This is the first time I have used this stack site so am not 100% sure this question is on topic (based on the tags I couldn't find) but thought someone may still be able to help me.

For those not familiar, in the UK we have the IET Wiring Regulations which set out regulations for electrical installations. This document also includes disconnection times for different fuse types so that the correct fuse can be selected for a system based on the PFC of the system and the required disconnection time.

Here is an example of one of the graphs for British Standard BS88 fuses;

Now I'm no mathematician but looking at the graph I'm sure there must be a way to deduce formula for the different fuse ratings (no formula are provided in the regulations). I'm currently updating an electrical design process where currently, the designer needs to manually refer to the graph to see which fuse should be used. I want to automate this process, hence wanting to find the formula for the graph.

Now, actually getting to the question, is it likely that the graph has been created using a formula (assuming it even has one), or could it just be data recorded during testing of the fuses with a "line of best fit" chucked over the top? I find it strange that I can't seem to find any formula for the graph anywhere online or even any clues.

I tried plugging in the values in the provided table into Excel and used the "show formula" option (I know, very crude) but using the formula provided didn't give me correct results when I manually checked them on the graph.

## Best Answer

The adiabatic equation gives earth sizes for disconnection times of 5 seconds

\$S = \frac{\sqrt{I^2}\times{T}}{k}\$

where \$T\$ is the disconnection time and \$k\$ is the factor chosen from tables in BS7671

But why square something then square root it? So just \$I\$.

So

\$\frac{S\times k}{ I} = T\$

where,