DC circuit breaker capacity vs time constant

[Yuma]

Dear all,
I have a question on the breaking capacity of a DC circuit breaker.
If a DC circuit breaker is able to break 50 kA with a time constant of 15 ms, how do you calculate the new breaking capacity for other time constant, say 45 ms for example?

Searching the web I came across the following formula: I2 = I1 * sqrt (t1/t2), so it would be 50 *sqrt(15/45) = 28,9 kA

But the formula was given 'as is', with no explanation.

Can anybody confirm that this formula is correct, and if so, explain where it comes from, or point me to a good reference where it is explained?

Thanks

 

[Compositepro]

I guess because power dissipated is proportional to I squared, and energy is P times t.

 

[waross]

I am sure that that formula is valid for something.
I suspect that it takes more than fun with numbers to re-rate a DC circuit breaker.
It may be safer to use the manufacturer's type tested and verified interrupting ratings.