behave as a Here a spherical cavity is expanded at a constant velocity 453bs_bs_query

401bs_bs_query rigid body. This was both a prerequisite of the analytical equa- and produces a plastic response immediately surrounding the 454bs_bs_query

402bs_bs_query tions and necessary due to the lack of validated failure data for cavity and an incompressible elastic region around that. If the 455bs_bs_query

403bs_bs_query the material model used for the cannonball. striking velocity is high enough, the plastic region can be rep- 456bs_bs_query

resented by a locked hydrostat. As the velocity of the penetrator 457bs_bs_query 404bs_bs_query 5.2. Analytical investigation decreases, there is a transition velocity, Vt , where the linear 458bs_bs_query

405bs_bs_query There is very little validation data for granite cannonball hydrostat is a better approximation [13,16]. This is governed by 459bs_bs_query

406bs_bs_query impacts. Anecdotal historical evidence exists for period, castle- target material properties, speciﬁcally the density and yield 460bs_bs_query

407bs_bs_query type targets but there is nothing in open literature for perfor- stress Y . 461bs_bs_query

408bs_bs_query mance of a granite sphere impacting a modern concrete target. The perpendicular force acting on a projectile is deﬁned in 462bs_bs_query

409bs_bs_query Therefore an analytical investigation was undertaken to provide [13] 463bs_bs_query

410bs_bs_query data points from which to compare the hydrocode simulations ⎡ ()ψ − ⎤ 464bs_bs_query 2 81 2 411bs_bs_query for the modern target. FaYA=+π ⎢ BV⎥ (5) ⎢ ψ 2 s ⎥ 412bs_bs_query The analytical equations used are only valid for normal ⎣ 24 ⎦ 465bs_bs_query

413bs_bs_query impacts so two different impact speeds were analysed, the

where 466bs_bs_query 414bs_bs_query muzzle velocity and ﬁnal velocity. These values provided the

415bs_bs_query full range of possible depths of penetration for the cannon. 467bs_bs_query A =()2 []1ln− ()η* (6)

416bs_bs_query The analytical model used here was derived [16] from the 3 468bs_bs_query

417bs_bs_query Forrestal Spherical Cavity Expansion model. Forrestal et al. ⎡ 2 ⎤ 469bs_bs_query ρ ⎛ ⎞2 ()ηηη3 −−() 418bs_bs_query developed the empirical equations for predicting the penetra- 0 ⎢3Y 3Y 34***⎥ B =+−η*⎜1 ⎟ + (7) 2 ⎢ ⎝⎜ ⎠⎟ ⎥ 419bs_bs_query tion depth of projectiles into concrete and earth-type targets γ ()−η Y ⎣⎢⎢ E 2E 21 * ⎦⎥ 470bs_bs_query

420bs_bs_query based on cavity expansion theory, taking into account the 1 421bs_bs_query bs_bs_query dimensions of the projectile (including nose shape), impact ⎡ 3 ⎤ 3 471 ⎛ Y ⎟⎞ 422bs_bs_query velocity and target properties [13]. γη=+⎢⎜ ⎟ −−()⎥ (8) ⎢⎝⎜1 ⎠⎟ 1 * ⎥ 2E 472bs_bs_query 423bs_bs_query Initially, an open-form analytical equation for penetration ⎣ ⎦

424bs_bs_query depth was used to estimate the depth of penetration [14]. This

Here, E is the Young’s Modulus, η* is the locked volumetric 473bs_bs_query 425bs_bs_query spit the penetration process into two regimes, a cratering phase ψ strain, taken as 0.04 [13], and is the calibre radius head of the 474bs_bs_query 426bs_bs_query (when the penetrator was less than two diameters into the ψ = projectile. In the case of a sphere or spherical nose 12; 475bs_bs_query 427bs_bs_query targets) and a tunneling phase after that. The depth of penetra-

for a cannonball, this therefore reduces Eq. (5) to 476bs_bs_query 428bs_bs_query tion, P, equation for this is shown below

