How do you "Proportionately Increase" an equipment grounding conductor per NEC® 250.122(B)?

Question

The National Electrical Code® (NEC®) 250.122(B) requires that "Where ungrounded conductors are
increased in size from the minimum size that has sufficient ampacity for the intended installation, wire-type equipment grounding conductors, where installed, shall be increased in size proportionately according to the circular mil area of the ungrounded conductors."
The NEC® Handbook section 250.122(B) has an example of how a "Proportionately Increased" equipment grounding conductor size calculation is accomplished. This example has been in the NEC® Handbook since the '96 cycle, when the sizing equipment grounding conductors section was located in 250.95, before it got moved to 250.122 in the '99 cycle.

Comments

1.  By example:
     If minimum ungrounded wire from #1 to 3/0 cu, the minimum ground wire is
     #6   grd   cu = 167800 cmil.
     If ungrounded wire is increased to 500kcmil:  500,000cmil/167800cmil=2.97
        Then:  26240 cmil x 2.97 = 77932.8 cmil.
Therefore, the next standard size ground wire is 83690 cmil or #1 awg.
Follow this example and you will pass your test.

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I am not following your example; you increase from #1 to 3/0 to 500; and it is NOT following the example I presented below that follows the example in the NEC® handbook. Please review the handbook example.

Answer 1

Did you know that if you increase a 20 amp circuit from #12 to 1/0, for what ever reason, that the proportionately increased equipment grounding conductor size works out to 1/0?

1/0=105,600 circular mills. #12=6,530 circular mills. (105,600/6,500)6,500=105600.

50 amp #8 circuit to #1. #8=16,510. #1=83,690. #10=10,380. (83,690/16,510)10,380=52,617. #3=52,620.

It works out 1 to 1 up for #14 - #10 normally sized ungrounded circuit conductors, then calculations are necessary to be conducted, accordingly.

Note: The NEC® does not require, but recommends voltage drop considerations. The Energy Conservation Codes require Voltage Drop considerations, logically so.