It is up to the individual airline to calc EO Dep, and not all of them do it the same way, especially when it comes to adding a turn into the mix. Each aircaft has its own quirks and limitations.
I have seen calcs to max bank angle that did not take into account any course correction while in the turn...and of course, the real voodoo in the mix, the winds.
There is no public criteria that defines how to do this, nor sets any parameters for each of the variables. It is blind, basically, it states, when you ask for DEP clearance, you are telling me that your aircraft meets the min requirements on the chart or the standard climb gradient. I am not going to tell you how to get there, you told me you could do it.
If there is a turn, there is a containment area associated with that, bank limiting and turn radius keep you in the containment area.
EO is an emergency, and is treated as such in the criteria. Just becuase there is an EO SID, doesnt mean you can use it.
From FAA:
http://www.aci-na.org/sites/default/..._-_4-17-12.pdf
One Engine Inoperative (OEI) Description
• Air Carriers are required to clear obstacles in one-engine out departure situation
• Each carrier maintains their own chart of critical obstacle height & locations
• Each carrier computes a 35 ft. obstacle clearance based on specific aircraft load and
performance – given reduced climb gradient
•FAA historically only protected for instrument approach procedures
• There are known impacts to departure payload due to obstacles in departure area