This article discusses the applicability of the various calibration formulae to archaeological finds. In other words, whether or not the formulae were actually followed in practice.
Washers and field-frames Edit
A number of field-frames from the Imperial Roman period have been found. If calibration formulae were adhered to, we could reasonably expect that the field-frames would have roughly the relative dimensions. This does not seem to be the case:
|Ballista||Ring hole Ø||Frame height||Ratio||Washer Ø||Bundle height||Ratio||Frame volume (cm^3)|
The data is taken from articles by Baatz (1974, 1977, 1978, 1981), Boube-Piccot (1994), Kayumov & Minchev (2010) and from the cheiroballistra manuscript. When measurements are given in textual format they're used as is. Those measurements which are not given have been estimated from the accompanying diagrams using a CAD program. Provided the original diagrams don't have any distortions or errors, the accuracy of the measurements should be at least 90%. The measurements for the cheiroballistra assume one dactyl is 1.93 cm; for discussion on this topic please refer to Iriarte (2000).
The column Frame volume refers to the volume of a cylinder that would just fit inside the field frame. It can be seen as a rough estimate of the relative power output of the weapon, assuming that
- The spring cord material being used is the same, or can store the same amount of energy for same volume
- The torsion spring is stressed the same amount in each case
Note that the additional height of the washers, as well as the width of the washer crossbar, would affect these results somewhat.
As can be seen, the Gornea field-frames seem very squat and the ones from Cheiroballistra very tall, whereas the rest are in roughly the same category. Of course, the ratio could be adjusted by modifying washer wall thickness and washer height, but the discrepancy between, say, Gornea and Orsova field-frames can't be explained away very easily using this method.
A particularly squat frame (e.g. Gornea) could be interpreted in several ways:
- It belongs to an outswinger, where arms can't be rotated much
- It belongs to an inswinger, where arms are not rotated much (even though they could)
- The spring cord material was very elastic
All of these explanations allow keeping the torsion spring stack at minimum. Similarly, a particularly slender spring (cheiroballistra) could indicate spring cord material that is fairly inflexible (sinew) in a weapon that has long draw (inswinger).
There are two archaeological finds where washers and field-frames have been preserved, and where the ratio of spring height and diameter can be calculated. In these cases (Lyon and Hatra) the difference is less pronounced than in the field-frames, but still significant.
All in all, the discrepancy in these numbers is too great in my opinion to suggest that any single formula was used.