BS88 Fuses

Do not worry - this is one that trips a few folk when they first meet the idea of adiabatic measurements

Well it will need to be pretty well lagged for  I^2*t to apply over 70,000 seconds. The whole idea of constant let-through energy really only works for things that happen really fast, so the energy is all in one place    - only in the melting fusewire, (or are in some super-lagged vacuum flask so no heat can escape.)
As a homely analogy consider that a mars bar and a small stick of dynamite both pack about 1megajoule, but the chemical decomposition of the mars bar does you less damage, as the energy is allowed to spread around the body and  dissipate slowly as a small temperature rise over hours. For things like fuses that hold in the hand, I2t is only really constant at times of a few seconds or less.

The cables too will cool over a few tens of seconds to minutes depending on size and installation method.

So look at the fuse curve again - your cable needs to carry 160A for ever, and maybe twice that for an hour or two. 35mm2 might do, maybe 50mm2. That is the near steady-state part of the operation.
Now slide you fingers along to the 'fires in seconds' part of the curve. Now we have thousands of amps, but not for very long at all,  and so we do not need a cable that can take those kilo-amps all day, just for the duration of the blowing time. That is where the approximation of a near constant I^2*t comes in.

Come back if there is no 'ahah' moment after you read this and I and the others can try again..

All the best
Mike

Do not worry - this is one that trips a few folk when they first meet the idea of adiabatic measurements

Well it will need to be pretty well lagged for  I^2*t to apply over 70,000 seconds. The whole idea of constant let-through energy really only works for things that happen really fast, so the energy is all in one place    - only in the melting fusewire, (or are in some super-lagged vacuum flask so no heat can escape.)
As a homely analogy consider that a mars bar and a small stick of dynamite both pack about 1megajoule, but the chemical decomposition of the mars bar does you less damage, as the energy is allowed to spread around the body and  dissipate slowly as a small temperature rise over hours. For things like fuses that hold in the hand, I2t is only really constant at times of a few seconds or less.

The cables too will cool over a few tens of seconds to minutes depending on size and installation method.

So look at the fuse curve again - your cable needs to carry 160A for ever, and maybe twice that for an hour or two. 35mm2 might do, maybe 50mm2. That is the near steady-state part of the operation.
Now slide you fingers along to the 'fires in seconds' part of the curve. Now we have thousands of amps, but not for very long at all,  and so we do not need a cable that can take those kilo-amps all day, just for the duration of the blowing time. That is where the approximation of a near constant I^2*t comes in.

Come back if there is no 'ahah' moment after you read this and I and the others can try again..

All the best
Mike