Measurements
Two general formulas were used in determining the size of the machine and the projectile it throws. The first is to determine the length of the bolt for a sharp-thrower, given as d = x / 9, where d is the diameter of the hole in the frame where the skein was threaded and x is the length of the bolt to be thrown. The second formula is for a stone thrower, given as d = (1.1)100m^(1/3), where d is the diameter of the hole in the frame where the skein was threaded and m is the weight of the stone. The reason for the development of these formulas is to maximize the potential energy of the skein. If it was too long, the machine could not be used at its full capacity. Furthermore, if it was too short, the skein produced a high amount of internal friction that would reduce the durability of the machine. Finally, being able to accurately determine the diameter of the frame’s holes prevented the sinews and fibers of the skein from being damaged by the wood of the frame. Once these initial measurements were made, corollary formulae could be used to determine the dimensions of the rest of the machines. A couple of examples below serve to illustrate this:
| Length/Weight of Missile | Diameter of torsion spring | Height of torsion spring | Machine length | Machine width |
|---|---|---|---|---|
| 31 cm | 3.4 cm | 22.1 cm | Hand-held | Hand-held |
| 54 cm | 5.6 cm | 36.4 cm | 1.4 | 0.8 m |
| 54 cm | 6.0 cm | 39.0 cm | 1.5 m | 0.9 m |
| 69 cm | 7.5 cm | 48.8 cm | 1.9 m | 1.1 m |
| 77 cm | 8.3 cm | 54.0 cm | 2.1 m | 1.2 m |
| 77 cm | 8.4 cm | 54.6 cm | 2.1 m | 1.2 m |
| 123 cm | 13.6 cm | 88.4 cm | 3.4 m | 1.9 m |
| 10 minas | 21.2 cm | 1.91 m | 6.4 m | 3.2 m |
| 15 minas | 24.3 cm | 2.19 m | 7.3 m | 3.6 m |
| 20 minas | 26.8 cm | 2.41 m | 8.0 m | 4.0 m |
| 30 minas | 30.7 cm | 2.76 m | 9.2 m | 4.6 m |
| 50 minas | 36.3 cm | 3.27 m | 10.9 m | 5.4 m |
| 1 talent | 38.4 cm | 3.46 m | 11.5 m | 5.8 m |
| 2 talents | 48.6 cm | 4.37 m | 14.6 m | 7.3 m |
d is measured in dactyls, and 1 dactyl = 1.93 cm
m is measured in minas, and 1 mina = 437 g
1 talent = 26 kg
Read more about this topic: Torsion Siege Engine, Construction