2 ⎡ ⎛ ⎞ ⎤ 477bs_bs_query 429bs_bs_query ⎛ ρ ⎞ 22B⎟ m NV1 ⎟ =+π ⎢ ⎜ ⎟ ⎥ P =+ln⎜14⎟+ a FaYA⎜ ⎟Vs (9) 2 ⎜ ⎟ (3) ⎣⎢ ⎝ ⎠ ⎦⎥ 2πaNρ ⎝ Sf ′ ⎠ 2 478bs_bs_query 430bs_bs_query c

Forces from both hydrostats can be written in the same form 479bs_bs_query 431bs_bs_query where 2 23 =+αβ 480bs_bs_query 432bs_bs_query − π ′ FVs (10) 2 = mVsc4 a Sf V (4) 481bs_bs_query 1 maN+ 4π 3 ρ 433bs_bs_query Allowing the depth to be calculated from 482bs_bs_query

bs_bs_query 434 where the projectile has mass m, radius a, nose factor N based dV dV 483bs_bs_query −=Fms =mV s (11) 435bs_bs_query on the calibre radius head, striking velocity Vs and initial tunnel s ρ dt dz 484bs_bs_query 436bs_bs_query region velocity V1. The target is deﬁned by density, ,

bs_bs_query ′ bs_bs_query 437 compressive strength, fc , and a dimensionless empirical Depth of penetration is then calculated for the locked 485

438bs_bs_query constant that multiplies the compressive strength, S. hydrostat and then added to the linear hydrostat solution [13]. 486bs_bs_query

I. Lewtas et al./Defence Technology ■■ (2015) ■■–■■ 7

487bs_bs_query Table 6

488bs_bs_query Depth of penetration values from analytical equations for maximum and

489bs_bs_query minimum velocities.

−1 490bs_bs_query Velocity location Speed/(m·s ) Depth of penetration/m

491bs_bs_query Muzzle velocity 319.1 0.205

492bs_bs_query Final velocity 209.2 0.096

493bs_bs_query

2 494bs_bs_query ⎛αβ+ ⎞ mV0 ⎟ P = ln⎜ ⎟ (12) t β ⎝⎜αβ+ 2 ⎠⎟ 495bs_bs_query 2 Vt

Fig. 8. Quarter symmetry examples of modern and three layer castle targets. 541bs_bs_query 2 496bs_bs_query ⎛ β ⎞ mV⎜ t ⎟ PP=+t ln⎜1 + ⎟ (13) β ⎝⎜ α ⎠⎟ 542bs_bs_query 497bs_bs_query 2

The majority of the stone found in the moorland of Dumfries 543bs_bs_query

498bs_bs_query where

and Galloway, the location of the castle, is granite. As there was 544bs_bs_query 2 bs_bs_query 499 α = πaYA (14) no validated failure and fracture model for granite available, a 545bs_bs_query

500bs_bs_query concrete model with a compressive strength of 200 MPa, gran- 546bs_bs_query 2 501bs_bs_query β = π (15) aYB ite’s minimum compressive strength [17], was used. The lime 547bs_bs_query

502bs_bs_query mortar was not explicitly modelled but simulated as interface 548bs_bs_query

503bs_bs_query The internal and external ballistics calculations provided the between the individual bricks with a break stress of 1.5 MPa. 549bs_bs_query

504bs_bs_query maximum and minimum impact velocities. The standard Values for the strength of the lime mortar varied from 0.58 MPa 550bs_bs_query

505bs_bs_query modern target was set as a 50 MPa monolithic concrete target. to 2.37 MPa [19], therefore, 1.5 MPa was used as the rounded 551bs_bs_query

506bs_bs_query The values in Table 6 show a penetration depth of less than median value. The castle target was simulated as a series of 552bs_bs_query

507bs_bs_query a radius of the cannonball for both impact velocities. The interlocking bricks in several layers with a steel surround to 553bs_bs_query

508bs_bs_query Muzzle Velocity impact is calculated from both hydrostats; help conﬁne the bricks. Fig. 8 shows the hydrocode set-up for 554bs_bs_query

