Been reading through CIGRE "TOOLS FOR THE SIMULATION OF EFFECTS OF THE INTERNAL ARC IN TRANSMISSION AND DISTRIBUTION SWITCHGEAR, REV 11.1". Annex C had a couple very interesting tidbits that I had not picked up on before. The first is that this is the first time that I've ever seen work trying to quantify the passing criteria for the cloth test strips used as part of arc resistant gear testing. What is interesting about it is that it seems to suggest that the passing criteria is 4 cal/cm^2 based on comparisons. This seems to fly in the face of the fact that the assumption is that arc resistant gear reduces the hazard down to under 1.2 cal/cm^2.

The second is that there is an equation for the Stoll curve given as E_Stoll = 50.204 kw/m^2*t^0.291 in kJ/m^2. This is slightly different from the equation recommended by ArcAd and is the first time I've seen anyone else promoting a time-dependent Stoll curve equation outside of what has been published on the Stoll curve that is used for instance for pass/fail data for calculating ATPV in the ASTM standard. Where does this equation come from? Is it valid? It would seem to suggest that the amount of energy decreases to zero and thus any amount of heat at zero time results in a burn which is nonsensical so at a minimum the curve should have a lower cutoff.

The equation actually does come from numerous researchers including A. Stoll. Stoll found that the results from her experiments could be predicted using Henrique's burn integral. Henriques and Moritz were the first to describe skin damage as a chemical rate process and show that first order Arrhenius rate equation could be used to determine the rate of tissue damage. The Arrhenius equation is a simple but remarkably accurate formula for the temperature dependence of reaction rates. Knowing the rate, reaction time (or time to produce damage) can be represented analytically as a function of either temperature or heat flux.

It is commonly known that the extent of damage or work produced by power is a function of time. Energy is a product of power and time, so no wonder 0 energy is delivered or produced in 0 seconds, subsequently no damage is done. As an example, time is required for an electric motor to produce mechanical work and no work is produced by motor if it is not given time to rotate. Similarly, in order to be burned by stove, one has to touch the glowing hot metal first. Although it may seem the damage has happened in no time, still it takes short but limited amount of time (t>0) for the damage to be produced.

A very interesting thing to know is that the infamous 1.2 cal/cm^2 threshold incident energy for a 2nd degree burn on bare skin cited in NFPA 70E and widely accepted in arc flash industry actually comes from misinterpretation of Alan Privettes' "Progress Report for ASTM Burn Study". As a matter of fact, Privettes' work is based upon tests where the test animals were shielded with flame retardant fabrics. Assuming Privettes' findings apply also to bare skin exposure is same as having a confidence you can safely touch the stove with bare hands as long as you have managed escaping damage by touching it previously while wearing protective gloves.

I encourage you to re-read this forum thread at http://arcflashforum.brainfiller.com/viewtopic.php?f=34&t=2221 and accompanying discussion for more information.

You may also want to check "Ocular and skin hazards from CO2 laser radiation" by A. Brownell for test evidence supporting a time-dependent Stoll curve equation outside of what has been published on the Stoll curve.

A quote from "Heat Transfer in Biotechnology" by A.Stoll summarizes the issue of using 1.2 cal/cm^2 as a threshold incident energy to 2nd degree burn. The quote reads:

"Serious misconceptions have crept into this field of research through adoption of rule-of-thumb terminology which has lost its identity as such and become accepted as fact. A glaring example of this process is the "critical thermal load". This quantity is defined as the total energy delivered in any given exposure required to produce some given endpoint such as a blister. Mathematically it is the product of the flux and exposure time for a shaped pulse. Implicit in this treatment is the assumption that thermal injury is a function of dosage as in ionizing radiation, so that the process obeys the "law of reciprocity," i.e., that equal injury is produced by equal doses. On the contrary, a very large amount of energy delivered over a greatly extended time produces no injury at all while the same "dose" delivered instantaneously may totally destroy the skin. Conversely, measurements of doses which produce the same damage over even a narrow range of intensities of radiation show that the "law of reciprocity" fails, for the doses are not equal."