Update on New Book by Giulio Fanti and Pierandrea Malfi

Thomas asks if Fanti’s approach to testing the age of linen really show promise. My response to that question would have to be: “Quite possibly. But that there are some big ‘howevers’ “.

Hugh has mentioned Fanti’s general approach, essentially measuring age-related changes in the spectral and mechanical properties of linen. You can find his related papers or references to them on Barrie Schwortz’s shroud.com web-site. Two in particular are: “Non-destructive dating of ancient flax textiles by means of vibrational spectroscopy” Authors: Giulio Fanti, Pietro Baraldi, Roberto Basso, Anna Tinti; and “A NEW CYCLIC-LOADS MACHINE FOR THE MEASUREMENT OF MICRO-MECHANICAL PROPERTIES OF SINGLE FLAX FIBERS COMING FROM THE TURIN SHROUD” Authors: Giulio Fanti, Pierandrea Malfi.

I will confine my technical comments to the mechanical testing, the Cyclic-Loads machine. Cyclic load testing has been used for several decades to measure the fatigue characteristics of engineering materials, particularly metallic materials such as steels and aluminium, and has a reputable history in engineering. It is particularly suitable for testing materials which are susceptible to very many cycles of heavy loading over the life of the different components, such as engine parts and highly stressed components in railway bridging where heavy loadings are repetitive. Typically all materials will fracture after a certain number of cycles for any given stress, down to a certain stress called the “endurance limit” below which no number of repetitions will produce fracture.

Another mechanical characteristic of materials is the “Young’s modulus”. This is the stress required to produce unit strain, All materials will stretch when subject to a tensile load. The strain is defined as the amount of extension divided by the length of the sample; the stress is the load divided by the cross-sectional area. Young’s modulus is calculated by dividing the stress by the strain. Several materials show elastic behaviour so that up to a certain elastic limit, strain is directly proportional to stress and Young’s modulus is fairly constant over this range. Many materials however, such as aluminium are not elastic, and their stretch behavior increases with loading, so that for these more plastic materials the modulus is defined by adopting an appropriate engineering convention for them over the range of loading.

The mechanical properties chosen by the authors as seemingly age-related were: breaking stress; two Young’s Moduli 1) relating to the last part of the increasing loading cycles, 2) relative to the first part of the decreasing loading cycles; two loss factors relating to dissipated and stored energies and other factors.

Mechanical properties of the flax fibres versus known ages of the samples were then correlated. The authors write: “This goal was reached performing stress-strain measurements in 350 loading-unloading cycles of 85 different flax fibers belonging to samples of 12 different historical and modern flax fabrics, see Ref. [14], dating back to up to more than five thousand years ago, obtaining approximately 16,000 manual acquisitions.”

The authors thus obtained five correlation curves for their five parameters. A measure of the “goodness of fit” when carrying out such work is the “Pearson’s correlation coefficient” = R. If R = 0.0, then there is no obvious correlation between the parameter and age and consequently no obvious relationship; If R = 1.0 then there is perfect fit and the parameter gives a very high predictability of true age. For the five parameters, the authors claim values of R between 0.90 and 0.95, which on the face of it would seem to be quite high correlation ratios.

Rather than taking a simple average of the five dating methods, the authors then proposed a “weighted mean” of the five methods giving greater weight to some apparently more reliable parameters than others. They claim: “The resulting uncertainty of the historical dates deriving from the measured mechanical parameters has a standard uncertainty of about 200 years.”

Taken singly, the five individual parameters give a very large range of possible dates for the TS, and with quite large margins of error. The oldest date is 556 BC, error 336 years; youngest date 456 AD error 538 years. However their weighted mean is 372 BC error 214 years. I might be happier with this last result, if the authors had given a correlation coefficient for their choice of the weighted mean formula.

There are many extraneous factors that can affect the mechanical properties of flax fibres. The authors note the possible historic effects of humidity and heat. They claim that these effects are manifest in the appearance of the fibres, such as their colour. Various fibres were rejected for testing on these grounds. Other effects, not evidently considered, result from the history of the parent fabric, such as repetitions of folding, rolling and methods of storage and their particular environment.

Gian Marco Rinaldi above has referred to the subjective selection of apparently older fibres, which may raise a doubt as to the integrity of the selection process.

I do not agree with Hugh’s conclusion that the results show such poor correlation that the method cannot be considered as useful. However we need to know a lot more about the raw data, than has been forthcoming to date. There is certainly the problem of obtaining sufficient calibration samples. Acceptance of any new scientific method always requires its replication and peer review by other independent investigators, and of course so far, this has not happened.

In principle however, the method of mechanical testing might provide a type of credibility check on other more established dating methods, but because of the importance of extraneous effects mentioned, and these will always be unknown, it seems likely that quite large errors of at least 200 years or more, can never be eliminated.