509bs_bs_query however, the Final Velocity impact is already below Vt and the two target types. 555bs_bs_query

510bs_bs_query therefore is drive solely by the linear hydrostat solution. 556bs_bs_query

511bs_bs_query The analytical model predicts a modern target standing up 5.3.1. Modern targets 557bs_bs_query

512bs_bs_query very well to a large calibre cannonball. These values for pen- Guided by the analytical equations and the results above, the 558bs_bs_query

513bs_bs_query etration depth were used as sanity checks and comparisons to 50 MPa concrete target was 2 m thick to provide a semi-inﬁnite 559bs_bs_query

514bs_bs_query make sure the hydrocode simulations were producing sensible target to properly predict depth of penetration. It was also over 560bs_bs_query

515bs_bs_query results. 20 times the cannonball radius in diameter in order to remove 561bs_bs_query

516bs_bs_query edge effects. Three impact scenarios were simulated to investi- 562bs_bs_query 517bs_bs_query 5.3. Hydrocode simulations

gate the range of possible penetration depths and any effect of 563bs_bs_query

518bs_bs_query Simulations were performed using the Lagrangian ricochet. 564bs_bs_query

519bs_bs_query hydrocode DYNA3D which has a proven capability of predict- Similar to the analytical modelling, the hydrocode predicted 565bs_bs_query

520bs_bs_query ing depth of penetration into different types of targets. penetration depths less than the radius of the cannonball. 566bs_bs_query

521bs_bs_query DYNA3D includes advanced material models as well as Fig. 9 below shows the ﬁnal state of the hydrocode model- 567bs_bs_query

522bs_bs_query advanced interface and fracture routines. ling for the normal impacts. Table 8 and Fig. 10 show the data Q5568bs_bs_query

523bs_bs_query The granite cannonball was modelled using a simple elastic and compares it to the analytical results. 569bs_bs_query

524bs_bs_query material model with a Young’s Modulus of 50 GPa and a Pois- The larger difference seen for the ﬁnal velocity impact simu- 570bs_bs_query

525bs_bs_query son’s Ratio of 0.17 [17]. This was modelled as a rigid body with lation is most likely due to the analytical model relying on the 571bs_bs_query

526bs_bs_query no failure or fracture. This presented the “best-case” in terms of linear hydrostat equations which may not be valid at the scales 572bs_bs_query

527bs_bs_query penetration where the cannonball itself does not deform or involved. 573bs_bs_query

528bs_bs_query break up and would therefore have a deeper penetration depth The ﬁnal velocity from the external ballistics exercise was 574bs_bs_query

529bs_bs_query than if it did fracture. also simulated with the angular impact (Table 7). This required 575bs_bs_query

530bs_bs_query Two targets types were modelled, a 2 m thick, semi-inﬁnite the simulation to be performed in half symmetry due to the 576bs_bs_query

531bs_bs_query 50 MPa concrete target (replicating the analytical work) and a asymmetrical impact conditions. The ﬁnal state of the 577bs_bs_query

532bs_bs_query castle-type target. Depending on the impact conditions the sce- hydrocode simulation for this angled impacts in shown in 578bs_bs_query

533bs_bs_query narios were either simulated in quarter or half symmetry to Fig. 11. 579bs_bs_query

534bs_bs_query reduce the computational load and run time. The hydrocode simulations are in close agreement with the 580bs_bs_query

535bs_bs_query The castle target was designed to be similar to Threave analytical modelling, within 6% for the higher velocity impacts, 581bs_bs_query

536bs_bs_query Castle, famously linked with Mons Meg. There is little available giving added conﬁdence to the hydrocode results. There is very 582bs_bs_query

537bs_bs_query information about the exact properties of the stone and mortar little difference between the normal and angled impacts for the 583bs_bs_query

538bs_bs_query that was used to construct Threave Castle but the stone was 209.2 m/s impact velocity. There is not enough engagement for 584bs_bs_query

539bs_bs_query most likely taken from the surrounding land and held together the angle of attack of the cannonball to have any pronounced 585bs_bs_query

540bs_bs_query with a lime mortar [18]. effect. 586bs_bs_query

8 I. Lewtas et al./Defence Technology ■■ (2015) ■■–■■

587bs_bs_query Fig. 9. Maximum depth of penetration for normal impacts at (a) 319.1 m/s and (b) 209.2 m/s.

