Can I determine a formula for fuse disconnection times?
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,


\$S\$ is size of conductor
\$I\$ is fault current
\$T\$ is disconnection time