On site quide is 75% rule of thumb corrected for cable temp rise during fault conditions. BS7671 is 'absolute max' - The actuall max may be calced, or rule of thumb used.
NICEIC charts show an 80% corrected figure.
Although your figures show 80% corrected.........so I am beginning to question my self!
Or, is the rule of thumb there due to testing conditions being at room temp and not operating temp.........Umm getting the grey matter working!
The OSG is the 80% value owing to the difference in conductor temperature at the time of testing. The tables in BS7671 are for the cable at its operating temperature i.e. 70ºC and the OSG (and GN3) for the cables listed at 10ºC.
Afaik 80% comes from the simplified coefficent of copper (0.004) multiplied by the temperature change (60ºC) + 1 = 1.24. For a decrease of 60ºC the 70ºC figure is divided by 1.24. The reciprocal of 1.24 is roughly 0.8 which is where I believe the 80% figure comes from.
There is some more info in the back of GN3.
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