588bs_bs_query

589bs_bs_query The data above shows that modern defensive structures 5.3.2. Period castle targets 613bs_bs_query

590bs_bs_query would hold up very well against a 13th century siege weapon. Castle construction often used stones and rock that were 614bs_bs_query

591bs_bs_query Even at point blank range the cannonball will, at most, leave a locally sourced and simply picked up from the ground which 615bs_bs_query

592bs_bs_query small dent in the concrete and most likely ricochet or bounce off meant that there is a wide range of stone sizes in most castle 616bs_bs_query

593bs_bs_query the target. walls. It is, however, difﬁcult, complicated and time consuming 617bs_bs_query

to replicate this construction in the simulations so the targets 618bs_bs_query

594bs_bs_query were designed with separate layers of interlocking bricks, with 619bs_bs_query

620bs_bs_query 595bs_bs_query Table 7 breakable “slideline” interfaces (described previously) between

596bs_bs_query Impact conditions for modern target hydrocode simulations. both the bricks and the separate layers. 621bs_bs_query −1 bs_bs_query 597bs_bs_query Velocity description Speed/(m·s ) Impact angle/(°) Threave Castle keep is described as being 3 m thick but the 622

number of bricks, cells and interfaces required to model this 623bs_bs_query 598bs_bs_query Muzzle velocity-normal 319.1 0.0

bs_bs_query 599bs_bs_query Final velocity-normal 209.2 0.0 size target is beyond the capability of DYNA3D to run in any 624

bs_bs_query 600 Final velocity-angled 209.2 21.3 sensible timeframe. Therefore this investigation looked at the 625bs_bs_query

penetration and perforation trend when the number of layers 626bs_bs_query 601bs_bs_query

and the thickness of the bricks ina3layered target are 627bs_bs_query

602bs_bs_query Table 8 increased. This data was then extrapolated into the penetration 628bs_bs_query

603bs_bs_query Maximum depth of penetration for hydrocode and analytical modelling and the performance of Mons Meg. 629bs_bs_query 604bs_bs_query difference between them.

The bricks used in this investigation were initially 630bs_bs_query 605bs_bs_query Impact condition DYNA3D/m Analytical/m Difference/% × × 260 mm 260 mm 520 mm. The target width and height was 631bs_bs_query −1 606bs_bs_query 319.1/(m·s ) 0.0° 0.194 0.205 −5.7 over 10 times the diameter of the cannonball to remove edge 632bs_bs_query + 607bs_bs_query 209.2/s 0.0° 0.127 0.096 24.4

effects in the simulation. For targets with multiple layers, the 633bs_bs_query

brick layout in the rows was staggered alternatively between 634bs_bs_query

608bs_bs_query

635bs_bs_query

609bs_bs_query Fig. 10. Graph of maximum depth of penetration in the hydrocode model

610bs_bs_query compared to the analytical model. The angled impact condition only has the

611bs_bs_query hydrocode result due to the analytic model being limited to normal impacts

612bs_bs_query only. Fig. 11. Maximum depth of penetration for 21.3°, 209.2/s impact. 636bs_bs_query

I. Lewtas et al./Defence Technology ■■ (2015) ■■–■■ 9

637bs_bs_query Table 9

638bs_bs_query Table summarizing the exit velocities and depths of penetration (DoP) against

639bs_bs_query varying period targets. The estimates of the exit velocity were necessary as the

640bs_bs_query cannonball had not completely cleared the target.

