Ancient & Medieval Artillery

Ancient & Medieval Artillery Artillery before gunpowder Jim Gandy How mechanical artillery works 1. Collect the muscle power of the crew. 2. Sto...
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Ancient & Medieval Artillery Artillery before gunpowder Jim Gandy

How mechanical artillery works

1.

Collect the muscle power of the crew.

2.

Store the energy until ready.

3.

Transfer the energy to the missile.

Types of energy storage

1.

Stretch (shanghai).

2.

Flexure (bow).

3.

Torsion (twisted rope).

4.

Gravity (lifted weight).

Torsion mechanism Skeins made of elastic rope.

Torsion catapults



Fragmentary data.



Skein ropes made of hair (horse or human) or sinew.



Range had to be greater than bowmen on walls > 150m.



Two types:



Ammunition stones have been found on many archaeological digs. Largest common size of ammo is 18Kg.

Ballista – could throw either spears or stones. Onager – only threw stones.

The gravity trebuchet

Types of trebuchet

Methods of analysis



Full mathematical analysis is theoretically possible for trebuchets and the formulae are available on the internet.



The formulae are exceedingly complex and lengthy.



Computer programs derived from them are also available.



I haven’t found the same for catapults.



Empirical methods using simple energy equations and model tests are, I believe, a more reliable method.

Energy equations Trebuchet Kinetic energy in missile Range at optimum angle of fire (45°) Potential energy stored in engine Solving equations assuming no losses: Upper limit for Range: Ro = Introduce a bugger factor, E representing the efficiency of the system: Actual Range: R =

Catapult

KE = ½.m.v^2 R = 2.v^2/g M.g.H

F.D

2.(M/m).H

2.(F/m/g).D

2.(M/m).H.E

2.(F/m/g).D.E

Meccano model

Vary M/m and plot Range Meccano 16 14 12

Range

10

W

8

F H

6 4 2 0 0

50

100 M/m

150

200

Vary M/m and plot efficiency 80% 70% 60%

E

50% Wheels

40%

No wheels

30%

Hanging weight

20% 10% 0% -10% 0.0

50.0

100.0 M/m

150.0

200.0

Vary arm length ratio and plot E v. M/m Hanging 60% 50%

E

40% 0.231

30%

0.166

20%

0.092

10% 0% -10% 0

50

100 M/m

150

200

Some model test results

Trebuchet

Onager

Ballista

Arrow (20g)

-

-

257 m

Golf ball (30g)

-

150 m

140 m

Arrow (175g)

-

-

125 m

Cricket ball (175g)

-

123 m

115 m

Bocce ball (720g)

102 m

58 m

48 m

Steel ball (2Kg)

91 m

-

-

Trebuchet configurations Hanging wt:

Simplest to build. Sand or gravel makes cheap weight. Easy to adjust range by shovelling sand. Efficient at high weight ratios. Recoil countered by backswing of weight.

Fixed weight:

Have to use metal weight – usually more expensive. Very efficient at low weight ratios. Recoil is a big problem – needs fore & aft bracing.

Wheeled:

More complex to build. Very efficient at low weight ratios. 20% more efficient than fixed due to flicking action. Recoil absorbed safely by machine thrashing about.

The hanging configuration was the most common historically.

Trebuchet Design

Fundamental parameter:

The BIGGER the BETTER.

Want more range ?

Use a longer arm.

Want to throw something bigger ? Use a bigger weight. To optimise efficiency:

Balance ratio of arm lengths with ratio of weights

Strength issues:

The arm & the sling are the only highly stressed items.

Torsion Catapult Design

The fundamental issues with catapult design are: •

Obtaining skein material with the right elasticity & strength



Making skein anchors of adequate strength.



Making a torsioning device strong enough to pretension the skein.



Making a winch strong & compact enough to cock it.



Optimising the geometry to maximise the arc of the arm.



Making the frame strong enough to withstand the stresses.

Efficiency of trebuchets

Compare trebuchets & catapults

Scaling up models

TREBUCHETS N times bigger will throw N^3 times the weight N times as far.

TORSION CATAPULTS N times bigger will throw N^2 times the weight N times as far.

Client brief for a trebuchet

1.

To provide comic relief at an architect’s weekend seminar at Cranbrook.

2.

To throw toilet pans and other interesting objects.

3.

To be aesthetically pleasing.

4.

To be demountable.

Compare model with engine Model

Engine

Ratio

Axle height, m

0.44

3.5

8

Long arm, m

0.53

4.8

9

Short arm, m

0.15

1.2

8

Drop, m

0.265

2.1

7.9

Weight, Kg

2.42

1,100

455

Missile weight, Kg

0.02

9

450

Weight ratio, M/m

121

122

Upper bound R, m

63

512

8.33

Range achieved, m

30

235

7.83

48%

46%

Efficiency, E

Feasibilty of historical engines

1.

Trebuchet to throw 50 Kg stone 300 m.

2.

Onager to throw 18 Kg stone 300 m.

3.

Ballista to throw 18 Kg stone 300 m.

4.

Ballista to throw 0.5 Kg arrow 500 m.

Compare the 4 engines Trebuchet

Onager

Ballista (S)

Ballista (A)

Missile, Kg

50

18

18

0.5

Range, m

300

300

300

500

5 tonnes sand

300 diam skein

2 x 208 diam skeins

2 x 136 diam skeins

Winch force, t

1.7

2.5

2.5

0.5

Arm length, m

9.5

3

2

3

Arm diam, mm (30 MPa)

400

300

208

136

Internal force, t

6

100

48

22

Power

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