I have looked, and can't find a reference to this. If the L/R ratio for a cable inductance/resistance exceeds the interruption time of the fuse, is the arc flash calculated from the longer of the two?

Please explain what you are using the L/R ratio for.

The L/R ratio is the inductance to resistance ratio. The ratio is in mS and defines an opposition to a change in current flow. I know that when you are selecting a fuse, you have to take this ratio into consideration.

In my application, I am looking at a 4/0 copper wire the Ibf is 24.721kA, and the voltage varies from 500 to 1000VDC. I had calculated the arc flash at ~17.8 cal/cm2 given an interrupt rating of 3 mS for the fuse R&D selected. The L/R ratio for 4/0 copper wire calculated to 4.87mS.

I was wonderring what affect the L/R ratio has on the overall arc flash rating.

Do you mean X/R ratio? The x being the inductive reactance in ohms.
This affects the asymmetry of the short circuit waveform. Typically the impedance of a conductor is provided with 2 components. The X value and the R value. The X/R ratio is dimensionless. When calculating the short circuit current, the total equivalent impedance of the conductor, source and other components are factored in and the X/R of the total impedance is part of the answer.

At the present time, the X/R ratio is not part of the IEEE 1584 arc flash calculations.

Are you using the dc arc flash calculations from NFPA 70E? The IEEE 1584 equations only apply to 50/60Hz ac systems.

To answer your question: L/R ratio isn't used to calculate DC arc flash. Calculate the arcing current (0.5xIbf), look up the clearing time in the TCC of the fuse and plug it in the maximum power method formula (0.01*V*Iarc*t/d^2, d=distance in cm). For 1000 VDC, this means 2.3 cal/cm2, assuming the clearing time of 3 ms is still correct.

oops! didn't catch the "DC" in the question.

The equations I have are:
L = 2l[2.303LOG[(2l/d)(1+x)] - x + 4/m + d/2l]]
x = sqrt(1+ (d/2l)^2)

where L = inductance in microHenries, l=length(1 foot), d=diameter, m=permeability

then L/R the ratio of the inductance (not inductive reactance) to resistance gives the time constant in mS.

I have found 3 different equations for cable inductance, and they, of course, give 3 different values for inductance. The problem is that I'm dealing with DC and not AC. I was presuming the customer was going to use 4/0, but was just informed they may use 350 MCM or even 500 MCM. SO, I just informed the customer that they need to give me the inductance of the cables they are using as specified by the cable manufacturer. That doesn't change the premise of my question though.

Though it will change the time constant based on whatever cable(s) they end up using for the installation (going from 4/0 to 500MCM doubles the time constant)

I realize that that ratio is not presently addressed by the IEEE 1584 arc flash calculations. I was more wonderring what the effect of the difference in the L/R time constant versus the fuse clearing time would have on an arc flash occurance.

Let me add a bit more, just in case my logic is unclear.

In any circuit where you have a coil (an inductor), you typically either put an RC network if you are supplying the coil with AC voltage or a flyback diode if you are supplying the coil with DC voltage. The reason being that you need to quench the arc on the contacts controlling the coil.

The line of thinking is to preserve the contacts and try to prevent arcing and welding when the contact opens because you have stored energy in the inductors oppposing a change in current, just as you have stored energy in capacitors opposing a change in voltage.

You have an inductor even in a straight piece of wire (albeit a very low-value inductor). So when the fuse clears, or attemps to clear, you have the inductance of the wire opposing a change in current. This is why tou have to take the L/R time constant into account when you are specifying fuses.

A very good question. I contacted one of my fuse guru friends to see what their view is on this.
In addition to the paper that I was given (and uploaded here) here are a few more thoughts on the subject.

The Circuit time constant (L/R) does affect clearing times, particularly for short clearing times. Basically, the higher the time constant, the longer it will take for the current to reach its steadt state value. Since the rms current is a weighted average of the instantaneous value over time it will be less than that value but growing over time. Since it is not a fixed value some modification of the tcc can be done to account for this. Basically, the higher the time constant the fuse will take longer to clear than what is shown for a fixed ac rms value on the tcc – particularly down in the 0.01 to 1.0 s region.

[color=#000000]Having said that, the effect of an arcing fault will be to reduce the time constant because the arc resistance will add to the source resistance. Clearing times of over current protective devices will require a good model of arc resistance.[/color]

Thanks, I appreciate the data.

Maybe this is a little off-topic, but section D.8.1.2 of the NFPA 70E refers to a document called "DC Arc Hazard Assessment Phase II Copyright Material Kinectrics Inc. Report No. K-012623-RA-0002-R00". Searching for that title only results in documents that refer to it, not the actual document. Anyone know where to get it, or what's in it?

If you really need to consider the time constant in determining clearing time, then you need to consider both the arc resistance (as noted by Jim) and the impedance of the source, not just the L/R of the cable.