−1 641bs_bs_query Brick size/mm Number of layers Exit velocity/(m·s ) DoP/mm × × 642bs_bs_query 260 260 520 1 162 N/A × × 643bs_bs_query 260 260 520 2 ~60 N/A × × 644bs_bs_query 260 260 520 3 ~24 N/A × × 645bs_bs_query 280 280 560 3 ~10 N/A × × 646bs_bs_query 300 300 600 3 ~4 N/A × × 647bs_bs_query 320 320 640 3 0 207 × × 648bs_bs_query 340 340 680 3 0 201

649bs_bs_query Fig. 13. Pre and post impact images of double layer brick target impacted 674bs_bs_query

normal at the muzzle velocity of Mons Meg showing brick interface issues. 675bs_bs_query

650bs_bs_query layers so there was not a single interface failure path through

676bs_bs_query 651bs_bs_query the thickness of the target. The number of cells in the simula-

652bs_bs_query tions, proportional to the computational load, was the limiting easily perforate a 260 mm thick single layer brick wall and has 677bs_bs_query

653bs_bs_query factor for the number of layers, restricting it to three. Each layer an exit velocity of 162 m/s. 678bs_bs_query

654bs_bs_query of bricks added roughly 635,000 cells, pushing the three layer The two layer target unfortunately encountered some 679bs_bs_query

655bs_bs_query target close to 2 million cells in quarter symmetry. numerical instability along the brick to brick interfaces which 680bs_bs_query

656bs_bs_query Due to the concern of the number of computational cells cause the simulation to crash before completion. It did however 681bs_bs_query

657bs_bs_query mentioned above, the simulations were limited to the “best run long enough for some initial conclusions to be made. 682bs_bs_query

658bs_bs_query penetration” case, a muzzle velocity of 319.1 m/s normal Fig. 13 shows the bricks in the second layer in the path of the 683bs_bs_query

659bs_bs_query impact, allowing the modelling to be performed in quarter cannonball, and central axis brick of the ﬁrst layer, have already 684bs_bs_query

660bs_bs_query symmetry. been pushed out and are travelling with a velocity greater than 685bs_bs_query

661bs_bs_query Table 9 shows the results for the period castle targets mod- the cannonball at the last time, implying they will have no 686bs_bs_query

662bs_bs_query elled. The size of the bricks used and the number of layers is further effect on the result. 687bs_bs_query

663bs_bs_query compared to the exit velocity and, if the cannonball was The velocity proﬁle of the cannonball has also plateaued at 688bs_bs_query

664bs_bs_query arrested by the target, their ﬁnal depth of penetration. roughly 60 m/s. All the bricks along the shot line, having failed 689bs_bs_query

665bs_bs_query Fig. 12 shows the impact against a single layer brick target. break interfaces, are moving out of the way. This is thus 690bs_bs_query

666bs_bs_query There are two different failure mechanism occurring: (i) the assumed to be the predicted exit velocity of the cannonball with 691bs_bs_query

667bs_bs_query brick along the central axis is simply pushed out of the way the caveat of qualitatively larger error bounds for this result. 692bs_bs_query

668bs_bs_query once the 1.5 MPa failure stress of the slideline is reached and is The impact against the three layer target was very similar in 693bs_bs_query

669bs_bs_query then free to move and (ii) the cannonball “tears” through the response to that seen in the two layer target. The velocity proﬁle 694bs_bs_query

670bs_bs_query other bricks as it passes through the wall. Mons Meg could of the cannonball plateaued at roughly 24 m/s. Fig. 14 shows 695bs_bs_query

the initial and ﬁnal state of the hydrocode modelling. 696bs_bs_query

If these three results are extrapolated, assuming a linear 697bs_bs_query

decreasing trend of exit velocity as the number of layers of 698bs_bs_query

bricks are increased, to stop the cannonball the wall requires at 699bs_bs_query

least four layers of 260 mm thick bricks. 700bs_bs_query

The thickness and size of the individual bricks in the three 701bs_bs_query

layer target were also increased in increments of 20 mm thick- 702bs_bs_query

671bs_bs_query

703bs_bs_query

672bs_bs_query Fig. 12. Pre and post impact images of single layer brick target impacted Fig. 14. Pre and post impact images of triple layer brick target impacted normal 704bs_bs_query

673bs_bs_query normal at the muzzle velocity of Mons Meg. at the muzzle velocity of Mons Meg showing brick interface issues. 705bs_bs_query

10 I. Lewtas et al./Defence Technology ■■ (2015) ■■–■■

deﬁne the material models and failure criteria. This would mean 745bs_bs_query

failure in the cannonball could be implemented which may 746bs_bs_query

dramatically affect the results. The design of the target can be 747bs_bs_query

made more representative of the “real life” structure by explic- 748bs_bs_query

itly including the mortar between the stones and rocks. The size 749bs_bs_query

and distribution of the stones can also be improved including 750bs_bs_query

have larger rocks spanning several layers. It would also be 751bs_bs_query

interesting to model the castle-type target for an angled impact. 752bs_bs_query

This would remove the mechanism of the bricks along the axis 753bs_bs_query

simply being pushed out the back. 754bs_bs_query

Uncited references Q7 755bs_bs_query

[20], [21], [22], [23], [24] 756bs_bs_query

757bs_bs_query

References 758bs_bs_query < [1] Wikipedia. Mons Meg – wikipedia [Online]. https://en.wikipedia.org/ 759bs_bs_query 706bs_bs_query Fig. 15. Graph showing cannonball velocity proﬁle through three layered > Q6 wiki/Mons_Meg ; 2015 [accessed 15.09.2015]. 760bs_bs_query

707bs_bs_query targets of differing thickness of brick. [2] Gaier C. The origin of Mons Meg. J Arms Armour Soc 1967;5(12): 761bs_bs_query

bs_bs_query 708bs_bs_query 425–31. 762

[3] Smith RD, Brown RR. Bombards: Mons Meg and her sisters. London: 763bs_bs_query

709bs_bs_query ness, as shown in Table 9. Fig. 15 presents the velocity proﬁles Trustees of The Royal Armouries; 1989. 764bs_bs_query

bs_bs_query 710 of the simulations and the results show that the 320 mm and [4] Kinard J. Artillery: an illustrated history of its impact. ABC-CLIO; 2007. 765bs_bs_query

711bs_bs_query 340 mm thick bricks stop the cannonball in the target. [5] Birchon D. Dictionary of metallurgy. London: Newnes; 1965. 766bs_bs_query

[6] Mallet R. On the physical conditions involved in the construction of 767bs_bs_query

bs_bs_query 712 6. Conclusions and recommendations artillery. 1856. 768bs_bs_query

[7] Gillet MHLJGC. A technological success in the 15th century: Jehan 769bs_bs_query

713bs_bs_query Internal ballistics codes and calculations provided an Gambier’s Mons Meg. J Ordinance Soc 2004;16:16–25. 770bs_bs_query

714bs_bs_query average expected muzzle velocity of 315.0 m/s for black [8] Anderson RFK. IBVHG2. U.S. Army Ballistic Research Laboratory; 771bs_bs_query

1987. 772bs_bs_query 715bs_bs_query powder available during Mons Meg’s operational lifetime. The

[9] Tschappat WH. Text-book of ordnance and gunnery. John Wiley; 1917. 773bs_bs_query 716bs_bs_query following external ballistics works investigates trajectory of the

[10] Richardson A. Vickers and Sons Maxim Ltd – their works and 774bs_bs_query

717bs_bs_query cannonball using this muzzle velocity.A value of 319.1 m/s was manufacturers. Strand: Ofﬁces of “Engineering”; 1902. 775bs_bs_query

718bs_bs_query also examined in the external and terminal ballistics sections [11] Falkovich G. Fluid mechanics. Cambridge University Press; 2011. 776bs_bs_query < 719bs_bs_query due time constraints. [12] NASA. Drag of a sphere [Online]. http://www.grc.nasa.gov/WWW/ 777bs_bs_query > k-12/airplane/dragsphere.html [accessed 15.09.15]. 778bs_bs_query 720bs_bs_query QQ-BDAS also correctly predicts the weak point in the

[13] Sedat Biringen C-YC. An introduction to computational ﬂuid mechanics 779bs_bs_query 721bs_bs_query cannon where it failed and postulates that the use of a more

by example. John Wiley & Sons; 2011. 780bs_bs_query 722bs_bs_query modern, powerful black powder could have been the cause of < [14] Wikipedia. Threave Castle – wikipedia [Online]. https://en.wikipedia 781bs_bs_query

723bs_bs_query the barrel bursting. > .org/wiki/Threave_Castle [accessed 15.09.15]. 782bs_bs_query

724bs_bs_query The Mons Meg trajectory model was used to investigate the [15] Jacobson MZ. Fundamentals of atmospheric modelling. 2nd ed. 783bs_bs_query

Cambridge University Press; 2005. 784bs_bs_query 725bs_bs_query effect of varying air temperature, initial angle and muzzle < [16] Dry air properties [Online]. http://www.engineeringtoolbox.com/dry 785bs_bs_query 726bs_bs_query velocity. > -air-properties-d_973.html [accessed 15.09.15]. 786bs_bs_query

727bs_bs_query The ﬁnal speed and trajectory of the internal ballistics’ [17] Forrestal MJ, Luk VK. Dynamic spherical cavity-expansion in a 787bs_bs_query

728bs_bs_query expected muzzle velocities was also calculated and carried compressible elastic-plastic solid. J Appl Mech 1988;55(2):275–9. 788bs_bs_query

729bs_bs_query forward to investigate the cannon’s terminal ballistic [18] Forrestal MJ, Luk VK. Penetration into semi-inﬁnite reinforced concrete 789bs_bs_query

targets with spherical and ogival nose projectiles. Int J Impact Eng 790bs_bs_query 730bs_bs_query performance.

1987;6:291–301. 791bs_bs_query 731bs_bs_query This section began talking about the siege of Threave Castle

[19] Forrestal MJ, Altman BS, Cargile JD, Hanchak SJ. An empirical equation 792bs_bs_query

732bs_bs_query and whether Mons Meg could break through the keep walls for penetration depth of ogive-nose projectile into concrete targets. Int J 793bs_bs_query

733bs_bs_query with enough residual velocity to remove the hand of a person Impact Eng 1994;15(4):395–405. 794bs_bs_query

734bs_bs_query inside. The hydrocode modelling has shown that, even with [20] Stone RL. Strenght and deformation properties of granite, basalt, 795bs_bs_query

limestone and tuff at various loading rates. Vicksburg, Mississippi: U.S. 796bs_bs_query 735bs_bs_query ideal conditions in terms of impact velocities, target design and

Army Engineer Waterways Experiment Station; 1969. 797bs_bs_query 736bs_bs_query rigid projectile material, the cannonball would fail to break

[21] Mackenzie W, Symson A. This history of Galloway: from the earliest 798bs_bs_query

737bs_bs_query through a 1.0 m period castle wall, let alone the 3 m thick keep period to the present time. Kirkcudbright: John Nickolson; 1841. 799bs_bs_query

738bs_bs_query walls of Threave Castle. This agrees with the lack of cannon [22] Pavia S, Fitzgerald B, Treacy E. An assessment of lime mortars for 800bs_bs_query

739bs_bs_query damage to the keep, which is still standing to this day. Mons masonry repairs. In: Concrete reseatch in Ireland colloquium. Dubline: 801bs_bs_query

2005. 802bs_bs_query 740bs_bs_query Meg is also predicted to have very little effect on modern

[23] McCoy RL. Modern exterior ballistics. Atglen, PA: Schiffer Publishing 803bs_bs_query 741bs_bs_query concrete targets.

Ltd.; 2012. 804bs_bs_query

742bs_bs_query These attempts to simulate period weaponry and castle [24] Subramanian RS. Drag on spherical particles and steady settling velocities 805bs_bs_query

743bs_bs_query targets have provided many lessons learnt. To accurately model < [Online]. http://web2.clarkson.edu/projects/subramanian/ch301/notes/ 806bs_bs_query > 744bs_bs_query the scenarios in the hydrocode, material tests will be needed to dragsphere.pdf [accessed 08.12.15]. 807bs_bs_query